LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Gats GENERAL THE PHYSICAL PAPERS OF HENRY AUGUSTUS ROWLAND THE PHYSICAL PAPERS OF HENRY AUGUSTUS ROWLAND PH.D., LL. D. Professor of Physics and Director of the Physical Laboratory in The Johns Hopkins University 1876-1901 COLLECTED FOR PUBLICATION BY A COMMITTEE OF THE FACULTY OF THE UNIVERSITY BALTIMORE THE JOHNS HOPKINS PRESS 1902 Copyright, 1902, by the JOHNS HOPKINS PRESS PRINTED BY BALTIMORE, RID., U. S. A. HENRY AUGUSTUS ROWLAND Born, Honesdale, Pennsylvania, November 27, 1848 Died, Baltimore, Maryland, April 16, 1901 Doctor of Philosophy (Ph. D.), Johns Hopkins University, 1880. (Hon- oris Causa.) Doctor of Laws (LL. D.), Yale University, 1895. Doctor of Laws (LL. D.), Princeton University, 1896. Fellow or Member of The British Association for the Advancement of Science. The Physical Society of London. The Philosophical Society of Cambridge, England. The Royal Society of London. The Royal Society of Gottingen. The Gioenian Academy of Natural Sciences, Catania, Sicily. The French Physical Society. The French Academy of Sciences. The Literary and Philosophical Society of Manchester. The Royal Lyncean Academy, Rome. The Academy of Sciences, Stockholm. The Italian Society of Spectroscopists. The Royal Society of Edinburgh. The Society of Arts, London. The Royal Astronomical Society of England. The Royal Society of Lombardy. The Royal Physiographic Society of Lund. The Royal Academy of Sciences, Berlin. The Royal Academy of Sciences and Letters, Copenhagen. The American Philosophical Society, Philadelphia. The American Academy of Arts and Sciences, Boston. The National Academy of Sciences, Washington. The American Physical Society, its first President. The Astronomical and Astrophysical Society of America. Delegate of the United States Government to the International Congress of Electricians, Paris, 1881. International Congress for the Determination of Electrical Units, Paris, 1882. Appointed Officer of the Legion of Honor of France. Electrical Congress, Philadelphia, 1884, President. International Chamber of Delegates for the Determination of Electrical Units, Chicago, 1893, President. PRIZES AND MEDALS. Rumford Medal, American Academy of Arts and Sciences. Draper Medal, National Academy of Sciences. Matteucci Medal. Prize awarded by the Venetian Institute in competition for a critical paper on the Mechanical Equivalent, of Heat. 102497 PREFACE Shortly after the death of Professor Rowland in April, 1901, a com- mittee of the Faculty of The 'Johns Hopkins University was appointed by President Gilman to suggest to the Trustees of the University a plan for a memorial of their colleague. The committee, consisting of Pro- fessors Remsen, Welch and Ames decided to recommend that a volume be prepared containing the physical papers and addresses of Professor Rowland, and also a detailed description of the dividing engines which had been designed and constructed by him for the purpose of ruling diffraction gratings, and that this volume be published by the University Press. This recommendation was approved by the Trustees of the University; and the same committee, with the addition of Professor R. W. Wood, was empowered to prepare the volume for publication. The editorial supervision has been mainly undertaken by Professor Joseph S. Ames. In deciding upon the scope of the proposed volume, it was thought best to include only the distinctly physical papers, inasmuch as Pro- fessor Rowland himself on several occasions when the question of the collection of his scientific papers was raised, had expressed himself as opposed to the republication of the purely mathematical ones. It was also decided to omit tables of wave-lengths, as these are extremely bulky, and copies can be easily obtained. Professor Rowland left many thousand pages of manuscript notes and outlines of lectures, but none of this material was ready for publication, and the committee were not in a position to undertake the task of its preparation. No attempt has been made to include a biography of Professor Rowland, for this would properly form a volume by itself, and would require much time for its preparation. There was at hand, moreover, the memorial address of Dr. Mendenhall, which tells so well, though briefly, the story of his life. vi PREFACE It was with difficulty, and only after a careful examination of many hundred volumes of scientific journals and transactions, that the com- mittee were able to obtain copies of all of Professor Eowland's numerous and scattered articles; but they are convinced that no paper of import- ance has escaped their notice. In preparing for publication these me- moirs and addresses, no alterations other than typographical have been made. For permission to reprint some of the most valuable papers, thanks are due to various publishers. The committee wish especially to express their appreciation of the kindness of Messrs. A. and C. Black, and of The Times (London) for permission to reprint from the Encyclopaedia Britannica the articles on " The Screw " and on " Diffraction Gratings," and of the Engineering Magazine Company, of New York, for permis- sion to reprint the article on " Modern Theories as to Electricity." The committee acknowledge their indebtedness also to Mr. 1ST. Mur- ray, Librarian of The Johns Hopkins University, who has personally superintended the details of publication, and whose advice has been often needed. The proofs have been revised by Mr. E. P. Hyde, Fellow in The Johns Hopkins University, who has thus been of the greatest assistance to the committee. THE JOHNS HOPKINS UNIVERSITY, BALTIMORE, MARYLAND, DECEMBER 1, 1902. CONTENTS PAGE PREFACE v ADDRESS BY DR. T. C. MENDENHALL 1 SCIENTIFIC PAPERS 19 PART I. EAKLY PAPERS. 21 *1. The Vortex Problem 23 Scientific American XIII, 308, 1865. 2. Paine's Electro-magnetic Engine 24 Scientific American XXV, 21, 1871. 3. Illustration of Resonances and Actions of a Similar Nature 28 Journal of the Franklin Institute XCIV, 275-278, 1872. 4. On the Auroral Spectrum 31 American Journal of Science (3), V, 320, 1873. PART II. MAGNETISM AND ELECTRICITY. 33 5. On Magnetic Permeability, and the Maximum of Magnetism of Iron, Steel and Nickel 35 Philosophical Magazine (4), XL VI, 140-159, 1873. 6. On the Magnetic Permeability and Maximum of Magnetism of Nickel and Cobalt 56 Philosophical Magazine (4), XLVHI, 321-340, 1874. 7. On a new Diamagnetic Attachment to the Lantern, with a Note on the Theory of the Oscillations of Inductively Magnetized Bodies.. 75 American Journal of Science (3), IX, 357-361, 1875. 8. Notes on Magnetic Distribution 80 Proceedings of the American Academy of Arts and Sciences, XI, 191, 192, 1876. 9. Note on Kohlrausch's Determination of the Absolute Value of the Siemens Mercury Unit of Electrical Resistance 82 Philosophical Magazine (4), L, 161-163, 1875. 10. Preliminary Note on a Magnetic Proof Plane 85 American Journal of Science (3), X, 14-17, 1875. * The numbers refer to corresponding ones in the Bibliography, page 681. viii CONTENTS PAGE 11. Studies on Magnetic Distribution 89 American Journal of Science (3), X, 325-335, 451-450, 1875. Ibid., XI, 17-29, 103-108, 1876. Philosophical Magazine (i\ L, 257-277, 348-367, 1875. 12. On the Magnetic Effect of Electric Convection 128 American Journal of Science (3), XV, 30-38, 1878. 13. Note on the Magnetic Effect of Electric Convection 138 Philosophical Magazine (5), VII, 442-443, 1879. 14. Note on the Theory of Electric Absorption 139 American Journal of Mathematics, I, 53-58, 1878. 15. Eesearch on the Absolute Unit of Electrical Eesistance 145 American Journal of Science (3), XV, 281-291, 325-336, 430-439, 1878. 17. On Professors Ayrton and Perry's NeAv Theory of the Earth's Mag- netism, with a Note on a New Theory of the Aurora 179 Philosophical Magazine (5), VIII, 102-106, 1879. Proceedings of the Physical Society, III, 93-98, 1879. 18. On the Diamagnetic Constants of Bismuth and Calc-spar in Absolute Measure. By H. A. Rowland and W. W. Jacques 184 American Journal of Science (3), XVIII, 360-371, 1879. 19. Preliminary Notes on Mr. Hall's recent Discovery 197 American Journal of Mathematics, II, 354-356, 1879. Philosophical Magazine (5), IX, 432-434, 1880. Proceedings of the Physical Society, IV, 10-13, 1880. 22. On the Efficiency of Edison's Electric Light. By H. A. Rowland and G. F. Barker 200 American Journal of Science (3), XIX, 337-339, 1880. 27. Electric Absorption of Crystals. By H. A. Rowland and E. L. Nichols 204 Philosophical Magazine (5), XI, 414-419, 1881. Proceedings of the Physical Society, IV, 215-221, 1881. 28. On Atmospheric Electricity 212 Johns Hopkins University Circulars Xo. 19, pp. 4, 5, 1882. 34. The Determination of the Ohm. Extract from a letter to the Inter- national Congress at Paris, 1884 217 Proces-Verbaux, Deuxieme Session, p. 37. Paris, 1884. 35. The Theory of the Dynamo 219 Report of the Electrical Conference at Philadelphia in November, 1884, pp. 72-83, 90, 91, 104, 107. Washington, 1886. 36. On Lightning Protection 236 Report of the Electrical Conference at Philadelphia in November, 1884, pp. 172-174. 37. On the Value of the Ohm 239 La Lumiere Electrique, XXVI, pp. 188, 477, 1887. CONTEXTS PAOE 38. On a Simple and Convenient Form of Water-battery ............... 241 American Journal of Science (3), XXXIII, 147, 1887. Philosophical Magazine (5), XXIII, 303, 1887. Johns Hopkins University Circulars No. 57, p. 80, 1887. 40. On an Explanation of the Action of a Magnet on Chemical Action. By H. A. Rowland and Louis Bell ................................ 242 American Journal of Science (3), XXXVI, 39-47, 1888. Philosophical Magazine (5), XXVI, 105-114, 1888. 43. On the Electromagnetic Effect of Convection-Currents. By H. A. Kowland and C. T. Hutchinson .................................. 251 Philosophical Magazine (5), XXVH, 445-460, 1889. 44. On the Ratio of the Electro-static to the Electro-magnetic Unit of Electricity. By H. A. Rowland, E. H. Hall, and L. B. Fletcher. . . 266 American Journal of Science (3), XXXVIII, 289-298, 1889. Philosophical Magazine (5), XXVIII, 304-315, 1889. 47. Notes on the Theory of the Transformer .......................... 276 Philosophical Magazine (5), XXXIV, 54-57, 1892. Electrical World, XX, 20, 1892. Johns Hopkins University Circulars No. 99, pp. 104, 105, 1892. 48. Notes on the Effect of Harmonics in the Transmission of Power by Alternating Currents ............................................ 280 Electrical World, XX, 368, 1892. La Lumiere Electrique, XLVII, 42-44, 1893. 53. Modern Theories as to Electricity ................................. 285 The Engineering Magazine, VIII, 589-596, 1895. 60. Electrical Measurement by Alternating Currents .................. 294 American Journal of Science (4), IV, 429-448, 1897. Philosophical Magazine (5), XLV, 66-85, 1898. 62. Electrical Measurements. By H. A. Rowland and T. D. Penniman.. 314 American Journal of Science (4), VIII, 35-57, 1899. 63. Resistance to Ethereal Motion. By H. A. Rowland, N. E. Gilbert and P. C. McJunckin ................................................ 338 Johns Hopkins University Circulars No. 146, p. 60, 1900. PART III. HEAT. 341 16. On the Mechanical Equivalent of Heat, with Subsidiary Researches on the Variation of the Mercurial from the Air-Thermometer and on the Variation of the Specific Heat of Water ................... 343 Proceedings of the American Academy of Arts and Sciences, XV, 75-200, 1880. 21. Appendix to Paper on the Mechanical Equivalent of Heat, Contain- ing the Comparison with Dr. Joule's Thermometer ............... 469 Proceedings of the American Academy of Arts and Sciences, XVI, 38-45, 1881. 20. Physical Laboratory; Comparison of Standards ................... 477 Johns Hopkins University Circulars No. 3, p. 31, 1880. x CONTENTS PAGE 26. On Geissler Thermometers 481 American Journal of Science (3), XXI, 451-453, 1881. PART IV. LIGHT. 485 29. Preliminary Notice of the Eesults Accomplished in the Manufacture and Theory of Gratings for Optical Purposes 487 Johns Hopkins University Circulars No. 17, pp. 248, 249, 1882. Philosophical Magazine (4), XIII, 469-474, 1882. Nature, 26, 211-213, 1882. 30. On Concave Gratings for Optical Purposes 492 American Journal of Science (3), XXVI, 87-98, 1883. Philosophical Magazine (5), XVI, 197-210, 1883. 31. On Mr. Glazebrook's Paper on the Aberration of Concave Gratings. 505 American Journal of Science (3), XXVI, 214, 1883. Philosophical Magazine (5), XVI, 210, 1883. 33. Screw 506 Encyclopaedia Britannica, Ninth Edition, Vol. 21. 39. On the Relative Wave-lengths of the Lines of the Solar Spectrum . . . 512 American Journal of Science (3), XXXIII, 182-190, 1887. Philosophical Magazine (5), XXIII, 257-265, 1887. 41. Table of Standard Wave-lengths 517 Philosophical Magazine (5), XXVII, 479-484, 1889. 42. A Few Notes on the Use of Gratings 519 Johns Hopkins University Circulars No. 73, pp. 73, 74, 1889. 46. Report of Progress in Spectrum Work 521 The Chemical News, LXIII, 133, 1891. Johns Hopkins University Circulars No. 85, pp. 41, 42, 1891. American Journal of Science (3), XLI, 243, 244, 1891. 49. Gratings in Theory and Practice 525 Philosophical Magazine (5), XXXV, 397-419, 1893. Astronomy and Astro-Physics, XII, 129-149, 1893. 50. A New Table of Standard Wave-lengths 545 Philosophical Magazine (5), XXXVI, 49-75, 1893. Astronomy and Astro-Physics, XII,. 321-347, 1893. 51. On a Table of Standard Wave-lengths of the Spectral Lines 548 Memoirs of the American Academy of Arts and Sciences, XII, 101-186, 1896. 52. The Separation of the Rare Earths 565 Johns Hopkins University Circulars No. 112, pp. 73, 74, 1894. 57. Notes of Observation on the Rontgen Rays. By H. A. Rowland, N. R. Carmichael and L. J. Briggs 571 American Journal of Science (4), I, 247, 248, 1896. Philosophical Magazine (5), XLI, 381-382, 1896. CONTENTS xi PAGE 58. Notes on Rontgen Bays. By H. A. Rowland, N. R. Carmichael and L. J. Briggs 573 Electrical World, XXVII, 452, 1896. 59. The Eontgen Ray and its Relation to Physics 576 Transactions of the American Institute of Electrical Engineers, XIII, 403-410, 430, 431, 1896. 64. Diffraction Gratings 587 Encyclopaedia Britannica, New Volumes, III, 458, 459, 1902. ADDRESSES 591 1. A Plea for Pure Science. Address as Vice-President of Section B of the American Association for the Advancement of Science, Minne- apolis, August 15, 1883 593 Proceedings of the American Association for the Advancement of Science, XXXII, 105-126, 1883. Science, II, 242-250, 1883. Journal of the Franklin Institute, CXVI, 279-299, 1883. 2. The Physical Laboratory in Modern Education. Address for Com- memoration Day of the Johns Hopkins University, February 22, 1886 614 Johns Hopkins University Circulars No. 50, pp. 103-105, 1886. 3. Address as President of the Electrical Conference at Philadelphia, September 8, 1884 619 Report of the Electrical Conference at Philadelphia in September, 1884, Washington, 1886. 4. The Electrical and Magnetic Discoveries of Faraday. Address at The Opening of the Electrical Club House of New York City, 1888 . 638 Electrical Review, Feb. 4, 1888. 5. On Modern Views with Respect to Electric Currents. Address Be- fore the American Institute of Electrical Engineers, New York, May 22, 1889 653 Transactions of the American Institute of Electrical Engineers, VI, 342- 357, 1889. 6. The Highest Aim of the Physicist. Address as President of the American Physical Society, New York, October 28, 1899 668 Science, X, 825-833, 1899. American Journal of Science (4), VIII, 401-411, 1899. Johns Hopkins University Circulars No. 143, pp. 17-20, 1900. BIBLIOGRAPHY 679 DESCRIPTION OF THE DIVIDING ENGINES DESIGNED BY PRO- FESSOR ROWLAND 689 INDEX. 699 HENRY A. ROWLAND COMMEMORATIVE ADDRESS BY DR. THOMAS C. MENDENHALL [Delivered before an assembly of friends, Baltimore, October 26, 1901.] In reviewing the scientific work of Professor Kowland one is most impressed by its originality. In quantity, as measured by printed page or catalogue of titles, it has been exceeded by many of his contem- poraries; in quality it is equalled by that of only a very, very small group. The entire collection of his important papers does not exceed thirty or forty in number and his unimportant papers were few. When, at the unprecedentedly early age of thirty-three years, he was elected to membership in the National Academy of Sciences, the list of his published contributions to science did not contain over a dozen titles, but any one of not less than a half-dozen of these, including what may properly be called his very first original investigation, was of such quality as to fully entitle him to the distinction then conferred. Fortunately for him, and for science as well, he liijed during a period of almost unparalleled intellectual activity, and his work was done during the last quarter of that century to which we shall long turn with admiration and wonder. During these twenty-five years the num- ber of industrious cultivators of his own favorite field increased enor- mously, due in large measure to the stimulating effect of his own enthu- siasm, and while there was only here and there one possessed of the divine afflatus of true genius, there were many ready to labor most assid- uously in fostering the growth, development, and final fruition of germs which genius stopped only to plant. A proper estimate of the magni- tude and extent of Eowland's work would require, therefore, a careful examination, analytical and historical, of the entire mass of contribu- tions to physical science during the past twenty-five years, many of his own being fundamental in character and far-reaching in their influ- ence upon the trend of thought, in theory and in practice. But it was 1 2 HENRY A. ROWLAND quality, not quantity, that he himself most esteemed in any perform- ance; it was quality that always commanded his admiration or excited him to keenest criticism; no one recognized more quickly than he a real gem, however minute or fragmentary it might be, and by quality rather than by quantity we prefer to judge his work to-day, as he would himself have chosen. Rowland's first contribution to the literature of science took the form of a letter to The Scientific American, written in the early Autumn of 1865, when he was not yet seventeen years old. Much to his sur- prise this letter was printed, for he says of it, " I wrote it as a kind of joke and did not expect them to publish it." Neither its humor nor its sense, in which it was not lacking, seems to have been appreciated by the editor, for by the admission of certain typographical errors he practically destroyed both. The embryo physicist got nothing but a little quiet amusement out of this, but in a letter of that day he de- clares his intention of some time writing a sensible article for the journal that so unexpectedly printed what he meant to be otherwise. This resolution he seems not to have forgotten, for nearly six years later there appeared in its columns what was, as far as is known, his second printed paper and his first serious public discussion of a scientific question. It was a keen criticism of an invention which necessarily involved the idea of perpetual motion, in direct conflict with the great law of the Conservation of Energy which Rowland had already grasped. It was, as might be expected, thoroughly well done, and received not a little complimentary notice in other journals. This was in 1871, the year following that in which he was graduated as a Civil Engineer from the Rensselaer Polytechnic Institute, and the article was written while in the field at work on a preliminary railroad survey. A year later, having returned to the Institute as instructor in physics, he published in the Journal of the Franklin Institute an article entitled " Illustra- tions of Resonances and Actions of a Similar Nature," in which he described and discussed various examples of resonance or " sympa- thetic " vibration. This paper, in a way, marks his admission to the ranks of professional students of science and may be properly con- sidered as his first formal contribution to scientific literature; his last was an exhaustive article on spectroscopy, a subject of which he, above all others, was master, prepared for a new edition of the Encyclopaedia Britannica, not yet published. Early in 1873 the American Journal of Science printed a brief note by Rowland on the spectrum of the Aurora, sent in response to a kindly and always appreciated letter from Pro- COMMEMORATIVE ADDRESS 3 fessor George F. Barker, one of the editors of that journal. It is inter- esting as marking the beginning of his optical work. For a year, or perhaps for several years previous to this time, however, he had been busily engaged on what proved to be, in its influence upon his future career, the most important work of his life. To climb the ladder of reputation and success by simple, easy steps might have contented Eowland, but it would have been quite out of harmony with his bold spirit, his extraordinary power of analysis and his quick recognition of the relation of things. By the aid of apparatus entirely of his own construction and by methods of his own devising, he had made an inves- tigation both theoretical and experimental of the magnetic permea- bility and the maximum magnetization of iron, steel and nickel, a subject in which he had been interested in his boyhood. On June 9, 1873, in a letter to his sister, he says: " I have just sent off the results of my experiments to the publisher and expect considerable from it; not, however, filthy lucre, but good, substantial reputation." What he did get from it, at first, was only disappointment and discourage- ment. It was more than once rejected because it was not understood, and finally he ventured to send it to Clerk Maxwell, in England, by whose keen insight and profound knowledge of the subject it was instantly recognized and appraised at its full value. Eegretting that the temporary suspension of meetings made it impossible for him to present the paper at once to the Eoyal Society, Maxwell said he would do the next best thing, which was to send it to the Philosophical Maga- zine for immediate publication, and in that journal it appeared in August, 1873, Maxwell himself having corrected the proofs to avoid delay. The importance of the paper was promptly recognized by European physicists, and abroad, if not at home, Eowland at once took high rank as an investigator. In this research he unquestionably anticipated all others in the dis- covery and announcement of the beautifully simple law of the magnetic circuit, the magnetic analogue of Ohm's law, and thus laid the founda- tion for the accurate measurement and study of magnetic permea- bility, the importance of which, both in theory and practice during recent years, it is difficult to overestimate. It has always seemed to me that when consideration is given to his age, his training, and the conditions under which his work was done, this early paper gives a better measure of Eowland's genius than almost any performance of his riper years. During the next year or two he continued to work along the same lines in Troy, publishing not many, but occasional, 4 HENRY A. BOWLAND additions to and developments of his first magnetic research. There was also a paper in which he discussed Kohlrausch's determination of the absolute value of the Siemens unit of electrical resistance, fore- shadowing the important part which he was to play in later years in the final establishment of standards for electrical measurement. In 1875, having been appointed to the professorship of physics in the Johns Hopkins University, the faculty of which was just then being organized, he visited Europe, spending the better part of a year in the various centres of scientific activity, including several months at Berlin in the laboratory of the greatest Continental physicist of his time, von Helmholtz. While there he made a very important investi- gation of the magnetic effect of moving electrostatic charges, a question of first rank in theoretical interest and significance. His manner of planning and executing this research made a marked impression upon the distinguished Director of the laboratory in which it was done, and, indeed, upon all who had any relations with Eowland during its pro- gress. He found what von Helmholtz himself had sought for in vain, and when the investigation was finished in a time which seemed incred- ibly short to his more deliberate and painstaking associates, the Director not only paid it the compliment of an immediate presentation to the Berlin Academy, but voluntarily met all expenses connected with its execution. The publication of this research added much to Eowland's rapidly- growing reputation, and because of that fact, as well as on account of its intrinsic value, it is important to note that his conclusions have been held in question, with varying degrees of confidence, from the day of their announcement to the present. The experiment is one of great difficulty and the effect to be looked for is very small and therefore likely to be lost among unrecognized instrumental and observational errors. It was characteristic of Eowland's genius that with compara- tively crude apparatus he got at the truth of the thing in the very start. Others who have attempted to repeat his work have not been uniformly successful, some of them obtaining a wholly negative result, even when using apparatus apparently more complete and effective than that first employed by Eowland. Such was the experience of Lecher in 1884, but in 1888 Eoentgen confirmed Eowland's experiments, detecting the existence of the alleged effect. The result seeming to be in doubt, Eowland himself, assisted by Hutchinson, in 1889 took it up again, using essentially his original method but employing more elaborate and sensitive apparatus. They not only confirmed the early experiments, COMMEMORATIVE ADDRESS 5 but were able to show that the results were in tolerably close agreement with computed values. The repetition of the experiment by Himstedt in the same year resulted in the same way, but in 1897 the genuineness of the phenomenon was again called in question by a series of experi- ments made at the suggestion of Lippmann, who had proposed a study of the reciprocal of the Rowland effect, according to which variations of a magnetic field should produce a movement of an electrostatically charged body. This investigation, carried out by Cremieu, gave an absolutely negative result, and because the method was entirely differ- ent from that employed by Eowland and, therefore, unlikely to be subject to the same systematic errors, it naturally had much weight with those who doubted his original conclusions. Realizing the neces- sity for additional evidence in corroboration of his views, in the Fall of the year 1900, the problem was again attacked in his own laboratory and he had the satisfaction, only a short time before his death, of seeing a complete confirmation of the results he had announced a quarter of a century earlier, concerning which, however, there had never been the slightest doubt in his own mind. It is a further satis- faction to his friends to know that a very recent investigation at the Jefferson Physical Laboratory of Harvard University, in which Row- land's methods were modified so as to meet effectively the objections made by his critics, has resulted in a complete verification of his conclusions. On his return from Europe, in 1876, his time was much occupied with the beginning of the active duties of his professorship, and especially in putting in order the equipment of the laboratory over which he was to preside, much of which he had ordered while in Europe. In its arrangement great, many of his friends thought undue, promi- nence was given to the workshop, its machinery, tools, and especially the men who were to be employed in it. He planned wisely, however, for he meant to see to it that much, perhaps most, of the work under his direction should be in the nature of original investigation, for the successful execution of which a well-manned and equipped workshop is worth more than a storehouse of apparatus already designed and used by others. He shortly found leisure, however, to plan an elaborate research upon the Mechanical Equivalent of Heat, and to design and supervise the construction of the necessary apparatus for a determination of the numerical value of this most important physical constant, which he determined should be exhaustive in character and, for some time to 6 HENRY A. EOWLAND come, at least, definitive. While this work lacked the elements of originality and boldness of inception by which many of his principal researches are characterized, it was none the less important. While doing over again what others had done before him, he meant to do it, and did' do it, on a scale and in a way not before attempted. It was one of the great constants of nature, and, besides, the experiment was one surrounded by difficulties so many and so great that few possessed the courage to undertake it with the deliberate expectation of greatly ex- celling anything before accomplished. These things made it attractive to Eowland. The overthrow of the materialistic theory of heat, accompanied as it was by the experimental proof of its real nature, namely, that it is essentially molecular energy, laid the foundation for one of those two great generalizations in science which will ever constitute the glory of the nineteenth century. The mechanical equivalent of heat, the num- ber of units of work necessary to raise one pound of water one degree in temperature, has, with much reason, been called the Golden Number of that century. Its determination was begun by an American, Count Eumford, and finished by Rowland nearly a hundred years later. In principle the method of Eowland was essentially that of Eumford. The first determination was, as we now know, in error by nearly 40 per cent; the last is probably accurate within a small fraction of 1 per cent. Eumford began the work in the ordnance foundry of the Elector of Bavaria at Munich, converting mechanical energy into heat by means of a blunt boring tool in a cannon surrounded by a definite quantity of water, the rise in temperature of which could be measured. Eowland finished it in an establishment founded for and dedicated to the in- crease and diffusion of knowledge, aided by all the resources and refine- ments in measurement which a hundred years of exact science had made possible. As the mechanical theory of heat was the germ out of which grew the principle of the conservation of energy, an exact determination of the relation of work and heat was necessary to a rigorous proof of that principle, and Joule, of Manchester, to whom belongs more of the credit for this proof than to any other one man or, perhaps, to all others put together, experimented on the mechanical equivalent of heat for more than forty years. He employed various methods, finally recurring to the early method of heating water by friction, improving on Eumford's device by creating friction in the water itself. Joule's last experiments were made in 1878, and most of Eowland's work was done in the year following. It excelled that of COMMEMOBATIVE ADDRESS 7 Joule, not only in the magnitude of the quantities to be observed, but especially in the greater attention given to the matter of thermometry. In common with Joule and other previous investigators, he made use of mercury thermometers, but this was only for convenience, and they were constantly compared with an air thermometer, the results being finally reduced to the absolute scale. By experimenting with water at different initial temperatures he obtained slightly different values for the mechanical equivalent of heat, thus establishing beyond question the variability of the specific heat of water. Indeed, so carefully and accurately was the experiment worked out that he was able to draw the variation curve and to show the existence of a minimum value at 30 degrees C. This elaborate and painstaking research, which is now classical, was everywhere awarded high praise. It was published in full by the Amer- ican Academy of Arts and Sciences with the aid of a fund originally established by Count Eumford, and in 1881 it was crowned as a prize essay by the Venetian Institute. Its conclusions have stood the test of twenty years of comparison and criticism. In the meantime, Rowland's interest had been drawn, largely per- haps through his association with his then colleague, Professor Hast- ings, toward the study of light. He was an early and able exponent of Maxwell's Magnetic Theory and he published important theoretical discussions of electro-magnetic action. Recognizing the paramount im- portance of the spectrum as a key to the solution of problems in ether physics, he set about improving the methods by which it was produced and studied, and was thus led into what will probably always be re- garded as his highest scientific achievement. At that time, the almost universally prevailing method of studying the spectrum was by means of a prism or a train of prisms. But the prismatic spectrum is abnormal, depending for its character largely upon the material made use of. The normal spectrum as produced by a grating of fine wires or a close ruling of fine lines on a plane reflect- ing or transparent surface had been known for nearly a hundred years, and the colors produced by scratches on polished surfaces were noted by Eobert Boyle, more than two hundred years ago. Thomas Young had correctly explained the phenomenon according to the undulatory theory of light, and gratings of fine wire and, later, of rulings on glass were used by Fraunhofer who made the first great study of the dark lines of the solar spectrum. Imperfect as these gratings were, Fraun- hofer succeeded in making with them some remarkably good measures 8 HENRY A. ROWLAND of the length of light waves, and it was everywhere admitted that for the most precise spectrum measurements they were indispensable. In their construction, however, there were certain mechanical difficulties which seemed for a time to be insuperable. There was no special trouble in ruling lines as close together as need be ; indeed, Nobert, who was long the most successful maker of ruled gratings, had succeeded in putting as many as a hundred thousand in the space of a single inch. The real difficulty was in the lack of uniformity of spacing, and on uniformity depended the perfection and purity of the spectrum pro- duced. Nobert jealously guarded his machine and method of ruling gratings as a trade secret, a precaution hardly worth taking, for before many years the best gratings in the world were made in the United States. More than thirty years ago an amateur astronomer, in New York City, a lawyer by profession, Lewis M. Rutherfurd, became inter- ested in the subject and built a ruling engine of his own design. In this machine the motion of the plate on which the lines were ruled was produced at first by a somewhat complicated set of levers, for which a carefully made screw was afterwards substituted. Aided by the skill and patience of his mechanician, Chapman, Rutherfurd continued to improve the construction of his machine until he was able to produce gratings on glass and on speculum metal far superior to any made in Europe. The best of them, however, were still faulty in respect to uniformity of spacing, and it was impossible to cover a space exceeding two or three square inches in a satisfactory manner. When Rowland took up the problem, he saw, as, indeed, others had seen before him, that the dominating element of a ruling machine was the screw by means of which the plate or cutting tool was moved along. The ruled grating would repeat all of the irregularities of this screw and would be good or bad just as these were few or many. The problem was, then, to make a screw which would be practically free from periodic and other errors, and upon this problem a vast amount of thought and experiment had already been expended. Rowland's solution of it was characteristic of his genius; there were no easy advances through a series of experiments in which success and failure mingled in varying proportions ; " fire and fall back " was an order which he neither gave nor obeyed, capture by storm being more to his mind. He was by nature a mechanician of the highest type, and he was not long in devis- ing a method for removing the irregularities of a screw, which aston- ished everybody by its simplicity and by the all but absolute perfection of its results. Indeed, the very first screw made by this process ranks COMMEMORATIVE ADDRESS 9 to-day as the most perfect in the world. But such an engine as this might only be worked up to its highest efficiency under the most favor- able physical conditions, and in its installation and use the most careful attention was given to the elimination of errors due to variation of tem- perature, earth tremors, and other disturbances. Not content, how- ever, with perfecting the machinery by which gratings were ruled, Kow- land proceeded to improve the form of the grating itself, making the capital discovery of the concave grating, by means of which a large part of the complex and otherwise troublesome optical accessories to the diffraction spectroscope might be dispensed with. Calling to his aid the wonderful skill of Brashear in making and polishing plane and concave surfaces, as well as the ingenuity and patience of Schneider, for so many years his intelligent and loyal assistant at the lathe and workbench, he began the manufacture and distribution, all too slowly for the anxious demands of the scientific world, of those beautifully simple instruments of precision which have contributed so much to the advance of physical science during the past twenty years. While willing and anxious to give the widest possible distribution to these gratings, thus giving everywhere a new impetus to optical research, Eowland meant that the principal spoils of the victory should be his, and to this end he constructed a diffraction spectrometer of extra- ordinary dimensions and began his classical researches on the Solar Spectrum. Finding photography to be the best means of reproducing the delicate spectral lines shown by the concave grating, he became at once an ardent student and, shortly, a master of that art. The out- come of this was that wonderful " Photographic Map of the Normal Solar Spectrum," prepared by the use of concave gratings six inches in diameter and twenty-one and a half feet radius, which is recognized as a standard everywhere in the world. As a natural supplement to this he directed an elaborate investigation of absolute wave-lengths, undertaking to give, finally, the wave-length of not only every line of the solar spectrum, but also of the bright lines of the principal ele- ments, and a large part of this monumental task is already completed, mostly by Rowland's pupils and in his laboratory. Time will not allow further expositions of the important conse- quences of his invention of the ruling engine and the concave grating. Indeed, the limitations to which I must submit compel the omission of even brief mention of many interesting and valuable investigations relating to other subjects begun and finished during these years of activity in optical research, many of them by Eowland himself and 10 HENRY A. KOWLAND many of them by his pupils, working out his suggestions and con- stantly stimulated by his enthusiasm. A list of titles of papers ema- nating from the physical laboratory of the Johns Hopkins University during this period would show somewhat of the great intellectual fertil- ity which its director inspired, and would show, especially, his continued interest in magnetism and electricity, leading to his important investi- gations relating to electric units and to his appointment as one of the United States Delegates at important International Conventions for the better determination and definition of these units. In 1883 a com- mittee appointed by the Electrical Congress of 1881, of which Rowland was a member, adopted 106 centimetres as the length of the mercury column equivalent to the absolute ohm, but this was done against his protest, for his own measurements showed that this was too small by about three-tenths of one per cent. His judgment was confirmed by the Chamber of Delegates of the International Congress of 1893, of which Rowland was himself President, and by which definitive values were given to a system of international units. Rowland's interest in applied science cannot be passed over, for it was constantly showing itself, often, perhaps, unbidden, an unconscious bursting forth of that strong engineering instinct which was born in him, to which he often referred in familiar discourse, and which would unquestionably have brought him great success and distinction had he allowed it to direct the course of his life. Although everywhere looked upon as one of the foremost exponents of pure science, his ability as an engineer received frequent recognition in his appointment as expert and counsel in some of the most important engineering operations in the latter part of the century. He was an inventor, and might easily have taken first rank as such had he chosen to devote himself to that sort of work. During the last few years of his life he was much occu- pied with the study of alternating electric currents and their applica- tion to a system of rapid telegraphy of his own invention. A year ago his system received the award of a grand prix at the Paris Exposition, and only a few weeks after his death the daily papers published cable- grams from Berlin announcing its complete success as tested between Berlin and Hamburg, and also the intention of the German Postal Department to make extensive use of it. But behind Rowland, the profound scholar and original investigator, the engineer, mechanician and inventor, was Rowland the man, and any estimate of his influence in promoting the interests of physical science during the last quarter of the nineteenth century would be COMMEMORATIVE ADDRESS 11 quite inadequate if not made from that point of view. Born at Hones- dale, Pennsylvania, on November 27, 1848, he had the misfortune, at the age of 11 years, to lose his father by death. This loss was made good, as far as it is possible to do so, by the loving care of mother and sisters during the years of his boyhood and youthful manhood. From his father he inherited his love for scientific study, which from the very' first seems to have dominated all of his aspirations, directing and con- trolling most of his thoughts. His father, grandfather, and great- grandfather were all clergymen and graduates of Yale College. His father, who is described as one " interested in chemistry and natural philosophy, a lover of nature and a successful trout-fisherman," had felt, in his early youth, some of the desires and ambitions that after- ward determined the career of his distinguished son, but yielding, no doubt, to the influence of family tradition and desire, he followed the lead of his ancestors. It is not unlikely, and it would not have been unreasonable, that similar hopes were entertained in regard to the future of young Henry, and his preparatory school work was arranged with this in view. Before being sent away from home, however, he had quite given himself up to chemical experiments, glass-blowing and other similar occupations, and the members of his family were often sum- moned by the enthusiastic boy to listen to lectures which were fully illustrated by experiments, not always free from prospective danger. His spare change was invested in copper wire and the like, and his first five-dollar bill brought him, to his infinite delight, a small galvanic battery. The sheets of the New York Observer, a treasured family newspaper, he converted into a huge hot-air balloon, which, to the astonishment of his family and friends, made a brilliant ascent and flight, coming to rest, at last, and in flames, on the roof of a neighbor- ing house, and resulting in the calling out of the entire fire department of the town. When urged by his boy friends to hide himself from the rather threatening consequences of his first experiment in aero- nautics, he courageously marched himself to the place where his balloon had fallen, saying, " No ! I will go and see what damage I have done/' When a little more than sixteen years old, in the spring of 1865, he was sent to Phillips Academy at Andover, to be fitted for entering the academic course at Yale. His time there was given entirely to the study of Latin and Greek, and he was in every way out of harmony with his environment. He seems to have quickly and thoroughly ap- preciated this fact, and his very first letter from Andover is a cry for relief. "Oh, take me home!" is the boyish scrawl covering the last 12 HENRY A. ROWLAND page of that letter, on another of which he says, " It is simply horrible; I can never get on here." It was not that he could not learn Latin and Greek if he was so minded, but that he had long ago become wholly absorbed in the love of nature and in the study of nature's laws, and the whole situation was to his ambitious spirit most artificial and irk- some. Time did not soften his feelings or lessen his desire to escape from such uncongenial surroundings, and, at his own request, Dr. Far- rand, Principal of the Academy at Newark, New Jersey, to which city the family had recently removed, was consulted as to what ought to- be done. Fortunately for everybody, his advice was that the boy ought to be allowed to follow his bent, and, at his own suggestion, he was sent, in the autumn of that year, to the Eensselaer Polytechnic Institute at Troy, where he remained five years, and from which he was graduated as a Civil Engineer in 1870. It is unnecessary to say that this change was joyfully welcomed by young Rowland. At Andover the only opportunity that had offered for the exercise of his skill as a. mechanic was in the construction of a somewhat complicated device by means of which he outwitted some of his schoolmates in an early attempt to haze him and in this he took no little pride. At Troy he gave loose rein to his ardent desires, and his career in science may almost be said to begin with his entrance upon his work there and before he was seventeen years old. He made immediate use of the opportunities afforded in Troy and its neighborhood for the examination of machinery and manufacturing processes, and one of his earliest letters to his friends contained a clear and detailed description of the operation of making railroad iron, the rolls, shears, saws, and other special machines being represented in uncommonly well executed pen drawings. One can easily see in this letter a full confirmation of a statement that he occasionally made later in life, namely, that he had never seen a machine, however complicated it might be, whose working he could not at once comprehend. In another letter, written within a few weeks of his arrival in Troy, he shows in a remarkable way his power of going to the root of things which even at that early age was sufficiently in evidence to mark him for future distinction as a natural philosopher. On the river he saw two boats equipped with steam pumps, engaged in trying to raise a half -sun ken canal boat by pumping the water out of it. He described engine?, pumps, etc., in much detail, and adds, "But there was one thing that I did not like about it; they had the end of their discharge pipe about ten feet above the water so that they had to overcome a COMMEMORATIVE ADDRESS 13 pressure of about five pounds to the square inch to raise the water so high, and yet they let it go after they got it there, whereas if they had attached a pipe to the end of the discharge pipe and let it hang down into the water, the pressure of water on that pipe would just have balanced the five pounds to the square inch in the other, so that they could have used larger pumps with the same engines and ths have got more water out in a given time." The facilities for learning physics, in his day, at the Eensselaer Poly- technic Institute were none of the best, a fact which is made the subject of keen criticism in his home correspondence, but he made the most of whatever was available and created opportunity where it was lacking. The use of a turning lathe and a few tools being allowed, he spent all of his leisure in designing and constructing physical apparatus of var- ious kinds with which he experimented continually. All of his spare money goes into this and he is always wishing he had more. While he pays without grumbling his share of the expense of a class supper, he cannot help declaring that " it is an awful price for one night's pleas- ure; why, it would buy another galvanic battery." During these early years his pastime was the study of magnetism and electricity, and his lack of money for the purchase of insulated wire for electro-magnetic apparatus led him to the invention of a method of winding naked copper wire, which was later patented by some one else and made much of. Within six months of his entering the Institute he had made a delicate balance, a galvanometer, and an electrometer, besides a small induction coil and several minor pieces. A few weeks later he an- nounces the finishing of a Euhmkorff coil of considerable power, a source of much delight to him and to his friends. In December, 1866, he began the construction of a small but elaborately designed steam engine which ran perfectly when completed and furnished power for his experiments. A year later he is full of enthusiasm over an investi- gation which he wishes to undertake to explain the production of electricity when water comes in contact with red-hot iron, which he attributes to the decomposition of a part of the water. Along with all of this and much more he maintains a good standing in his regular work- in the Institute, in some of which he is naturally the leader. He occa- sionally writes: "I am head of my class in mathematics," or "I lead the class in Natural Philosophy," but official records show that he was now and then " conditioned " in subjects in which he had no special interest. As early as 1868, before his twentieth birthday, he decided that he must devote his life to science. While not doubting his ability 14 HENRY A. EOWLAND "to make an excellent engineer" as he declares, he decides against engineering, saying, " You know that from a child I have been ex- tremely fond of experiment; this liking instead of decreasing has gradu- ally grown upon me until it has become a part of my nature, and it would be folly for me to attempt to give it up; and I don't see any reason why I should wish it, unless it be avarice, for I never expect to be a rich man. I intend to devote myself hereafter to science. If she gives me wealth, I will receive it as coming from a friend, but if not, I will not murmur." He realized that his opportunity for the pursuit of science was in becoming a teacher, but no opening in this direction presenting itself he spent the first year after graduation in the field as a civil engineer. This was followed by a not very inspiring experience as instructor in natural science in a Western college, where he acquired, however, experience and useful discipline. In the spring of 1872 he returned to Troy as instructor in physics, on a salary the amount of which he made conditional on the purchase by the Institute of a certain number of hundreds of dollars' worth of physical apparatus. If they failed in this, as afterward happened, his pay was to be greater, and he strictly held them to the contract. His three years at Troy as instructor and assistant professor were busy, fruitful years. In addition to his regular work he did an enormous amount of study, purchasing for that purpose the most recent and most advanced books on mathematics and physics. He built his electro- dynamometer and carried out his first great research. As already stated, this quickly brought him reputation in Europe and what he prized quite as highly, the personal friendship of Maxwell, whose ardent admirer and champion he remained to the end of his life. In April, 1875, he wrote, " It will not be very long before my reputation reaches this country," and he hoped that this would bring him opportunity to devote more of his time and energy to original research. This opportunity for which he so much longed was nearer at hand than he imagined. Among the members of the Visiting Board at the West Point Military Academy in June, 1875, was one to whom had come the splendid conception of what was to be at once a revelation and a revolution in methods of higher education. In selecting the first faculty for an institution of learning which, within a single decade, was to set the pace for real university work in America, and whose influence was to be felt in every school and college of the land before the end of the first quarter of a century, Dr. Oilman was guided by an instinct 15 which more than all else insured the success of the new enterprise. A few words about Eowland from Professor Michie, of the Military Academy, led to his being called to West Point by telegraph, and on the banks of the Hudson these two walked and talked, " he telling me," Dr. Oilman has said, " his dreams for science and I telling him my dreams for higher education/' Eowland, with characteristic frank- ness, writes of this interview, " Professor Gilman was very much pleased with me," which, indeed, was the simple truth. The engage- ment was quickly made. Eowland was sent to Europe to study labor- atories and purchase apparatus, and the rest is history, already told and everywhere known. Eowland's personality was in many respects remarkable. Tall, erect and lithe in figure, fond of athletic sports, there was upon his face a certain look of severity which was, in a way, an index of the exacting standard he set for himself and others. It did not conceal, however, what was, after all, his most striking characteristic, namely, a perfectly frank, open and simple straightforwardness in thought, in speech and in action. His love of truth held him in supreme control, and, like Galileo, he had no patience with those who try to make things appear otherwise than as they actually are. His criticisms of the work of others were keen and merciless, and sometimes there remained a sting of which he himself had not the slightest suspicion. "I would not have done it for the world," he once said to me after being told that his pitiless criticism of a scientific paper had wounded the feelings of its author. As a matter of fact he was warm-hearted and generous, and his occasionally seeming otherwise was due to the complete separation, in his own mind, of the product and the personality of the author. He possessed that rare power, habit in his case, of seeing himself, not as others see him, but as he saw others. He looked at himself and his own work exactly as if he had been another person, and this gave rise to a frankness of expression regarding his own performance which some- times impressed strangers unpleasantly, but which, to his friends, was one of his most charming qualities. Much of his success as an investi- gator was due to a firm confidence in his own powers, and in the unerring course of the logic of science which inspired him to cling tenaciously to an idea when once he had given it a place in his mind. At a meeting of the National Academy of Science in the early days of our knowledge of electric generators, he read a paper relating to the fundamental principles of the dynamo. A gentleman who had had large experience with the practical working of dynamos listened to the paper, and at the 16 HENRY A. ROWLAND end said to the Academy that unfortunately practice directly contra- dicted Professor Rowland's theory, to which instantly replied Rowland, " So much the worse for the practice," which, indeed, turned out to be the case. Like all men of real genius, he had phenomenal capacity for concen- tration of thought and effort. Of this, one who was long and intimately associated with him remarks, " I can remember cases when he appeared as if drugged from mere inability to recall his mind from the pursuit of all-absorbing problems, and he had a triumphant joy in intellectual achievement such as we would look for in other men only from the gratification of an elemental passion." So completely consumed was he by fires of his own kindling that he often failed to give due attention to the work of others, and some of his public utterances give evidence of this curious neglect of the historic side of his subject. As a teacher his position was quite unique. Unfit for the ordinary routine work of the class room he taught as more men ought to teach, by example rather than by precept. Says one of his most eminent pupils, " Even of the more advanced students only those who were able to brook severe and searching criticism reaped the full benefit of being under him, but he contributed that which, in a University, is above all teaching of routine, the spectacle of scientific work thoroughly done and the example of a lofty ideal." Returning home about twenty years ago after an expatriation of several years, and wishing to put myself in touch with the development of methods of instruction in physics and especially in the equipment of physical laboratories, I visited Rowland very soon after, as it happened, the making of his first successful negative of the solar spectrum. That he was completely absorbed in his success was quite evident, but he also seemed anxious to give me such information as I sought. I questioned him as to the number of men who were to work in his laboratory, and although the college year had already begun he appeared to be unable to give even an approximate answer. " And what will you do with them ? " I said. " Do with them ? " he replied, raising the still drip- ping negative so as to get a better light through its delicate tracings, " Do with them ? I shall neglect them." The whole situation was in- tensely characteristic, revealing him as one to whom the work of a drill- master was impossible, but ready to lead those who would be led and could follow. To be neglected by Rowland was often, indeed, more stimulating and inspiring than the closest personal supervision of men lacking his genius and magnetic fervor. COMMEMORATIVE ADDRESS 17 In the fulness of his powers, recognized as America's greatest physi- cist, and one of a very small group of the world's most eminent, he died on April 16, 1901, from a disease the relentless progress of which he had realized for several years and opposed with a splendid but quiet courage. It was Eowland's good fortune to receive recognition during his life in the bestowal of degrees by higher institutions of learning; in elec- tion to membership in nearly all scientific societies worthy of note in Europe and America; in being made the recipient of medals of honor awarded by these societies; and in the generously expressed words of his distinguished contemporaries. It will be many years, however, be- fore full measure can be had of his influence in promoting the interests of physical science, for with his own brilliant career, sufficient of itself to excite our profound admiration, must be considered that of a host of other, younger, men who lighted their torches at his flame and who will reflect honor upon him whose loss they now mourn by passing on something of his unquenchable enthusiasm, something of his high regard for pure intellectuality, something of his love of truth and his sweetness of character and disposition. SCIENTIFIC PAPERS PART I EARLY PAPERS THE VOKTEX PROBLEM [Scientific American, XIII, 308, 1865] Messrs. Editors: In a late number of your paper an inquiry was made why a vortex was formed over the orifice of an outlet 1 pipe; as, for instance, in a bath tub, when the water is running out. If the water be first started, the explanation will be on the same principle that a ball and string will, if started, wind itself up upon the hand; the ball being attached to the string will, as the string winds up, get nearer the hand, and, consequently, will have less far to go to make one revo- lution, and thus the momentum, though perhaps not great enough to carry it around in the great circle, is still sufficient to make it revolve in the smaller one. Therefore, as the string is continually winding up, and the ball con- tinually nearing the hand, it will, if the resistance of the air is not too great, continue to revolve until the string is wound up. Now, in the case of the water, each particle of it will represent the ball, the force of the water rushing toward the outlet will be the string, and, the water running out, and thus causing the particles to come nearer the center at every revolution, will represent the winding-up process. Thus, we see this case is analogous to the preceding, and the same reason that will apply to one will apply to the other. I suppose that some slight motion existing among the particles of the water, united to the motion produced by the outlet, causes the vortex to begin, and, once begun, it will continue until the water is exhausted. Such motion could either previously exist, or might be produced by the form * of the vessel, which would cause the water, in running to the outlet, to assume a certain direction. H. A. R. Troy, N. T., October, 1865. '[In the original article this reads "outlet of an orifice," an obvious misprint.] MIn the original article this word is "power," an obvious misprint.] PAINE'S ELECTRO-MAGNETIC ENGINE [Scientific American, XXV, 21, 1871] To the Editor of the Scientific American: Having noticed several articles in your paper with reference to Paine's electro-magnetic machine, I believe I cannot do better than describe a visit which I paid it about three months ago. Entering the office in company with a friend, at about twelve o'clock one day, I was told that the machine was not running then, but would be in operation at one. Proceeding there alone, at about that time, I was, after the formality of sending up my name, conducted by a small boy, through numerous by-ways and passages, to the second story of a back building, where I was met by the illustrious inventor and a few select friends. Mr. Paine began by showing the small model machines, which he set in motion by a battery of four cups, of about a gallon capacity each. These models revolved very well, but apparently with no power, for they could be stopped easily. I then began to reason with him on the absurdity of his position, and adduced in my support the experiments of Joule, Mayer, Faraday and others. He, evidently, had no very high opinion of these, and pronounced the conservation of force an old fashioned idea, which had been overthrown in these enlightened days by his " experiments," though what the latter were I have never determined. After conversing some time, to no purpose, he prepared to over- throw me and my authority at one blow, by an exhibition of The Machine. This was standing in front of a chimney, on one side of the room, with the axis of its wheels parallel to the wall. The wheel to which the magnets were attached was, unlike the models, inclosed in a cast iron case, which enveloped it closely above, but spread out into a rectangular base below. The latter rested directly on the floor. The axis of the wheel projected on each side, and, to one end, a pulley was attached, and to the other, the brake for operating the magnets. The machine had the general appearance of a fan blower with an enlarged pulley. The battery was attached to two binding screws, fixed to a PAINE'S ELECTBO-MAGNETIC ENGINE 25 standard on the chimney, and the current was supposed to pass from these, along wires, to the break piece, and thence to the magnets. A belt on the pulley connected with a shaft overhead, whence another belt proceeded to the pulley of a small circular saw. As soon as the connection was made with the battery, the whole apparatus began to move, and soon the saw attained great velocity, shaking the building with violence. The latter effect was caused by a heavy fly wheel on the saw arbor, which probably was not well balanced. When well in motion, boards were applied and sawed with the greatest ease. To show the excess of power, they were sometimes placed on edge and passed over the saw, so as wholly to envelop it, and the cut made from end to end, without the velocity being at all diminished. On throwing off the belt from the saw, the machine still proceeded at the same velocity, with entire indifference to external resistance. On mentioning this to Mr. Paine, he informed me that when the saw was attached, and the resistance greater, the increased pull on the magnets brought them nearer together, by bending the heavy iron frame; and, as magnetic attraction varies inversely as the square of the distance, it only required a small change of distance to account for the increased power. I clearly indicated that I was skeptical on this point, and sug- gested that it would also work without variation if the power pro- ceeded from some well governed steam engine in the neighborhood. On this he intimated that, if I were not careful, a force might proceed from his body which would act in conjunction with gravitation in causing me to be projected through the window, and strike with vio- lence on the ground below. The exhibition being over, on going down stairs in company with the rest, I tried the door of the room below, but found it locked, and the windows covered with papers. I desired to get in, but was met with the assurance that the room was rented by a man who was then absent. This, 1 believe, is the last visit paid by an outsider to this wonderful invention. I have been there several times since, but there has been no admittance to me, or to any one else. I have since been to the owner of the building, and find that Mr. Paine rents the room to which I sought admittance, and also rents power in that same room, which is directly below that containing his machine. The engine from which the power comes generally stops work at twelve and starts again at one, but sometimes works all day. My visits there have established the following facts: First, That my friend and I were denied admittance at twelve o'clock, but were 26 HENEY A. KOWLAND invited to come at one. Second, That the shaft in the room below does not revolve between the hours of twelve and one. Third, That the room below, containing power, was rented by Mr. Paine, but that he kept it carefully locked, and misguided me as to the tenant. Fourth, That the working parts are concealed in an unnecessarily strong case, well adapted to the concealment of another source of power. Fifth, That part of the apparatus is attached to the wall, so that the machine must always occupy the same position on the floor. Sixth, That the models have not a power proportionate to their size. Seventh, That the machine runs at the same velocity, whether producing one horse power or a fraction of a horse power, and this without a governor. These are the facts of the case. Where the power of the machine comes from I am unable to say. Is there some secret connection be- tween this machine and the shaft below, and does the battery serve only to make this connection? Or does the battery, when applied, connect the apparatus with a larger battery? I leave these questions to others; but, unless the reasoning and experiments of a host of our greatest men be false, and unless the greatest development of modern science be overthrown, this machine cannot but derive its power from some extraneous source. In a late communication to your paper, Mr. Paine sets himself up as the peer of Faraday, Tyndall and others, and gives as the reason, his long devotion to science. He evidently does not consider that to be ranked with such men requires something more than devotion; it requires brains; brains to discriminate between true science and quack- ish nonsense; brains to discover and originate. And pray what fact, among the thousands of science, does Mr. Paine pretend to have proved beyond doubt ? Let him answer. As to Mr. Paine's " science," I assert that it is a tissue of error and ignorance, from beginning to end. Even his vaunted invention of metallic foil, wherewith to envelop his magnets or wire, can operate in no other manner than to the detriment of his machine, as any such metallic coating lengthens the demagneti- zation, which is the very thing to be guarded against. This is due to an induced current, which forms in the coating, and, being in the same direction as the primary current, operates in the same manner to keep up the magnetism. His reason for the machine's keeping at the same velocity also shows great ignorance of the subject. In the first place, the law of magnetic force, under these circumstances, is stated entirely wrong. For this case, the true law is complex, but most nearly ap- proaches to that of inversely as the distance, instead of as the square of PAINE'S ELECTRO-MAGNETIC ENGINE 27 the distance. (See Joule, and also Tyndall, in the London, Edinburgh and Dublin Philosophical Magazine for 1850.) And, in the second place, approach of the poles would not necessarily increase the effi- ciency; in this kind of machine there is a distance of maximum effi- ciency; and if the magnets revolve at a distance greater than this, the attraction becomes too small; and if at a less distance, the times of magnetizing and demagnetizing the magnets become too great, and the machine goes too slowly. The distance in this machine is, undoubtedly, within the limit, for Mr. Paine prides himself upon its smallness, and so further reduction, could it take place, can act in no other manner than the opposite of that claimed. But it is my opinion that all the force brought to bear on the magnets could not move them one two- hundredth of an inch, when attached to such a frame. As to Mr. Paine's disregard for the conservation of force, I have little to say. His assertions are made directly in the face of this principle, and yet he has never adduced one experiment, or even a plaus- ible reason, to prove what he says. He takes you into a building where shafts are revolving by the vulgar power of steam, and directs you to look while he evokes power from nothing. You must not touch any- thing; you must not enter the room below; you must not be there while the engine next door is at rest; but you must simply look, and by that renowned maxim of fools, that " seeing is believing/' you must believe that the whole structure of science has fallen, and that above its ruins nothing remains but Mr. Paine and his wonderful electro-magnetic machine. HENRY A. EOWLAND, C. E. Newark, N. J. ILLUSTRATION OF RESONANCES AND ACTIONS OF A SIMILAR NATURE [Journal of the Franklin Institute, XCIV, 275-278, 18721 At the present day, when scientific education is beginning to take its proper place in the public estimation, anything which can help toward imparting a clear idea of any physical phenomenon becomes im- portant. There are a number of these phenomena, of which resonance is one, which play quite an important part in nature, but which as yet have not been illustrated with sufficient clearness in the lecture-room. Among these are the following: A person carrying water may so time his steps as to produce waves which shall rise and fall in unison with the motion of his body; soldiers in crossing a bridge must not keep step, or they may transmit such a vibration to it as to break it down; window-panes are sometimes cracked by sounding a powerful organ- pipe to which they can vibrate ; a tuning-fork will respond to another of equal pitch sounded near it; and others will readily suggest themselves to the reader. In all these cases we have two bodies which can vibrate in equal times, connected together either directly or by some medium which transmits the motion from one to the other. We can, then, readily reproduce the circumstances in the lecture-room. The vibrating bodies which I have found most convenient are pendu- lums; they are easily made, are seen well at a distance, and their time of vibration can be easily and quickly regulated. The apparatus can be prepared in the following manner: Fix a board, about a foot long, in a horizontal position; suspend a piece cf small stiff wire, of equal length, beneath its edge, parallel to it, and an inch or two distant, by means of threads. To one end of the board suspend a pendulum, con- sisting of a thread about ten or twenty inches long, to which is attached a ball weighing two or three ounces; join the thread of this pendulum to the horizontal wire by taking a turn of it around the wire, so that when the pendulum oscillates, it causes the wire to move back and forth in unison with it. To complete the apparatus, prepare a number of small pendulums by suspending bullets to threads, and let them have small hooks of wire to hang by. ILLUSTRATION OF KESONANCES 29 Having then set the heavy pendulum in motion, hang some of the light ones on the horizontal wire, and note the result: those which are shorter or longer than the heavy one will not be affected, but if any of them are nearly of the same length, they will begin to vibrate to a small extent, but will soon come to rest, after which they will com- mence again, but stop as before ; but if any one happens to be of exactly the proper length, its motion will soon become very great, and im- mensely surpass in amplitude that of the heavy one, although the motion is derived from it. Of course the heavy pendulum must be retarded in giving motion to the light one, but it is hardly perceptible when there is great difference in the weight. In the same manner a tuning-fork will undoubtedly come to rest sooner when producing resonance than when vibrating freely. To show this retardation more clearly, suspend two pendulums, equal in weight and length, to the edge of a horizontal board, and connect their two threads together by a horizontal thread tied to each at a point an inch or two from the top, and drawn so tight as to pull each of the pendulums a little out of plumb. On starting one of these pendulums the other will gradually move, and finally absorb all the motion from the first, and bring it entirely. to rest; the action will then begin anew, and the motion will be entirely given back to the first ball. This experiment differs from that of resonance, inasmuch as in the case of the pendulums all the motion of the first ball is finally stored up in the second; but in the case of resonance the confined air is constantly giving out its motion to the atmosphere in waves of sound. To imitate this to some extent we must attach a rather large piece of paper to the second pendulum, so that it will meet with resistance, and then both balls will come to rest sooner than otherwise. If one of the balls is only two or three times heavier than the other, they will then also interchange motions; but when the heavy ball has the motion, the arc of its vibration will not be so great as that of the other when it vibrates. To illustrate the use of Helmholtz resonance globes, or Koenig's apparatus for the analysis of sounds, we can enlarge and modify the first apparatus somewhat. Make the board six or eight feet long, and suspend at one end four or five of the heavy pendulums, and at the other the same number of light ones, each of which corresponds in time of vibration with one of the heavy ones. On now causing any of the heavy pendulums to vibrate, as No. 3, we shall meet with no response from any of the light ones except No. 7. If Nos. 1, 2 and 4 are set going at one time, the wire A will be drawn hither and thither by the 30 HENKY A. ROWLAND conflicting pulls with no seeming regularity, but each of the balls 5, 6 and 8 will pick out from the confused motion the vibration due to itself, and will move in unison, but No. 7 will remain quiet. The short pendulums always produce the effect sooner than the long ones. To remedy this to some extent it is well to bend the wire A into the shape shown in the figure. It is not well to make the pendulum more than twenty inches long, if a quick response is wished. There seems to be no limit to the number of pendulums which can be used or the distance to which the effect can be transmitted, though it is more decided when there are but few pendulums and they are near together. It may some- times be more convenient to suspend the pendulums from a wire, :wm tightly stretched, than from a board. To make the balls visible at a distance, it may be well in some cases to make them of polished steel, and illuminate them by a beam from the electric lamp. These experiments have many advantages which recommend them to teachers; they can be performed without purchased apparatus, and can be made to illustrate resonance and the kindred phenomena in all their details. Indeed, any one will be well repaid for spending an hour in performing them, simply for their own beauty. 4 ON THE AUKORAL SPECTRUM I American Journal of Science [3], F, 320, 1873] A letter from Henry A. Rowland, at present Instructor in Physics in the Rensselaer Polytechnic Institute at Troy, informs us that he observed the line of wave-length 431 in the auroral spectrum of last October. He says : " The observations were made with an ordinary chemical spectroscope of one prism, in which the scale was read by means of a lamp. Great care was taken in the readings, and after com- pleting them the spectroscope was set aside until morning, when the readings were taken on the lines of comparison without altering the instrument in any way or even regulating the slit. The wave-lengths of the known lines were taken from Watts's * Index of Spectra/ but as he does not give the wave-lengths of lines in the flame spectrum I am not quite certain that they are correct." On the scale of his instru- ment, Li a was at 13.5, Ca a 21, Naa27.5 , Ca/336 , Ca r 95.5, and K/s 110. The aurora lines were as follows: Scale-reading. Wave-lengths. 1 19 628.3 2 35.5 554.3 3 95 425 " The wave-lengths of the auroral lines were obtained by graphical interpolation on such a large scale as to introduce little or no error." PART II MAGNETISM AND ELECTRICITY ON MAGNETIC PERMEABILITY, 1 AND THE MAXIMUM OF MAGNETISM OF IRON, STEEL, AND NICKEL [Philosophical Magazine [4], XL VI, 140-159, 1873] More than three years ago I commenced the series of experiments the results of which I now publish for the first time. Many of the facts which I now give were obtained then; but, for satisfactory reasons, they were not published at that time. The investigations were com- menced with a view to determine the distribution of magnetism on iron bars and steel magnets; but it was soon found that little could be done without new experiments on the magnetic permeability of sub- stances. Few observations have been made as yet for determining the mag- netic permeability of iron, and none, I believe, of nickel and cobalt, in absolute measure. The subject is important, because in all theories of induced magnetism a quantity is introduced depending upon the mag- netic properties of the substance, and without a knowledge of which the problem is of little but theoretical interest; this quantity has always been treated as a constant, although the experiments on the maximum of magnetism show that it is a variable. However, the form of the function has never been determined, except so far as we may deduce it from the equation of Miiller, which, as will be shown, leads to wrong results. The quantities used by different persons are as follows: , Neumann's coefficient, or magnetic susceptibility (Thomson). Tc, Poisson's coefficient. /*, coefficient of magnetization (Maxwell), or magnetic permeability (Thomson). ^-, introduced for convenience in the following paper. 1 The word "permeability" has been proposed by Thomson, and has the same meaning as "conductivity" as used by Faraday ('Papers on Electricity and Magnet- ism,' Thomson, p. 484; Maxwell's 'Electricity and Magnetism,' vol. ii, p. 51.) 36 HEXRY A. ROWLAND The relations of these quantities are given by the following equa- tions : , _ - 3k A The first determination of the value of any of these quantities was made by Thalen. But more important experiments have been made by Weber, Von Quintus Icilius, and more recently by M. Eeicke and Dr. A. Stoletow. 2 The first three of these in their experiments used long cylindrical rods, or ellipsoids of great length; the last, who has made by far the most important experiments on this subject, has used an iron ring. The method of the ring was first used by Dr. Stoletow in September, 1871; but more than eight months before that, in Jan- uary, 1871, I had used the same method, but with different apparatus, to measure the magnetism. He plots a curve showing the variation of K ; but he plots it with reference to E as abscissa instead of R * , and thus fails to determine the law. His method of experiment is much more complicated than mine, so that he could only obtain results for one ring; while by my method I have experimented on about a dozen rings and on numerous bars, so that I believe I have been enabled to find the true form of the function according to which /* varies with the magnetism of the bar or the magnetizing-force. Many experiments have been made on the magnetism of iron without giving the results in absolute measure. Among these are the experi- ments of Muller, Joule, Lenz and Jacobi, Dub, and others. The ex- periments have been made by the attraction of electromagnets, by the deflection of a compass-needle, or, in one case, by measuring the in- duced current in a helix extending the whole length of the bar. By the last two methods the change in the distribution of magnetism over the bar when the magnetism of the bar varies is disregarded, if indeed it was thought of at all : even in a recent memoir of M. Cazin * we have the statement made that the position of the poles is independent of the strength of the current. He does not give the experiment from which he deduces this result. Now it is very easy to show, from the formula 'Phil. Mag., January, 1873. 3 Annales de Chimie et de Physique, Feb., 1873, p. 171. MAGNETIC PERMEABILITY OF IROX, STEEL AND XICKEL 37 of Green for the distribution of magnetism on a bar-magnet combined with the known variation of K, that this can only be true for short and thick bars; and it has also been remarked by Thomson that this should be the case. 4 An experiment made in 1870 places this beyond doubt. A small iron wire (No. 16), 8 inches long, was wound with two layers of fine insulated wire; a small hard steel magnet inch long suspended by a fibre of silk was rendered entirely astatic by a large magnet placed about 2 feet distant; the wire electromagnet was then placed near it, so that the needle hung H inch from it and about 2 inches back from the end. On now exciting the magnet with a weak current, the needle took up a certain definite position, indicating the direction of the line of force at that point. When the current was very much increased, the needle instantly moved into a position more nearly parallel to the magnet, thus showing that the magnetism was now distributed more nearly at the ends than before. This shows that nearly all the experi- ments hitherto made on bar-magnets contain an error; but, owing to its small amount, we can accept the results as approximately true. I believe mine are the first experiments hitherto made on-this subject in which the results are expressed and the reasoning carried out in the language of Faraday's theory of lines of magnetic force ; and the utility of this method of thinking is shown in the method of experimenting adopted for measuring magnetism in absolute measure, for which I claim that it is the simplest and most accurate of any yet devised. Whether Faraday's theory is correct or not, it is well known that its use will give correct results; at the present time the tendency of the most advanced thought is toward the theory 5 ; and indeed it has been pointed out by Sir William Thomson that it follows, from dynamical reasoning upon the magnetic rotation of the plane of polarization of light, that the medium in which this takes place must itself be in rotation, the axis of rotation being in the direction of the lines of force. 8 Some substances must of necessity be more capable of assum- ing this rotary motion than others; and hence arises the notion of magnetic " conductivity '"' and " permeability." Thomson has pointed out several analogies which may be used in calculating the distribution and direction of the lines of force under various circumstances. He has shown that the mathematical treatment 4 Papers on Electricity and Magnetism, p. 512. 5 "On Action at a Distance," Maxwell, 'Nature,' Feb. 27 and March 6 and 13, 1873. "Thomson's 'Papers on Electricity and Magnetism,' p. 419, note; and Maxwell's 'Treatise on Electricity and Magnetism,' vol. ii, chap. xxi. 38 HENRY A. EOWLAND of magnetism is the same as that of the flow of heat in a solid, as the static induction of electricity, and as the flow of a frictionless incom- pressible liquid through a porous solid. It is evident that to these analogies we may add that of the conduction of electricity. 7 We readily see that the reason of the treatment being the same in each case is that the elementary law of each is similar to Ohm's law. Mr. Webb 8 has shown that this law is useful in electrostatics; and I hope, in a sequel to this paper, to apply it to the distribution of magnetism: I give two equations derived in this way further on. The absolute units to which I have reduced my results are those in which the metre, gramme, and second are the fundamental units. The unit of magnetizing-force of helix I have taken as that of one turn of wire carrying the unit current per metre of length of helix, and is 4?r times the unit magnetic field. This is convenient in practice, and also because in the mathematical solution of problems in electrodynam- ics the magnetizing-force of a solenoid naturally comes out in this unit. The magnetizing-force of any helix is reduced to this unit by multiply- ing the strength of current in absolute units by the number of coils in the helix per metre of length. These remarks apply only to endless solenoids, and to those which are very long compared with their diam- eter. The unit of number of lines of force I have taken as the number in one square metre of a unit field measured perpendicular to their direction. As my data for reducing my results to these units, I have taken the horizontal force of the earth's magnetism at Troy as 1-641, and the total force as 6-27. The total force, which will most seriously affect my results, is well 'known to be nearly constant at any one place for long periods of time. From the analogy of a magnet to a voltaic battery immersed in water I have obtained the following, on the assumption that // is constant, and that the resistance to the lines of force passing out into the medium is the same at every point of the bar. Let R = resistance to lines of force of one metre of length of bar. E' = resistance of medium along 1 metre of length of bar. Q' = lines of force in bar at any point. Q f = lines of force passing from bar along small distance I. e =base of Napierian system of logarithms. x = distance from one end of helix. 1 Maxwell's 'Treatise on Electricity and Magnetism,' arts. 243, 244 and 245. s "Application of Ohm's Law to Problems in Electrostatics," Phil. Mag. S. 4, vol. xxxv, p. 325 (188). MAGNETIC PERMEABILITY OF IRON, STEEL AND NICKEL 39 & = total length of helix. s' = resistance at end of helix of the rest of bar and medium. M = magnetizing-f orce of helix. We then obtain Ml -A / rx r (-*)-) (l\ 1M M 1 A m - ~ A fe r 4-1 s n e r (-*)^ f9\ s' ~f 2R A^- I ( IJE -VTT in which and for near the centre of an infinitely long bar, where x > and < &, and 6=00 , we have Q.= 0,and V=%. . .-'. (3) For a ring-magnet, s' = 0; .-. & = 0,and Q=X ...... (4) And if a is the area of the bar or ring, al =B = -ir ori = iSr ..... (5) in which A is the same as in the equations previously given. These equations show that we may find the value of ^, and hence the permea- bility, by experimenting either on an infinitely long bar or on a ring- magnet. Equations (4) evidently apply to the case where the diameter of the ring is large as compared with its section. The fact given by these equations can be demonstrated in another and, to some persons, more satisfactory manner. If n is the number of coils per metre of helix and n' the number on a ring-magnet, i the strength of current, and p the distance from the axis of the ring to a given point in the Formulae giving the same distribution as this have been obtained by Biot and also by Green. See Biot's Traite de Physique, vol. iii, p. 77, 10 and 'Essay on the Ap- plication of Mathematical Analysis to the Theories of Electricity and Magnetism,' by Green, 17th section. IO [In the original paper this was " vol. iv, p. 669." The correction was made later by Professor Rowland.] 40 HENRY A. KOWLAND interior of the ring-solenoid, the magnetic field at that point will, as is well known, be 2n'i - , f> and at a point within an infinitely long solenoid If the solenoid contain any magnetic material, the field will be for the ring and for the infinite solenoid 4x/ttft, Therefore the number of lines of force in the whole section of a ring- magnet of circular section will be, if a is the mean radius of the ring, S Q'= n' in dx = J B a x or, since n' = 2 * an and M = in, we have, by developing, Qf= ^jfoorj?) (i + \ f + i jr + & c .y . . (6) For the infinite electromagnet we have in the same way for a circular section, Q' = 4*Mn(*B*) ......... (7) When the section of the ring is thin, equation (6) becomes the same as equation (7), and either of them will give which is the same as equation (5). In all the rings used the last parenthesis of (6) is so nearly unity that the difference has in most cases been neglected, the slightest change in the quality of the iron producing many times more effect on the permeability than this. Whenever the difference amounted to more than -^TT it was not rejected. The apparatus used to measure Q' was based upon the fact discovered by Faraday, that the current induced in a closed circuit is proportional to the number of lines of force cut by the wire, and that the deflection of the galvanometer-needle is also, for small deflections, proportional to that number. In the experiments of 1870-71 an ordinary astatic galvanometer was used; but in those made this year a galvanometer was MAGNETIC PERMEABILITY OF IRON, STEEL AND XICKEL 41 specially constructed for the purpose. It was on the principle of Thom- son's reflecting instrument, but was modified to suit the case by increas- ing the size of the mirror to of an inch, by adding an astatic needle just above the coil without adding another coil, by loading the needle to make it vibrate slowly, and, lastly, by looking at the reflected image of the scale through a telescope instead of observing the reflection of a lamp on the scale. The galvanometer rested on a firm bracket attached to the wall of the laboratory near its foundation. In most of the ex- periments the needle made about five single vibrations per minute. The astatic needle was added to prevent any external magnetic force from deflecting the needle; and directive force was given by the magnet above. Each division of the scale was 075 inch long; and the extrem- ities of the scale were reached by a deflection of 7 in the needle from 0. The scale was bent to a radius of 4 feet, and was 3 feet from the instru- ment. At first a correction was made for the resistance of the air, &c. ; but it was afterwards found by experiment that the correction was very exactly proportional to the deflection, and hence could be dispensed with. This instrument gave almost perfect satisfaction; and its accu- racy will be shown presently. The tangent-galvanometer was also a very fine instrument, and was constructed expressly for this series of experiments. The needle was 1*1 inch long, of hardened steel; and its deflections were read on a circle graduated to half degrees, and 5 inches in diameter. The aver- age diameter of the ring was 16^ inches nearly, and was wound with several coils; so that the sensibility could be increased or diminished at pleasure, and so give the instrument a very wide range. The value of each coil in producing deflection was experimentally determined to within at least ^ of 1 per cent by a method which I shall soon publish. The numbers to multiply the tangent of the deflection by, in order to reduce the current to absolute measure, were as follows: Number of coils. Multiplier. 1 -05377 3 -01800 9 " . -006007 27 -002018 48 " . -001143 By this instrument I had the means of measuring currents which varied in strength several hundred times with the same accuracy for a large as for a small current. For greater accuracy a correction was 42 HENEY A. ROWLAND applied according to the formula of Blanchet and De la Prevostaye for the length of the needle, the position of the poles being estimated; this correction in the deflections used was always less than -6 per cent. To eliminate any error in the position of the zero-point, two readings were always taken with the currents in opposite directions, each one being estimated with considerable accuracy to ^ of a degree. The experiments were carried on in the assay laboratory of the Institute, which was not being used at that time; and precautions were taken that the different parts of the apparatus should not interfere with each other. The disposition of the apparatus is represented in Plate II. The current from the battery A, of from two to six large Chester's " electropoion " cells No. 2, joined according to circumstances, passed to the commutator B, thence to the tangent-galvanometer C, thence to another commutator D, thence around the magnet E (in this case a ring), and then back through the resistance-coils K to the battery. To measure the magnetism excited in E, a small coil of wire F was placed around it, 11 which connected with the galvanometer H, so that, when the magnetism was reversed by the commutator D, the current induced in the coil F, due to twice cutting the lines of force of the ring, produced a sudden swing of the needle of H. As the needle swung very freely and would not of itself come to rest in ten or fifteen min- utes, the little apparatus 7 was added : this consisted of a small horse- shoe magnet, on one branch of which was a coil of wire ; and by sliding this back and forth, induced currents could be sent through the wire, which, when properly timed, soon brought the needle to rest. This arrangement was very efficient; and without it this form of galvano- meter could hardly have been used. To compare the magnetism of the ring with the known magnetism of the earth, and thus reduce it to absolute measure, a ring G supported upon a horizontal surface was included in the circuit; when this was suddenly turned over, it produced an induced current, due to twice cutting the lines of magnetic force which pass through the ring from the earth's magnetism. The induced current in the case of either coil, F or G, is proportional to the number of the lines of force cut by the coils " and to the number of wires in the coil, which latter is self evident, but may be deduced from the law of Gaugain. 1 * It is evident, then, that if c is the deflection from coil G, 11 If a bar was used, this coil was placed at its centre. 12 Faraday's Experimental Researches, vol. iii, series 29. 13 Dagnin's Traite de Physique, vol. iii, p. 691. MAGNETIC PERMEABILITY OF IRON, STEEL AND NICKEL 43 and h that from helix F, the number of lines of force passing through the magnet E, expressed in the unit we have chosen, will he (9) where ri is the number of coils in the ring G, n the number in the helix F, R the radius of G, 6- 27 the total magnetism of the earth, and 7450' the dip. The quantity 2n'(6-27 sin 7450')^E 2 is constant for the coil, and had the value 14* 15. This is the number of square metres of a unit field which, when cut once by a wire from the galvanometer, would produce the same deflection as the coil when turned over. The experiments being made by reversing the magnetism of the bars, a rough experiment was made to see whether they had time to change in half a single vibration of the needle; it was found that this varied from sensibly to nearly 1 second, so that there was ample time. It was also proved that the sudden impulse given to the needle by the change of current produced the same deflection as when the change was more gradual, which has also been remarked by Faraday, though he did not use such sudden induced currents. As a test of the method, the horizontal force of the earth's magnetism was determined by means of a vertical coil; it was found to be 1' 634. while the true quantity is 1-641. It is sometimes assumed that some of the action in a case like the present is due to the direct induction of the helix around the magnet on the coil F. I think that this is not correct; for when the helix is of fine wire closely surrounding the bar or ring, all the lines of force which affect F must pass through the bar, and so no correction should be made. However, the correction is so small that it will hardly affect the result. If it were to be made, -^ (equation 5) should be diminished CL by 47r/lf ; but, for the above reasons, it has not been subtracted. As a test of the whole arrangement, I have obtained the number of lines of force in a very long solenoid: the mean of two solenoids gave me Q' = 12-67 M(xR<); while from theory we obtain, by equation (7) (n 1), which is within the limits of error in measuring the diameter of the tubes, &c. All the rings and bars with which I have experimented have had a circular section. In selecting the iron, care must be used to obtain a 44 HEXET A. KOWLAND homogeneous bar; in the case of a ring I believe it is better to have it welded than forged solid; it should then be well annealed, and after- wards have the outside taken off all round to about -J of an inch deep in a lathe. This is necessary, because the iron is " burnt " to a consider- able depth by heating even for a moment to a red heat, and a sort of tail appears on the curve showing the permeability, as seen on plotting Table III. To get the normal curve of permeability, the ring must only be used once; and then no more current must be allowed to pass through the helix than that with which we are experimenting at the time. If by accident a stronger current passes, permanent magnetism is given to the ring, which entirely changes the first part of the curve, as seen on comparing Table I with Table II. The areas of the bars and rings were always obtained by measuring their length or diameter across, and then calculating the area from the loss of weight in water. The following is a list of a few of the rings and bars used, the dimensions being given in metres and grammes. In the fourth column " annealed " means heated to a red heat and cooled in open air, " C annealed " means placed in a large crucible covered with sand, and placed in a furnace, where, after being heated to redness, the fire was allowed to die out ; " natural " means that its temper was not altered from that it had when bought. Results given in Table. Quality of substance. How made. Temper. Spec, grav. Weight. Mean diam. Area. State. 0000 M "Burden best" iron. Welded and turned. Annealed. 17-63 148-61 0677 916 Normal. II. u 11 <{ u 7-63 148-61 0677 916 Magnetic. III. It II " M C an- nealed. 17-63 148-01 0677 912 Burnt. :v.j Bessemer steel. Turned from large bar. Natural. 7-84 38-34 0420 371 Normal. M Norway iron Welded and turned. C an- nealed. J7-83 39-78 0656 7695 Magnetic. VI. { Cast nickel. 14 Turned from button. .... 8-83 4-806 0200 0869 Normal. VII. | Stubs' steel. Hard-drawn wire. Natural. 7-73 0969 Normal. The first three Tables are from the same ring. Besides these I have used very many other bars and rings ; but most of them were made before I had discovered the effect of burning upon 14 Almost chemically pure before melting. MAGNETIC PERMEABILITY OF IKON, STEEL AND NICKEL 45 the iron, and hence did not give a normal curve for high magnetizing- powers. However, I have collected in Table VIII some of the results of these experiments; but I have many more which are not worked up yet. In the following Tables Q= -^ has been measured as previously described. It is evident that if, instead of reversing the current, we simply break it, we shall obtain a deflection due to the temporary mag- netism alone. In this manner the temporary magnetism has been measured; and on subtracting this from Q, we can obtain the permanent magnetism. The following abbreviations are made use of in the Tables, the other quantities being the same as previously described. C.T.G. Number of coils of tangent-galvanometer used. D.T.G. Deflection of tangent-galvanometer. D.C. Deflection from coil G. D.F. Deflection from helix F on reversing the current. Q. Magnetic field in interior of bar (total). D.B. Deflection from F on breaking current. T. Magnetic field of bar due to temporary magnetism. P. Magnetic field of bar due to permanent magnetism. n. Number of coils in helix F. Each observation given is almost always the mean of several. D.T.G. is the mean of four readings, two before and two after the observations on the magnetism; D.C. is the mean of from four to ten readings; D.F. mean of three; D.B. mean of two, except in Table I, where the deflec- tion was read only once. In all these Tables the column containing the temporary magnetism T can only be accepted as approximate, the experiments having been made more to determine Q than T. The value of n was generally varied by coiling a wire more or less around the ring, but leaving its length the same. The change in the value of D.C. is due to the change in the resist- ance of the galvanometer from change of temperature, copper wire increasing in resistance about 1 per cent for every 2 -60. rise. In Table I the temperature first increased slowly, and then, after remain- ing stationary for a while, fell very fast. 46 HEXEY A. BOWLAND STABLE i. " BURDEN BEST" IRON, NORMAL. T. M? C.T.G. D.T.G. M. B.C. 71. D.F. D.F. 2n. ' D.B. n. Q. A A Calcu- lated. A ^=S- T. P. P. M.' 3627- 48 4-5 1456 23-4 30 6-6 1083 1 08 715 4910 5845 390-7 528 187- 1284- 7080- 16-45 5501 54-6 910 59 6005 10920 10885 868-7 3894 2111- 3838- 7746- 20-2 6815 87-9 1-465 80 9667 14180 14074 1129 5280 4387- 6437- 8786- 28-6 ! 1-011 23-3 io 74-2 3-71 1-34 24600 24330 24000 1936 8882 15718- 15550- 8766- 31-1 1-119 88-2 4-41 1-48 29230 26120 26050 2078 9811 19419- naso- 8819- 31-9 1.155 92'6 4-63 1-53 30820 26690} 26660 2124 10180; 20640' 17870- ?8205- 41-12 1-623 "z 28-8 7-45 2-0 49590 30570 30740 2433 13310 36280- 22370- 94BO- 27 28-35 1-766 23-1 32-8 8-20 2-5 54820 31030 31050 2470 16710 38110- 21570- 9517- 29-6 1-861 34-6 8-65 2-65 57820 31070 31100 2472 17710 40110' 21550- 8812- 33-4 2-162 23-1 39-8! 9-95 2-85 66510 30770 30776 2448 19050 1 47460- 21950- 8115- 37-45 2-512 44-711-18 3-05 74730 29750 29930 : 2367 20390 54340- 21630- 7985- 44-45 3-223 53-513-38 3-85 89430 27750 27390 ! 2208 25740 63690- 19760- 7674- 52-1 4-225 60-315-08 4-85 100800 23860 24730 : 1899 32420! 67380' 15950" 7070- '9 34-65 6-744 73-1 18-28 7-10 122700 18210 18410 1448 47680 75020- 11130- 6519- 39-8 8-136 23-0 77-319-32 7-90 129700 15940 16130 1 1269 53040 76660- 9423- 6403- 44-3 9-543 "\ 40-620-30 9-1 136300 14280 13920 1137 611001 75200' 7881- 4666- 55-1 14-04 43-521-75 9-8 145400 10360 10760 824'1 65510- 79890- 5690- 2816- '3 42-95 27-18 47-423-70 11-5 157700 5803 6350 461-8 76540; 81160- 2985- 2300- 51-3 36-60 49-124-55 12-7 162700 4445 4523 353.8 84180! 78520- 2145- 1702- 60-15 51-18 23-4 50-325-15 13-2 166000 3243 3310 358.0 87120, 78880- 1541- 00 175000 1 TABLE II. "BURDEN BEST" IRON, MAGNETIC. M. Q. A. M. M. Q. A. M. 1456 426 2920 232 2-930 82720 28240 2247 5699 3346 5987 476 4-210 100900 23950 1906 6962 5700 8189 652 6-769 122800 18140 1444 1-080 24350 22550 1795 7.273 124300 17090 1360 1-191 29280 24580 1956 7-626 127100 16670 1326 1-537 46150 30020 2389 11-10 139500 12570 1000 1-590 49070 30260 2408 13-61 144700 10630 846 1-933 59680 30860 2456 22-10 154600 6965 554 2-377 71660 30150 2399 > TABLE III. BURDEN BEST" IRON, BURNT. M. Q. A. M- T. M. Q. A. M. T. P. P. 143 1001 7039 560 1020 3.810 116900 30730 2446 8 .553 9395 16980 1351 5115 4-283 120200 28060 2233 4280- 682 16550 24240 1929 6835 4-722 123900 26240 2088 30830 9715- 962 37330 38780 3086 9454 6.565 133100 20270 1613 27876- 1-070 42920 40130 3194 10300 9-326 141200 15140 1200 3981032620- 1-153 48830 42340 3369 10530 11-00 144400 13120 1045 38300- 1-317 59490 45180 3595 11650 13-44 147500 10970 873 44070 47840- 103430- 1-340 59580 44450 3538 13700 23-41 155500 6642 529 51030 45880- 104470- a 127 90180 42400 3374 18470 32-73 159400 4870 387 71710- 2-501 98560 39400 3136 19920 32-56 158400 48641 387 78640- 2-864 104000 36310 2890 24600 51-03 165800 3250 259 56100 79400- 109700- 3-151 108200 34330 2732 24610 83590- 15 [Columns 1, 15, 16 were added to the original paper by Professor Rowland, after its publication.] 16 [The last two columns of Tables III, IV, V, VII were added by Professor Row- land after the paper was published.] MAGNETIC PEEMEABILITY or IKON, STEEL AND XICKEL 47 STABLE iv. BESSEMER STEEL, NORMAL. M. Q. A. M- T. M. Q. A. *. T. P. P. 1356 327 2412 192 309 2-756 39960 14500 1154 13080 IS- 26880- 2793 817 2995 238 727 3-219 50550 15700 1250 16350 90- 34200- 5287 1726 3264 260 1471 3-551 56310 15860 1262 15980 255- 40330- 9398 3833 4079 325 3106 4-469 71380 15970 1271 18340 727- 53040- 1-421 7702 5421 431 5576 5-698 85530, 15010 1195 23610 2126- 61920- 1-880 14080 7487 596 8972 11-44 119550 10450 832 28020 5108- 91530- 1-947 15420 7920 630 8938 20-69 138300 6685 532 41360 6482- 96940- 2-300 24830 10800 859 11320 38-99 153700 3942 314 52930 13510- 100770- "TABLE V. NORWAY IRON, MAGNETIC. M. Q. A. /* T. M. Q. A. M. T. P. P. 1344 865 6439 512 2-290 105900 46240 3680 35240 70660- 2673 2550 9910 759 1892 4-393)134100 30520 2429 54970 658- 79130- 516l! 13000 25200 2005 5857 5-910 142400 24090 1917 62810 7143- 79590- 5572 15310) 27480 2187 8110 7-874 149100 18940 1507 68490 7200- 80610- 6725 30140 44820 3567 8921 13-77 156800 11390 906 77060 21220- 79740 9305 53800J 57820 4602 13970 26-84 165800 6038 480 84710 39830- 81090- 1-362 77700 57110 4545 21630 36-86 168500 4572 364 87860 56070- 80740- 1-788 93000 52020 4140 28200 64800- TABLE VI. CAST NICKEL, NORMAL. M. Q. A. M- T. M. Q. A. (* T. 1-433 852 595 47-4 13-43 27100 2018 160-6 11260 2-904 2377 819 65-1 16-53 31050 1878 149-5 13530 3-527 3685 1070 85-1 21-02 34950 1663 132-3 16480 5-555 10080 1815 144-4 32-17 41980 1305 103-8 22300 6-783 13680 2017 160-5 5120 33-92 42650 1257 100-0 23360 7-401 15270 2063 164-2 5614 60-91 50860 855 66-4 29540 9-273 19600 2114 168-2 7644 82-36 53650 651 51.8 33460 11.78 24720 2098 167-0 9902 105-2 55230 525 41-8 35120 STABLE vn. STUBS' STEEL WIRE, NORMAL. M. Q. A. M. T. M. Q. A. /* T P. P. 1673 159 953 75-9 13-65 54300 3978 316-6 20900 33400- 6237 678 1087 86-5 598 19-35 77770 4020 319-9 29480 80- 48290- 1.084 ! 1197 1104 87-9 1101 27-43100800 3676 292-6 38590 96- 62210- 2-043 ! 2448 1199 95-4 2257 33-39111300 3335 265-4 45110 191- 66190- 2-714 j 3446 1270 101-0 3095 35-58115000 3228 256-9 45950 351- 69050- 4-221 i 6278 1487 118-4 5145 38-64 119400 3092 246-0 48060 1133- 71340- 10-26 33700 3286 261 5 16170 17530- 48 HENUY A. EOWLAND The best method of studying these Tables is to plot them: one method of doing this is to take the value of the magnetizing-force as the abscissa, and that of the permeability as the ordinate; this is the method used by Dr. Stoletow; but, besides making the complete curve infinitely long, it forms a very irregular curve, and it is impossible to get the maximum of magnetism from it. Another method is to employ the same abscissas, but to use the magnetism of the bar as ordinates; this gives a regular curve, but has the other two disadvantages of the first method; however, it is often employed, and gives a pretty good idea of the action. In Plate II, I have given a plot of Table V with the addition of the residual or permanent magnetism, which shows the general features of these curves as drawn from any of the Tables. It is observed that the total magnetism of the iron at first increases very fast as the magnetizing-force increases, but afterwards more and more slowly until near the maximum of magnetism, where the curve is parallel to the axis of Q. The concavity of the curve at its commence- ment, which indicates a rapid increase of permeability, has been noticed by several physicists, and was remarked by myself in my experiments of January, 1871; it has now been brought most forcibly before the public by Dr. Stoletow, whose paper refers principally to this point. 17 M. Miiller has given an equation of the form to represent this curve; but it fails to give any concavity to the first part of the curve. A formula of the same form has been used by M. Cazin ; 18 but his experiments carry little weight with them, on account of the small variation of the current which he used, this being only about five times, while I have used a variation in many cases of more than three hundred times. Weber has obtained, from the theory that the particles of the iron are always magnetic and merely turn round when the magnetizing- force is applied, an equation which would make the first part of the curve coincide with the dotted line in Plate II ; 19 and Maxwell, by addi- tion to the theory, has obtained an equation which replaces the first 17 On the Magnetizing Function of Soft Iron, especially with the weaker decom- posing powers. By Dr. A. Stoletow, of the University of Moscow. Translated in the Phil. Mag., January, 1873. See particularly p. 43. 18 Annales de Chimie et de Physique, February 1873, p. 182. 19 This is according to Maxwell's integration of Weber's equation, Weber having made some mistake in the integration. MAGNETIC PERMEABILITY OF IRON, STEEL AND NICKEL 49 part of the curve by the broken line. 20 I believe that I have obtained at the least a very close approximation to the true equation of the curve, and will show further on that Q and M must satisfy the equation D It is very probable that Weber's theory may be so modified as to give a similar equation. Space will not permit me to discuss the curves of temporary and permanent magnetism; but I will call attention to the following facts which the Tables seem to establish. 1. Nearly or quite all the magnetism of a bar is, with weak magnetizing- forces, temporary; and this is more apparent in steel than in soft iron. 2. The temporary magnetism increases continually with the current. 3. The permanent magnetism at first increases very fast with the current, but afterwards diminishes as the current increases, when the iron is near its maximum of magnetism. 21 I have now described the methods of plotting the Tables hitherto used; and I will now describe the third, which is, I believe, new. This is by using the values of the magnetism of the bar as abscissas, and those of the permeability as ordinates. In this way we obtain a per- fectly regular curve, which is of finite dimensions, and from which the maximum of magnetism can be readily obtained. Plate III shows this method of plotting as applied to Table I. If we draw straight lines across the curve parallel to the axis of Q and mark their centres, we find that they always fall very exactly upon a straight line, which is therefore a diameter of the curve. The curve of nickel shown upon the same Plate has this property in common with iron. I have made several attempts to get a ring of cobalt; but the button has always been too porous to use. However, I hope soon to obtain one, and thus make the law general for all the magnetic metals. There are two equations which may be used to express the curve : one is the equation of an inclined parabola; but this fails for the two ends of the curve; the other is an equation of the general form (11) 20 Treatise on Electricity and Magnetism, Maxwell, vol. ii, chap. vi. 21 The last clause of this sentence cannot be considered yet as entirely settled, though I have other curves than those shown here which show it well. [This note was added to the original paper by Professor Rowland.] 4 50 HEJSTRY A. ROWLAND in which A, H, D, and a are constants depending upon the kind and quality of the metal used. A is the maximum value of X, and gives the height of the curve E D, Plate III; a establishes the inclination of the diameter; H is the line A 0; and D depends upon the line A 0. The following equation, adapted to degrees and fractions of a degree, is the equation from which the values of ^ were found, as given in Table I: A = 81-100 sin The large curve in Plate III was also drawn from this, and the dots added to show the coincidence with observation; it is seen that this is almost perfect. As X enters both sides of the equation, the calculation can only be made by successive approximations. We might indeed solve with reference to Q ; but in this case some values of ^ as obtained from experiment may be accidentally greater than A, and so give an imagi- nary value to Q. By plotting any Table in this way and measuring the distance C, we have the maximum of magnetism. I have given in the same Plate the curve drawn from the observations on the nickel ring with Q on the same scale, but ^ on a scale four times as large as the other. The curve of nickel satisfies the equation quite well, but not so exactly as in the case of iron. This ring, when closely examined, was found to be slightly porous, which must have changed the curve slightly, and perhaps made it depart from the equation. In Table VIII, I have collected some of the values of the constants in the formula when it is applied to the different rings and bars, and have also given some columns showing the maximum of magnetism. When any blank occurs, it is caused by the fact that for some reason or other the observations were not sufficient to determine it. The values of a, H, D, and the value of X, when Q = 0, can in most cases only be considered approximate ; for as they all vary so much, I did not think it necessary to calculate them exactly. For comparison, I have plotted Dr. Stoletow's curve and deduced the results given in the Table, of course reducing them to the same units as mine. It will be observed that the columns headed "maximum of mag- netism " contain, besides the maximum magnetic field, two columns MAGNETIC PERMEABILITY OF IRON, STEEL AND NICKEL 51 * M O 5) (H !i c 'S "S 1=11 pa x- ^ Burnt. Normal. Magnetic. Normal. ii Burnt. 5 7. Burnt, Magnetic. o 3 * "* "7? O O o o o o 1-1 T*< e* o g to O O O O C5 to o eg r-l X CO CO So cocS sg i 00 ~c t- t- 1- > t- i- i> t- I- t- i- 00 P |8 O C5 1 1 o 1C 4 o o . 00 35 o 1 X o o o o 1C CO O t- O O O O O O O CO O o o o o c = P o o o o CO CO 0^00 00 co :i2 ^ ^ S i - 1 1 1 >o b - 5O 1- 1C 35 I-l ^H 1C 00 i| :r. -f 1 >c o CO o 04 Greatel meabi 000 o o o 35 O i-( 35 CO -J ^-1 O o o o o o O O to o CM O ?! Q ?} o CO OO CO O 1 1 t- |ll . O 5 O5 OO iH t~ CO cr. to oo etism. o c _ So go ' I- t- rH r-l OO H CO t- t- iH i-l TH Jl o* o 00 i e S 3 Tension of lines in kil. per square centim. " i i i 1 ? r-l r-t r-l ? 1 S "K 5 O O O O .00 i-H -H I 177000 o o o : o o o o s o l- 1-H Temper. I } , (12) 173240000 Ibs. per square inch, from which the quantities in the Table were calculated. It is seen that the maximum of magnetism of ordinary bar iron is about 175,000 times the unit field, or 177 Ibs. on the square inch, and for nickel 63,000 times, or 22-9 Ibs. on the square inch. For pure iron, however, I think it may reach 180,000, or go even above that. It is seen that one of the Norway rings gave a very high result; this is explained by the following considerations. All the iron rings were welded except this one, which was forged solid from a bar 2 inches wide and then turned. Even the purest bar iron is somewhat fibrous; and between the fibres we often find streaks of scale lying lengthwise in the bar and so diminishing the section somewhat if the ring be welded from the bar; when, however, it is forged solid, these streaks are thoroughly disintegrated; and hence we find a higher maximum of magnetism for a ring of this kind, and one approaching to that of pure iron. But a ring made in this way has to be exposed to so much heating and pounding that the iron is rendered unhomogeneous, and a tail appears to the curve like that in Table III. It is evident that this tail must always show itself whenever the section of the ring is not homogeneous throughout. Hence we may conclude that the greatest weight which can be sus- tained by an electromagnet with an infinite current is, for good but not pure iron, 354 Ibs. per square inch of section, and for nickel 46 Ibs. Joule 2 * has made many experiments on the maximum sustaining- power of magnets, and has collected the following Table, which I give complete, except that I have replaced the result with his large magnet by one obtained later. It is seen that these are all below my estimate, as they should be. 23 Treatise on Electricity and Magnetism, vol. ii, p. 256. 2* Phil. Mag., 1851. MAGNETIC PERMEABILITY OF IRON, STEEL AND NICKEL 53 For comparison, I have added a column giving the values of Q which would give the sustaining-power observed; some of these are as high as any I have actually obtained, thus giving an experimental proof that my estimate of 354 Ibs. cannot be far from correct, and illustrating the beauty of the absolute system of electrical measurement by which, from the simple deflection of a galvanometer-needle, we are able to predict how much an electromagnet will sustain without actually trying the experiment. TABLE IX. Magnet belonging to Least area of section, square inch. Weight sustained. Weight sus- tained -r least area. Q. f 1. . 10. 2775 277 154700 I 2. . 196 49 250 147000 Mr. Joule. ^ * 0436 12 275 154100 j 4 0012 202 162 118300 Mr. Nesbit 4-5 1428 317 165500 Prof. Henry 3-94 750 190 128200 Mr. Sturgeon 196 50 255 148500 In looking over the columns of Table VIII, which contain the values of the constants in the formula, we see how futile it is to attempt to give any fixed value to the permeability of iron or nickel; and we also see of how little value experiments on any one kind of iron are. Iron differs as much in magnetic permeability as copper does in electric conductivity. It is seen that in the three cases when iron bars have been used, the value of a is negative; we might consider this to be a general law, if I did not possess a ring which also gives this negative. All these bars had a length of at least 120 times their diameter. The mathematical theory of magnetism has always been considered one of the most difficult of subjects, even when, as heretofore, fj. is considered to be a constant; but now, when it must be taken as a func- tion of the magnetism, the difficulty is increased many fold. There are certain cases, however, where the magnetism of the body is uniform, which will not be affected. Troy, June 2, 1873. (54) ON THE MAGNETIC PEEMEABILITY AND MAXIMUM OF MAGNETISM OF NICKEL AND COBALT [Philosophical Magazine [4], XL VIII, 321-340, 1874J Some time ago a paper of mine on the magnetic permeability of iron, steel, and nickel was published in the Philosophical Magazine (August, 1873); and the present paper is to be considered as a continuation of that one. But before proceeding to the experimental results, I should like to make a few remarks on the theory of the subject. The mathe- matical theory of magnetism and electricity is at present developed in two radically different manners, although the results of both methods of treatment are in entire agreement with experiment as far as we can at present see. The first is the German method; and the second is Faraday's, or the English method. When two magnets are placed near each other, we observe that there is a mutual force of attraction or repulsion between them. Now, according to the German philosophers, this action takes place at a distance without the aid of any intervening medium: they know that the action takes place, and they know the laws of that action; but there they rest content, and seek not to find how the force traverses the space between the bodies. The English philosophers, however, led by Newton, and preeminently by Faraday, have seen the absurdity of the proposition that two bodies can act upon each other across a perfectly vacant space, and have attempted to ex- plain the action by some medium through which the force can be trans- mitted along what Faraday has called " lines of force." These differences have given rise to two different ways of looking upon magnetic induction. Thus if we place an electromagnet neat" a compass-needle, the Germans would say that the action was due in part to two causes the attraction of the coil, and the magnetism induced in the iron by the coil. Those who hold Faraday's theory, on the other hand, would consider the substance in the helix as merely " conduct- ing " the lines of force, so that no action would be exerted directly on the compass-needle by the coil, but the latter would only affect it in virtue of the lines of force passing along its interior, and so there could be no attraction in a perfectly vacant space. MAGNETIC PEEMEABILITY OF NICKEL AND COBALT 57 According to the first theory, the magnetization of the iron is repre- sented by the excess of the action of the electromagnet over that of the coil alone; while by the second, when the coil ia very close around the iron, the whole action is due to the magnetization of the iron. The natural unit of magnetism to be used in the first theory is that quantity which will repel an equal quantity at a unit's distance with a unit of force; on the second it is the number of lines of force which pass through a unit of surface when that surface is placed in a unit field perpendicular to the lines of force. The first unit is 4?r times the second. Now when a magnetic force of intensity & 1 acts upon a mag- netic substance, we shall have 33 = +4-$, in which 33 is the mag- netization of the substance according to Faraday's theory, and is what I formerly called the magnetic field, but which I shall hereafter call, after Professor Maxwell, the magnetic induction. % is the intensity of magnetization according to the German theory, expressed in terms of the magnetic moment of the unit of volume. Now, when the sub- stance is in the shape of an infinitely long rod placed in a magnetic field 01 parallel to the lines of force, the ratio 2 ==// is called the magnetic permeability of the substance, and the ratio = K is Neumann's co- efficient of magnetization by induction. Now experiment shows that for large values of Q the values of both n and K decrease, so that we may expect either $ or both 33 and % to attain a maximum value. In my former paper I assumed that 33 as well as $ attain a maxi- mum; but on further considering the subject I see that we have no data for determining which it is at present. If it were possible for 53 to attain a maximum value so that // should approach to 0, K would be negative, and the substance would then become diamagnetic for very high magnetizing forces. 2 This is not contrary to observation; for at present we lack the means of producing a sufficiently intense magnetic field to test this experimentally, at least in the case of iron. To pro- duce this effect at ordinary temperatures, we must have a magnetic field greater than the following for iron 175,000, for nickel 63,500, and for 1 1 shall hereafter in all my papers use the notation as given in Professor Maxwell's ' Treatise on Electricity and Magnetism ;' for comparison with my former paper I give the following: 33 in this paper = Q in former one. 6 " = 4;rM " 3 " =-M 'See Maxwell's 'Treatise on Electricity and Magnetism,' art. 844. J. C. M. 58 HENEY A. ROWLAND cobalt about 100,000 (?). These quantities are entirely beyond our reach at present, at least with any arrangement of solenoids. Thus, if we had a helix 6 inches in diameter and 3 feet long with an aperture of 1 inch diameter in the centre, a rough calculation shows that, with a battery of 350 large Bunsen cells, the magnetic field in the interior would only be 15,000 or 20,000 when the coils were arranged for*the best effect. We might obtain a field of greater intensity by means of electromagnets, and one which might be sufficient for nickel; but we cannot be certain of its amount, as I know of no measurement of the field produced in this way. But our principal hope lies in heating some body and then subjecting it to a very intense magnetizing-f orce ; for I have recently found, and will show presently, that the maximum of magnetization of nickel and iron decreases as the temperature rises, at least for the two temperatures C. and 220 C. I am aware that iron and nickel have been proved to retain their magnetic properties at high temperatures, but whether they were in a field of sufficient intensity at the time cannot be determined. The experiment is at least worth try- ing by some one who has a magnet of great power, and who will take the trouble to measure the magnetic field of the magnet at the point where the heated nickel is placed. This could best be done by a small coil of wire, as used by Verdet. But even if it should be proved that 33 does not attain a maximum, but only $, it could still be explained by Faraday's theory; for we should simply have to suppose that the magnetic induction 33 was composed of two parts the first part, 4 Trig, being due to the magnetic atoms alone, and the second, >, to those lines of force which traversed the aether between the atoms. To determine whether either of these quantities has a maximum value can probably never be done by experi- ment; we may be able to approach the point very nearly, but can never arrive at it, seeing that we should need an infinite magnetizing-force to do so. Hence its existence and magnitude must always be inferred from the experiments by some such process as was used in my first paper, where the curve of permeability was continued beyond the point to which the experiments were carried. Neither does experiment up to the present time furnish any clue as to whether it is 33 or $ which attains a maximum. As the matter is in this undecided state, I shall hereafter in most cases calculate both $ and * as well as 33 and //, as I am willing to admit that $ may have a physical significance as well as 33, even on Faraday's theory. MAGNETIC PEEMEABILITY OF NICKEL AND COBALT 59 There is a difficulty in obtaining a good series of experiments on nickel and cobalt which does not exist in the case of iron. It is prin- cipally Giving to the great change in magnetic permeability of these substances by heat, and also to their small permeability. To obtain sufficient magnetizing-force to trace out the curve of permeability to a reasonable distance, we require at least two layers of wire on the rings, and have to send through that wire a very strong current. In this way great heat is developed; and on account of there being two layers of wire it cannot escape; and the ring being thus heated, its permeability is changed. So much is this the case, that when the rings are in the air, and the strongest current circulating, the silk is soon burned off the wire; and to obviate this I have in these experiments always immersed the rings in some non-conducting liquid, such as alcohol for low tem- peratures and melted paraffin for high temperatures, the rings being suspended midway in the liquid to allow free circulation. But I have now reason to suspect the efficacy of this arrangement, especially in the case of the paraffin. The experiments described in this paper were made at such odd times as I could command, and the first ones were not thoroughly discussed until the series was almost completed; hence 1 have not been so careful to guard against this error as I shall be in the future. This can be done in the following manner namely, by letting the current pass through the ring for only a shirt time. But there is a difficulty in this method, because if the current is stopped the battery will recruit, and the moment it is joined to the ring a large and rapidly decreasing current will pass which it is impossible to measure accu- rately. I have, however, devised the following method, which I will apply in future experiments. It is to introduce into the circuit between the tangent-galvanometer and the ring a current-changer, by which the current can be switched off from the ring into another wire of the same resistance, so that the current from the battery shall always be con- stant. Just before making an observation the current is turned back into the ring, a reading is taken of the tangent-galvanometer by an assistant, and immediately afterward the current is reversed and the reading taken for the induced current; the tangent-galvanometer is then again read with the needle on the other side of the zero-point. The pressure of outside duties at present precludes me from putting this in practice. But the results which I have obtained, though probably influenced in the higher magnetizing-forces by this heating, are still so novel that they must possess value notwithstanding this defect; for they contain the only experiments yet made on the permeability of 60 HENRY A. KOWLAXD cobalt at ordinary temperatures, and of iron, nickel, and cobalt at high temperatures. The rings of nickel and cobalt which I have used in the experiments of this paper were all turned from buttons of metal obtained by fusing under glass in a French crucible, it having been found that a Hessian crucible was very much attacked by the metal. The crucibles were in the fire three or four hours, and when taken out were very soft from the intense heat. As soon as taken out, the outside of the crucible was wet with water, so as to cool the metal rapidly and prevent crystalliza- tion; but even then the cooling inside went on very slowly. As the physical and chemical properties of these metals exercise great influence on their magnetic properties, I will give them briefly. A piece of nickel before melting was dissolved in HC1; it gave no precipitate with H 2 S , and there were no indications of either iron or cobalt. A solution of the cobalt gave no precipitate with H 2 S, but contained small traces of iron and nickel. After melting the metals no tests have been made up to the present time; but it is to be expected that the metals absorbed some impurities from the crucibles. They probably did not contain any carbon. One button of each metal was obtained, from each of which two rings were turned. The cobalt was quite hard, but turned well in the lathe, long shavings of metal coming off and leaving the metal beautifully polished. The metal was slightly malleable, but fin- ally broke with a fine granular fracture. The rings when made were slightly sonorous when struck; and the color was of a brilliant white slightly inclined to steel-color, but a little more red than steel. The nickel was about as hard. as wrought iron, and was tough and difficult to turn in the lathe, a constant application of oil being necessary, and the turned surface was left very rough; the metal was quite malleable, but would become hard, and finally fly apart when pounded down thin if not annealed. When the rings were struck, they gave a dead sound as if made of copper. In both cases the specific gravity was considerably higher than that generally given for cast metal ; but it may be that the metal to which they refer contained carbon, in which case it would be more easily melted. There is great liability to error in taking the specific gravity of these metals, because they contract so much on cool- ing, and unless this is carried on rapidly crystals may form, between which, as the metal contracts, vacant spaces may be left. As the specific gravity of my rings approaches to that of the pure metals pre- cipitated by hydrogen, I consider it evidence of their purity. The dimensions of the rings and their other constants are as follows: VNI\ MAGNETIC PERMEABILITY OF XICKEL AND COBALT 61 King. Weight in vacuo, in grammes. Loss in water at 4 C.,in grammes. Specific gravity. Mean dia- meter, in centimetres. Nickel No I 21-823 2-4560 8-886 3-28 Nickel No II 8-887 Cobalt No I 10-011 1 1435 8-7553 2-48 Cobalt No. II 4-681 5346 8 7550 1-81 Ring. Mean circum- ference, in centimetres. Number of coils of wire on ring. Coils per metre of cir- cumference. Area of sec- tion, in square centimetres. Nickel No I 10 304 318 3086 2384 Nickel' No. II. Cobalt, No. I 7-791 243 3119 1467 Cobalt No. II 5-686 158 2779 09403 Up to the present time cnly the rings whose dimensions are given have been used. The following Tables from the nickel ring No. I leave little to be desired in point of regularity, and confirm the fact proved in my first paper, that the laws deduced for iron hold also for nickel, and also confirm the value given in my other paper for the maximum value of magnetization of nickel. But the most important thing that they show is the effect of heat upon the magnetization of nickel; and Table III contains the first numerical data yet obtained on the effect of heat on the magnetic properties of any substance. As all the rings were wound with two layers of wire, a slight correc- tion was made in the value of S) for the lines of inductive force which passed through the air and not through the metal. In all the experi- ments of this paper greater care was used to obtain T than in the first paper. Each value of >, 33, and T is the mean of four readings. In all the Tables I have left the order of the observations the same as that in which they were made, and have also put down the date, as I now have reason to suspect that the leaving of a ring in the magnetized state in which it is after an experiment will in time affect its properties to a small extent. Let me here remark that the time necessary to simply make the observations is only a Very small fraction of that required to prepare for them and to afterwards discuss them. And this, with the small amount of time at my disposal, will account for the late day at which I publish my results. The following is the notation used, the measurements being made on that absolute system in which the metre, gramme, and second are the fundamental units. 62 HENRY A. ROWLAND $ is the magnetizing-force acting on the metal. 23 is the magnetic induction within the metal (see Maxwell's ' Trea- tise on Electricity and Magnetism/ arts. 400, 592, and 604). i fj. is the magnetic permeability of the metal s=_=4*-H. s? T is the portion of 23 which disappears when the current is broken. P is the portion of 33 which remains when the current is broken. qa a $ is the intensity of magnetization = - ow ic is Neumann's coefficient of induced magnetization = ^. *Q TABLE I. CAST NICKEL, NOKMAL, AT 15 C. Experiments made November 29, 1873. a S3 Ob- served. Calcu- lated. Error. T. P. 3. K. Ob- served. K. Calcu- lated. Error. 12-84 675 52-6 46-4 6-2 52-7 4-10 3 65 -45 26-85 2169 80-8 80-6 .3 1263 906 170-5 6-35 6-27 08 45 14 7451 165-1 166-8 1-7 2894 4557 589-3 13-06 13-08 02 56-12 11140 198-5 199-1 6 3788 7352 882-0 15-72 15-70 02 70-78 15410 217-8 217-5 -3 5018 10392 1221 17-25 17-21 04 77-52 17100 220-6 220-6 5454 11646 1355 17-47 17-47 90-76 20180 222-3 222-0 - -3 6483 13697 1599 17-61 17-60 01 115-4 25170 218-2 214-3 3-9 8313 16857 1994 17-28 16-98 30 139-4 28540 204-7 204-3 -4 10100 18440 2260 16-21 16-18 .03 172-9 32460 187-8 186-6 1-2 12530 19930 2569 14-86 14-93 07 195-3 34630 177-3 179-1 1-8 13320 21310 2740 14-03 14-12 09 229-5 37340 162-8 165-5 2-7 15720 21620 2953 12-87 13-02 15 275-9 40860 148-1 146-3 1-8 17960 22900 3230 11-71 11-46 25 415-2 46470 111-9 112-8 9 22560 23910 3665 8-82 8-77 05 727-0 52690 72-5 72-8 3 28020 24670 4135 5-69 5-64 05 1042 55680 53-4 52-8 -6 30680 25000 4344 4-17 4-17 63420 4940 ooo = 222 sin /"= 359 =17 6 sin 28 TABLE II. CAST NICKEL, MAGNETIC, AT 12 C. Experiments made December 6, 1873. 6. to. M. T. P. 3- K. 23-25 1245 53-55 97-2 4-18 47-69 7786 163-3 3095 4691 615-8 12-91 57-78 11460 198-3 3740 7720 907-3 15-70 73-43 16040 218-5 5032 11008 1270-6 17-30 88-23 19790 224-3 6554 13236 1568 17-77 107-3 23530 219-2 7620 15910 1864 17-36 153-8 30160 196-1 10940 19220 2388 15-52 206-3 35880 174-0 14030 21850 2839 13-76 296-4 41310 139-4 18390 22920 3264 11-01 421-8 46520 110-3 22520 24000 3668 8-70 MAGNETIC PERMEABILITY OF NICKEL AND COBALT 63 TABLE III. CAST NICKEL, MAGNETIC, AT 220 C. Experiments made December 6, 1873. . as. n- T. P. 3- K. 22-60 4502 199-2 2671 1831 356-4 15-77 45-06 14000 310-8 5470 8530 1111 24-65 52-96 16660 314-6 6350 10310 1322 24-96 67-42 20300 301-1 7722 12578 1602 23-88 80-69 22540 279-3 8914 13626 1787 22-15 106-4 26420 248-3 11140 15280 2094 19-68 150-8 30740 203-8 14040 16700 2434 16-14 191-0 33530 175-6 15940 17590 2653 13-89 294-8 38300 129-9 20240 18060 ! 3024 10-26 553-6 42630 77-0 24360 18270 3348 6-05 789-8 43900 55-6 26060 17840 3431 4-345 Experiments made December 10, 1873. 13-00 1537 118-2 109-2 9-33 22-37 4262 190-5 337-4 15-08 25-15 5337 212-2 422-7 16-81 33-19 94S6 285-8 4055 5431 752-3 22-15 43-28 13570 313-6 5357 8213 1076 24-88 In Table I are given the results for nickel at about 15 C., together with the values of // and < calculated from the formulae given below the Table. We see that the coincidence is almost perfect in both cases, which thus shows that the formula which we have hitherto used for X and ;j. can also be applied to , at least within the limit of experiments hitherto made, although it must at last depart from one or the other of the curves. The greatest relative error is seen to be in the first line, where ) is small: this does not indicate any departure from the curve, but is only due to the too small deflections Of the galvanometer; and the error indicates that of only a small fraction of a division at the galvanometer. In the calculation of /J- and K a method was used which may be of use to others in like circumstances, who have to calculate a large num- ber of values of one variable from a function which cannot be solved with reference to that variable, but can be solved with reference to the other. Thus we have which can be solved with reference to S3 but not to //; for we have (1) (2) 64 HENEY A. ROWLAND Suppose we have values of 33, and wish to find the corresponding values of .//. We first calculate a few values of 33 from (2) so that we can plot the curve connecting 33 and [JL. We then from the plot select a value of p which we shall call //, as near the proper value as possible, and calculate the corresponding value of 33, which we shall call 33'. Our problem then is, knowing 33' and //, to find the value of /JL corresponding to 33 when this is nearly equal to 33'. Let 33' receive a small increment J33', so that 33 = 33' + J33' ; then we have, from Taylor's theorem, since ' + J33') and fjf= Remembering that the constants in (1) refer to degrees of arc and not to the absolute value of the arc, we have &c, which is in the most convenient form for calculation by means of Barlow's Tables of squares, &c., and is very easy to apply, being far easier than the method of successive approximation. On comparing the magnetic curve Table II with the normal curve Table I, we see that the magnetic curve of nickel bears the same rela- tion to the normal curve as we have already found for iron; that is, the magnetic curve falls below the normal curve for all points before the vertex, but afterwards the two coincide. Hence we see that at ordinary temperatures the magnetic properties of nickel are a complete reproduction of those of iron on a smaller scale. But when we come to study the effect of temperature we shall find a remarkable difference, and shall find nickel to be much more susceptible than iron to the influence of heat. In Table III we have experiments on the permeability of nickel at a high temperature, the ring being maintained at 220 C. by being placed in a bath of melted paraffin: in this bath the silk covering of the wire remained quite perfect, but after many hours became some- what weak. After completing the experiments on this and the cobalt rings, on unwinding some of them I found the outside layer quite per- fect; but, especially in the smallest ring, the silk on the inside layer was much weaker, although the insulation was still perfect when the wire was in place. I can only account for this by the electric current generating heat in the wire, which was unable to pass outward because MAGNETIC PERMEABILITY OF NICKEL AND COBALT 65 of the outside layer and also of the pieces of paper which were used to separate the layers of wire; hence the ring at high magnetizing-powers must have been at a somewhat higher temperature than the bath, to an amount which it is impossible to estimate. It is probable that it was not very great, however; for at this high temperature continued for hours it requires but little increase of heat to finally destroy the silk. We can, however, tell the direction of the error. We see, on comparing Tables I and II with Table III, the great effect of heat on the magnetic properties of nickel. We see that for low magnetization the permeability is greatly increased, which is just opposite to what we might expect; but on plotting the curve we also notice the equally remarkable fact, that the maximum of magnetization ZO.OOO 40.000 eo.ooo 1. Curve at 15 C. 2. Curve at 220 C. is decreased from 33= 63,400 or 3 = 4940 to 33= 49,000 or $ = 3800. This curious result is shown in the annexed figure, where we see that for low magnetizing-f orces p is increased to about three or four times its value at 15 C., and the maximum value of // is increased from 222 to 315. When 33 has a value of 32,000, p is not affected by this change of temperature, seeing that the two curves coincide; but above that point fji is less at 220 C. than at 15 C. In other words, if nickel is heated from 15 C. to 220 C., the magnetization of nickel will increase if the magnetizing-f orce is small, but will decrease if it is large. It is impos- sible to say at present whether increase of temperature above 220 will always produce effects in the same direction as below it or not. These remarkable effects of heat, it seems to me, will, when followed out, lead to the discovery of most important connections between heat and magnetism, and will finally result in giving us much more light upon the nature of heat and magnetism, and that equally important 5 66 HENRY A. EOWLAND question of what is a molecule. To accomplish this we must obtain a series of curves for the same ring between as wide limits of temperature as possible. We must then plot our results in a suitable manner; and from the curves thus formed we can find what would probably happen if the temperature were lowered to the absolute zero, or were increased to the point at which nickel is said to lose its magnetism. In such inquiries as these the graphical method is almost invaluable, and little can be expected without its aid. In applying the formula to this curve, we do not find so good an agreement as at the lower temperature. I do not consider this conclu- sive that the formula will not agree with observation at this tempera- ture; for I have noticed that the curves of different specimens of iron and nickel seem to vary within a minute range, not only in their elements but also in their form. This might perhaps be accounted for by some small want of homogeneity, as in the case of burning in iron and nickel; but at present the fact remains without an explanation. But the amount of the deviation is in all cases very small when all the precautions are taken to insure good results. The nature of the devia- tion is in this case as follows: when the constants in the formula are chosen to agree with the observed curve at the vertex and at the two ends, then the observed curve falls slightly below the curve of the formula at nearly all other points. In a curve plotted about 5 inches high and broad, the greatest distance between the two curves is only about -^ of an inch, and could be much reduced by changing the con- stants. For the benefit of those who wish to study this deviation, I have calculated the following values, which will give the curve touching the vertex and the two ends of the observed curve of Table III. They are to be used by plotting in connection with that Table. K. 3. 140 3802 12.75 205 2833 18-75 455 2269 22-5 703 1835 25 1206 3 + 25/C + 140 I have not as yet obtained a complete curve of iron at a high temper- ature; but as far as I have tried, it does not seem to be affected much, at least for high magnetizing-powers. I have, however, found that the maximum of magnetization of iron decreases about 2 per cent by a MAGNETIC PEEMEABILITY OF NICKEL AND COBALT 67 rise of temperature from 15 C. to 222 C., while that of nickel de- creases 22-7 per cent. The experiments which 1 have made with cobalt do not seem to be so satisfactory as those made with nickel and iron. There are some things about them which I cannot yet explain; but as they are the only exact experiments yet made on cobalt, they must possess at least a transient value. The difficulties of getting a good cobalt-curve are. manifold, and are due to the following properties (1) its small permea- bility, (2) its sensitiveness to temperature, and (3) its property of having its permeability increased by rise of temperature at all magnetizing- powers within the limits of experiment. The following are the results with No. I : TABLE IV. CAST COBALT, NORMAL, AT 5 C. Experiments made November 27, 1873. fi. 8. M. T. P. 3- K. Ob- served. K. Calcu- lated. Error. 49-33 4303 87-24 3702 601 338-5 6-86 6-75 11 58-83 5608 95-32 4526 1082 441-6 7-51 7-44 07 76-47 8409 109-95 6175 2234 663-1 8-67 8-79 12 93-15 11623 124-8 7826 3797 917-5 9-85 9-81 04 113-0 14993 132-7 9805 5188 1193-1 10-48 10-44 04 129-3 17439 134-9 10580 6859 1387-8 10-66 10-72 06 159-4 22309 140-0 14090 8219 1775-3 11-06 11-00 06 189-0 26769 141-6 16260 10509 2130-3 11-19 10-97 22 219-6 30580 139-3 18200 12380 2433-5 11-01 10-83 18 264-7 35525 134-2 21120 14405 2827-0 10-60 10-50 10 351-1 43421 123-7 25670 17751 3455-0 9-76 9-73 03 400-0 46640 116-6 27830 18810 3711-5 9-20 9-34 14 552-1 55410 100-4 34090 21320 4409-0 7-91 8-16 25 732-1 63400 86-6 39850 23550 5045-0 6-81 6-93 12 999-8 71800 71-8 47310 24490 5714-0 5-63 5-55 08 1471 80770 54-9 55870 24900 6430-0 4-29 3-98 31 8160 c* +190* + 120 ... -|i ain *y 46 TABLE V. CAST COBALT, MAGNETIC, AT 5 C. Experiments made November 28, 1873. . 93. M. T. P. 3- K. 48-47 3702 76-37 3287 415 290-8 6-00 76-74 7254 94-54 5760 1494 571-1 7-44 112-8 14370 127-5 9388 4982 1134-5 10-06 167-6 24130 144-0 14490 9640 1907 11-38 264-2 35860 135 7 20420 15440 2833 10-72 539-9 53940 99-91 33010 20930 4249 7-87 1473 80760 54-84 55920 24840 6310 4-28 i G8 HENRY A. ROWLAND TABLE VI. CAST COBALT, MAGNETIC, AT 230 C. Experiments made February 3, 1874. ft. S3. M. T. P. 3- K. 13-34 1357 101-8 1165 192 107 8-02 25-67 2916 113-6 2662 254 230 8-96 38-55 4940 128-2 4397 543 390 10-12 55-56 9400 169-1 7440 I960 743-5 13-38 75-16 15800 210-2 10050 5750 1143 16-65 101-4 23920 235-9 14260 9660 1895 18-70 132-7 31260 235-5 17710 13550 2475 18-66 172-9 38060 220-2 21820 16240 3015 17-44 281-8 52520 186-4 31160 21360 4174 14-76 393-6 63430 161-2 39070 24360 5039 12-75 702-9 82070 117-0 54920 27150 6515 9-27 989-3 95600 96-63 66750 28850 7584 7-67 1282 106200 82-87 75820 30380 8422 6-57 From Table IV we see that at ordinary temperatures cobalt does not offer any exception to the general law for the other magnetic metals that as the magnetization increases, the magnetic permeability first increases and then decreases. We also see that the results satisfy to a considerable degree of accuracy the equation which I have used for the other magnetic metals. The departure from the equation is of exactly the nature that can be accounted for in either of two ways either by the heating of the ring by the current for the higher magnetizing- forces, or by some want of homogeneity in the ring. According to the first explanation, the maximum of magnetization at C. will be some- what lower than the curve indicates; but by the second it must be higher. I, however, incline to the first, that it is due to heating, for two reasons: first, it is sufficient; and secondly, the smaller cobalt ring gives about the same maximum as this. Hence we may take as the provisional value of the maximum of magnetization of cobalt in round numbers 3= 8000, or SB = 100,000. We also see from Table IV that, at least in this case, the permeability of cobalt is less than that of nickel, though we could without doubt select specimens of cobalt which should have this quality higher than a given specimen of nickel. The formula at the foot of the Table also shows, by the increased value of the coefficient of K in the right-hand member, that the diameter of the curve is much less inclined to the axis of $ in this case than in the case of nickel or iron. In this re- spect the three metals at present stand in the following order cobalt, nickel, iron. This is the inverse order also of their permeability; but MAGNETIC PERMEABILITY OF NICKEL AND COBALT 69 at present I have not found any law connecting these two, and doubt if any exact relation exists, though as a general rule the value of the constant is greater in those curves where the permeability is least. In a short abstract in the ' Telegraphic Journal/ April 1, 1874, of a memoir by M. Stefan, it is stated " that the resistance of iron and nickel to magnetization is at first very great, then decreases to a mini- mum value, which is reached when the induced magnetic moment is become a third of its maximum." This will do for a very rough approx- imation, but is not accurate, as will be seen from the following Table of this ratio from my own experiments : Experiments published in Augnst, 1873. Iron. Tables I and II. Iron. Table III. Bessemer Iron Tabfe'iv. j TableV " Nickel. Table VI. Steel. Table VII. 1 3-02 1 2-64 1 1 1 3-15 1 2-46 2-65 2-68 Experiments of present paper. Nickel. Tables I and II. Nickel. Table III. Cobalt. Tables IV and V. 1 3-23 1 3-14 1 4-2 The average of these is, if we include Bessemer steel with the iron, as it is more iron than steel: Hence the place of greatest permeability will vary with the kind of metal. From these, however, we can approximate to the value of 6 in the formula; for we have 27,000 f AT- i i ^ 11,000 for Iron, b = - ; for Nickel, * = = ; p " for Cobalt, b = 26,000. In Table V we have the results for cobalt in the magnetic state. We here find the same effect of magnetization as we have before found for iron and nickel. 70 HENRY A. KOWLAND In Table VI we have results for cobalt at a high temperature, and see how greatly the permeability is increased by rise of temperature, this being for the vertex of the curve about 70 per cent. But on plot- ting the curve I was much surprised to find an entire departure from that regularity which I had before found in all curves taken from iron and nickel when the metal was homogeneous. At present I am not able to account for this, and especially for the fact that one of the measure- ments of 33 is higher than that which we have taken for the maximum of magnetization, at, however, a lower temperature. The curve is exactly of the same nature as that which I have before found for a piece of nickel which had been rendered unhomogeneous by heating red-hot, and thus burning the outside. The smaller cobalt ring gives a curve of the same general shape as this, but has the top more rounded. I will not attempt without fresh experiments to explain these facts, but will simply offer the following explanations, some one of which may be true. First, it may be due to want of homogeneity in the ring; but it seems as if this should have affected the curve of Table IV more. Secondly, it may be at least partly due to the rise in temperature of the ring at high magnetizing-powers ; and indeed we know that this must be greater in paraffin than in alcohol for several reasons : there is about twice as much heat generated in copper wire at 230 C. as at with the same current; and this heat will not be conducted off so fast in paraffin as in alcohol, on account of its circulating with less freedom; it probably has less specific heat also. Thirdly, it may be due to some property of cobalt, by which its permeability and maximum of magneti- zation are increased by heat and the curve changed. The experiments made with the small ring confirm those made with the large one as far as they go; but as it was so small, they do not possess the weight due to those with the larger one. But, curious as it may seem, although they were turned from the same button side by side, yet the permeability of the larger is about 45 per cent greater than that of the smaller. I have satisfied myself that this is due to no error in experiment, but illustrates what extremely small changes will affect the permeability of any metal. We have now completed the discussion of the results as far as they refer to the magnetic permeability, leaving the discussion of the tem- porary and permanent or residual magnetism to the future, although these latter, when discussed, will throw great light upon the nature of the coercive force in steel and other metals. The whole subject seems to be a most fruitful one, and I can hardly understand why it has MAGNETIC PERMEABILITY OF NICKEL AND COBALT 71 been so much neglected. It may have been that a simple method of experiment was not known; but if so, I believe that my method will be found both accurate and simple, though it may be modified to suit the circumstances. Professor Maxwell has suggested to me that it would be better to use rods of great length than rings, because that in a ring we can never determine its actual magnetization, but must always con- tent ourselves with measuring the change on reversing or breaking the current. This is an important remark, because it has been found by MM. Marianini and Jamin, and was noticed independently by myself in some unpublished experiments of 1870, that a bar of steel which has lain for some time magnetized in one direction will afterwards be more easily magnetized in that direction than in the other. This fact could not have been discovered from a ring; and indeed if a ring got a one- sided magnetism in any way we might never know it, and yet it might affect our results, as indeed we have already seen in the case of the magnetic curve. But at the same time I think that greater errors would result from using long bars. I have tried one of iron 3 feet long and inch diameter; and the effect of the length was still appar- ent, although the ratio of length to diameter was 144. To get exact results it would probably have to be several times this for the given specimen of iron, and would of course have to be greater for a piece of iron having greater permeability. This rod must be turned and must be homogeneous throughout conditions which it would be very difficult to fulfil, and which would be impossible in the case of nickel and cobalt. We might indeed use ellipsoids of very elongated form; and this would probably be the best of all, as the mathematical theory of this case is complete, and it is one of the few where the magnetization is uniform, and which consequently will still hold, although the permea- bility may vary with the amount of magnetization. This form will, of course, satisfy Professor Maxwell's objection. The method of the ring introduces a small error which has never yet been considered, and which will affect Dr. Stoletow's results as well as mine. The number of lines of induction passing across the circular section of a ring-magnet we have seen to be /+ J ~Jp y* Jn a, x in which a is the mean radius of the ring, E the radius of the section, n' the number of coils in the helix, and i the intensity of the current. Xow in integrating this before, I assumed that ft was a constant throughout the section of the ring: now we have found that 11 is a 72 HENET A. EOWLAND function of the magnetization, and hence a function of the magnetizing- force; but the latter varies in different parts of the section, and hence n must vary. But the correction will be small, because the average value will be nearly the same as if it were a constant. We may estimate the correction in the following manner. Let // and be the values of those quantities at any point in the section of the ring, // and ' the values at the centre of the section, and fjt t and , the observed values. Then, by Taylor's theorem, But = 2n ' 1 and ft' = , and so we have a x a \ 4 a* 2// dJQ r \ a 2 Jp' 2 d z >j. I R* , q K But in my Tables I have already calculated Q 1 A*J = a &c. . t / i T53 \ J ,lfV (l + i ^ + fto.) and as ft l is very nearly equal to fjf, and $, to ^)', we have approximately 6, din. I IP 3 If . -- . 2 4 a 4 which will give the value of // corresponding to Q' and >'. Hence the correct values of the quantities will be //, ', and S3' = ^V. The quantities -^- and ^/- can be obtained either by measuring a "/ **/ plot of the curve, or from the empirical equation = sn when we know the values of the constants. In this case dp _ , ft, *$/ " ^V/ d? in which MAGNETIC PERMEABILITY OF NICKEL AND COBALT 73 In all these the upper signs are to be taken for all values of >, less than , and the lower signs for greater values. t> On applying these formulas to the observations, I have found that the corrections will in no way influence my conclusions, being always very small; but at the same time the calculation shows that it would be well R to diminish the ratio as much as possible. In all my rings this ratio a did not depart very much from - ; but I would advise future experi- o'o menters to take it at least as small as ^: the amount of correction R will be very nearly proportional to the square of . ct Summary. The following laws have been established entirely by my own experi- ments, though in that part of (2) which refers to iron I have been anticipated in the publication by Dr. Stoletow (Phil. Mag. Jan. 1873). When any measurements are given, they are on the metre, gramme, second system. (1) Iron, nickel, and cobalt, in their magnetic properties at ordinary temperatures, differ from each other only in the quantity of those properties and not in the quality. (2) As the magnetizing-force is increased from upwards, the resist- ance of iron, nickel, and cobalt to magnetization decreases until a minimum is reached, and after that increases indefinitely. This mini- mum is reached when the metal has attained a magnetization of from 24 to -38 of the maximum of magnetization of the given metal. (3) The curve showing the relation between the magnetization and the magnetic permeability, or Neumann's coefficient, is of such a form that a diameter can be drawn bisecting chords parallel to the axis of 33, and is of very nearly the form given by the equation where B, &, and D are constants, jut is the ratio of the magnetization to the magnetizing-force in an infinitely long bar, and 33 is the amount of magnetization. (4) If a metal is permanently magnetized, its resistance to change of magnetism is greater for low magnetizing-powers than when it is in the normal state, but is the same for high magnetizing-powers. This 74 HENRY A. EOWLAND applies to the permanent state finally attained after several reversals of magnetizing-f orce ; but if we strongly magnetize a bar in one direction and then afterwards apply a weak magnetizing-force in the opposite direction, the change of magnetization will be very great. (5) The resistances of nickel and cobalt to magnetization vary with the temperature; but whether it is increased or not in nickel depends upon the amount of magnetization : for a moderate amount of magneti- zation it decreases with rise of temperature very rapidly; but if the magnetization is high the resistance is increased. In cobalt it appar- ently always decreased, whatever the magnetization. The resistance of iron to magnetization is not much affected by the temperature. (6) The resistance of any specimen of metal to magnetization de- pends on the kind of metal, on the quality of the metal, on the amount of permanent magnetization, on the temperature, and on the total amount of magnetization, and, in at least iron and nickel, decreases very much on careful annealing. The maximum of magnetization depends on the kind of metal and on the temperature. (7) Iron, nickel, and cobalt all probably have a maximum of magneti- zation, though its existence can never be entirely established by experi- ment, and must always be a matter of inference; but if one exists, the values must be nearly as follows at ordinary temperatures. Iron when 33 = 175,000 or when 3 = 13,900; nickel when 33 =63,000 or when 3 = 4940; cobalt when 33 = 100,000( ?) or when 3 = 8000 (?). (8) The maximum of magnetization of iron and nickel decreases with rise of temperature, at least between 10 C. and 220 C., the first very slowly and the second very rapidly. At 220 C. the maximum for iron is when 33 = 172,000 and 3 = 13,600, and for nickel when 33 = 49,000 and 3 = 3800. The laws which govern temporary and residual magnetism, except so far as they have been hitherto given, I leave for the future, when I shall have time for further experiment on the subject to develop some points which are not yet quite clear. Troy, New York, U. S. A., April, 1874. ON A NEW DIAMAGNETIC ATTACHMENT TO THE LANTERN, WITH A NOTE ON THE THEOEY OF THE OSCILLATIONS OF INDUCTIVELY MAGNETIZED BODIES [American Journal of Science [8], IX, 357-361, 1875] 1. DESCRIPTION OF APPARATUS Some time ago, in thinking of the theory of diamagnetism, I came to the conclusion that apparatus of large size was by no means neces- sary in diamagnetic experiments, and on testing my conjectures experi- mentally, I was much pleased to find that they were true. So that for more than a year I have been in the habit of illustrating this subject to my classes by means of a small apparatus weighing only about a pound or two, which I place in my lantern and magnify to a large size on the screen. The effects obtained in this way are very fine and are not surpassed by those with the largest magnets; and we are by no means confined, to strongly diamagnetic substances, but, with proper care, can use any- thing, even the most feeble. The apparatus which I used consisted of a horseshoe electro-magnet, made of an iron bar half an inch in diam- eter and about ten inches long, bent into the proper form, and sur- rounded with four or five layers of No. 16 wire. But the following apparatus will, without doubt, be found much more convenient. It can be made of any size, though the dimensions given will probably be found convenient. d d r j 3 be the resistance at a given point to passing down the rod, s be the resistance at the end of the rod, Q' 4 be the number of lines of induction passing along the rod at a given point, $'. 5 be the number of lines of induction passing from the rod into the medium along a small length of the rod JL, L be the distance from the end of the rod to a given point, R ' A _ V RR' + s , dL + dp= ,57 To find ft, the ordinary equation for the resistance of a derived cir- cuit gives whence 4 These are the surf ace-integrals of magnetic induction (see Maxwell's ' Electricity,' art. 402) the first across the section of the bar, and the second along a length AZ, of the surface of the bar. 5 It is to be noted that Q', when A is constant, is nearly proportional to the so- called surface-density of magnetism at the given point. 92 HENRY A. EOWLAND and To find Q', we have whence and fV^AT HAT ^ _-"). . . (3) When L is very large, or s =*/RR' , we have Q' = Cf L > and C: in which L / is reckoned from an origin at any point of the rod. These equations give the distribution on the part outside the helix; and we have now to consider the part covered by the helix. Let us A: c: E FIG. 1. limit ourselves to the case where the helix is long and thin, so that the field in its interior is nearly uniform. As we pass along the helix, the change of magnetic potential due to the helix is equal to the product of the intensity of the field multiplied by the distance passed over ; so that in passing over an elementary dis- tance dy the difference of potential will be &dy. The number of lines of force which this difference of potential causes in the rod will be equal to Qdy divided by the sum of the resistances of the rod in both direc- tions from the given point. These lines of force stream down the rod on either side of the point, creating everywhere a magnetic potential which can be calculated by equation (2), and which is represented by the curves in Fig. 1. In that figure A B is the rod, C D the helix, and cPQ' This could have been obtained directly from the equation ,? 9 =Q / r y , and Q/ e from Cl-Li' dQ' the equation Q f e = -V A L. STUDIES ON MAGNETIC DISTEIBUTION 93 E the element of length dy. Now, if we take all the elements of the rod in the same way and consider the effect at H F, the total magnetic potential at this point will, by hypothesis No. 1, be equal to the sum of the potentials due to all the elements dy. Let 4Q' be the number of lines of force produced in the bar at the point E due to the elementary difference of potential at that point, Qdy, AQ" be the number o* lines of force arriving at the point F due to the same element, Q" be the number of lines passing from bar along length JL, /> be the sum of the resistances of the bar in both directions from E, /> z be resistance at F in direction of D, y be the distance D E, x be the distance D F, 6 be the distance C D, s" and s' be the resistance of the bar, &c., respectively at C in the direction of A, and at D in direction of B, be the magnetizing-force of helix in its interior. Let At y jt^t -r * AH *v jm, T * ** ~ * ^ 9 " ' j---,^ ^>^ 7i 9 f>* = ft 4- e _ ~ 2R'r A'A"-1 This gives the positive part of Q"- To find the negative part, change x into & a;, A' into A", and A" into A', and then change the sign of the whole. When the helix is symmetrically placed on the bar, we have s' = s", A'=A"; whence, adding the positive and negative parts together, we have 94 HENRY A. ROWLAND " = J -/ y * ~ A ' ( e r (-*> rx> ) (5^) ZVTU? A'? b 1 v which gives the number of lines of induction passing out from the rod along the length AL when the helix is symmetrically placed on the rod. To get the number of lines of induction passing along the rod at a given point, we have f\Z (L 1 A I where c rt 1 When the bar extends a distance L' out of both ends of the helix, so that if = */RW and A' = we have It may be well, before proceeding, to define what is meant by mag- netic resistance, and the units in which it is measured. If ft is the magnetic permeability of the rod, we can get an idea of the meaning of magnetic resistance in the following manner. Suppose we have a rod infinitely long placed in a magnetic field of intensity parallel to the lines of force. Let Q' be the number of lines of inductive force passing through the rod, or the surface-integral of the magnetic induc- tion across its section; also let a be the area of the rod. Then by definition n = -sL. If L is the length of the rod, the difference of flEty potential at the ends will be LS& ; hence 0' - L and fl - - L - L ^ X ' ~ IT ~^' and R in the formula? becomes R _ R, _ . 1 -ft -jL . L* a/j. It is almost impossible to estimate R' theoretically, seeing that it will vary with the circumstances. We can get some idea of its nature, however, by considering that the principal part of it is due to the cylindric envelope of medium immediately surrounding the rod. The resistance of such an envelope per unit of length of rod is STUDIES ox MAGNETIC DISTRIBUTION 95 where D is the diameter of the envelope, d of the rod, and /JL } the permea- bility of the medium. But we are not able to estimate D. If, however, we have two magnetic systems similar in all their parts, it is evident that beyond a certain point similarly situated in each system we may neglect the resistance of the medium, and -r will be the same for the two systems. Hence R' is approximately constant for rods of all diam- eters in the same medium, and r takes the form r = ^ It is evident that the reasoning would apply to rods of any section as well as circular. In Green's splendid essay (Eeprint, p. Ill, or Maxwell's ' Treatise on Electricity and Magnetism,' art. 439) we find a formula similar to equation (5), but obtained in an entirely different manner, and applying only to rods not extending beyond the helix. In the ' Keprint,' ft corresponds to my r; and its value, using my notation, is obtained from the equation 231863 2 hyp. log p + 2p = _ 4 , , .... (8) rd where p = -=-. rd If we make p a constant in this formula, we must have p == -^ = constant; hence which is the same result for this case as from equation (7). When fj. in the two formula is made to vary, the results are not exactly the same; but still they give approximately the same results for the cases we shall consider; and since the formula is at the best only approximate, we shall not spend time in discussing the merits of the two. III. Among the various methods of measuring linear magnetic distribu- tion, we find few up to the present time that are satisfactory. Coulomb used the method of counting the number of vibrations made by a magnetic needle when near various points of the magnet. Thus, in 96 HENRY A. KOWLAND the curve of distribution most often reproduced from his work, he used a magnetized steel bar 27 French inches long and 2 lines in diameter placed vertically; opposite to it, and at a distance of 8 lines, he hung a magnetic needle 3 lines in diameter and 6 lines long, tempered very hard; and the number of oscillations made by it was determined. The square of this number is proportional to the magnetic field at that point, supposing the magnetism of the needle to be unchanged; and this, corrected for the magnetism of the earth, gives the magnetic field due to the magnet alone. This for points near the magnet and distant from the ends is nearly proportional to the so-called magnetic surface-density opposite the point. At the end Coulomb doubled the quantity thus found, seeing that the bar extended only on one side of the needle. It will be seen that this method is only approximate, and almost incapable of giving results in absolute measure. The effect on the needle depends not only on that part of the bar opposite the needle, but on portions to either side, and gives, as it were, the average value for some distance; in the next place, the correction at the end, by multiplying by 2, seems to be inadequate, and gives too small a result compared with other parts. For at points distant from the end the average surface-density at any point will be nearly equal to the average for a short distance on both sides, while at the end it will be greater than the average of a short distance measured back from the end. To these errors must be added those due to the mutual induction of the two magnets. The next method we come to is that which has been recently used by M. Jamin, and consists in measuring the attraction of a piece of soft iron applied at different points of the magnet. In this case it does not seem to have been considered that the attraction depends not only on the magnetic density at the given point, but also on that around it, and that a piece of soft iron applied to a magnet changes the distri- bution immediately at all points, but especially at that where the iron is applied. The change is of course less when the magnet is of very hard steel and the piece of soft iron small. Where, however, we wish to get the distribution on soft iron, it becomes a quite serious difficulty. Another source of error arises from the fact that the coefficient of magnetization of soft iron is a function of the magnetization: this source of error is greatest when the contact-piece is long and thin, and is a minimum when it is short and thick and not in contact with the magnet. Hence this method will give the best results when the con- tact-piece is small and in the shape of a sphere and not in contact with STUDIES ON MAGNETIC DISTRIBUTION 97 the magnet, and when the method is applied to steel magnets. But after taking all these precautions, the question next arises as to how to obtain the magnetic surface-density from the experiments. Theory indicates, and M. Jamin has assumed, that the attractive force is nearly proportional to the square of the surface-density. But experiment does not seem to confirm this, except where there is some distance between the two bodies, at least in the case of a sphere and a plane surface, as in Tyndall's experiments (Phil. Mag., April, 1851). It is not necessary at present to consider the cause of this apparent dis- crepancy between theory ar>d experiment; suffice it to say that the explanation of the phenomenon is without doubt to be sought for in the variable character of the magnetizing-function of iron. All I wish to show is that the attraction of iron to a magnet, especially when the two are in contact, is a very complicated phenomenon, whose laws in general are unknown, and hence is entirely unsuitable for experiments on magnetic distribution. A third method is that used in determining the correction for the distribution on the magnets in finding the intensity of the earth's magnetism. Usually the distribution is not explicitly found in this case; but it is easy to see how it might be. Thus, one way would be as follows: Take the origin of coordinates at the centre of the magnet. Develop the distribution in an ascending series of powers of x with unknown constant coefficients. Calculate the magnetic force due to this distribution for any points along the axis, or else on a line perpen- dicular to the magnet at its centre. Determine the force at a series of points extending through as great a range and as near the magnet as possible. These experiments give a series of equations from which the coefficients in the expansion can be determined. Other and better methods of expansion might be found, except for short magnets, where the method suggested is very good. The similarity of this method to that used by Gauss in determining the distribution on the earth is apparent. A fourth method is similar to the above, except that the lines of force around the magnet are measured and calculated instead of the force. The last two methods are very exact, but are also very laborious, and therefore only adapted to special investigations. Thus, by the change in direction of the lines of force around the magnet, we have a delicate means of showing the change in distribution, as, for instance, when the current around an electro-magnet varies. 98 HENEY A. EOWLAND The fifth method is that used lately in some experiments of Mr. Sears (American Journal of Science, July, 1874), but only adapted to temporary magnetization. At a given point on the bar a small coil of wire is placed, and the current induced in it measured by the swing of the galvanometer-needle when the bar is demagnetized. It does not seem to have been noticed that what we ordinarily consider the mag- netic distribution is not directly measured in this way; and indeed, to get correct results, the magnetization should have been reversed, seeing that a large portion of the magnetization will not disappear, on taking away the magnetizing-force, where the bar is long. The quantity which is directly measured is the surface-integral of the temporary magnetic induction across the section of the bar, while the magnetic surface- density is proportional to the surface-integral of magnetic induction along a given portion of the Itar. In other words, the quantity measured is Q instead of -^L. We can, however, derive one from the other very easily. The sixth and last method is that which I used first in 1870, and by which most of my experiments have been performed. This consists in sliding a small coil of wire, which just fits the bar and is also very narrow, along the bar inch by inch, and noting the induced current over each inch by the deflection of a galvanometer-needle. This meas- ures Q f , except for some corrections which I now wish to note. In the first case, to give exact results, the lines of force should pass out per- pendicular to the bar, or the coil must be very small. But even when the last condition is fulfilled errors will be introduced at certain por- tions of the bar. The error is vanishingly small in most cases, except near the ends; and even there it is not large, except in special cases; for at this part the lines of force pass forward toward the end of the bar, and so the observation next to the end may be too small, while that at the end is too large. The correction can be made by finding where the lines of force through the centre of the section of the coil in its two positions meet the bar. The error from this source is not large, and may be avoided to a great extent. One very great advantage in the method of induced currents is the facility with which the results can be reduced to absolute measure by including an earth-inductor in the circuit as I have before described (Phil. Mag., August, 1873). There is also no reaction (except a tem- porary one) between the magnet and current; so that the distribution remains unchanged. Hence it seems to me that this method is the only one capable of giving exact results directly. STUDIES ON MAGNETIC DISTRIBUTION 99 The coils of wire which I used consisted of from twenty to one hundred turns of fine wire wound on thin paper tubes which just fitted the bar and extended considerably beyond the coils. The coils were mostly from -1 to -25 of an inch wide and from -1 to -2 inch thick. A measure being laid by the side of the given bar under experiment, the coil was moved from one division of the rule to the next very quickly, and the deflection produced on an ordinary astatic galvanometer noted. After experience this could be done with great accuracy. It might be better in some cases to have the coil slide over a limited distance on the tube, though for the use to which I intend to put the results the other is best. Up to 35 Q f is nearly proportional to the deflection; and when any larger value is put down in the Tables, it is the sum of two or more deflections. I have not the data in most cases to reduce my results to absolute measure, but took pains to ensure that certain series of ex- periments should be comparable among themselves. Having measured Q e at all points of a rod, we may find Q by adding up the values of Q f from the end of the rod. The magnetizing force to which the bar was subjected was in all cases a helix placed at some part of the bar. The iron bars were of course demagnetized thoroughly before use by placing them in the proper position with reference to the magnetic meridian and striking them. In the Tables L is the distance in inches from the zero-point, Q f is the deflection of the galvanometer when the helix is passed between the points indicated in the first column. Thus, in Table II, 34-7 is the deflection on the galvanometer when the helix was moved from the tenth to the eleventh inch from the zero-point; and so we may con- sider it as the value of Q f at 10 inches; so that the values of Q ( refer to the half inches, but Q to the even inches. In all the calculations the constants in the formulae were taken to represent Q most nearly, and then the corresponding formulae for Q e taken with the same constants. For ease in calculating by ordinary logarithmic Tables, we may put -rL 1 /ymSrt IV. Table I is from a bar 17 inches long with a magnetizing helix 1 inch long at one end, the zero-point being at the other. Table II is from a bar 9 feet long with a helix 4$ inches long quite near one end, the zero-point being at 1 inch from the helix toward the long end. 100 HENRY A. EOWLAND Table III is from a bar 2 feet long with a helix 4r| inches long near one end, so that its centre was 19f inches from the end on which the experiments were made, the zero-point being at the end. In adapting the formula to apply to the case of Table I, we may assume that at the end of the bar s =o> and (7 = 0, which is equivalent to assuming that the number of lines of induction which pass out at the end of the rod are too small to be appreciated. TABLE I. BAR -18 INCH DIAMETER. AT END OF BAR. L. < Q'. Calcu- Error of at Q'. Calcu- Error of served. lated. Q,. served. lated. 3 .... 2-7 3-5 + -8 5 6 7 8 9 10 11 12 13 14 2-0 2-5 3-2 3-7 4-3 5-3 6-5 7-7 9-5 2-0 2-4 2-8 3-5 4-3 5-2 6-5 8-0 9-9 -1 -4 -2 -1 + -3 + -4 5-9 7-9 10-4 13-6 17-3 21-6 26-9 33-4 41-1 50-6 6-6 8-6 11-0 13-8 17-3 21-6 26-8 33-3 41-3 51-2 + -7 + -7 + -6 + -2 -1 -1 + -2 + -6 n^iCi,=,54 (e +e -, In Table II observations were not made over the whole length of the rod, and the zero-point was not at the end of the bar. It is evident, however, that by giving a proper value to s we may suppose the bar to end at any point. As the rod is very long, expressions of the form Q'C" = 0'^ L C" and Q' t = rC'e-* L will apply. In Table II the observations were near the end of the rod, and were repeated several times. Neglecting the end of the rod, we have s=oo . In these Tables we see quite a good agreement between theory and observation; but on more careful examination we observe a certain law in the distribution of errors. Thus in Table I the errors of Q' are all positive between and 8 inches; and this has always been found to be the case at this part of the bar in all my experiments. The explanation of this is very simple. In obtaining the formulae,, we assumed that the magnetic permeability of the bar fj. was a constant STUDIES ON MAGNETIC DISTRIBUTION 101 TABLE II. BAR -39 INCH DIAMETER. AT 1 INCH FROM HELIX. L. served. Calcu- lated. Error of Q^- Q'-C". Ob- served. Q'-C". Calcu- lated. Error of Q'- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 21 23 25 27 29 31 825-2 753-5 688-3 628-8 575-3 524-1 477-4 434-2 394-2 357-0 322-3 290-6 261-1 235-4 209-9 187-9 166-4 146-4 127-3 94-8 67-3 44-3 25-8 11-3 902-5 825-9 755-1 689-8 629-5 574-3 523-1 476-0 432-5 392-5 355-6 321-5 290-1 261-2 234-5 210-0 187-3 166-4 147-1 129-4 97-8 71-1 48-6 29-0 12-6 1-2 + -7 + 1-6 + 1-5 + -7 1-0 1-0 1-4 1-7 1-7 1-4 -8 -5 + -1 -9 + -1 -6 + -7 + 2-1 + 3-0 + 3-8 + 4-3 + 3-2 + 1-3 1-2 71-7 65-2 59-5 53-5 51-2 46-7 43-2 40-0 37-2 34-7 31-7 29-5 25-7 25-5 22-0 21-5 20-0 19-1 32-5 27-5 23-0 18-5 14-5 11-3 70-8 65-3 60-2 55-5 51-2 47-2 43-5 40-1 37-0 34-1 31-4 28-9 26-6 24-6 22-7 20-9 19-3 17-8 31-5 26-7 22-8 19-4 16-5 14-0 -9 + -1 + -7 + 2-0 + -5 + -3 + -1 -2 -6 -3 -6 + -9 -9 + -7 -6 .7 1-3 1-0 -8 -2 + -9 + 2-0 + 2-7 Qf _C' // =983r-o8i35z;_80-5=983-(10)--o, whence for the positive part of Q' f ' we have 2R'r l and for the negative part (1 + e* _ -rxN . 8 When considering surface-density, we should also allow for the direct action of the helix, though this is always found too small to be worth taking into account except in very accurate experiments. STUDIES ox MAGNETIC DISTRIBUTION therefore the real value is Q,, _ &AL f ( Z _ b} , b _ o\ , f -rx\ . U< ~ 2R'r C And if x is reckoned from the end of the rod, we have 113 (10) When x = 0, this becomes and when x = b, it becomes the ratio of which is and this is the ratio of the values of Q" at the ends of the helix. When & is 12 inches, as in this case, we get the following values of this ratio : r 05. 1. 15. 20. 30. 00. -*(-*-!) = 2 2256 4-43 3494 2-86 4173 2-40 4546 2-20 4863 2-06 500 2-00 e-'-* 1 To compare this with our experiments, let us plot Table X once more, rejecting, however, the end observations and completing the curve by the eye, thus getting rid of the error introduced at this point. We then find for this ratio, according to the different curves, B. C. D. 2-1 2-3 3-2 It is seen that these are all above the limit 2, as they should be though it is possible that it may fall below in some cases, owing to the variation of the permeability. As the magnetization increases, the values of the above ratio show that r decreases, as we should expect it to do from the variation of /*. To find the neutral point in this case, we must have in formula (10) 114 HENRY A. EOWLAND where x is the distance of the neutral point from the end. Making b = 12, we have from this : r= x= 05. 10. 15. 20. 30. 00 . 10-1 8-96 8-31 7-89 7-39 6-00 By experiment we find that the neutral point is, in all the cases we have given in Table X, between 7-5 and 8-1 inches, which are quite near the points indicated by theory for the proper values of r, though we might expect curve D to pass through the point x = 9, except for the disturbing causes we have all along considered. Our formulae, then, express the general facts of the distribution in this case with considerable accuracy. These experiments and calculations show the change in distribution in an electromagnet when we place a piece of iron against one pole only. In an ordinary straight electromagnet the neutral point is at the centre. When a paramagnetic substance is placed against or near one end, the neutral point moves toward it; but if the substance is diamag- netic it moves from it. The same thing will happen, though in a less degree, in the case of a steel magnet; so that its neutral point depends on external conditions as well as on internal. We now come to practically the most interesting case of distribution, namely that of a straight bar magnetized longitudinally either by a helix around it, or by placing it in a magnetic field parallel to the lines of force; we shall also see that this is the case of a steel magnet mag- netized permanently. This case is the one considered by Biot (Traite de PJiys., tome iii, p. 77) and Green (Mathematical Papers of the late George Green, p. Ill, or Maxwell's ' Treatise/ art. 439), though they apply their formula? more particularly to the case of steel magnets. Biot obtained his formula from the analogy of the magnet to a Zamboni pile or a tourmaline electrified by heat. Green obtained his for the case of a very long rod placed in a magnetic field parallel to the lines of force, and, in obtaining it, used a series of mathematical approxima- tions whose physical meaning it is almost impossible to follow. Prof. Maxwell has criticised his method in the following terms (' Treatise/ art. 439) : " Though some of the steps of this investigation are not rigorous, it is probable that the result represents roughly the actual magnetization in this most important case." From the theory which STUDIES ON MAGNETIC DISTKIBUTION 115 I have given in the first part of this paper we can deduce the physical meaning of Green's approximations; and these are included in the hypotheses there given, seeing that, when my formula is applied to the special case considered by Green, it agrees with it where the permea- bility of the material is great. My formula, however, is far more gen- eral than Green's. It is to Green that we owe the important remark that the distribu- tion in a steel magnet may be nearly represented by the same formula that applies to electromagnets. As Green uses what is known as the surface-density of magnetization, let us first see how this quantity compares with those I have used. Suppose that a long thin steel wire is so magnetized in the direction of its length that when broken up the pieces will have the same mag- netic moment. While the rod is together, if we calculate its effect on exterior bodies, we shall see that the ends are the only portions which seem to act. Hence we may mathematically consider the whole action of the rod to be due to the distribution of an imaginary magnetic fluid over the ends of the rod. As any case of magnetism can be represented by a proper combination of these rods, we see that all cases of this sort can be calculated on the supposition of there being two magnetic fluids distributed over the surfaces of the bodies, a unit quantity of which will repel another unit of like nature at a unit's distance with a unit of force. The surface-density at any point will then be the quantity of this fluid on a unit surface at the given point; and the linear density along a rod will be the quantity along a unit of length, supposing the density the same as at the given point. Where we use induced currents to measure magnetism we measure the number of lines of force, or rather induction, cut by the wire, and the natural unit used is the number of lines of a unit field which will pass through a unit surface placed perpendicular to the lines of force., The unit pole produces a unit field at a unit's distance; hence the num- ber of lines of force coming from the unit pole is 4 x, and the linear density is ' = & ....... < H > and the surface-density These really apply only to steel magnets ; but as in the case of electro- magnets the action of the helix is very small compared with that of the 116 HENKY A. ROWLAND iron, especially when it is very long and the iron soft, 9 we can apply these to the cases we consider. Transforming Green's formula into my notation, it gives (13) in which < is Neumann's coefficient of magnetization by induction, and is equal to This equation then gives c f r(/;.-i) ~- , .... (U) Equation (5) can be approximately adapted to this case by making s' oo , which is equivalent to neglecting those lines of force which pass out of the end section of the bar. This gives A' = 1 : hence 2 / 1 Now we have found (equation 7) that r -=- J nearly; and this in Green's formula (equation 14) gives which is identical with my own when JJL is large, as it always is in the case of iron, nickel, or cobalt at ordinary temperatures. When x is measured from the centre of the bar, my equation becomes (17) The constant part of Biot's formula is not the same as this; but for any given case it will give the same distribution. Both Biot and Green have compared their formulae with Coulomb's experiments, and found them to represent the distribution quite well. Hence it will not be necessary to consider the case of steel magnets very extensively, though I will give a few results for these further on. 9 I take this occasion to correct an error in Jenkin's 'Textbook of Electricity,' where it is stated that by the introduction of the iron bar into the helix, the num- ber of lines of force is increased 32 times. The number should have been from a quite small number for a short thick bar and hard iron to nearly 6000 for a long thin bar and softest iron. STUDIES ON MAGNETIC DISTRIBUTION 117 At present let us take the case of electromagnets. For observing the effect of the permeability, I took two wires 12-8 inches long and -19 inch in diameter, one being of ordinary iron and the other of Stubs' steel of the same temper as when purchased. These were wound uniformly from end to end with one layer of quite fine wire, making 600 turns in that distance. In finding / from Q" f) the latter was divided by 4~JL, except at the end, where the end-section was included with JL in the proper manner. x was measured from the end of the bar in inches. The observations in Table XI are the mean of four observations made on both ends of the bar and with the current in both directions. TABLE XI. IKON ELECTROMAGNET. x = distance from end. I Q- 4irA. Observed. . Observed. 4irA. Computed. Error. 22-5 41-1 33-9 7-2 } 12-6 25-1 26-9 ' +1-8 1 19-3 19-3 18-9 0-4 12-0 12-0 11-7 -3 6-6 6-6 7-1 + -5 4 3-9 3-9 4-0 + -1 5 6 2-9 2-9 1.7 1-2 4jr2. = 42 The agreement with the formula in this Table is quite good; but we still observe the excess of observation over the formula at the end, as we have done all along. Here, for the first time, we see the error introduced by the method of experiment which I have before referred to (p. 98) in the apparently small value of 4;rA at x= -75. On trying the steel bar, I came across a curious fact, which, how- ever. I have since found has been noticed by others. It is, that when an iron or steel bar has been magnetized for a long time in one direction and is then demagnetized, it is easier to magnetize it again in the same direction than in the opposite direction. The rod which I used in this experiment had been used as a permanent magnet for about a month, but was demagnetized before use. From this rod five cases of distribu- tion were observed: first, when the bar was used as an electromagnet with the magnetization in the same direction as the original mag- 118 HENKY A. EOWLAND netism; second, ditto with magnetization contrary to original mag- netism; third, when used as a permanent magnet with magnetism the same as the original magnetism; fourth, ditto with magnetism oppo- site; and fifth, same as third, but curve taken after several days. The permanent magnetism was given by the current. The observations in Tables XI and XII can be compared together, the quantities being expressed in the same unknown arbitrary unit. It is to be noted that the bars in Tables XI and XII were subjected to the same magnetizing force. TABLE XII. STUBS' STEEL. Electromagnet. Permanent Magnet. X. Magnetism same as original. Magnetism opp site to original. Magnetism same as original. Magnetism opposite to original. Same as third, after three or four days. Qe- 4irA. Qe- 47TA. Qe- 4irA. Qe- 4rrA. Qe- 4irA. i 23-3 11-5 42-5 23-0 15-9 7-7 29-0 15-4 I 14-4 13-7 4-8 4-6 12-8 12-2 H 8-2 6-1 16-4 12-2 5-9 4-3 11-8 8-6 I 8-2 8-2 4-0 4-0 7-3 7-3 7-4 7-4 5-5 5-5 5-3 5-3 2-9 2-9 4-8 4-8 3 8-6 3-6 2-7 2-5 3-0 3-0 1-6 1-6 2-9 2-9 4 6 1-7 8 1-0 5 2-2 1-1 9 4 2-0 1-0 First of all, from these Tables and figures (p. 119) we notice the change in distribution due to the quality of the substance; thus in Fig. 5 we see that the curves for steel are much more steep than that of iron, and would thus give greater values to r in the formula a result to be expected. We also observe in both figures the great change in distri- bution due to the direction of magnetization. In the case of the elec- tromagnet this amounts to little more than a change in scale; but in the permanent magnet there is a real change of form in the curve. It seems probable that this change of form would be done away with by using a sufficient magnetizing power or magnetizing by application of permanent magnets; for it is probable that the fall in the curve E is due to the magnetizing force having been sufficient to change the polarity completely at the centre, but only partially at the ends. On comparing the distribution on electromagnets with that on perma- nent magnets, we perceive that the curve is steeper toward the end in STUDIES ON MAGNETIC DISTRIBUTION 119 electromagnets than in permanent magnets. At first I thought it might be due to the direct action of the helix, but on trial found that the latter was almost inappreciable. I do not at present know the explanation of it. As before mentioned, Coulomb has made many experiments on the distribution of magnetism on permanent magnets; and so I shall only consider this subject briefly. I have already given one or two results in Table XII. 654321 FIG. 5. Results from electromagnets. A. Iron, from Table XI. B. Steel, from Table XII, magnetized same as originally. C. Steel, from Table XII, magnetized opposite to its original magnetism. 6 S 4 3 2 1 O FIG. 6. Results from steel permanent magnets. D. Magnetized in its original direction, Table XII. E. Magnetized opposite to its original direction, Table XII. Scale four times that of Fig. 5. The following Tables were taken from two exactly similar Stubs' steel rods not hardened, one of which was subsequently used in the experiments of Table XII. They were 12-8 inches long and -19 inch in diameter. The coincidence of these observations with the formula is very re- 120 HENRY A. ROWLAND markable; but still we see a little tendency in the end observation to rise above the value given by the formula. In equation (7), and also from Green's formula, we have seen that * T for a given quality and temper of steel p = r - is a constant. From to Coulomb's experiments on a steel bar -176 inch in diameter (whose quality and temper is unknown, though it was probably hardened) Green has calculated the value of this constant, and obtained -05482, which was found from the French inch as the unit of length, but which is constant for all systems. From Tables XIII and XIV we find the value TABLE XIII. X. Q<- Observed. 47TA. Observed. 47TA. Computed. Error. 1-28 2-56 3-84 5-12 6-40 46-6 23-8 12-6 7-2 2-3 34-9 18-6 9-8 5-6 1-8 34-26 18-60 9-88 4-77 1-41 -6 + -1 8 4 47 r ;i=-117<10' 203(& - a:) -10' 203!t ). TABLE XIV. X. Qe- Observed. Observed. 4irA. Computed. Error. 1 .98 42-6 31-9 30-74 1-2 2-56 21-4 16-7 16-72 3- 84 10-9 8-5 8-86 + -4 5-12 5-4 4-2 4-28 + -1 6-40 1-7 1-33 1-27 -1 47rA=-105(10' 203(6 - z) -10' !i031 ). of r to be -4674, whence ^= -04440 for steel not hardened. As the steel becomes harder this quantity increases, and can probably reach about twice this for very hard steel. To show the effect of hardening. I broke the bar used in Table XIV at the centre, thus producing two bars 6-4 inches long. One of these halves was hardened till it could scarcely be scratched by a file ; but the other half was left unaltered. The following Table gives the distribu- tion, using the same unit as that of Tables XIII and XIV. The bars were so short that the results can hardly be relied on ; but they will at least suffice to show the change. STUDIES ON MAGNETIC DISTKIBUTION 121 In Fig. 7 I have attempted to give the curve of distribution from Table XV, and have made the curves coincide with observation as nearly as possible, making a small allowance, however, for the errors intro- duced by the shortness of the bar. It is seen that the effect of harden- ing in a bar of these dimensions is to increase the quantity of magnetism, but especially that near the end. Had the bar been very long, no increase TABLE XV. X. Soft Steel, A. Hard Steel, B. Or 4.A. Qe- 47TA. 64 1-28 1-92 3-20 20-4 9-8 6-0 3-8 29-1 15-3 9-4 3-0 47-7 13-9 7-0 2-6 68-1 21-7 11-0 2-0 -Results from permanent magnets. A. Soft steel. B. Hard steel. in the total quantity of magnetism would have taken place; but the distri- bution would have been changed. From this we deduce the important fact that hardening is most useful for short magnets. And it would seem that almost the only use in hardening magnets at all is to concentrate the magnetism and to reduce the weight. Indeed I have made magnets from iron wire whose magnetization at the central section was just as intense as in a steel wire of the same size; but to all appearance it was less 122 HENRY A. KOWLAND strongly magnetized than the steel, because the magnetism was more diffused; and as the magnetism was not distributed so nearly at the end as in the steel, its magnetic moment and time of vibration were less. It is for these reasons that many makers of surveyors' compasses find it unnecessary to harden the needles, seeing these are long and thin. We might deduce all these facts from the formulae on the assumption that r is greater the harder the iron or steel. Having now considered briefly the distribution on electromagnets and steel magnets, and found that the formulae represent it in a general way, we may now use them for solving a few questions that we desire to solve, though only in an approximate manner. VI. M. Jamin, in his recent experiments on magnetic distribution, has obtained some very interesting results, although I have shown his method to be very defective. In his experiments on iron bars mag- netized at one end, he finds the formula s rl to apply to long ones as I have done. Now it might be argued that as the two methods apparently give the same result, they must be equally correct. But let us assume that the attraction of his piece of soft iron F varied as some unknown power n of the surface-density d. Then we find F=Ce nrL , which shows that the attractive force or any power of that force can be represented by a logarithmic curve, though not by the same one. Hence the error introduced by M. Jamin's method is insidious and not easily detected, though it is none the less hurtful and misleading, but rather the more so. However, his results with respect to what he calls the normal mag- net 10 are to some extent independent of these errors ; and we may now consider .them. Thus, in explaining the effect of placing hardened steel plates on one another, he says, " Quand on superpose deux lames aimante'es pareilles, les courbes qui represontent les valeurs de F [the attractive force on the piece of soft iron] s'e!6vent, parce que le magnetisme quitte les faces que 1'on met en contact pour se refugier sur les parties ex- te"rieures. En meme temps, les deux courbes se rapprochent 1'une dc 1'autre et du milieu de 1'aimant. Get effet augmente avec une troisieme 10 on electrifying the disc -)- the north pole moved toward the axis, and on changing the electrification, the north pole moved away from the axis. With motion and -(- electrification, the north pole moved away from the axis, and with electrification, it moved toward the axis. The direction is therefore that in which we should expect it to be. To prevent any suspicion of currents in the gilded surfaces, the latter, in many experiments, were divided into small portions by radial scratches, so that no tangential currents could take place without suffi- cient difference of potential to produce sparks. But to be perfectly certain, the gilded disc was replaced by a plane thin glass plate which could be electrified by points on one side, a gilder induction plate at zero potential being on the other. With this arrangement, effects in the same direction as before were obtained, but smaller in quantity, seeing that only one side of the plate could be electrified. The inductor plates were now removed, leaving the disc perfectly free, and the latter was once more gilded with a continuous gold sur- face, having only an opening around the axis of 3-5 cm. The gilding of the disc was connected with the axis and so was at a potential of zero. On one side of the plate, two small inductors formed of pieces of tin- foil on glass plates, were supported, having the disc between them. On electrifying these, the disc at the points opposite them was electrified by induction but there could be no electrification except at points near the inductors. On now revolving the disc, if the inductors were very small, the electricity would remain nearly at rest and the plate would as it were revolve through it. Hence in this case we should have conduction without motion of electricity, while in the first experi- ment we had motion without conduction. I have used the term " nearly at rest " in the above, for the following reasons. As the disc revolves the electricity is being constantly conducted in the plate so as to retain its position. Now the function which expresses the potential producing these currents and its differential coefficients must be con- tinuous throughout the disc, and so these currents must pervade the whole disc. Ox THE MAGNETIC EFFECT OF ELECTRIC CONVECTION 131 To calculate these currents we have two ways. Either we can con- sider the electricity at rest and the motion of the disc through it to produce an electromotive force in the direction of motion and propor- tional to the velocity of motion, to the electrification, and to the surface resistance; or, as Professor Helmholtz has suggested, we can consider the electricity to move with the disc and as it comes to the edge of the inductor to he set free to return by conduction currents to the other edge of the inductor so as to supply the loss there. The problem is capable of solution in the case of a disc without a hole in the centre but the results are too complicated to be of much use. Hence scratches were made on the disc in concentric circles about -6 cm. apart by which the radial component of the currents was destroyed and the problem became easily calculable. For, let the inductor cover -th part of the circumference of any n one of the conducting circles; then, if C is a constant, the current in the circle outside the inductor will be +-, and inside the area of the 1 n inductor C^ n ~ l \ On the latter is superposed the convection cur- fi rent equal to -\-C. Hence the motion of electricity throughout the whole circle is - what it would have been had the inductor covered the n whole circle. In one experiment n was about 8. By comparison with the other experiments we know that had electric conduction alone produced effect we should have observed at the telescope 5- mm. Had electric con- vection alone produced magnetic effect we should have had -j- 5- 7 mm. And if they both had effect it would have been -f- -7 mm., which is prac- tically zero in the presence of so many disturbing causes. No effect was discovered, or at least no certain effect, though every care was used. Hence we may conclude with reasonable certainty that electricity pro- duces nearly if not quite the same magnetic effect in the case of con- vection as of conduction, provided the same quantity of electricity passes a given point in the convection stream as in the conduction stream. The currents in the disc were actually detected by using inductors covering half the plate and placing the needle over the uncovered por- tion; but the effect was too small to be measured accurately. To prove 132 HENRY A. KOWLAXD this more thoroughly numerical results were attempted, and, after weeks of labor, obtained. I give below the last results which, from the precautions taken and the increase of experience, have the greatest weight. The magnetizing force of the disc was obtained from the deflection of the astatic needle as follows. Turning the two needles with poles in the same direction and observing the number n of vibrations, and then turning them opposite and finding the number n' of vibrations in that position, we shall find, when the lower needle is the strongest, Y -p, w 2 n" 1 n' 2 A w n . JL JL 5; jz = *. 72 77 ** I .... (1) w 2 + n ' i? + n D where X' and X are the forces on the upper and lower needle re- spectively, A the deflection, D the distance of the scale and H the horizontal component of the earth's magnetism. As X' and n' are very small the first term is nearly X X'. The torsion of the silk fibre was too small to affect the result, or at least was almost eliminated by the method of experiment. The electricity was in the first experiment distributed nearly uni- formly over the disc with the exception of the opening in the centre and the excess of distribution on the edge. The surface density on either side was V y a* - V - -V being the difference of potential between the disc and the outside plates, /? the thickness of the disc and B the whole distance apart of the outside plates. The excess on the edge was (Maxwell's Electricity, Art. 196, Eq. 18), *=* ' < 3 > where C is the radius of the disc. We may calculate the magnetic effect on the supposition that, as in the conducted current, the magnetizing force due to any element of surface is proportional to the quantity of electricity passing that element in a unit of time. The magnetic effect due to the uniform distribution has the greatest effect. With an error of only a small Ox THE MAGNETIC EFFECT OF ELECTEIC CONVECTION 133 fraction of a per cent, we may consider the two sides of the disc to coincide in the centre. Taking the origin of coordinates at the point of the disc under the needle and the centre of the disc on the axis of X. we find for both sides of the disc, the radial component of the force parallel to the disc, r c ~ f J_ (C+b) J. x)dxdy (a 1 + a? + f> - (b where a is the distance of the needle from the disc and & that from the axis; N is the number of revolutions of the disc per second and v = 28,800,000,000 centimetres per second according to Maxwell's de- termination. The above integral can be obtained exactly by elliptic integrals, but as it introduces a great variety of complete and incom- plete elliptic integrals of all three orders, we shall do best by expanding as follows: V 4-JW 7, faNff f . . A a >. -r.v X= - P - (A! + A* + A 3 + &c.), ... (4) A, = 2jfarc tan -=^ + arc tan ^-^ - a log, 4 , \ a a ] JV 2sb + a2) loge (5s 3 &c., &c., where -, , . /it) From this must be subtracted the effect of the opening in the centre, for which the same formula will apply. The magnetic action of the excess at the edge may be calculated on the supposition that that excess is concentrated in a circle of a little smaller diameter, C", than the disc; therefore, 134 HEXEY A. EOWLAXD where fc = ^-i^jL^, and F(Jc) and E(k) are complete elliptic V c? + ( C? + 0) integrals of the second and first orders respectively. The determination of the potential was by means of the spark which Thomson has experimented on in absolute measure. For sparks of length I between two surfaces nearly plane, we have on the centimetre, gram, second system, from Thomson's experiments, V- V = 117-5 (1 + . 0135), and for two balls of finite radius, we find, by considering the distribu- tion on the two sheets of an hyperboloid of revolution, V-V' = 117-5 (I + -0135) where r is the ratio of the length of spark to diameter of balls and had in these experiments a value of about 8. In this case V V = 109-6 (I + -0135) . (6) A battery of nine large jars, each 48- cm. high, contained the store of electricity supplied to the disc, and the difference of potential was determined before and after the experiment by charging a small jar and testing its length of spark. Two determinations were made before and two after each experiment, and the mean taken as representing the potential during the experiment. The velocity of the disc was kept constant by observing a governor. The number of revolutions was the same, nearly, as determined by the sizes of the pulleys or the sound of a Seebeck siren attached to the axis of the disc; the secret of this agreement was that the driving cords were well supplied with rosin. The number of revolutions was 61- per second. In such a delicate experiment, the disturbing causes, such as the changes of the earth's magnetism, the changing temperature of the room, &c., were so numerous that only on few days could numerical results be obtained, and even then the accuracy could not be great. The centimetre, gram, second system, was used. First Series, a = 2-05, & = 9-08, w=-697, Z> = 110-, H -182 nearly, 5 = 1-68, /?=-50, (7 = 10-55, N 61-, v = 28,800,000,000-, 7Z ' =-0533, C" = 10. ON THE MAGNETIC EFFECT OF ELECTRIC CONVECTION 135 Direction of Electrifica- motion. tion of disc. Scale reading in mm. Deflection on reversing electriflcat'n in mm. Length of spark. - 99- 107-5 101-5 7-25 295 7 68-5 76-5 68-0 8-25 290 - 97- 91-5 100- 7-00 282 1 59- 65-5 58-5 6-75 265 - i 92-5 85- 91-0 6-75 290 ' 52-5 57-5 51-5 5-50 285 + 82-0 76-0 81-7 5-85 285 1 36-5 43-0 36-5 6-50 275 - 68-0 61-0 68-0 7-00 290 27-5 33-5 26-5 6-50 288 Mean values. 6-735 2845 Hence From equation (1), X- -99X' =, 305700' Bv calculation from the electrification we find = 00000327. 136 HENEY A. ROWLAND 1 X--992T 1 = ; = 00000337. 296800- The effect on the upper needle, X', was about Jg- of that on the lower X. Second Series. Everything the same as before except the following. & = 7-65, n'=-Q525. Direction of motion. Electrifica- tion of disc. Scale reading in mm. Deflection on reversing electriflcat'n in mm. Length of spark. + 172-5 + 165-5 7-0 300 + 172-5 + 120-0 + 127-5 121-5 7-5 295 129-0 163-5 + + 170-5 163-0 7-25 297 + 170-5 + 118-0 + 127-0 120-0 8-25 270 127-5 Mean values. 7-50 2955 Hence for this case we have from equation (1), 1 315000- And from the electrification, T -QQ JT' - =00000317. = -00000349 . Third Series. Everything the same as in the first series, except = 8-1, n' = -0521, D = 114. ON THE MAGNETIC EFFECT OF ELECTRIC CONVECTION 137 Direction of motion. Electrifica- tion of disc. Scale reading in mm. Deflection on reversing electrificat'n in mm. Length of spark. + 151-0 158-5 7.50 287 + 151-0 + 192-0 + 185-5 7-25 292. + 193-5 157-5 + 148-5 157-5 8-25 295 + 150-0 185-0 + + 192-5 185-5 7-75 302 + 193-5 151-0 -1- 143-5 7-25 287 150-5 Mean values. 7-60 2926 J = -380, For this case from equation (1) 1 295000 and from the electrification = -2926. = -00000339 , = -00000355 . 281500- The error amounts to 3, 10 and 4 per cent respectively in the three series. Had we taken Weber's value of v the agreement would have been still nearer. Considering the difficulty of the experiment and the many sources of error, we may consider the agreement very satis- factory. The force measured is, we observe, about ^inr of the hori- zontal force of the earth's magnetism. The difference of readings with -f- and - - motion is due to the magnetism of rotation of the brass axis. This action is eliminated from the result. It will be observed that this method gives a determination of v, the ratio of the electromagnetic to the electrostatic system of units, and if carried out on a large scale with perfect instruments might give good results. The value v = 300,000,000- metres per second satisfies the first and last series of the experiments the best. Berlin, February 15, 1876. 13 NOTE ON THE MAGNETIC EFFECT OF ELECTRIC CONVECTION [Philosophical Magazine [5], VII, 442, 443, 18791 JOHNS HOPKINS UNIVERSITY, BALTIMORE, April 8, 1878. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN: Some three years since, while in Berlin, I made some experiments on the magnetic effect of electric convection, which have since been published in the ' American Journal of Science ' for Jan- uary, 1878. But previous to that, in 1876, Professor Helmholtz had presented to the Berlin Academy an abstract of my paper, which has been widely translated into many languages. But, although Helm- holtz distinctly says, " Ich bemerke dabei, das derselbe den Plan f iir seine (Rowland's) Versuche schon gefasst und vollstandig iiberlegt hatte, als er in Berlin ankam, ohne vorausgehende Einwirkung von meiner Seite," yet nevertheless I now find that the experiment is being constantly referred to as Helmholtz's experiment and that if I get any credit for it whatever, it is merely in the way of carrying out Helmholtz's ideas, instead of all the credit for ideas, design of appar- atus, the carrying out of the experiment, the calculation of results, and everything which gives the experiment its value. Unfortunately for me, Helmholtz had already experimented on the subject with negative results; and I found, in travelling through Ger- many that others had done the same. The idea occurred in nearly the same form to me eleven years ago; but as I recognized that the experiment would be an extremely delicate one, I did not attempt it until I could have every facility, which Helmholtz kindly gave me. Helmholtz kindly suggested a more simple form of commutator than I was about to use, and also that I should extend my experiments so as to include an uncoated glass disk as well as my gilded vulcanite ones; but all else I claim as my own, the method of experiment in all its details, the laboratory work, the method of calculation indeed every- thing connected with the experiment in any way, as completely as if it had been carried out in my own laboratory 4000 miles from the Berlin labor- atory. Yours truly, H. A. ROWLAND. 14 XOTE OX THE THEORY OF ELECTRIC ABSORPTION [American Journal of Mathematics, J, 53-58, 1878] In experimenting with Leyden jars, telegraph cables and condensers of other forms in which there is a solid dielectric, we observe that after complete discharge a portion of the charge reappears and forms what is known as the residual charge. This has generally been explained by supposing that a portion of the charge was conducted below the surface of the dielectric, and that this was afterwards conducted back again to its former position. But from the ordinary mathematical theory of the subject, no such consequence can be deduced, and we must conclude that this explanation is false. Maxwell, in his ' Trea- tise on Electricity and Magnetism,' vol. 2, chap X, has shown that a substance composed of layers of different substances can have this property. But the theory of the whole subject does not yet seem to have been given. Indeed, the general theory would involve us in very complicated mathematics, and our equations would have to apply to non-homo- geneous, crystalline bodies in which Ohm's law was departed from and the specific inductive capacity was not constant; we should, moreover, have to take account of thermo-electric currents, electrolysis, and electro-magnetic induction. Hence in this paper I do not propose to do more than to slightly extend the subject beyond its present state and to give the general method of still further extending it. Let us at first, then, take the case of an isotropic body in general, in which thermo-electric currents and electrolysis do not exist, and on and in which the changes of currents are so slow that we can omit electro-magnetic induction. The equations then become 1 , in which y is the specific inductive capacity of the substance, If the 'Maxwell's Treatise, Art. 325. 140 HENET A. BOWLAND electric conductivity, V the potential, p the volume density of the elec- tricity, and t the time. The subtraction of one equation from the other gives To introduce the condition that there shall be no electric absorption, we must observe that when that phenomenon exists, a charge of elecr tricity appears at a point where there was no charge before; in other words, the relative distribution has been changed. Hence, if the rela- tive distribution remains the same, no electric absorption can take place. Our condition is, then, where c is independent of t, and // and p' are the densities at the points x, y, z, and x', y' z'. This gives where c is a function of t only and not of x, y, z, and p is the value of p at the time t = 0. As we have 1 dV dm dV d /,-. k\ . dV d /, k\ . dV d /, k where m = - and n is a line in the direction of the current at the given I point, equation (1) becomes _1_ d V dm 1 dp 4rr p _ ft m dn dn ~lc ^IT ~ ~^~ ' From equation (2) P = f and hence _!_ dV dm m dn dn If we denote the strength of current at the point by 8, we have NOTE ox THE THEORY OF ELECTRIC ABSORPTION 141 8- -k dV k Wi' and 1 dm _. j^ /*. cm - 4:rw 8 dn IS JL this equation (3) gives the value of - =m at all points of the body and at all times so that the phenomenon of electric absorption shall not take place. As this equation makes m a function of x, y, z, S and t, the relation in general is entirely too complicated to ever apply to physical phenomena, without some limitation. Firstly then, as c is only an arbitrary function of t, we shall assume that it is constant ; .. . cm 47:w 2 dn 6' The most important case is where m is a constant. Then dm _ ~ ~dn ~ and c = 4:xm, S=S a s-, p = p.e-. In this case, therefore, we see that both the electrification and the currents die away at the rate c. The case where Ohm's law is true and the specific inductive capacity is constant is included in this case, seeing that when Jc and % are both constants their ratio, m, is constant. But it also includes the cases where k and # are both the same functions of V, S, or x, y, z, seeing that their ratio, m, would be constant in this case also. When m is not constant, the chances are very small against its satis- fying equation (4). Hence, we may in general conclude, that electric absorption will almost certainly take place unless the ratio of conductivity to the specific inductive capacity is constant throughout the body. This ratio, m, may become a variable in several manners, as follows : 1st manner. The body may not be homogeneous. This includes the case, which Maxwell has given, where the dielectric was composed of layers of different substances. 2d manner. The body may not obey Ohm's law; in this case k would be variable. 3d manner. The specific inductive capacity, , may vary with the electric force. 142 HEXRY A. KOWLAND It is to be noted that the cases of electric absorption which we observe are mostly those of condensers formed of two planes, or of one cylinder inside another, as in a telegraph cable. Our theory shows that different explanations can be given of these two cases. The case of parallel plates does not admit of being explained, except on the supposition that m varies in the first manner above given, or in this manner in combination with the others, for we can only conceive of the conductivity and the specific inductive capacity as being func- tions of the ordinate or of the electric force. As the latter is constant for all points between the plates, m would still be constant although it were a function of the electric force, and thus electric absorption would not take place. We may then conclude that in the case of parallel plates, omitting explanations based on electrolysis or thermo-electric currents, the only explanation that we can give at present is that which depends on the non-homogeneity of the body, and is the case which Maxwell has given in the form of two different materials. Our equations show that the form of layers is not necessary, but that any departure from homo- geneity is sufficient. It is to be noted that the homogeneity, which we speak of, is electrical homogeneity, and that a mass of crystals with their axes in different directions would evidently not be electrically homogeneous and would thus possess the property in question. In the case of glass it is very possible that this may be the case and it would certainly be so for ice or any other crystalline substance which had been melted and cooled. In the case of hard india rubber, the black color is due to the particles of carbon, and as other materials are incorporated into it during the process of manufacture, it is certainly not electrically homogeneous. As to the ordinary explanation that the electricity penetrates a little below the surface and then reappears again to form the residual charge, we see that it is in general entirely false. We could, indeed, form a condenser in which the surface of the dielectric would be a better con- ductor than the interior and which would act thus. But in general, the theory shows that the action takes place throughout the mass of the dielectric, where that is of a fine grained structure and apparently homogeneous, as in the case of glass, and consists of a polarization of every part of the dielectric. To consider more fully the case of a condenser made of parallel plates, let us resume our original equations. Without much loss of generality we can assume a laminated structure of the substance in NOTE ON THE THEORY OF ELECTRIC ABSORPTION 143 the direction of the plane YZ, so that m and V will be only functions of the ordinate x. Our equations then become d A ~- dx dx j dt Eliminating p we find if A _ 4- dt dx \dx dx dx Now let us make p = x -=- and as t and x are independent, we find CvtC on integration, (P Pj + 4 " (P m jOoWo) = 0, where p is the value of p for some initial value of x, say at the surface of the condenser, and is an arbitrary function of t, seeing that we may vary the charge at the surface of the body in any arbitrary manner. This equation establishes p as a function of m and t only, and as we have 1 dp ~~ - p will also be a function of these only. Let us now suppose that at the time t = 0, the condenser is charged, having had no charge before, and let us also suppose that the different strata of the dielectric are infinitely thin and are placed in the same order and are of the same thickness at every 'part of the substance, so that a finite portion of the substance will have the same properties at every part. In this case m will be a periodic function of x, returning to the same value again and again. As p is a function of this and of t only, at a given time t, it must return again and again to the same value as we pass through the substance, indicating a uniform polarized structure throughout the body. This conclusion would have been the same had we not assumed a laminated structure of the dielectric. In all other cases, except that of two planes, electric absorption can take place, as we have before remarked, even in perfectly homogeneous bodies, provided that Ohm's law is departed from or that the electric induction is not proportional to the electric force, as well as in non-homogeneous bodies. But where the body is thus homogeneous, electric absorption is not due to a uni- 144 HENRY A. KOWLAND form polarization, but to distinct regions of positive and negative electrification. In the whole of the investigation thus far we have sought for the means of explaining the phenomenon solely by means of the known laws of electric induction and conduction. But many of the phenomena of electric absorption indicate electrolytic action, and it is possible that in many cases this is the cause of the phenomenon. The only object of this note is to partially generalize Maxwell's explanation, leaving the electrolytic and other theories for the future. 15 RESEARCH ON THE ABSOLUTE UNIT OF ELECTEICAL RESISTANCE * [American Journal of Science [3], XV, 281-291, 325-336, 430-439, 1878] PEELIMINAEY REMABKS Since the classical determination of the absolute unit of electrical resistance by the Committee on Electrical Standards of the British Association, two re-determinations have been made, one in Germany and the other in Denmark, which each differ two per cent from the British Association determination, the one on one side and the other on the other side, making a total difference of four per cent between the two. Such a great difference in experiments which are capable of consider- able exactness, seems so strange that I decided to make a new deter- mination by a method different from any yet used, and which seemed capable of the greatest exactness; and to guard against all error, it was decided to determine all the important factors in at least two different ways, and to eliminate most of the corrections by the method of experi- ment, rather than by calculation. The method of experiment depended upon the induction of a current on a closed circuit, and in this respect, resembled that of Kirchhoff, but it differed from his inasmuch as, in my experiment, the indiiction current was produced by reversing the main current, and in Kirchhoff's by removing the circuits to a distance from each other. And it seems to me that this method is capable of greater exactness than any other, and it certainly possessed the greatest simplicity in theory and facility in experiment. In the carrying out of the experiment I have partly availed myself of my own instruments and have partly drawn on the collection of the University, which possesses many unique and accurate instruments for electric and magnetic measurements. To insure uniformity and accur- acy, the coils of all these instruments have been wound with my own hands and the measurements reduced to a standard rule which was 1 1 am greatly indebted to Mr. Jacques, Fellow of the University, who is an excel- lent observer, for his assistance during the experiment, particularly in reading the tangent galvanometer. 10 146 HENRY A. KOWLAND again compared with the standard at Washington. Unlike many Ger- man instruments, quite fine wire has always been used and the number of coils multiplied, for in this way the constants of the coils can be more exactly determined, there is less relative action from the wire connecting the coils, and above all we know exactly where the current passes. The experiment was performed in the back room of a small house near the University, which was reasonably free from magnetic and other physical disturbances. As the magnetic disturbance was eliminated in the experiment, it was not necessary to select a region entirely free from such disturbance. The small probable error proves that sufficient precaution was taken in this respect. The result of the experiment that the British Association unit is too great by about -88 per cent, agrees well with Joule's experiment on the heat generated in a wire by a current, and makes the mechanical equiv- alent as thus obtained very nearly that which he found from friction: it is intermediate between the result of Lorenz and the British Asso- ciation Committee; and it agrees almost exactly with the British Asso- ciation Committee's experiments, if we accept the correction which I have applied below. The difference of nearly three per cent which remains between my result and that of Kohlrausch is difficult to explain, but it is thought that something has been done in this direction in the criticism of his method and results which are entered into below. My value, when introduced into Thomson's and Maxwell's values of the ratio of the electromagnetic to the electrostatic units of electricity, caused a yet further deviation from its value as given in Maxwell's electromagnetic theory of light: but experiments on this ratio have not yet attained the highest accuracy. HISTORY The first determination of the resistance of a wire in absolute meas- ure was made by Kirchhoff 2 in 1849 in answer to a question propounded by Neumann, in whose theory of electrodynamic induction a constant appeared whose numerical value was unknown until that time. His method, like that of this paper, depended on induction from currents: only one galvanometer was used and the primary current was measured by allowing only a small proportion of it to pass through the galvano- 2 Bestimmung der Constanten von welcher die Intensitat inducirter elektrischer Strome abhangt. Fogg. Ann., Bd. 76, S. 412. Ox THE ABSOLUTE UNIT OF ELECTRICAL RESISTANCE 147 meter by means of a shunt, while all the induced current passed through it. But, owing to the heating of the wires, the shunt ratio cannot be relied upon as constant, and hence the defect of the method. At pres- ent this experiment has only historical value, seeing that no exact record was kept of it in a standard resistance. However, we know that the wire was of copper and the temperature R. and that the result obtained gave the resistance of the wire $ smaller than Weber found for the same wire at 20 R. in 1851. In 1851, "Weber published 8 experiments by two methods, first by means of an earth inductor, and second by observing the damping of a swinging needle. Three experiments gave for the resistance of the circuit 1903 -10 8 , 1898 -10 8 , and 1900 -10 s , , but it is to be noted sec. that a correction of five-eighths per cent was made on account of the time, two seconds, which it took to turn the earth-inductor, and that no account was taken of the temperature, although the material was copper. He finds for the value of the Jacobi unit, 598 -10 7 ^. Three OCC'B years after that, in 1853, Weber made another determination of the specific resistance of copper. 4 But these determinations were more to develope the method than for exact measurement, and it was not until 1862 5 that Weber made an exact determination which he expected to be standard. In this last determination he used a method compounded of his first two methods by which the constant of the galvanometer was eliminated, and the same method has since been used by Kohlrausch in his experiments of 1870. The results of these experiments were embodied in a determination of the value of the Siemens unit and of a standard which was sent by Sir Wm. Thomson. As the old Siemens units seem to vary among themselves one or two per cent, and as the result from Thomson's coil differs more than one per cent from that which would be obtained with any known value of the Siemens unit, we cannot be said to know the exact result of these experiments at the present time. Beside which, it was not until the experiments of Dr. Matthiessen on the electric permanence of metals and alloys, that a suitable material could be selected for the standard resistance. The matter was in this state when a committee was appointed by the 3 Elektrodynamische Maasbestimmungen ; or Pogg. Ann., Bd. 82, S. 337. 4 Abh. d. Kon. Ges. d. Wissenchaften zu Gottingen, Bd. 5. 5 Zur Galvanometrie, Gottingen, 1862. Also Abb. d. K. Ges. d. Wis. zu Gottingen, Bd. 10. 148 HENRY A. BOWLAXD British Association in 1861, who, by their experiments which have ex- tended through eight years, have done so much for the absolute system of electrical measurements. But the actual determination of the unit was made in 1863-4. The method used was that of the revolving coil of Sir William Thomson, the principal advantage of which was its sim- plicity and the fact that the local variation of the earth's magnetism was entirely eliminated and only entered into the calculation as a small correction. The principle of the method is of extreme beauty, seeing that the same earth's magnetism which causes the needle at the centre of the coil to point in the magnetic meridian also causes the current in the revolving coil which deflects the needle from that meridian. When- ever a conducting body moves in a magnetic field, currents are gener- ated in it in such direction that the total resultant action is such that the lines of force are apparently dragged after the body as though they met with resistance in passing through it : and so we may regard Thom- son's method as a means of measuring the amount of this dragging action. But, however beautiful and apparently simple the method may appear in theory, yet when we come to the details we find many reasons for not expecting the finest results from it. Nearly all these reasons have been stated by Kohlrausch, and I can do barely more in this direction than review his objections, point out the direction in which each would affect the result, and perhaps in some cases estimate the amount. In the first place, as the needle also induced currents in the coil which tended in turn to deflect the needle, the needle must have a very small magnetic moment in order that this term may be small enough to be treated as a correction. For this reason the magnetic needle was a small steel sphere 8 mm. diameter, and not magnetized to satur- ation. It is evident that in a quiescent magnetic field such a magnet would give the direction of the lines of force as accurately as the large magnets of Gauss and Weber, weighing many pounds. But the mag- netic force due to the revolving coil is intermittent and the needle must show as it were the average force, together with the action due to induced magnetization. Whether the magnet shows the average force acting on it or not, depends upon the constancy of the magnetic axis, and there seems to be no reason to suppose that this would change in the slightest, though it would have been better to have made the form of the magnet such that it would have been impossible. The induced magnetism of the sphere would not affect the result, were it not for the time taken in magnetization: on this account the needle is dragged Ox THE ABSOLUTE UNIT OF ELECTRICAL EESISTAXCE 149 with the coil, and hence makes the deflection greater than it should be, and the absolute value of the Ohm too small by a very small quantity. The currents induced in the suspended parts also act in the same direction. Neither of these can be estimated, but they are evidently very minute. The mere fact that this small magnet was attached to a comparatively large mirror which was exposed to air currents could hardly have affected the results, seeing that the disturbances would have been all eliminated except those due to air currents from the revolving coil, and which we are assured did not exist from the fact that no deflection took place when the coil was revolved with the circuit broken. In revolving the coil in opposite directions very different results were obtained, and the explanation of this has caused considerable discussion. As this is of fundamental importance I shall consider it in detail. The magnet was suspended by a single fibre seven feet long, and the deflection was diminished by its torsion -00132. No mention is made of the method used for untwisting the fibre, and we see that it would require only 2-11 turns to deflect the needle 1 from the meridian. To estimate the approximate effect of this, we may omit from Maxwell's equation * all the other minor corrections and we have GKw cos (l + /)/7~ $t "\nearly, 1 ; sin where we have substituted

= 102 and (p is about ^V we have a= 12 - nearly, which is a value so large that it would surely have been noticed. Hence we may conclude that no reasonable amount of torsion in the silk fibre could have produced the difference in the results from positive and negative rotation, as has been stated by Mr. Fleming Jenkin in his ' Keport on the New Unit of Electrical Eesistance/ r The greatest value which we can possibly assign to a which might have remained unnoticed is y 1 ^, which would not have affected the the experiment to any appreciable extent. Another source of error which may produce the difference we are discussing is connected with the heavy metal frame of the apparatus, in which currents can be induced by the revolving coil. The coil passes so near the frame-work that the currents in it must be quite strong and produce considerable magnetic effect. Kohlrausch has pointed out the existence of these currents, but has failed to consider the theory of them. Now, from the fact that after any number of revolutions the number of lines of force passing through any part of the apparatus is the same as before, we immediately deduce the 1 ' Reports on Electrical Standards,' London, 1873, p. 191. ON THE ABSOLUTE UNIT OF ELECTEICAL EESISTAXCE 151 fact that, if Ohm's law be correct, the algebraical sum of the currents at every point in the frame is zero, and hence the average magnetic action on the needle zero. But although these currents can have no direct action, they can still act by modifying the current in the coil; for while the coil is nearing one of the supports the current in the coil is less than the normal amount, and while it is leaving it is greater; and although the total current in the coil is the normal amount, yet it acts on the needle at a different angle. By changing the direction of rotation, the effect is nearly but not quite eliminated. The amount of the effect is evidently dependent upon the velocity of rotation and increases with it in some unknown proportion, and the residual effect is evidently in the direction of making the action on the needle too small and thus of increasing R. If these currents are the cause of the different values of R obtained with positive and negative rotation, we should find that if we picked out those experi- ments in which this difference was the greatest, they should give a larger value of R than the others. Taking the mean of all the results " in which this difference is greater than one per cent, we find for the Ohm 1.0033 earth ^ uadt , and when it is less than one per sec. cent, -9966 r - SC*r which is in accordance with the theory, the sec. average velocities being ^ and *^ nearly. But the individual observations have too great a probable error for an exact comparison. But whatever the cause of the effect we are considering, the follow- ing method of correction must apply. The experiments show that R is a function of the velocity of rotation, and hence, by Taylor's theorem, the true resistance R must be R = R (1 -f- Aw + Bw 2 + &c.), and when R is the mean of results with positive and negative rotations, R = R (1 -f Bw 2 + DW* + &c.). Supposing that all the terms can be omitted except the first two, and using the above results for large and small velocities, we find .R _ . 9926 earth quad. But if we - ect the two resu i ts i n wn i c h the sec. 8 In the table published by the Committee the different columns do not agree, and I have thought it probable that the last two numbers in the next to the last column should read 1-0032 and 1-0065 instead of 1-0040 and -9981, and in my discussion I have considered them to read thus. 152 HENEY A. EOWLAND difference of positive and negative rotations is over seven per cent, we find sec. The rejection of all the higher powers of w renders the correction uncertain, but it at least shows that the Ohm is somewhat smaller than it was meant to be, which agrees with my experiments. It is to be regretted that the details of these experiments have never been published, and so an exact estimate of their value can never be made. Indeed we have no data for determining the value of the Ohm from the experiments of 1863. All we know is that, in the final result, the 1864 experiments had five times the weight of those of 1863, and that the two results differed -16 per cent, but which was the larger is not stated. Now the table of results pub- lished in the report of the 1864 experiments contains many errors, some of which we can find out by comparison of the columns. The following corrections seem probable in the eleven experiments : No. 4, second column, read 4-6375 for 4-6275. No. 10, fourth and fifth columns, read 1-0032 and + 0-32 in place of 1-0040 and +0-40. No. 11, fourth and fifth columns, read 1-0065 and + 0-65 in place of 0-9981 and 0-19. Whether we make these corrections or not the mean value is entirely incompatible with the statement with respect to the 1863 experiments. With the corrections the mean value of the 1864 experiments is 1 Ohm = 1-00071 earth ^ uad \ and without them, using sec. the fourth column, it is 1-00014. With the corrections the difference between fast and slow rotation is 6 per cent. In the year 1870 Professor F. Kohlrausch made a new determination of Siemen's unit in absolute measure, the method being one formed out of a combination of Weber's two methods of the earth inductor and of damping, by which the constant of the galvanometer was eliminated, and is the same as Weber used in his experiments of 1862. His formula for the resistance of the circuit, omitting small corrections, is approximately, where 8 is the surface of the earth inductor, T is the horizontal inten- sity of the earth's magnetism, K the moment of inertia of the magnet, t the time of vibration of the magnet, ^ the logarithmic decrement, and A and B are the arcs in the method of recoil. ON THE ABSOLUTE UNIT OF ELECTRICAL EESISTANCE 153 One of the principal criticisms I have to offer with respect to this method is the great numher of quantities difficult to observe, which enter the equation as squares, cubes, or even fourth powers. Thus S 2 depends upon the fourth power of the radius of the earth inductor. Now this earth inductor was wound years before by W. Weber, and the mean radius determined from the length of wire and controlled by measuring the circumference of the layers. Now the wire was nearly 3-2 mm. diameter with its coating, and the outer and inner radii were 115- mm. and 142 mm. Hence the diameter of the wire occupied two per cent of the radius of the coil, making it uncertain to what point the radius should be measured. As the coil is wound, each winding sinks into the space between the two wires beneath, except at one spot where it must pass over the tops of the lower wires. The wire must also be wound in a helix. All these facts tend to diminish 8 and make its value as deduced from the length of the wire too large; and any kinks or irregularities in the wire tend in the same direction. And these errors must be large in an earth-inductor of such dimensions, where the wire is so large and many layers are piled on each other. If we admit an error of one-half a millimetre in the radius as deter- mined in this way, it would diminish the value of S 2 1-4 per cent, and make Kohlrausch's result only -6 per cent greater than the result of the British Association Committee. Three other quantities, T, X and K, are very hard to determine with accuracy, and yet T enters as a square. It is to be noted that this earth-inductor is the same as that used by Weber in his experiment of 1862, and which also gave a larger value to the Ohm than those of the British Association Committee. Indeed, the results with this inductor and by this method form the only cases where the absolute resistance of the Ohm has been found greater than that from the experiments of the British Association Committee, There seems to be a small one-sided error in A and B which Kohl- rausch does not mention, but which Weber, in his old experiments of 1851, considered worthy of a -6 per cent correction, and which would diminish by 1-2 per cent. This is the error due to loss of time in turning the earth-inductor. As Kohlrausch's needle had a longer time of vibration than Weber's, the correction will be much smaller. In Weber's estimate the damping was not taken into account, and indeed it is impossible to do so with exactness. To get some idea of the value of the correction, however, we can assume that the current 154 HENRY A. KOWLAND from the earth-inductor is uniform through a time t'", and the com- plete solution then depends on the elimination of nine quantities from ten complicated equations, and which can only be accomplished approx- imately. If f is the true value of the angular velocity, as given to the needle by the earth-inductor, and f is the velocity as deduced from the ordinary equation for the method of recoil, I find where A is the logarithmic decrement, the base of the natural system of logarithms, T the time of vibration of the needle, and t the time during which the uniform current from the earth-inductor flows. In the actual case, the current from the earth-inductor is nearly propor- tional to sin t, and hence it will be more exact to substitute / / \2 /iir / / 4 (--) I taiiitdt = l( V * / / v * in the place of t 2 . The formula then becomes This modification is more exact when ), is small than when it is large, but it is sufficiently exact in all cases to give some idea of the magni- tude of the error to be feared from this source. Kohlrausch does not state how long it took him to turn his earth-inductor, but as T = 34 seconds, we shall assume -^ J^ and as / = \ nearly, we have -?- = 1-0008, r which would diminish the value of the resistance by -16 per cent. As the time we have allowed for turning the earth-inductor is prob- ably greater than it actually was, the actual correction will be less than this. The correction for the extra current induced in the inductor and galvanometer, as given by Maxwell's equation, 9 has been shown by Stoletow to be too small to affect the result appreciably. We may sum up our criticism of this experiment in a few words. The method is defective because, although absolute resistance has the dimensions of - , yet in this method the fourth power of space and 9 ' Electricity and Magnetism,' art. 762. ON THE ABSOLUTE UNIT OF ELECTEICAL RESISTANCE 155 the square of time enter, besides other quantities which are difficult to determine. The instruments are defective, because the earth-inductor was of such poor proportion and made of such large wire that its average radius was difficult to determine, and was undoubtedly over- estimated. It seems probable that a paper scale, which expands and contracts with the weather was used. And lastly, the results with this inductor and by this method have twice given greater results than anybody else has ever found, and greater than the known values of the mechanical equivalent of heat would indicate. The latest experiments on resistance have been made by Lorenz of Copenhagen, 10 by a new method of his own, or rather by an application of an experiment of Faraday's. It consists in measuring the difference of potential between the centre and edge of a disc in rapid rotation in a field of known magnetic intensity. A lengthy criticism of this experiment is not needed, seeing that it was made more to illustrate the method than to give a new value to the Ohm. The quantity primarily determined by the experiment was the absolute resistance of mercury, and the Ohm will have various values according to the different values which we assume for the resist- ance of mercury in Ohms. One of the principal defects of the experiment is the large ratio between the radius of the revolving disc and the coil in which it revolved. In conclusion I give the following table of results, reduced as nearly as possible to the absolute value of the Ohm in earth q uad \" sec. iPogg. Ann., Bd. cxlix, (1873), p. 251. 11 Since this was written, a new determination has been made by H. F. Weber, of Zurich, in which the different results agree with great accuracy. The result has been expressed in Siemen's units, and the comparison seems to have been made simply with a set of resistance coils and not with standards. The modern Siemen's units seem to be reasonably exact, but from the table published by the British Association Committee in 1864, it seems that at that time there was uncertainty as to its value. He obtains 1 8. U. = -9550 ---', which is greater or less than sec. the British Association determination, according as we take the different ratios of the Siemen's to the British Association unit, ranging from -14 per cent above to 1-92 per cent below. In any case the result agrees reasonably well with my own. The apparatus used does not seem to have been of the best, and the exact details are not given. But wooden coils to wind the wire on seem to have been used, which should immediately condemn the experiment where a pair of coils is used, seeing that in that case the constant, both of magnetic effect and of induction, depend on the dis- tance of the coils. It is unfortunate that sufficient details are not given for me to enter into a criticism of the experiment. 156 HENRY A. EOWLAND Date. Observer. Value of Ohm. Remarks. 1849 Kirchhoff 88 to -90 Approximately. 1851 Weber 95 to -97 1862 Weber ( 1-088 From Thomson's unit. 1863-4 1870 B. A. Committee. Kohlrausch { 1-075 1-0000 * -993 1-0196 From Weber's value of Siemen's unit. Mean of all results. Corrected to a zero velocity of coil. 1873 Lorenz -970 Taking ratio of quicksilver unit to Ohm = 962. 1876 Rowland \ -980 9912 Taking ratio of quicksilver unit to Ohm= 953. From a preliminary comparison with the B. A. unit. THEORY OF THE METHOD When a current is induced in a circuit by magnetic action of any kind, Faraday has shown that the induced current is proportional to the number of lines of force cut by the circuit and inversely as the resist- ance of the circuit. If we have two circuits near each other, the first of which carries a current, and the second is then removed to an infinite distance, there will be a current in it proportional to the number of lines of force cut. Let now a unit current be sent through the second circuit and one of strength E through the first; then, on removing the second circuit, work will be performed which we easily see is also proportional to the number of lines of force cut. Hence, if EM is the work done, Q is the induced current, and R is the resistance of the second circuit, -, where C is a constant whose value is unity on the absolute system. When the current in the first circuit is broken, the lines of force contract on themselves, and the induced current is the same as if the second circuit had been removed to an infinite distance. If the current is reversed the induced current is twice as great; hence in this case = ^ or = K V Hence, to measure the absolute resistance of a circuit on this method, we must calculate M and measure the ratio of Q to E. M is known as the mutual potential of the two circuits with unit currents, and mathematical methods are known for its calculation. The simplest and best form in which the wire can be wound for the Ox THE ABSOLUTE UXIT OF ELECTKICAL KESISTAXCE 157 calculation of M is in parallel circular coils of equal size and of as small sectional area as possible. For measuring E a tangent galvano- meter is needed, and we shall then have E= ^ tanfl. 6r where H is the horizontal intensity of the earth's magnetism at the place of the tangent galvanometer, and G the constant of the galvano- meter. For measuring Q we must use the ballistic method, and we have . which for very small values of ), becomes ^ G' - s ' ' H' ~W Tain*? I + *A - * A 2 ' where H' is the horizontal component of the earth's magnetism at the place of the small galvanometer, G' its constant, T the time of vibra- tion of the needle, and X the logarithmic decrement. The ratio of H' to H can be determined by allowing a needle to vibrate in the two positions. But this introduces error, and by the following method we can eliminate both this and the distance of the mirror from the scale by which we find 0' and the error of tangent galvanometer due to length of needle. The method merely consists in placing a circle around the small galvanometer and then taking simultaneous readings with the current passing through it and the tangent galvanometer, before and after each experiment. Let and a' be the deflections of the tangent galvanometer and the other galvano- meter respectively, and let G" be the constant of the circle at the point where the needle hangs, then TT JJ I -^ tan a = -^j- tan a', and we have finally TT G tan a' tan 6 \ R=M- T G 71 ' ta.na sin*0' l+JA U' which does not contain H or H', and the distance of the mirror from the scale does not enter except as a correction in the ratio pf sin # and tan a'; and, as a and can be made nearly equal, the correction 158 HENEY A. EOWLAND of the tangent galvanometer for the length of needle is almost elimi- nated. When the method of recoil is used, we must substitute - ~TA for the term involving /, and sin $A f -f- sin %B' in the place of sin ^ 6' A' and B' being the greater and smaller arcs in that method. This is on the supposition that X is small. The ratio of G" to G must be so large, say 12,000, that it is difficult to determine it by direct experiment, but it is found readily by measure- ment or indirect comparison. It is seen that in this equation the quantities only enter as the first powers, and that the only constants to be determined which enter the equation are M, G and G", which all vary in simple proportion to the linear measurement. It is to be noted also that the only quantities which require to be reduced to standard measure are M and T, and that the others may all be made on any arbitrary scale. No correction is needed for temperature except to M. Indeed, I believe that this method exceeds all others in simplicity and probable accuracy and its freedom from constant errors, seeing that every quantity was varied except G" and G, whose ratio was determined within probably one in three thousand by two methods. Having obtained the resistance of the circuit by this method, we have next to measure it in ohms. For this purpose the resistance of the circuit was always adjusted until it was equal to a certain German silver standard, which was afterward carefully compared with the ohm. This standard was about thirty-five ohms. By this method, the following data are needed. 1. Eatio of constants of galvanometer and circle. 2. Eatio of the tangents of the two deflections of tangent galvano- meter. 3. Eatio of the deflection to the swing of the other galvanometer. 4. Mutual potential of induction coils on each other. 5. Time of vibration of the needle. 6. Eesistance of standard in ohms. For correction we need the following : 1. The logarithmic decrement. 2. Distance of mirror from scale. 3. Coefficient of torsion of suspending fibre. 4. Eate of chronometer. 5. Correction to reduce to standard metre. Ox THE ABSOLUTE UNIT OF ELECTRICAL KESISTANCE 159 6. Variation of the resistance of German silver with the temperature. 7. Temperature of standard resistance. 8. Arc of swing when the time of vibration is determined. 9. Length of needle in tangent and other galvanometer (nearly com- pensated by the method). 10. The variation of resistance of circuit during the experiment. The following errors are compensated by the method of experiment. 1. The local and daily variation of the earth's magnetism. 2. The variation of the magnetism of the needle. 3. The magnetic and inductive action of the parts of the apparatus on each other. 4. The correction for length of needle in the tangent galvanometer (nearly). 5. The axial displacement of the wires in the coils for induction. 6. The error due to not having the coils of the galvanometer and the circle parallel to the needle. 7. Scale error (partly). 8. The zero error of galvanometers. CALCULATION OF CONSTANTS Circle. For obtaining the ratio of G to G", it is best to calculate them separately and then take their ratio, though it might be found by Maxwell's method ('Electricity,' article 753). But as the ratio is great, the heating of the resistances would produce error in this latter method. For the simple circle, where A is its radius and B the distance of the plane of the circle to the needle on its axis. Galvanometer for Induction Current. For the more sensitive galvano- meter, we must first assume some form which will produce a nearly uniform field in its interior, without impairing its sensitiveness. If we make the galvanometer of two circular coils of rectangular section whose depth is to its width as 108 to 100, and whose centres of sections are at a radius apart from each other, we shall have Maxwell's modifi- cation of Helmholtz's arrangement. The constant can then be found by calculation or comparison with another coil. 160 HEXKY A. EOWLAXD Maxwell's formulae are only adapted to coils of small section. Hence we must investigate a new formula. 13 Let N be the total number of windings in the galvanometer. Let R and r be the outer and inner radii of the coils. Let X and x be the distances of the planes of the edges of the coils from the centre. Let a be the angle subtended by the radius of any winding at the centre. Let & be the length of the radius vector drawn from the centre to the point where we measure the force. Let 6 be the angle between this line and the axis. Let c be the distance from the centre to any winding. Let w be the potential of the coil at the given point. Then (Maxwell's 'Electricity,' Art. 695), for one winding. W = 2n ] 1 COS a + sin 2 a ( Q[ (a) $1 (#) ( \c and for two coils symmetrically placed on each side of the origin, W = 4:r \ COS a sin 2 a ( * f ) O 2 ' (a) Q 2 (0) I \ * \ c 1 where Q 2 (0), Q^(0), &c., denote zonal spherical harmonics, and Q 2 '()> Q'i(a) &c., denote the differential coefficients of spherical harmonics with respect to cos a. As the needle never makes a large angle with the plane of the coils, it will be sufficient to compute only the axial component of the force, which we shall call F. Let us make the first computation without substitution of the limits of integration, and then afterward substitute these: F = * f C^-dxdr, r)(X x)J J dx and we can write %*N &c. 12 A formula involving the first two terms of my series, but applying only to the special case of a needle in the centre of a single circle of rectangular section, is given by Weber in his 'Elektrodynamische Maasbestimmungen inbesondere Wider- standsmessungen,' S. 872. ON THE ABSOLUTE UNIT OF ELECTRICAL RESISTANCE 161 where H^ x log. (r + / y? + r 2 ) , o _ 1.3.5. . 2t- '2 1 (2* -1)2 ' 2t - 3 (it - l)(2i - 3) 2.4 D = C 2 *' 8 _ i(t'-l)..(* 6) '2i 5 (2i-i)(2t 3)(2i - 5) 2.4.6' E t = &c., &c. Substituting the limits for x, r and a, we find + V ^ 2 o = i / 1 f ^ ___ ^_ 1 / If r 3 \\ \ X \(ff + X z )l (r 2 + JT')i "^ ^ + a?)l (r 2 + z*)*J J ' The needle consisted of two parallel lamina? of steel of length, Z, and a distance, W, from each other. As the correction for length is small, we may assume that the magnetism of each lamina is concentrated in two points at a distance n / from each other, where n is a quantity to he determined. Hence W where cos & /71 .., _,, seeing that the needle hangs parallel to * the coils. In short thick magnets, the polar distance is about Z and the value of n will be about f . For all other magnets it will be between this and unity. In the present case n = f nearly. As all the terms after the first are very minute, this approximation is sufficient, and will at least give us an idea of the amount of this source of error. 11 162 HENRY A. KOWLAND INDUCTION COILS The induction coils were in the shape of two parallel coils of nearly equal size and of nearly square section. Let A and a he the mean radii of the coils. Let & he the mean distance apart of the coils. Let C Supposing the coils concentrated at their centre of section we know that where F(c) and E(c) are elliptic integrals. If and y are the depth and width of each coil, the total value of M will he, when A = a nearly, and we find nc (1 O -2 _ 12^ A ^2 COEBECTIONS Calling /? and <5 the scale deflections corresponding to tan a' and sin , we may write our equation for the value of the resistance 8 1--35 where R' is the resistance of the circuit at a given temperature 17-0 C., and E = 2^M-^ Ff (l + a -f & + etc.), in which ^, 5, etc. and a, 6, etc. are the variable and constant corrections respectively. a. Correction for damping. ON THE ABSOLUTE UNIT OF ELECTRICAL KESISTANCE 163 I. Torsion of fibre. The needle of the tangent galvanometer was sustained on a point and so required no correction. The correction for the torsion in the other galvanometer is the same for /? and d and hence only affects T. Therefore, if t is the coefficient of torsion, b= - It. c. Rate of chronometer. Let p be the number of seconds gained in a day above the normal time P ~ 86400* d. Reduction to normal metre. The portion of this reduction which depends on temperature must be treated under the variable corrections. Let m be the excess of the metre used above the normal metre, ex- pressed in metres; then d = + m. e. Correction of T for the arc of vibration. This arc was always the same, starting at c^ and being reduced by damping to about c n , where c^ and c a are the total arcs of oscillation. /. Correction for length of needles. For the tangent galvanometer, the correction is variable. For the circle it is /= + where I is half the distance between the poles of the needle and A the radius of circle. For the other galvanometer it is included in the formula for G. A. Reduction to normal metre. As the dimension of R is a velocity and the induction coils were wound on brass, the correction is where f is the coefficient of expansion of brass or copper, t' the actual and t" the normal temperature. B. Correction of standard resistance for temperature. Let a be the variation of the resistance for 1 C., ?" be the actual and T the normal temperature 17- C. ; then 164 HENRY A. BOWL AND C. Correction for length of needle in tangent galvanometer, C = + J^ sin (a + ')f -|r-Y(a' ~ a ) ' \-A-l where V is half the distance between the poles of the needle and A' is the radius of the coil. D. The resistance of the circuit was constantly adjusted to the standard, but during the time of the experiment the change of temper- ature of the room altered the resistance slightly; this change was measured and the correction will be plus or minus one-half this. The resistance was adjusted several times during each experiment. The correction is Z). Some of the errors which are compensated by the experiment need no remark and I need speak only of the following. No. 3. By the introduction of commutators at various points all mutual disturbance of instruments could be compensated. No. 5. In winding wire in a groove, it may be one side or the other of the centre. By winding the coils on the centre of cylinders which set end to end, on reversing them and taking the mean result, this error is avoided. No. 6. The circle was always adjusted parallel to the coils of the galvanometer. Should they not be parallel to the needle, G and 0" will be altered in exactly the same ratios and will thus not affect the result. The same may be said of the deflection of the magnet from the magnetic meridian due to torsion. No. 7. /? and 3 both ranged over the same portion of the scale and so scale error is partly compensated. No. 8. The zero-point of all galvanometers was eliminated by equal deflections on opposite sides of the zero-point. INSTRUMENTS Wire and coils. The wire used in all instruments was quite small silk-covered copper wire, and was always wound in accurately turned ls brass grooves in which a single layer of wire just fitted. The separate layers always had the same number of windings, and the wire was wound so carefully that the coils preserved their proper shape through- 13 To obtain an accurate coil an accurate groove is necessary, seeing that otherwise the wire will be heaped up in certain places. The circle of the tangent galvanometer, which was made to order in Germany, had to be returned in this country before use, and much time was lost before finding out the source of the difficulty. ON THE ABSOLUTE UNIT OF ELECTRICAL EESISTANCE 165 out. No paper was used between the layers. As the wire was small, very little distortion was produced at the point where one layer had to rise over the tops of the wires below. Corrections were made for the thickness of the steel tape used to measure the circumference of each layer; also for the sinking of each layer into the spaces between the wires below, seeing that the tape measures the circumference of the tops of the wires. The steel tape was then compared with the standard. The advantages of small wire over large are many; we know exactly where the current passes; it adapts itself readily to the groove without kinks; it fills up the grooves more uniformly; the connecting wires have less proportional magnetic effect; and lastly, we can get the dimensions more exactly. The size of wire adopted was about No. 22 for most of the instruments. The mean radius having been computed, the exterior and interior radii are found by addition and substraction of half the depth of the coil. The sides of the coil were taken as those of the brass groove. All coils were wound by myself personally to insure uniformity and exactness. Tangent galvanometer. This was entirely of brass or bronze, and had a circle about 50 cm. diameter. The needle was 2-7 cm. long and its position was read on a circle 20- cm. diameter, graduated to 15'. The graduated circle was raised so that the aluminium pointer was on a level with it, thus avoiding parallax. The needle and pointer only weighed a gram or two, and rested on a point at the centre which was so nicely made that it would make several oscillations within 1 and would come to rest within 1' or 2' of the same point every time. I much prefer a point with a light needle carefully made to any suspended needle for the tangent galvanometer, especially as a raised circle can then alone be used. The needle was suspended at a distance from any brass which might have been magnetic. There were a series of coils ascending nearly as the numbers 1, 3, 9, 27, 81, 243, whose constants were all known, but only one was used in this experiment. The proba- ble error of a single reading was about 1'. Galvanometer for induction current. This was a galvanometer on a new plan, especially adapted for the absolute measurement of weak currents. It was entirely of brass, except the wooden base, and was large and heavy, weighing twenty or twenty-five pounds. It could be used with a mirror and scale or as a sine galvanometer. It will be 166 HENKY A. EOWLAND necessary to describe here only those portions which affect the accuracy of the present experiment. The coils were of the form described above in the theoretical portion, and were wound on a brass cylinder about 8-2 cm. long and 11-6 cm. diameter in two deep grooves about 3- cm. deep and 2-5 cm. wide. The opening in the centre for the needle was about 5-5 cm. diameter and the cylinder was split by a saw-cut so as to diminish the damping effect. This coil was mounted on a brass column rising from a gradu- ated circle by which the azimuth of the coil could be determined by two verniers reading to 30". Through the opening in the coil beneath the needle passed a brass bar 95 cm. long and 2 cm. broad, carrying a small telescope at one end. In the present experiment, this bar was merely used in the comparison of the constant of the instrument with that of another instrument. For this purpose the instrument is used as a sine galvanometer by which a great range can be secured, and it could be compared with a coil having a constant twenty-three times less and which was used with telescope and scale. The coils contained about five pounds of No. 22 silk-covered copper wire in 1790- turns. Two needles were used in this galvanometer, each constructed so that its magnetic axis should be invariable; this was accomplished by affixing two thin laminae of glass-hard steel, to the two sides of a square piece of wood, with their planes vertical. This made a sort of compound magnet very strong for its length, and with a constant magnetic axis. The first needle had a nearly rectangular mirror 2-4 by 1-8 cm. on the sides and -22 cm. thick. The other needle had a circular mirror 2-05 cm. diameter and about 1 mm. thick. The needle of the first was 1-27 cm. and of the second 1-20 cm. long, and the pieces of wood were about -45 cm. and -6 cm. square respectively. The moment of inertia of both was much increased by two small brass weights attached to wires in extension of the magnetic axis, thus extending the needles to a length of 4-9 cm. and 4-2 cm. respectively. The total weights were 5-1 and 5-6 grams and the times of vibration about 7-8 and 11-5 seconds. They were suspended by three single fibres of silk about 43 cm. long. In front of the needle was a piece of plane-parallel glass. This and the mirrors were made by Steinheil of Munich, and were most perfect in every way. In the winding of the coils every care was taken, seeing that a small error in so small a coil would produce great relative error. And for Ox THE ABSOLUTE UNIT OF ELECTRICAL RESISTANCE 167 this reason the constant was also found by comparison with another coil. The following were the dimensions: Mean radius 4-3212 cm. R - 5-6212 r = 3-0212 X= 3-475565 x= -935565 R r = 2-6000 X x = 2-54000 ^=1790- whence F= 1832-25 1-70&'& (0) - 4-50i 4 & (0) + -90 6 () 6 (0) - &c. Taking the mean dimensions of the two needles, we have 1 = 1-23, w = -52, w = |, cos 6' = -748. Q t (0') = + 339 , Q t (6'} = - -354 , Q 6 (a') = - -275 . .-. G = 1832-25 -083 + -071 - -002 + &c. = 1832-24. The coil with which this galvanometer was compared was the large coil of an electro-dynamometer similar to that described in Maxwell's 'Electricity/ Art. 725, but smaller. The coil was on Helmholtz's principle with a diameter of 27-5 cm., and was very accurately wound on the brass cylinder. There was a total of 240 windings in the coil. The constant of this coil was 78-371 by calculation. To eliminate the difference of intensity of the earth's magnetism, an observation was first made and then the positions of the instruments were changed so that each occupied exactly the position of the other: the square root of the product of the two results was the true result free from error. The coils of the galvanometer could be separated so that an outer and inner pair could be used together. By comparing these parts separately and adding the constants together we find G. Hence two comparisons are possible, one with the coils together and the other with them separate. The results were for the ratio of the constants 23-3931 and 23-4008, which give G = 1833-37 and 1833-98. The mean result is 1833-67 -09, and this includes seven determinations with two reversals of instru- ments. This result is one part in thirteen hundred greater than found by direct calculation, which is to be accounted for by the small size of the galvanometer coils and the consequent difficulty of their accurate measurement. As comparison with the electro-dynamometer has such 168 HENET A. KOWLAND a small probable error, and as it is a much larger coil, it seems best to give this number twice the weight of that found by calculation : we thus obtain (7 = 1833-19 as the final result. It does not seem probable that this can be in error more than one part in two or three thousand. Telescope, scale, &c. The telescope, mirrors and plane-parallel glass were all from Steinheil in Munich, and left nothing to be desired in this direction, the image of the scale being so perfect that fine scratches on it could be distinguished. The telescope had an aperture of 4 cm. and a magnifying power of 20 was used. The scale was of silvered brass, one metre long and graduated to millimetres. Induction coils. A coil was wound in a groove in the centre of each of three accurately turned brass cylinders of different lengths. Two of them only were used at a time, by placing them end to end, the ends being ground so that they laid on each other nicely. The two coils could be placed in four positions with respect to each other, in each of which they were very exactly the same distance apart. This distance for each of the four positions, was determined at three parts of the circumference by means of a cathetometer, with microscopic objective, reading to ^ mm. The mean of all twelve determinations was the mean distance. In using the coils they were always used in all four positions. The probable error of each set of twelve readings was -001 mm. The data are as follows, naming the coils, A, B and C : Mean radius of A = 13-710, of B = 13-690, of C = 13-720. Mean distance apart of A and 5 = 6-534, of A and (7 = 9-574, of B and (7=11-471. N= 154 for each coil, == -90, y = -84. For A and B we have M= 3774860- + T V (74250- 66510-) = 3775500- The remaining terms of the series are practically zero, as was found by dividing one of the coils into parts and calculating the parts sepa- rately and adding them. For A and C M = 2561410- -f T V (34000- 27230-) = 2561974- For B and (7 M = 2050600- + T V (27500- 19800-) = 2051320- The calculation of the elliptic integrals was made by aid of the tables of the Jacobi function, q, given in Bertrand's ' Traite de Calcul Inte- ON THE ABSOLUTE UNIT OF ELECTRICAL RESISTANCE 169 grale ' as well as by the expansions in terms of the modulus after trans- forming them hy the Landen substitution. The Circle. The circle whose constant we have called G" and which was around the galvanometer whose constant was G, was a large wooden one containing a single coil of No. 22 wire. 14 To prevent warping, it was laid up out of small pieces of wood with the grain in the direction of the circumference, and was carefully turned with a minute groove near one edge in which the wire could just lie. It was about 5- cm. broad, 1-8 thick and 82-7 cm. diameter. As the room had no fire in it, the circle remained perfect throughout the experiment. The wire was straightened by stretching and measured before placing on the circle, which last was done with great care to prevent stretching; after the experiment it was measured and found exact to T ' T mm. The circle was adjusted parallel and concentric with the coils of the galvanometer, but at a distance of 1-1 cm. to one side, in order to allow the glass tube with the suspending fibre to pass. The length of wire was 259-58 cm. which gives a mean radius of 41-31344 cm. These data give G" = -151925. Preliminary results were also obtained by use of another circle. Chronometer. To obtain the time of vibration, a marine chronometer giving mean solar time was used. The rate was only half a second per day. Wheatstone bridge. To compare the resistance of the circuit with the arbitrary German silver standard, a bridge on Jenkin's plan, made by Elliott of London, was used. A Thomson galvanometer with a single battery cell gave the means of accurately adjusting the resistance, one division of the scale representing one part in fifty thousand. 4 Thermometers. Accurate thermometers graduated to half degrees were used for finding the temperature of the standard. The arbitrary standard. This was made of about seventy feet of German silver wire, mounted in the same way as the British Association Standard. Immediately after use, two copies, one in German silver and the other in platinum-silver alloy, were made. It had a resistance of about 35 ohms. The temperature was taken as 17 C. To obtain the accurate resistance of this standard in ohms, I had two standards of 10 ohms and one of 1, 100, and 1,000 ohms. The 1-ohm, and one of the 10-ohm standards, were made by Elliott of London, and u ln another part of my paper I have criticised the use of wooden circles for coil, but it is unobjectionable in the case of a single wire, especially when the needle i& suspended near its centre. 170 HENRY A. EOWLAND the others by Messrs. Warden, Muirhead and Clark of the same place. But on careful comparison I found that Warden, Muirhead and Clark's 10-ohm standard was 1-00171 times that of Messrs. Elliott Bros. On stating these facts to the two firms I met no response from the first firm, but the second kindly undertook to make me a standard which should be true by the standards in charge of Professor Maxwell at Cambridge." At present I give the result of the comparison with these standards, as well as some others, and also with a set of resistance coils by Messrs. Elliott Bros. Commutators. No commutators except those having mercury con- nections were used, and those in the circuit whose resistance was deter- mined were so constructed as to offer no appreciable resistance. The commutator by which the main current was reversed, could be operated in a fraction of a second, so as to cause no delay in the reversal. Connecting wires. These were of No. 22 or No. 16 wire and were all carefully twisted together. The insulation was tested and found to be excellent. Inductor for damping. This has already been described in my first paper on ' Magnetic Permeability,' and merely consisted of a small horse-shoe magnet with a sliding coil, which was introduced into the secondary circuit. By moving it back and forth, the induced current could be used to stop the vibrations of the needle and make it stationary at the zero point. This is necessary in the method where the first throw of the galvanometer needle constitutes the observation, but in the method of recoil it is not necessary to use it very often. I prefer the method of the first throw as a general rule, but I have used both methods. This method of damping will be found much more efficient than that of the damping magnet as taught by Weber, and after practice a single movement will often bring the needle exactly to rest at the zero point. Arrangement of apparatus. Two rooms on the ground floor of a small building near the University were set aside for the experiment, making a space 8 m. long by 3-7 m. wide. The plan of the arrange- ment is seen at Fig. 1. The current from the battery, in the Univer- sity, entered at A, the battery being eighteen one-gallon cells of a chromate battery, arranged two abreast and eight for tension. The 18 As this is nearly a year since, and as I cannot tell when the standard will arrive, I now publish the results as so far obtained, hoping to make a more exact comparison in future. ON THE ABSOLUTE UXIT OF ELECTRICAL EESISTANCE 171 resistance of the circuit was about 20 ohms, and of the whole battery about ^ ohm, thus insuring a reasonably constant current. At B some resistance could be inserted by withdrawing plugs so as to vary the current. At C is the tangent galvanometer with commutator on a brick pier. The nearness of the commutator produces no error, seeing that we only wish to determine the ratio of two currents. The effect of currents in the commutator was, however, vanishingly small in any case. At D is the principal commutator which reversed the current in the induction coils, L, or in the circle, F, when it was in the circuit. FIG. 1. The secondary circuit included the induction coil, L, the damping inductor, M, and the galvanometer 0. At H was the Jenkin's bridge, with standard at P, in a beaker of water, and a Thomson galvanometer at J K. The secondary circuit could be joined to the bridge by raising a U-shaped piece of wire out of the mercury cups. The telescope and scale, E, were on a heavy wooden table, and the two galvanometers on brick piers with marble tops. A row of gas-burners at Q illuminated the silvered scale in the most perfect manner. Adjustments and tests. The circle, F, must be parallel to coils of galvanometer, G. The circle and coils of galvanometer were first adjusted with their planes vertical and then adjusted in azimuth by 172 HENKY A. EOWLAND measurement from the end of the bar, R, to the sides of the circle, F. The adjustment was always within 30', which would only cause an error of one part in 25000. The needle must hang in the magnetic meridian by a fibre without torsion, and the coils must be parallel to it. These adjustments were carefully made, but, as has been shown, the error from this source is compensated. The needle must hang in the centre of the galvanometer coils and on the axis of the circle. The error from this source is vanishingly small. The scale must be perpendicular to the line joining the zero point and the galvanometer needle, it must be level and not too much below the galvanometer needle. All errors from this source are partially or entirely compensated by the method of experiment. The induction coils, L, must be horizontal, and at the same level as the two galvanometers, so as not to produce any magnetic action on them. The error from this source is exactly compensated by this method of experiment, but could never amount to more than 1 part in 2000. The tangent galvanometer should have the plane of its coils in the magnetic meridian, but all errors are compensated. The connecting wires must be so twisted together and arranged as to produce no magnetic action, but tests were made in all cases where the error was not compensated, and found to be practically zero. The insulation of all coils, wires and commutators was carefully tested. Method of experiment. As has been stated before, the method gener- ally used was that of the first throw of the needle, though the method of recoil was also used. For the successful use of the first method a quickly vibrating needle and the damping inductor are indispensable, seeing that with a slow moving needle we can never be certain of its being at rest. By this method it is not necessary to have the needle at rest at the zero point, but, if it vibrates in an arc of only a millimetre or two, we have only to wait till it comes to rest at its point of greatest elongation on either side of the zero point and then reverse the commu- tator. The error by this method is in the direction of making the throw greater in proportion of the cosine of the phase to unity. The smallest throw used was 100 mm. Hence, if the needle vibrated through a total arc of 2 mm., the error would be 1 in 17,000. In reality the needle was always brought to rest much more nearly than this. The method of recoil was used once with the needle vibrating in 7-8 ON THE ABSOLUTE UNIT OF ELECTRICAL EESISTANCE 173 seconds, but the time of vibration was too short and another needle was constructed vibrating in 11-5 seconds, which was a sufficiently long period to be used successfully after practice. There seems to be no error introduced by the time taken to reverse the commutator in the method of recoil, seeing that the breaking of the current stops the needle and the making starts it in the opposite direction. As the time was only a fraction of a second the error is minute in any case. While the current is broken in the reversal, the battery may re- cuperate a little and there is also some action from the extra current, but there seems to be no doubt that long before the four or six seconds which the needle takes to reach its greatest elongation everything has again settled to its normal condition and the current resumes its original strength. Hence the error from these sources may be con- sidered as vanishingly small. Some experiments were made by simply breaking the current and they gave the same result as by reversal. The following is the order of observations corresponding to each experiment. 1st. The time of vibration of needle was observed. 2d. The current was passed around the circle, F, so as to observe y3 and a. Simultaneous readings were taken at the two galvanometers. The commutator at the tangent galvanometer was then reversed and readings again taken. After that the commutator to the circle was reversed and the operation repeated. This gave four readings for the circle and eight for the tangent galvanometer, as both ends of the needle were read. In some cases these were increased to six and twelve respectively. This operation was repeated three times with currents of different strengths, constituting three observations each of a and /?. To eliminate any action due to the induction coils, they were sometimes connected in one way and sometimes in the opposite way. 3d. The resistance of the circuit was adjusted equal to the arbitrary standard. 4th. The circle, F, was thrown out of the circuit and the observations of 6 and d begun. Two throws, d, one on either side of zero were observed and one reading of d taken. The commutators at s and C were then reversed, and the operation repeated. This whole operation was then repeated with currents of three different strengths. The position of the two induction coils was now reversed and observations again made with the three currents. The resistance was now com- 174 HENRY A. ROWLAND pared with the standard, the difference noted, and the resistance again adjusted. The observations were completed by turning the induction coils into the two other positions which they could occupy with respect to each other, followed by another comparison of resistance with standard. 5th. Observations of a and ft were again made as before. 6th. The time of vibration was again determined. The observations as here explained furnished data for three compu- tations of the resistance of the circuit, one with each of the three cur- rents. In each of these three computations, a was the mean of 16 readings, ft of 8 or sometimes 12, 6 of 16 and 3 of 16. In using the method of recoil nearly the same order was observed. The time of vibration was determined by allowing the needle to vibrate for about ten seconds and making ten observations of transits before and after that period. During the experiment, I usually ob- served at the telescope and Mr. Jacques at the tangent galvanometer. The methods of obtaining the corrections require no explanation. RESULTS The constant corrections are as follows for the first needle. a=-J^+ T ^A= - -00711. J = - H = -00020 , c = -000006 , d = + -000074 at 20' C . / = + -00003 , a + b + c + d + e +/ '00718. For method of recoil it becomes -00016. Hence for A and B, log JT= 11-4536030 Hence for A and 0, log # = 11-2852033 Hence for B and C, log #=11-1886619 For method of recoil using A and B, log K = 11-4566.630. For second needle and method of recoil, a = } f V = - -000050 , V * / &=}$= - -00025, c = -000006 , d = + -000074 , ON THE ABSOLUTE UNIT or ELECTRICAL EESIRTANCB 175 e*Tt at the centre of section and 27 and c are the width and depth of the groove in which the coil is wound. We can calculate this quantity best by the formula of Maxwell (Electricity, Art. 700), Thus we finally find M= ^A t {l + T V + } A tll rl Q' tll + i (5, - 3) etc. It is by aid of this equation that we find the coefficients A t , A lu , etc. in the expansion of the magnetic potential, V. For, let the coil be moved in the field from a position where M has the value M' to where it has the value M " : then if the coil be joined to a galvanometer the current induced will be equal to M' - M" R where R is the resistance of the circuit. If an earth inductor is in- cluded in the circuit whose integral area is E, when it is reversed the 2 J-fW current is ^- where H is the component of the earth's magnetism DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 187 perpendicular to the plane of the inductor. The current as measured by the galvanometer in the first case will be C sin \ S (1 -j- /) and in the second C sin D (1 + /), where C is the constant of the galvano- meter and ^ is the logarithmic decrement. Hence T[f' _ Tif" * sm In this way we can obtain a series of equations containing A t , A llt , etc., and can thus find these by elimination. This completes the exploration, and we have as a result a formula giving the magnetic potential of the field in absolute measure through- out a certain small region in which we can experiment. The next process is to consider the action of this field upon any body which we may hang in it. CRYSTALLINE BODY IN MAGNETIC FIELD Let the body have such feeble magnetic action that the magnetic field is not very much influenced by its presence. In all crystalline substances we know there exist in general three axes at right angles to each other, along which the magnetic induction is in the direction of the magnetic force. Let k 1} Jc 2 and k a be the coefficients of magnetiza- tion in the directions of these axes and let a set of coordinate axes be drawn parallel to these crystalline axes, the coordinates referred to which are designated by x', y' and z', and the magnetic components of the force parallel to which are X', Y' and Z'. The energy of the crystalline body will then be E = - \fff (k,Z' 2 + Jc, Y n + fc s Z") dx'dy'dz' In most cases it is more convenient to refer the equation to axes in some other direction through the crystal. Let these axes be X, Y, Z. Then Y , dV dV dV dV X =d^ = ^ a + ^ a + dz a Y' = etc. 188 HENEY A. EOWLAND Hence Z' - Xa+Ya' where a, /?, f ; a!, /3', -f ; and a", /5", /' are the direction cosines of the new axes with reference to the old. We then find E= - \fff{ X* (jfcy + JkJP + V) + Y* ( V 2 + V + V 2 ) + Z\k + 2YZ The most simple and in many respects the most interesting cases are when the crystal has only one optic or magnetic axis. In this CclSG $2 ' ' ~ wy Hence where , a! and a!' are the direction cosines of the magnetic axis with respect to the coordinate axes. The first case to consider is that of a mass of crystal in a uniform magnetic field. The magnetic forces which enter the equation are those due to the magnetic action of the body as well as to the field in which the body is placed. In the case of very weak magnetic or diamagnetic bodies the forces are almost entirely those of the field alone. Hence in the case under consideration we may put F = and Z = 0. Hence and if v is the volume of the body As this expression is the same at all points of the field there is no force acting to translate the body from one part of the field to another. The moment of the force tending to increase - v _ ~~dr ~ also let the section of the bar be a = dy dz and let the axis of the bar pass through the origin from which we have developed the potential in terms of spherical harmonics. We can then write as before where Q t , Q ltl , etc., are zonal spherical harmonics with reference to the angle 6, from which we have the following: X* = A'Q* + SA*,^ + 25^-#f + QA^Q.Q^ ^Q&i* + MA ltt A,Q M QS + etc., * + ZA.A^Q'ff^ '&i* + ZA^A^&r* + etc.} sin-*, The moment of the force tending to increase 6 is dE ~W whence we may write, *i * + *,) + B ((^ - kj '* + h) C (Tc, - 2 ) ' \, 190 HENEY A. EOWLAND where d + l V2 7 . a d X*ar = sin - Y*dr = sin - I Y 2 dr, diJL J_, tJ /*+' fi /+' C = - ~ I ZXYdr = sin 6 " I ZXYdr, dv J -i a/jLj_, where I is half the length of the bar and cosd. = U*m0\ A]Q t Q' t + | A* ,#&]* + ^ A'Q.QP + A t A tll ( + Q,Q'J P + A t A v (Q'& + Q& ) ^ + V- A UI J T (J. + L',u 3 + L" + etc. }, B = U sin e \ MIL + M'ff + etc. \, C = M{N+iy t n + JV'V + etc. }, where the values of L, M, etc., are apparent. To sum up we may then write as before = - J a\A [(^ - *,) 2 + &,] + 5[(^ - *,) ' 2 + * s ] - C' (&, - *,) '} where A, B and (7 are the quantities we have found, a is the cosine of the angle made by the axis of the crystal with the axis of the bar, and a' is the cosine of the angle made by the same axis with a horizontal line at right angles to the bar. The equation # = gives equilibrium at some angle depending on a and a', and if either of these is zero the angle can be either = or -J-, one of which will be stable and the other unstable according as the body is para- or dia- magnetic. For a diamagnetic crystal like bismuth with the axis at right angles to the bar we can put n = cos = sin (/> and a = , and we can write 192 HENEY A. EOWLAND = J a\4lk (Lfji + L>jf* + etc.) &,) a' 2 + k,][M;j. + M'/S + etc.]} or for very small values of // we can write in terms of - 2al<>> \lc,L + ((&! - &,) ' 2 + & 2 ) M\. If I is the moment of inertia of the bar and t is the time of a single vibration, we may write =/-#. If we hang up the bar so that a' we have and if we hang it up so that a' = %TT we have again 2a" whence 7T 2 / 1 where x - ^ - u t A n F + (II ^: /y + v- ^ A) ^- -v/ *,** + -VV/ For a cleavage bar of calc spar we must use the general equation. For equilibrium we have h {Aa* + Ba' 3 - Caa'\ + k, { A (1 a 2 ) + B (1 - a' 2 ) + Caa' \ = 0, which gives us the ratio of Jc 1 to Tc 2 . For this experiment it is best to hang up the bar so that the axis is in the horizontal plane and we should then have a 2 = I a' 2 . For obtaining another relation it is best to suspend the bar with ' = and we then have the position of stable equilibrium at the point 6 \K which gives T?I t* whence DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 193 these various equations give the complete solution of the problem of finding the various coefficients of magnetization. PART II. BY W. W. JACQUES In the foregoing part of this paper there have been deduced mathe- matical expressions for the constants He and ~k' both for bismuth and for calc-spar crystals. In these expressions it is necessary to substitute certain quantities obtained by a series of experiments, and it is the purpose of the remaining portion of the paper to describe briefly the way in which these quantities were obtained. These experiments are naturally divided into two parts. First, the exploration of the small magnetic field between the two poles of the electromagnet, and second, the determination of the time of swing and certain other constants relating to little bars of the substances experi- mented upon when suspended in this field. In order to insure the constancy of the magnetic field, a galvano- meter and variable resistance were inserted in the circuit through which the magnetizing current circulated. This space between the poles of the electromagnet in which the experiments were performed was a little larger than a hen's egg. The method of exploring this field was as follows : In the line join- ing the centre of the two poles was placed a little brass rod, along which a very small coil of fine wire was made to slide. To this rod were fixed two little set-screws to regulate the distance through which the coil could be moved. Starting now always from the centre, the coil was moved successively through distances a, & and c, and the cor- responding deflections of a delicate mirror galvanometer contained in the circuit were noted. To each of these deflections was added the deflection due to quickly pulling the coil away from the centre to a distance such that the magnetic potential was negligibly small. Of course, experiments were made on both sides of the centre of the field in order to eliminate any want of symmetry, and the distances through which the coil moved were all carefully measured with a dividing engine. In order to reduce the deflections of the galvanometer to absolute 13 194 HENRY A. EOWLAND measure, an earth inductor was included in the circuit with the little coil and galvanometer and the deflections produced by this were com- pared with those produced by moving the little coil. These deflections were taken between every two observations with the little coil. The deflections due to moving the little coil, those due to the earth inductor and that due to pulling the coil away from the centre are given in the following table: Distance a. Distance 6. Distance c. Coil 4-407 cm. 9-655 cm. 6-363 cm. Earth inductor 33-138 cm. 33-137 cm. 33-162 cm. Drawing coil away from centre 57-416 cm. In order to determine the proper quantities for substitution in the expression for the magnetic potential of the field, it was necessary to measure, besides, the deflections due to the little coil when moved through various distances and those due to the earth inductor. The mean radius of the small coil = -3912 cm. Number of turns = 83 Width if coil = -182.4 cm. Depth of coil = -1212 cm. Integral area of earth inductor = 20716-2 cm. Horizontal intensity of earth's magnetism. . . . = -1984cgs. The quotient of the mean radius of the coil by the distance moved gave tan d. The linear measurements were made with a dividing engine. The horizontal intensity of the earth's magnetism was determined by measuring the time of swing of a bar magnet and its effect upon a smaller galvanometer needle. The proper substitution of these quan- tities in the formula given gave the expression in absolute measure for the magnetic potential at any part of the field. The remaining part of the experiment and the part that was attended with greatest difficulty, was to prepare little bars of the substances and to determine the times of vibration of these when suspended, first with the axis vertical and then with it horizontal in the magnetic field. Besides this, the dimensions and the moment of inertia of each bar had to be determined, and, in the case of the calc-spar, the angle the bar made with the equatorial line of the poles when in its position of equi- librium, had to be measured. Bismuth and calc-spar were the two crystals experimented upon; quite a number of other substances were tried but failed to give good DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-&PAR 195 results because of the iron contained in them as an impurity. The bars were each about 15 mm. long and about 2 mm. in cross section. The force to be measured being only about -00000001 of that exerted in the case of iron it was necessary to carry out the experiments with the very greatest care. In order to obtain bars free from iron, very fine crystals of chemically pure substances were selected and the bars cleaved from them. They were then polished with their various sides parallel to the cleavage planes by rubbing on clean plates of steatite with oil. In order to remove any particles of iron that might have collected upon them during these processes, they were carefully washed with boiling hydro- chloric acid and with distilled water and then wrapped in clean papers, and never touched except after washing the hands with hydrochloric acid and distilled water. In order to reduce to a minimum the causes that might interfere with the accurate determination of the times of vibration of these bars the poles of the magnet were encased by a box of glass. From the top of this a tube four feet long extended up toward the ceiling, and inside this was hung a single fibre of silk so small as to be barely visible to the naked eye. The bars were placed in little slings of coarser silk fibre and suspended by this. Outside the glass case was a microscope placed horizontally and having a focus of about six inches. This was directed toward the suspended bar, and when the latter was at rest the cross hairs of the microscope fell upon a little scratch in one end of the bar. Near by was a telegraph sounder arranged to tick seconds. The bar was set swinging through a small arc by making and breaking the current, and the interval between two successive transits of the little scratch on the bar by the cross hairs of the microscope was measured in seconds and tenths of a second by the ear. By keeping count through a large number of successive transits the time of a single swing could be determined with very great accuracy. The bar was caused to swing only through a few degrees of arc and such small correction for ampli- tude as was found necessary was applied. The time of swing was deter- mined first with the axis vertical and then with it horizontal. But besides the time of swing of each bar it was necessary to measure : the length ; area of section; moment of inertia in each position ; and for the calc-spar bar the angle it made with the equatorial plane of the magnet when in its position of equilibrium. This was not necessary in the case of bismuth, because its position of equilibrium lay in the equatorial plane. 196 HENRY A. ROWLAND BISMUTH. Time of swing. Axis, vertical 7'18 sec. Axis, horizontal 5'76 sec. Moment of Half Area of inertia. length. section. 10976 cgs. 10943 cgs. 7709 cm. 03778 cm, CALC-SPAR. Half length. Area of section. 8015cm. -0300cm. 50 30' Time of Moment of swing. inertia. Axis, vertical 46'35sec. '0303cgs. Axis, horizontal 43-39 sec. '0300 cgs. The linear measurements were made with a dividing engine, the moments of inertia were calculated from the dimensions of the bars. The angle at which the calc-spar stood was measured by projecting the linear axis on a scale placed at a distance. The above quantities being all determined and properly substitutedj the solution of the equations gave for Bismuth , . .Tc, = Calc-spar 000 000 012 554 000000014324 000 000 037 930 000000040330 19 PRELIMINARY NOTES ON ME. HALL'S RECENT DISCOVERY * [Philosophical Magazine [5], IX, 432-434, 1880 ; Proceedings of the Physical Society, IV, 10-13, 1880; American Journal of Mathematics, II, 354-356, 1879] The recent discovery by Mr. Hall 3 of a new action of magnetism on electric currents opens a wide field for the mathematician, seeing that we must now regard most of the equations which we have hitherto used in electromagnetism as only approximate, and as applying only to some ideal substance which may or may not exist in nature, but which cer- tainly does not include the ordinary metals. But as the effect is very small, probably it will always be treated as a correction to the ordinary equations. The facts of the case seem to be as follows, as nearly as they have yet been determined: Whenever a substance transmitting an electric current is placed in a magnetic field, besides the ordinary electromotive force in the medium, we now have another acting at right angles to the current and to the magnetic lines of force. Whether there may not be also an electromotive force in the direction of the current has not yet been determined with accuracy; but it has been proved, within the limits of accuracy of the experiment, that no electromotive force exists in the direction of the lines of magnetic force. This electromotive force in a given medium is proportional to the strength of the current and to the magnetic intensity, and is reversed when either the primary current or the magnetism is reversed. It has also been lately found that the direction is different in iron from what it is in gold or silver. To analyze the phenomenon in gold, let us suppose that the line A B represents the original current at the point A, and that B C is the new effect. The magnetic pole is supposed to be either above or below the paper, as the case may be. The line A C will represent the final resultant electromotive force at the point A. The circle with arrow represents the direction in which the current is rotated by the mag- netism. 1 From the American Journal of Mathematics. Communicated by the Physical Society. * Phil. Mag. [5], vol. ix, p. 225. 198 HENKY A. ROWLAND It is seen that all these effects are such as would happen were the electric current to be rotated in a fixed direction with respect to the lines of magnetic force, and to an amount depending only on the mag- netic force and not on the current. This fact seems to point imme- diately to that other very important case of rotation, namely the rota- tion of the plane of polarization of light. For, by Maxwell's theory, light is an electrical phenomenon, and consists of waves of electrical displacement, the currents of displacement being at right angles to the direction of propagation of the light. If the action we are now con- sidering takes place in dielectrics, which point Mr. Hall is now investi- gating, the rotation of the plane of polarization of light is explained. I give the following very imperfect theory at this stage of the paper, hoping to finally give a more perfect one either in this paper or a later one. North Pole above. North Pole below. Let $ be the intensity of the magnetic field, and let E be the original electromotive force at any point, and let c be a constant for the given medium. Then the new electromotive force E' will be and the final electromotive force will be rotated through an angle which will be very nearly equal to c>. As the wave progresses through the medium, each time it (the electromotive force) is reversed it will be rotated through this angle; so that the total rotation will be this quan- tity multiplied by the number of waves. If ^ is the wave-length in air, and i is the index of refraction, and c is the length of medium, then the number of waves will be and the total rotation The direction of rotation is the same in diamagnetic and ferromag- netic bodies as we find by experiment, being different in the two; for it PRELIMINARY NOTES ON MR. HALL'S RECENT DISCOVERY 199 is well known that the rotation of the plane of polarization is opposite in the two media, and Mr. Hall now finds his effect to be opposite in the two media. This result I anticipated from this theory of the magnetic rotation of light. But the formula makes the rotation inversely proportional to the wave-length, whereas we find it more nearly as the square or cube. This I consider to be a defect due to the imperfect theory ; and it would possibly disappear from the complete dynamical theory. But the for- mula at least makes the rotation increase as the wave-length decreases, which is according to experiment. Should an exact formula be finally obtained, it seems to me that it would constitute a very important link in the proof of Maxwell's theory of light, and, together with a very exact measure of the ratio of the electromagnetic to the electrostatic units of electricity which we made here last year, will raise the theory almost to a demonstrated fact. The determination of the ratio will be published shortly; but I may say here that the final result will not vary much, when all the corrections have been applied, from 299,700,000 metres per second; and this is almost exactly the velocity of light. We cannot but lament that the great author of this modern theory of light is not now here to work up this new confirmation of his theory, and that it is left for so much weaker hands. But before we can say definitely that this action explains the rota- tion of the plane of polarization of light, the action must be extended to dielectrics, and it must be proved that the lines of electrostatic action are rotated around the lines of force as well as the electric cur- rents. Mr. Hall is about to try an experiment of this nature. I am now writing the full mathematical theory of the new action, and hope to there consider the full consequences of the new discovery. Addition. I have now worked out the complete theory of the rota- tion of the plane of polarization of light, on the assumption that the displacement currents are rotated as well as the conducted currents. The result is very satisfactory, and makes the rotation proportional to ~ , which agrees very perfectly with observation. The amount of rota- tion calculated for gold is also very nearly what is found in some of the substances which rotate the light the least. Hence it seems to me that we have very strong ground for supposing the two phenomena to be the same. 22 ON THE EFFICIENCY OF EDISON'S ELECTRIC LIGHT BY H. A. ROWLAND AND GEORGE F. BARKER \American Journal of Science, [31, XIX, 337-339, 1880] The great interest which is now being felt throughout the civilized world in the success of the various attempts to light houses by elec- tricity, together with the contradictory statements made with respect to Mr. Edison's method, have induced us to attempt a brief examina- tion of the efficiency of his light. We deemed this the more important because most of the information on the subject has not been given to the public in a trustworthy form. We have endeavored to make a brief but conclusive test of the efficiency of the light, that is, the amount of light which could be obtained from one horse power of work given out by the steam engine. For if the light be economical, the minor points, such as making the carbon strips last, can undoubtedly be put into practical shape. Three methods of testing the efficiency presented themselves to us. The first was by means of measuring the horse power required to drive the machine, together with the number of lights which it would give. But the dynamometer was not in very wood working order, and it was difficult to determine the number of lights and their photometric power, as they were scattered throughout a long distance, and so this method was abandoned. Another method was by measuring the resist- ance of, and amount of, current passing through a single lamp. But the instruments available for this purpose were very rough, and so this method was abandoned for the third one. This method consisted in putting the lamp under water and observing the total amount of heat generated in the water per minute. For this purpose, a calorimeter, holding about 1^ kil. of water, was made out of very thin copper: the lamp was held firmly in the centre, so that a stirrer could work around it. The temperature was noted on a delicate Baudin thermometer graduated to 0-1 C. As the experiment was only meant to give a rough idea of the efficiency within two or three per cent, no correction was made for ON THE EFFICIENCY OF EDISON'S ELECTRIC LIGHT 201 radiation, but the error was avoided as much as possible by having the mean temperature of the calorimeter as near that of the air as possible, and the rise of temperature small. The error would then be much less than one per cent. A small portion of the light escaped through the apertures in the cover, but the amount of energy must have been very minute. In order to obtain the amount of light and eliminate all changes of the engine and machine, two lamps of nearly equal power were gener- ally used, one being in the calorimeter while the other was being measured. They were then reversed and the mean of the results taken. The apparatus for measuring the light was one of the ordinary Bunsen instruments used for determining gas-lights, with a single candle at ten inches distance. The candles used were the ordinary standards, burning 120 grains per hour. They were weighed before and after each experiment, but as the amount burned did not vary more than one per cent from 120 grains per hour, no correction was made. As the strips of carbonized paper were flat, very much more light was given out in a direction perpendicular to the surface than in the plane of the edge. Two observations were taken of the photometric power, one in a direction perpendicular to the paper, and the other in the direction of the edge, and we are required to obtain the average light from these. If L is the photometric power perpendicular to the paper, and I that of the edge, then the average, I, will evidently be very nearly Xo COS a sin a d a + I I Sin 2 a d a, / I Ft A = J L + p. In the paper lamps we found l = The lamps used were as follows: nearly; hence x =|L nearly No. Kind of Carbon. Size of Carbon. Approximate resistance when cold. 580 Paper. Large. 147 ohms. 201 n it 147 850 it Small. 170 " 809 it *i 154 " 817 Fibre. Large. 87 The capacity of the calorimeter was obtained by adding to the capac- ity of the water, the copper of the calorimeter and the glass of the 202 HENRY A. ROWLAND lamp and thermometer. The calorimeter and cover weighed 0-103 kil. and the lamps about 0-035 kil. First experiment, No. 201 in calorimeter and No. 580 in photometer; capacity of calorimeter = 1-153 + -009 + -007 = 1-169 kil. The temperature rose from 18 -28 C. to 23 -11 C. in five minutes, or l-75 F. in one minute. Taking the mechanical equivalent as 775-, which is about right for the degrees of this thermometer, this corresponds to an expenditure of 3486 foot pounds per minute. The photometric power of No. 580 was 17-5 candles maximum, or 13-1 mean, /. When the lamps were reversed, the result was 3540 foot pounds for No. 580, and a power of 13-5 or 10-1 candles mean. The mean of these two gives, therefore, a power of 3513 foot pounds per minute for 11-6 candles, or 109-0 candles to the horse power. To test the change of efficiency when the temperature varied, we tried another experiment with the same pair of lamps, and also used some others where the radiating area was smaller, and, consequently, the temperature had to be higher to give out an equal light. We combine the results in the following table, having calculated the number of candles per indicated horse power by taking 70 per cent of the calculated value, thus allowing about 30 per cent for the friction of the engine, and the loss of energy in the magneto-electric machine, heating of wires, etc. As Mr. Edison's machine is undoubtedly one of the most efficient now made, it is believed that this estimate will be found practically correct. The experiment on No. 817 was made by observing the photometric power before and after the calorimeter experiment, as two equal lamps could not be found. As the fibre was round, it gave a nearly equal light in all directions as was found by experiment. Lamps used in Photometric Power. -! 06 . c i on cS ti A + p This gives us an equation which may be solved with respect to fi. The curve for the magnetic permeability is of this nature (Fig. 7). It will be of a more or less flat form, according to the value of I and p. Therefore, in increasing the magnetic force upon the magnet, it becomes easier and easier to magnetize it until a certain point is reached, and after that it becomes harder and harder. In practice the core should have sufficient cross-section to produce a very strong magnetic field, but not so great as to require too much wire to wind it. The two must be balanced, which can only be done by calculation or, better, by experi- ments on the machine. By examining the force of the magnet at each point, and in that way getting an idea of how these lines of force go, we can see whether the cross-section of the core is large enough to produce all the lines of force necessary for our purpose or not. Of course, in order to have sufficient magneto-motive force to send lines of force across the opening in sufficient quantity, we must have sufficient wire. As the thickness of the coil is increased, we have to use more wire in proportion for a certain diameter of core, which is a disadvan- 15 226 HEXRY A. BOWL AND tage, since each coil acts very nearly the same as every other in produc- ing force. But if the core is very short indeed, wire must be piled on it to a very great extent in order to get sufficient magneto-motive force, and as iron is cheaper than copper it might he better to lengthen out the core. I do not know where the lengthening should end, but I should suppose when the requisite wire on the magnet makes a moder- ately thin layer. Of course, as we lengthen out the magnet, the resist- ance of the circuit to magnetization becomes greater; but that is a very small quantity. I do not suppose the increase is very much for a considerable lengthening of the magnet. As I said before, the magnetic conductivity of iron is many times greater than that of air, and we can lengthen out the cores without producing much loss on account of that lengthening. Some persons have suggested that there might be a slight gain from FIG. 7. the fact that iron, after it has been magnetized a great number of times in the same direction, rather likes to be magnetized in the same direc- tion afterwards. If the core is made of any material similar to steel, such as wrought iron or anj'thing of that sort, it might be possible to have some gain from the coercive power of the magnet. There would be loss from that cause at first; but from the continual use of the machine I think it very likely the iron might get a set in the direction of the force. If the core were of steel, for instance, it might be that one could send a strong current through at first and magnetize the steel, and then be able to diminish the current considerably and still keep up a very large magneto-motive force. I do not know how practical that would be, but it seems to me that one could produce a very strong field in that way. In the commencement of the operation of the machine, we would have to send a powerful current to magnetize the steel, and then, without stopping the current, to diminish it. Then the set of THE THEORY OF THE DYNAMO 227 the steel would be in the same direction with the current and produce the field with less expenditure of energy than if it were simply iron. There is no difference between a shunt and a series machine. The magnetizing force on the magnet I have set down as proportional to the number of turns multiplied by the current; that is, proportional to the cross-section of the coils multiplied by the current per unit of cross- section, so that the magnetizing action can be the same either from a strong current or a weak current. Therefore, if the exterior dimen- sions of the coils are the same in both cases, the same energy is ex- pended in each in order to produce the same force, so that there is no FIG. 8. difference between a shunt machine and a series machine as far as the economy of the magnet is concerned. I do not wish to take up too much of your time, and will go on to the heating of the armature. Of course the amount of energy expended in the heating of the armature will be dependent on the resistance of the armature. It is well known that the efficiency of the circuit will merely depend upon the relation between the resistance of the arma- ture and the exterior circuit. There is one other point in regard to losses ; ' dead wire,' I think, is the technical term for it; I mean that portion of the wire which does not cut the lines of force. In the Gramme pattern the armature is 228 HEXKY A. EOWLAXD inside of the rings. In the Siemens pattern the coils are around the ends of the armature. In a section of the Gramme ring (Fig. 8), the outside portion of the wire (a) is active, since the lines of force follow the core and the outside of the ring around; but the lines of force do not go through the core of the ring, so that the inside portion (6) is dead, so that we can say nearly half the wire is dead wire. In the Siemens armature one cannot see immediately how much dead wire there will be, because it depends upon the length of the armature. The wire is wound around in that way (Fig. 9), and this portion (a a) is active, and this portion (6 &) is dead. If the armature is very thick we would have more dead wire than when it is simply long. I cannot say which has the more dead wire, but I dare say the Gramme has more I 1 I I J 4_l i 1 i 1 i FIG. 9. than the Siemens. Furthermore, either in the Gramme ring or the Siemens armature (Fig. 10) we have the lines of force running across here (arrows) ; that portion is active ; but these portions (a a) in between the poles are dead, and when the armature revolves we have the lines of force turning around, and I think that would add more dead wire. I believe an attempt has been made to throw out these coils. There is no necessity to go further. As I have said, the efficiency of the circuit depends upon the ratio of the resistance of the armature to the resistance of the wires, and therefore, as far as this point is con- cerned, any machine can be made as efficient as one pleases by putting in greater and greater external resistance. But as the magnet remains the same, we would find a point where the efficiency as a whole would not increase for an increase of external resistance, but would actually diminish. There are other things to be taken account of, such as losses THE THEORY OF THE DYNAMO 229 due to the self induction of the coils which produce sparks in them. I have requested Professor Fitzgerald to take up that point, and will leave it for him to consider. There is another point with regard to the dynamo which can be treated in this simple manner with no use of the calculus. This is very simple reasoning if you only know the principles. I shall con- sider two machines similar in all respects, except that one is larger than the other, or rather consider one machine, and see what the effect will be when that machine gradually changes in size. The point from which we start shall be that the magnetic field is con- stant in the two machines. For, owing to the fact that there is a limit in the magnetization of a magnet, we cannot have a field with more FIG. 10. than certain strength produced by iron, and I will suppose that the strength is reasonably near that maximum for iron. It cannot be up to the maximum strength, of course, but somewhere near it. I made some experiments many years ago upon an ordinary magnet, the results of which were published in Silliman's Journal, by means of what I call the magnetic proof plane. (Am. J. Sci., vol. 10, 1875, p. 14.) It applies beautifully to dynamo machines, and I obtained everything with it that I have referred to here. If I remember right, I found in that magnet about one-third of the field that an iron magnet could pos- sibly have. It is theoretically possible to get a force equal to the magnetizability of the iron, but practically, I suppose that instance is about the case of the ordinary dynamo machine. We start, then, with the supposition that the field of force in the two machines, one of which is larger than 230 HEXEY A. KOWLAKD the other, is constant. That is to say, the magnetizing force at any point of one machine is equal to that at a similar point in the other machine. In making a drawing of the machines., it would not matter about the scale of dimensions; the force at a certain point is a certain amount whatever the scale. Next consider what must be the current through the wire in the two machines. There are the same numbers of turns of wire around the magnet, and everything is the same except the dimensions. Consider the current passing around the coil of a tangent galvanometer. If the galvanometer grow, in order to produce the same effect at the centre (and not only at the centre but at every point), the current must in- crease in direct proportion to the radius of the coil. When the coil is twice as large the current must be twice as large, in order to produce the same force at every point. Thus, if there is no difference in the material of the two machines, we have their currents in direct propor- tion to their linear dimensions. Make a machine twice as large and the current in the coils must be twice as great to produce the same magneto-motive force. Of course the wire has increased in size; if the machine has increased to twice its original size the cross-section of the wire has increased four times. In other words, from that cause the current per unit of area will vary inversely as the square of I, the linear dimensions; and since we have found the current to vary directly as I, in order to retain the same force in the field, by a combination of the two results, it varies inversely, as I. Therefore, so far as the magnets are concerned, the heating effect, which depends upon the current per unit of cross-section, will decrease with the size, while the surface will increase in proportion to the square of the size. There will, therefore, be less danger of heating in a large magnet than in a small magnet, but this is only with respect to the magnet. The resistance of any part of the machine varies, of course, directly as the length of the wire, and inversely as the cross-section. The cross- section varies as Z 2 , so that resistance varies inversely as I. Therefore the larger the machine the less the resistance ; one machine being twice as large as the other, the resistance will be half as great. This applies not only to the work of the magnets, but to the work of the armature. I will now consider the electro-motive force. The electro-motive force is proportional to the product of the current and the resistance, or we may write E = RC. We have the current proportional to I, and the resistance inversely proportional to I; therefore the electro-motive force is constant. As we are running the machine, it turns out that THE THEORY OF THE DYXAMO 231 the electro-motive force does not vary with the size, but we shall pres- ently see how this is modified so as to get greater electro-motive force for the larger machine. The work done is C 2 R in any part of the machine, or in the whole machine, just as you please. This varies directly as I. Therefore the one machine which is twice as large as the other requires twice as much power to run it, and twice as much electrical energy comes out of it. But it is to be remembered that the weight of the machine varies as I s , and we only get work proportional to I out of it. So far as results go, we have constructed two machines which differ only in size. The efficiency of these two machines is a constant quan- tity. That will be rather startling to some, who think a large machine is more efficient than a small one. As far as we have gone in any two machines, one of which is simply larger than the other, the efficiency is the same. But if we calculate the angular velocity of the armature to keep the proper current we shall find that it varies inversely as the square of the linear dimensions. In other words, in one machine twice as large as another the velocity of the armature must be only one-fourth as great in order to produce the proper current in the wires. This takes account, I think, of every irregularity in the machine. The two machines are exactly the same in every respect. I have not added the loss for the self-induction of the coil. I have an idea that this also should be taken into account, but Mr. Fitzgerald will consider that point. ISfow the question comes up, can we increase the velocity of the arma- ture above that point? Is it practically necessary that we should run one machine at one-fourth of the angular velocity if it is twice as large ? It is a practical question; but I should certainly think the velocity was not in that proportion. I should think it would be more nearly in- versely as the size and not inversely as the square of the size. If so, then by so arranging the wire of the armature as to increase the pro- portion of external resistance we can have the same current per unit of section when running the armature faster and the same electro- motive force. If we do that, this whole theory applies; but we shall have increased the external resistance of the machine in comparison with the resistance of the armature, and when we do that we increase the efficiency of the machine. I think it is from this cause that we find large machines more efficient than smaller ones; but it is also evident that there is a limit to this, 232 HENRY A. KOWLAND which can only be obtained, I suppose, from practically making the machines and seeing how much faster they may be run without flying to pieces. As far as this theory goes, the increase comes not from the size of the machine, but from the fact that we can get a greater electro- motive force with the same angular velocity, and so can reduce the internal resistance in proportion. In very large machines we can make the wire with one turn, not several turns simply bars on the machines. We thus decrease the resistance of the machine, and at the same time, if we run it above this proportion which I have pointed out, we obtain the proper electro-motive force. In other words, the proper electro- motive force is more easily obtained from the large than the small machine, because it is not practically necessary to decrease the velocity so as to keep it inversely as the square of the size. [Discussion by Professor Elihu Thomson and others.] With respect to Mr. Thomson's remarks, I am very glad to see the matter taken up in this spirit and to have my principles intelligently criticised. However, there was one remark which I wish to state imme- diately as an error, of course, with regard to the steel. Steel can be magnetized to exactly the same degree as soft iron. There is no differ- ence between soft iron and steel in that respect, except that we require an immensely greater force to magnetize steel to the same extent as iron. There are some old papers of mine, which were published in the ' Philosophical Magazine/ I believe, in 1873, relating to experiments where I took iron and steel and several other metals, and showed that the maximum magnetization was the same in all cases. But with respect to a number of statements with regard to flat mag- nets and round magnets I am very glad to see my remarks criticised in the manner that they were, because it shows the need of exactly what I stated; and that is experiments upon this subject. The question is one of quantity. My reasoning gave results in one direction, and Mr. Thomson gave reasons for making the magnet in another way, and it is a quantitative question of course as to which is the best; and for that reason I want very much to see experiments made in the manner which I have described by means of this ' magnetic proof plane/ so as to find out what the escape of the lines of magnetic force in all cases is. I think we can decide on one point that was brought up without any trouble, and that is with respect to the dynamo made with extended pole piece (Fig. 2), where it was assumed that the lines of force had a THE THEORY or THE DYNAMO 233 tendency to go in a particular direction, that it was a sort of gun shoot- ing the lines of force through the armature. That is not true, because they do not have any tendency to go that way at all, and we would only add that much to the area of the end of the magnet. Very few lines of force will go out there, and by putting this additional magnet on we add to the area of the magnet. The lines of force will go out at the sides probably in greater numbers than they would at the end, so that I do not think that particular objection holds in that particular case. It is a question of quantity; the thing should be measured and found out. I see very plainly in my own mind that more lines of force would go out the side by adding this iron here (Fig. 2) than would go out at the end of it by leaving it vacant, as in Fig. 1. But it is a matter of mere opinion. Another reason for having fewer magnets is that the surface is greater in the case of the larger number than of the smaller number for the lines of force to escape from. There was another point brought up here with respect to the machine which was made in this way (Fig. 4). It was stated that there was some gain from the magnetic action of this coil on the iron outside. There is undoubtedly a gain: the question is how much, and whether more lines do not escape than would make up for that. With no experiments to go on, it is a case of judgment. My own judgment would be that there would be very little gain ; but, as I said before, the thing should be measured, and then we could find out about that point. [Discussion by Professors Sylvanus Thompson and Anthony and others.] I am very glad that that point of hollow magnets has been brought up, as I think that the question of hollow magnets, hollow lightning rods, and a great many similar things, causes more difficulty, especially to practical men, than almost anything else. It can be explained in a very few words. Take a hollow bar having the magnetizing coil around it acting to send lines of force along it. They have got to go out to make their complete circuit. They could only end at a certain point if we had free magnetism, that is, a separate magnetic fluid. I speak not from a physical sense but from a mathematical point of view. The principal resistance to the propagation of these lines of force is in the air and not in the magnet. If we take away a large portion of the interior of that magnet we will have the surface the same as it was before, and consequently the external resistances are the 234 HENRY A. EOWLAND same. In such a case as that we leave the magnet about as strong as it was before. But that would not be the case if we compress magnet- ism until we get it up to the point of magnetization of the centre. In that case we should need the whole mass, and it is almost impossible to magnetize to any extent without the centre coming in. It depends on the length of the bar. If we bring the bar around, making a com- plete magnetic circuit of the thing, so that the lines of force do not have to pass out into the air at all when we put a wire around it so as to wind it like a ring at every point, in that case the whole cross-section becomes equally magnetized, if it is not bent too much. If it is a large ring of small cross-section, it is perfectly magnetized across from side to side. We know that perfectly well; it is a result of the law of con- servation of energy. The case of dynamos is like that. We require the whole cross-section to transmit these lines around. The resistance to the magnetization comes partly from this opening and partly from the iron. We have no gain in making these cylinders hollow; indeed we rather increase the outside surface to let lines of force flow into the air. In the case of a dynamo machine, the solid form is not only desirable, but by far the most efficient. I have thought of that matter a great deal, and experimented upon it. Indeed this closed circuit is the very idea from which the permea- bility of the iron is determined. All the calculations upon that sub- ject are based upon that law. I think there can be no doubt that in the dynamo the solid form is the proper form, and that the whole cross- section is effective. The whole cross-section of a round piece is just as effective as the whole cross-section of a flat piece. The flat piece ex- poses more surface to the air, and there is more surface for the force to escape from. That is another reason for not making the magnets flat. The round form is that in which there is the least surface, and therefore the least liability of the lines of force to escape. You can conduct the lines of force by a round piece to any point you desire much better than by a flat piece. [Discussion by Professor Sylvanus Thompson.] I do not know that the theory bears upon the solidity of the core. Of course, the more iron in there the better is the efficiency of the machine. I suppose there would be no objection to dividing that cylinder up into a number, so that the Foucault currents could not exist, if the exterior form was round; but I do have an objection to THE THEORY OF THE DYNAMO 235 making it any other shape. Indeed, currents could be more thoroughly eliminated by dividing up the cross-section than by making it of a very elongated form. [Discussion by Professor Elihu Thomson.] I do not like to rise so often, but I think there is some misapprehen- sion. I have not said anything about large masses of iron. There are the same masses of iron in my method as in any other. The only question is as to making them round or elongated. Of course by dividing this core up it becomes similar to a core of the Euhmkorff coil, and the currents change very rapidly. From Professor Sylvanus Thompson's remarks, I thought that that was desirable. One cannot say that the current is transferred from the core to the wires outside. The same current might take place, and, if the resistances are the same, would take place in the wires outside in both cases. By lengthen- ing the time of action one decreases the electro-motive force or de- creases the external current. If the time is ten minutes one would have one electro-motive force for the external current: if it is five minutes, the electro-motive force would be somewhere near twice as great as before, the whole quantity of electricity passing being the same in both cases. 36 [Report of the Electrical Conference at Philadelphia in November, 1884, pp. 172-17-t; Washington, 1886] As this is an important question, especially in some of the Western States, I will say a few words. In order to protect buildings from lightning we must have a space into which the lightning cannot come, and have the house situated in that space. What sort of a space do we know in electrical science into which electricity cannot enter from the outside ? It is a closed space I mean a space inclosed by a very good conducting body. All the light- ning in the world might play around a hollow copper globe and it would not affect in the slightest degree anything inside the globe; but the the walls of the vessel need not be solid metal. Of course, if solid, it is all the better ; but if it is made of a net-work of very good conducting material it would protect the inside from lightning strokes. A spark striking on one side of such wire cage would find it easier to go around through the wire of the cage to the other side than it would to go through the centre. This is Maxwell's idea, with reference to protec- tion of houses from lightning, viz., to enclose the house in a rough cage of conducting material. Suppose, for instance, this box is the house, and suppose we start from the roof and run a rod diagonally to each corner and thence down to the earth. We thus make a rough cage. Of course there are openings on the sides; and if we wished to make a better protection we could put rods down the sides wherever we wished. Now, there is ground underneath the house, and the lightning might, by jumping across the centre, find a good conductor through the middle of the house and go down to the earth in that way. How do we prevent that? By running the lightning-rods clear across underneath the house. Then the lightning would find it easier to go around the house than to jump across, even if there were a good conductor through the middle. A house inclosed in a cage of that sort would be perfectly protected, even if it were a powder magazine, or anything of that sort. Of course, in the case of petroleum storage reservoirs, where fumes are given off, there would be danger then, as the stroke might ignite the ON LIGHTNING PROTECTION 237 fumes of the petroleum. That would not be the case of a powder magazine. The protection in that case could be made perfect. It is not necessary to have lightning-rods insulated. Indeed the question is, can we insulate a lightning-rod ? We may insulate it for a small potential, but lightning coming from a mile or two to strike a house is not going to pay any attention to such an insulator; we may just as well nail the lightning-rod directly to the house as far as that goes. The idea of having the lightning-rods inclose the bottom as well as the sides of the house is very important, because we do not know, and we have no right to assume, that the earth is a good conductor. We are perfectly certain if the earth forms a good conductor that then the lightning could go down at the sides into the earth. By inclosing the house in a case both below and above we obviate all that difficulty, and it makes no difference whether the earth is a good conductor or not. I am glad of this public opportunity to say something with regard to a peculiar form of lightning-rod; it is in reference to a form of a rod shaped like the letter U. I think the idea is that the lightning strikes on one side, and that it goes down and has inertia and flies up again. The company which advocated this idea had the impudence to bring a lawsuit against a scientific man who said it was a humbug. A company of course can make a great deal of trouble to one man; but when there is such a gross humbug as that around, one would like to undergo the danger of a lawsuit. There is nothing scientific about it; it will endan- ger life in any house in which it is placed. Mr. SCOTT. I would like to ask whether a building constructed of iron would not be completely protected from lightning ? Professor EOWLAND. Yes, if it has a floor of iron too. If a gas-pipe came up into the centre the lightning might find it easier to go across to the pipe than to go around. But if we made a floor of iron the lightning would find it easier to go around than across to the pipe. It must be an entirely inclosed house. Mr. SCOTT. Then would not a petroleum tank entirely constructed of iron with an iron bottom be the safest inclosure possible for petro- leum? Professor ROWLAND. The peculiarity of that is that the fumes of petroleum are all the time coming out from the cracks. The whole out- side is probably covered with petroleum. I suppose also the ground is saturated with petroleum. The petroleum as far as the inside goes would be perfectly safe. 238 HENKY A. ROWLAND Lieutenant FISKE. I would like to ask how far lightning obeys the ordinary law of currents, whether it takes the path of least resistance or not. Do high potentials always do that? In general across a nar- row space the resistance is greater than going around by the iron, and the question is, to what extent does the lightning obey the law of circuits ? Professor ROWLAND. I would like to say one word more with respect to petroleum. In the case of the tank you have a mixture of the petro- leum vapor and air which probably would explode. Unless the tank was a very good conductor there might be also a little spark in the interior, not enough to hurt a man in there; but the smallest spark inside the tank would cause an explosion. I am not certain whether the iron of the tank is a good enough conductor to prevent every trace of spark in the interior. Indeed, suppose we had a tank with a cover upon it. That is supposed to be a closed vessel, yet the lightning would have to pass from top to bottom between the cover and the tank, and perhaps a little spark would take place in the interior; and possibly in going from one of the plates of the iron tank to the other it may find some resistance and jump over some small plate in the interior of the tank. It would be a most difficult thing to protect. With regard to that other question, lightning in the air, of course, does not obey Ohm's law; it is entirely a discontinuous anomaly. It is like the breaking of a metal. A piece of metal is supposed to break at a certain strain; but it does not always break then; it pulls out in strings or something of that sort. One cannot measure the distance and say the lightning is going to jump across that distance. 37 THE VALUE OF THE OHM [La Lumieve filectrique, XXVI, pp. 188, 189, 477, 1887] La Yaleur de PTJnite de Besistance de 1'Association Britannique. A la derniere reunion de 1' Association britannique, le professeur H. A. Eowland a donne la valeur definitive de 1'unite de resistance electrique de 1'Association, telle qu'elle a ete determined par la com- mission americaine. La valeur donnee en 1876 etait : unite B. A. = 0-9878 ohm. Dans la derniere determination, on s'est servi des methodes de Kirch- hoff et de celle de Lorenz. La premiere a donne une valeur de 0-98646 40 et la seconde 0-9864 18; son erreur probable est done de moins de la moitie de celle de la premiere methode. Le professeur Eowland a egalement determine la resistance d'une colonne de mercure de 1 mm. 2 de section et de 100 centimetres de lon- gueur, et a trouve 0-95349 unites B. A. Valeur de 1'Etalon B. A. de 1'Ohm, d'apres les Mesures de la Com- mission, Americaine, par Eowland. Les observations ont ete terminees en 1884 deja, mais les calculs viennent d'etre termines et seront publics prochainement. En 1786: Eowland a trouve 1 unite B. A. = 0-9878 ohm. Kimball a trouve 1 unite B. J.. = 0-9870 ohm. Maintenant Eowland trouve par la methode de Kirchhoff et a 1'aide de 73 observations 1 unite B. A. = (0-98627 40) ohms et Kimball par la methode de Lorenz et au moyen de 43 observations 1 unite B. A. = (0-98642 18) ohms. En combinant les deux resultats, on trouve que 1'unite mercurielle est egale a 0-95349 unites B. A., c'est-a-dire que 1'ohm de mercure cor- respond a une colonne de mercure de 106-32 cm. Eappelons ici les valeurs obtenues par diiferents physiciens et qui se rapprochent le plus du resultat ci-dessus : 240 HENEY A. KOWLAND Lord Eayleigh 106-25 cm. Glazebrook 106-29 cm. Wiedemann 106-19 cm. Mascart 106-37 cm. Weber . ,.106-16 cm. 38 ON A SIMPLE AND CONVENIENT FOEM OF WATER BATTERY [American Journal of Science [3], XXXI21, 147, 1887 ; Philosophical Magazine [5], XXIII, 303, 1887 ; Johns Hopkins University Circulars, No. 57, p. 80, 1887] For some time I have had in use in my laboratory a most simple, convenient and cheap form of water battery whose design has been in one of my note-books for at least fifteen years. It has proved so useful that I give below a description for the use of other physicists. Strips of zinc and copper, each two inches wide, are soldered to- gether along their edges so as to make a combined strip of a little less than four inches wide, allowing for the overlapping. It is then cut by shears into pieces about one-fourth of an inch wide, each composed of half zinc and half copper. A plate of glass, very thick and a foot or less square, is heated and coated with shellac about an eighth of an inch thick. The strips of copper and zinc are bent into the shape of the letter IT, with the branches about one-fourth of an inch apart, and are heated and stuck to the shellac in rows, the soldered portion being fixed in the shellac, and the two branches standing up in the air, so that the zinc of one piece comes within one-sixteenth of an inch of the copper of the next one. A row of ten inches long will thus contain about thirty elements. The rows can be about one-eighth of an inch apart and therefore in a space ten inches square nearly 800 elements can be placed. The plate is then warmed carefully so as not to crack and a mixture of beeswax and resin, which melts more easily than shellac, is then poured on the plate to a depth of half an inch to hold the elements in place. A frame of wood is made around the back of the plate with a ring screwed to the centre so that the whole can be hung up with the zinc and copper elements below. When required for use, lower so as to dip the tips of the elements into a pan of water and hang up again. The space between the ele- ments being -fa inch, will hold a drop of water which will not evaporate for possibly an hour. Thus the battery is in operation in a minute and is perfectly insulated by the glass and cement. This is the form I have used, but the strips might better be soldered face to face along one edge, cut up and then opened. 16 40 ON AN EXPLANATION OF THE ACTION OF A MAGNET ON CHEMICAL ACTION 1 BY HENRY A. ROWLAND AND Louis BELL [American Journal of Science [3], XXXVI, 39-47, 1888; Philosophical Magazine [5]. XXVI, 105-114, 1888] In the year 1881 Prof. Eemsen discovered that magnetism had a very remarkable action on the deposition of copper from one of its solu- tions on an iron plate, and he published an account in the American Chemical Journal for the year 1881. There were two distinct phe- nomena then described, the deposit of the copper in lines approximat- ing to the equipotential lines of the magnet, and the protection of the iron from chemical action in lines around the edge of the poles. It seemed probable that the first effect was due to currents in the liquid produced by the action of the magnet on the electric currents set up in the liquid by the deposited copper in contact with the iron plate. The theory of the second kind of action was given by one of us, the action being ascribed to the actual attraction of the magnet for the iron and not to the magnetic state of the latter. It is well known since the time of Faraday that a particle of magnetic material in a magnetic field tends to pass from the weaker to the stronger portions of the field, and this is expressed mathematically by stating that the force acting on the particle in any direction is proportional to the rate of variation of the square of the magnetic force in that direction. This rate of variation is greatest near the edges and points of a mag- netic pole, and more work will be required to tear away a particle of iron or steel from such an edge or point than from a hollow. This follows whether the tearing away is done mechanically or chemically. Hence the points and edges of a magnetic pole, either of a permanent or induced magnet, are protected from chemical action. One of Prof. Remsen's experiments illustrates this most beautifully. He places pieces of iron wire in a strong magnetic field, with their axes along the lines of force. On attacking them with dilute nitric acid they are eaten away until they assume an hour-glass form, and are 1 Read at the Manchester meeting of the British Association, September, 1887. ACTION OF A MAGNET ox CHEMICAL ACTION 243 furthermore pitted on the ends in a remarkable manner. On Prof. Remsen's signifying that he had abandoned the field for the present, we set to work to illustrate the matter in another manner by means of the electric currents produced from the change in the electrochemical nature of the points and hollows of the iron. The first experiments were conducted as follows: Two bits of iron or steel wire about 1 mm. in diameter and 10 mm. long were imbedded side by side in insulating material, and each was attached to an insulated wire. One of them was filed to a sharp point, which was exposed by cutting away a little of the insulation, while the other was laid bare on a portion of the side. The connecting wires were laid to a reflecting galvanometer, and the whole arrangement was placed in a small beaker held closely between the poles of a large electromagnet, the iron wires being in the direction of the lines of force. When there was acid or any other substance acting upon iron in the beaker, there was always a deflection of the galvanometer due to the slightly different action on the two poles. When the magnet was excited the phenomena were various. When dilute nitric acid was placed in the beaker and the magnet excited, there was always a strong throw of the needle at the moment of making circuit, in the same direction as if the sharp pointed pole had been replaced by copper and the other by zinc. This throw did not usually result in a permanent deflection, but the needle slowly returned toward its starting point and nearly always passed it and produced a reversed deflection. This latter effect was disregarded for the time being, and attention was directed to the laws that governed the apparent ' protective throw,' since the reversal was so long delayed as to be quite evidently due to after effects and not to the immediate action of the magnet. With nitric acid this throw was always present in greater or less degree, and sometimes remained for some minutes as a temporary deflection, the time varying from this down to a few seconds. The throw was independent of direction of current through the magnet, and apparently varied in amount with the strength of acid and with the amount of deflection due to the original difference between the poles. This latter fact simply means that the effect produced by the magnet is more noticeable as the action on the iron becomes freer. When a pair of little plates exposed in the middle were substituted for the wires, or when the exposed point of the latter was filed to a flat surface, the protective throw disappeared, though it is to be noted that the deflection often gradually reversed in direction when the cur- 244 HENRY A. EOWLAND rent was sent through the magnet; i. e., only the latter part of the previous phenomenon appeared under these circumstances. When the poles, instead of being placed in the field along the lines of force, were held firmly perpendicular to them, the protective throw disappeared completely, though as before there was a slight reverse after-effect. Some of Professor Eemsen's experiments on the corrosion of a wire in strong nitric acid were repeated with the same results as he obtained, viz.: the wire was eaten away to the general dumb-bell form, though the protected ends instead of being club-shaped were perceptibly hol- lowed. When the wire thus exposed was filed to a sharp point the extreme point was very perfectly protected, while there was a slight tendency to hollow the sides of the cone, and the remainder of the wire was as in the previous experiments. In both cases the bars were steel and showed near the ends curious corrugations, the metal being left here and there in sharp ridges and points. In one case the cylinder was eaten away on sides and ends so that a ridge of almost knife-like sharpness was left projecting from the periphery of the ends. These were the principal phenomena observed with nitric acid. Since this acid is the only one which attacks iron freely in the cold, in Prof. Eemsen's experiment, this was the one to which experiments were in the main confined. With the present method, however, it was pos- sible to trace the effect of the magnet whenever there was the slightest action on the iron, and consequently a large number of substances, some of which hardly produce any action, could be used with not a little facility. In thus extending the experiments some difficulties had to be encountered. In many cases the action on the iron was so irregular that it was only after numerous experiments under widely varying conditions that the effect of the magnet could be definitely determined. Frequently the direction of the original action would be reversed in the course of a series of experiments without any apparent cause, but in such case the direction of the effect due to the magnet remained always unchanged, uniformly showing protection of the point so long as the wires remained parallel to the lines of force. When, however, the original action and the magnetic effect coincided in direction, the repe- tition of the latter showed a decided tendency to increase the former. When using solutions of various salts more or less freely precipitated by the iron, it frequently happened that the normal protective throw was nearly or quite absent, but showed itself when the magnet circuit was broken as a violent throw in the reverse direction, showing that the combination had been acting like a miniature storage batterv which ACTION OF A MAGNET ON CHEMICAL ACTION 245 promptly discharged itself when the charging was discontinued by breaking the current through the magnet. The gradual reversal of the current some little time after exciting the magnet was noted fre- quently in these cases, as before. Owing to this peculiarity and their generally very irregular action, the various salts were disagreeable sub- stances to experiment with, though as a rule they gave positive results. Unless the poles were kept clean experimenting became difficult from the accumulation of decomposition products about them and oxidation of their surfaces. A few experiments showed how easily the original deflection could be modified, nearly annulled or even reversed in direc- tion by slight differences in the condition of the poles. These difficul- ties of the method are, however, more than counterbalanced by its rapidity and delicacy when proper precautions are taken. Xearly thirty substances were tested in the manner previously de- scribed; but comparatively few of them gave very decided effects with the magnet, though, as later experiments have shown, the protective action is a general one. The substances first tried were as follows. The table shows the various acids and salts tried, and their effects as shown by the original apparatus: Substances. Effect due to Magnet. Notes. Nitric acid Sulphuric " Hydrochloric acid. Acetic Formic Oxalic Tartaric Chromic Perchloric Chloric Bromic Phosphoric Permanganic Chlorine water Bromine (l Iodine " Copper sulphate " nitrate " acetate " chloride " tartrate Mercuric bromide " chloride Mercurous nitrate Ferric chloride Silver nitrate Platinum tetrachloride. Strong. Little or none. n None. Some effect. K None. Slight effect. Decided " Some. Slight. Some. Decided. Some. Always powerful protective throw. Does not act very readily on the iron. Sometimes quite distinct throw, irregular. Much less marked than with chromic. Hardly any effect on iron. More than with perchloric. Mainly showing as throw, on breaking. Throw, on breaking. Very slight solution, weak. Mainly as throw on breaking, [breaking. Both protective throw, and sometimes on Action very irregular. 246 HEXKY A. EOWLAND Several things are worthy of note in this 'list. In the first place those solutions of metallic salts which are precipitated by iron all show distinct signs of protective action when the current is passed through the magnet. Of the various acids this is not generally true ; only those show the magnetic effect, which act on iron without the evolution of hydrogen, and are powerful oxidizing agents. In general, substances which acted without the evolution of hydrogen gave an effect with the magnet. From these experiments it was quite evident that the protective action, whatever its cause, was more general than at first appeared and steps were next taken to extend it to the other magnetic metals. Small bars were made of nickel and cobalt and tried in the same manner as before. These metals are acted on but very slightly by most acids, and the range of substances which could be used was therefore very small, but all the substances which gave the magnetic effects with iron poles gave a precisely similar, though much smaller effect, whenever they were capable of acting at all on the nickel and cobalt. This was notably the case with nitric acid, bromine water, chlorine water, and platinum tetrachloride, which were the substances acting readily on the metals in question. Even with these powerful agents, however, the magnetic action was very much less than with iron, and experimentation on metals even more weakly magnetic was evidently hopeless. As a preliminary step toward ascertaining the cause* of the magnetic action and its non-appearance where the active substance evolved hydro- gen, it now became necessary to discover and if possible eliminate the cause of the reversal of the current which regularly followed the protec- tive throw. Experiments soon showed that it could not be ascribed to accumulation of decomposition products around the electrodes, and polarization, while it could readily neutralize the original deflection, could not reverse its direction. Whatever the cause, it was one which did not act with any great regularity, and it was soon found that stirring the liquid while the magnet was on, uniformly produced the effect ob- served. Since one pole was simply exposed over a small portion of its side while the other had a sharp projecting point, it was the latter which was most freely attacked when there were currents in the liquid, whether these were stirred up artificially or were produced by the change in gal- vanic action due to the presence of the magnet. AVhen the poles were placed in fine sand saturated with acid this reversing action was much diminished, and in fact anything which tended to hinder free circulation of the liquid produced the same effect. Several materials were tried and .Acxiox OF A MAGNET ox CHEMICAL ACTION 247 of these the most successful was an acidulated gelatine which was allowed to harden around the poles. In this case the protective throw was not nearly as large as in the free acid, since the electrodes tended to become polarized while the gelatine was hardening, and only weakly acid gelatine would harden at all; but the reversing action completely disappeared, so that, when the magnet was put on, a permanent deflec- tion was produced instead of a transitory throw. This point being cleared up attention was next turned to the negative results obtained with acids which attack iron with evolution of hydro- gen. The galvanometer was made much more sensitive and removed from any possible disturbing action due to the magnet; and with these precautions the original experiments were repeated, it seeming probable that even if the magnetic effect were virtually annulled by the hydrogen evolved, some residual effect might be observed. This residual effect was soon detected, first with hydrobromic acid, and then with hydrochloric, hydriodic, sulphuric and others. The strongest observed effect was with hydriodic acid, but as this may pos- sibly have contained traces of free iodine it may be regarded as some- what doubtful. The effect in all these cases was very small, and though now and then suspected in the previous work, could not have been definitely determined, much less measured. Some rough measurements were made on the electromotive forces involved in this class of phenomena by getting the throw of the galvano- meter for various small known values of the E. M. F. The values found varied greatly, ranging from less than 0-0001 volt in case of the acids evolving hydrogen, up to 0-02 or 0-03 volts with nitric acid and certain salts. These were the changes produced by the magnet, while the initial electromotive forces normally existing between the poles would be, roughly speaking, from 0-0001 to nearly 0-05 volts, never disappear- ing and rarely reaching the latter figure. From these experiments it therefore appears that the protective action of the magnetic field is general, extending to all substances which act chemically on the magnetic metals. While this is so, the strongest effect is obtained with those substances which act without the evolution of hydrogen. But the series is really quite continuous, perchloric acid for instance producing but little more effect than hydrobromic, while this in turn differs less from perchloric than from an acid like acetic. It seems probable that the action of the hydrogen evolved is partially to shield the pole at which it is evolved, and lessen the difference be- tween the poles produced by the magnet. It probably acts merely 248 HENRY A. BOWLAND mechanically, for it is to be noted that those acids which evolve a gas other than hydrogen (perchloric acid, for instance), which is not ab- sorbed by the water, tend to produce little magnetic effect compared with those which act without the evolution of any gas. As to the actual cause of the protective action exercised by the mag- netic field, all these experiments go to show that it is quite independent of the substance acting, with the exception above noted, and is probably due to the attractive action of the magnet on the magnetic metals forming the poles subjected to chemical action, as we have before explained. In the first place, whenever iron is acted upon chemically in a mag- netic field those portions of it about which the magnetic force varies most rapidly are very noticeably protected, and this protection as nearly as can be judged varies very nearly with the above quantity. Wherever there is a point there is almost complete protection, and wherever there is a flat surface, no matter in how strong a field, it is attacked freely. Whenever in the course of the action there is a point formed, the above condition is satisfied and protection at once appears. Thus, in the steel bars experimented on, whenever the acid reached a spot slightly harder than the surrounding portions it produced a little elevation from which the lines of force diverged, and still further shielding it produced a ridge or point, sharp as if cut with a minute chisel. Mckel and cobalt tend to act like iron, though they are attacked with such diffi- culty that the phenomena are much less strongly marked. With the non-magnetic metals they are completely absent. Now, turning to the experiments with the wires connected with a galvanometer, the same facts appear in a slightly different form. When the poles were placed perpendicular to the lines of force instead of parallel to them, the magnet produced no effect whatever, showing, first, that the effect previously observed depended not merely on the existence of magnetic force but on its relation to the poles, and, sec- ondly, that when the poles were so placed as to produce little deflection of the lines of force the protective effect disappeared. When the pointed pole was blunted the effect practically disappeared, the poles remaining parallel to the lines of force, and when plates were substituted for the wires no effect was produced in any position, show- ing that the phenomena were not due to the directions of magnetization but to the nature of the field at the exposed points. In short, whatever the shape or arrangement of the exposed surfaces, if at any point or points the rate of variation of the square of the magnetic force is ACTION OF A MAGNET ox CHEMICAL ACTION 249 greater than elsewhere, such points will be protected, while if the force is sensibly constant over the surfaces exposed there will be no protection at any point. With all the forms of experimentation tried this law held without exception. It therefore appears that the particles of magnetic material on which the chemical action could take place are governed by the general law of magnetic attraction and are held in place against chemical energy precisely as they would be held against purely mechanical force. To sum up: When the magnetic metals are exposed to chemical action in a magnetic field such action is decreased or arrested at any points where the rate of variation of the square of the magnetic force tends toward a maximum. It is quite clear that the above law expresses the facts thus far obtained, and while in any given case the action of the magnet is often complicated by subsidiary effects due to currents or by-products, the mechanical laws of motion of particles in a magnetic field hold here as elsewhere and cause the chemical action to be confined to those points where the magnetic force is comparatively uniform. The effect of currents set up in the liquid during the action of the magnet cannot be disregarded especially in such experiments as those of Xichols (this Journal, xxxi, 272, 1886) where the material acted on was powdered iron and the disturbances produced by the magnet would be particularly potent. The recent experiments of Colardeau (Journal de Physique, March, 1887) while perhaps neglecting the question of direct protection of the poles, have furnished additional proof of the purely mechanical action of the magnet by reproducing some of the characteristic phenomena where chemical action was eliminated and the only forces acting were the ordinary magnetic attractions. An attempt was made to reverse the magnetic action, i. e. to deposit iron in a magnetic field and increase its deposition where there was a sharp pole immediately behind the plate on which the iron was being deposited. This attempt failed. The action was very irregular and the results not decisive. The question of stirring effect was also examined. Usually stirring the liquid about one pole increased the action on that pole, but sometimes produced little effect or even decreased it. This however is in entire agreement with the irregular action sometimes observed in the case of the after-effect in the original experiments. An excellent method of experiment is to imbed an iron point in wax leaving the minute point exposed: imbed a flat plate also in wax and expose a point in its centre. Place the point opposite to the plate, but 250 HENRY A. EOWLAND not too near and place in the liquid between the poles of a magnet and attach to the galvanometer as before. There is a wide field for experiment in the direction indicated above, for it is certainly very curious that the effect varies so much. If hydro- gen were as magnetic as iron, of course acids which liberated it would have no action. But it is useless to theorize blindly without further experiment; and we are drawn off by other fields of research. In this Journal for 1886, (1. c.) Professor E. L. Nichols has investi- gated the action of acids on iron in a magnetic field. He remarks that the dissolving of iron in a magnetic field is the same as removing it to an infinite distance and hence the amount of heat generated by the reaction should differ when this takes place within or without the magnetic field. Had he calculated this amount of heat due to the work of withdrawing it from the field, he would probably have found his method of experiment entirely too rough to show the difference, for it must be very small. He has not given the data, however, for us to make the calculation. The results of the experiments were inconclu- sive as to whether there was greater or less heat generated in the field than without. In the same Journal for December, 1887, he describes experiments on the action of the magnet on the passive state of iron in the magnetic field. In a note to this paper and in another paper in this Journal for April, 1888, he describes an experiment similar to the one in this paper but without our theory with regard to the action of points. Indeed he states that the ends of his bars acted like zinc, while the middle was like platinum, a conclusion directly opposite to ours. The reason of this difference has been shown in this paper to be probably due to the cur- rents set up in the liquid by the reaction of the magnet and the electric currents in the liquid. In conclusion we may remark that our results differ from Professor Nichols in this: First, we have given the exact mathematical theory of the action and have confirmed it by our experiments, having studied and avoided many sources of error, while Professor Nichols gives no theory and does not notice the action of points. Secondly, our experi- ments give a protective action to the points and ends of bars, while Professor Nichols thinks the reverse holds and that these are more easily dissolved than unmagnetized iron. 43 ON THE ELECTROMAGNETIC EFFECT OF CONVECTION- CURRENTS BY HENRY A. ROWLAND AND CABY T. HUTCHINSOX [Philosophical Magazine [5], XXVII, 445-460, 1889] The first to mention the probable existence of an effect of this kind was Faraday/ who says : " If a ball be electrified positively in the middle of a room and then be moved in any direction, effects will be produced as if a current in the same direction had existed." He was led to this conclusion by reasoning from the lines of force. Maxwell, writing presumably in 1872 or 1873, outlines an experi- ment, similar to the one now used, for the proof of this effect. The possibility of the magnetic action of convection-currents occurred to Professor Rowland in 1868, and is recorded in a note-book of that date. In his first experiments, made in Berlin in 1876, Prof. Rowland used a horizontal hard rubber disk, coated on both sides with gold, and revolving between two glass condenser-plates. Each coating of the disk formed a condenser with the side of the glass nearer it; the two sides of the disk were charged to the same potential. The needle was placed perpendicular to a radius, above the upper condenser-plate, and nearly over the edge of the disk. The diameter of the hard rubber disk was 21 cm., and the speed 61 per second. The needle system was entirely protected from direct electrostatic effect. On reversing the electrification, deflexions of from 5 to 7-5 mm. were obtained, after all precautions had been taken to guard against possible errors. Measurements were made, and the deflexions as calculated and observed agreed quite well; but it was not possible to make the measurements with as great accuracy as was desired, and hence the present experiment. Helmholtz, 2 in 1875 and later, carried out some experiments bearing i Experimental Researches, vol. i, art. 1644. *Wiss. Abh. i, p. 778. 252 HEXRY A. EOWLAXD on this subject. According to the " potential theory " of electrody- namics which he wished to test, unclosed circuits existed. The end of one of these open circuits would exert an action on a close magnetic or electric circuit. So the following experiment was made by M. Schiller, 3 under his direction. A closed steel ring was uniformly magnetized, the magnetic axis coin- ciding with the mean circle of the ring. This was hung by a long fibre and placed in a closed metal case. A point attached to a Holtz machin.j was fixed near the box, and a brush-discharge was kept up from this point. If the point acted as a current-end, a deflexion would be ex pected, on the potential theory. No deflexion was observed, although the calculated deflexion was 23 scale-divisions. The inference is tha', either the potential theory is untrue, or else that there is no unclosed circuit in this case, i. e. that the convection-currents completing the circuit have an electromagnetic effect. Schiller's further work, not bearing directly upon convection-cur- rents, leads him to the conclusion that all circuits are closed, and that displacement-currents have an electromagnetic effect. Dr. Lecher is reported to have repeated Professor Eowland's experi- ment, with negative results. His paper has not been found. Rontgen* has discovered a similar action; he rotates a dielectric disk between the enlarged plates of a horizontal condenser and gets a de- flexion of his needle. He apparently guards against the possibility of this being due to a charge on his disk. A calculation of the force he measures shows it to be almost one-eighth of that in the Berlin experi- ment. His apparatus is not symmetrically arranged, the disk being much closer to the upper condenser-plate; the distances from the upper and lower plates are 0-14 and 0-25 cm. respectively. He uses a difference of potential corresponding to a spark-length of 0-3 cm. in air between balls of 2 cm. diameter, i. e. about 33 electrostatic units, equal to the sparking potential between plane surfaces : t 0-26 cm. The disk is an imperfect conductor, and altogether it does not seem clear, in spite of the precautions taken, that this is not diu- to convection-currents. In the Berlin apparatus, as stated above, the needle is near the edge of the disk; the magnetic effect produced is assumed to be proportional to the surface-density multiplied by the linear velocity; hence the force will be much greater at the edge of the disk than near the centre : but 3 Pogg. Ann. clix, p. 456. * Sitzb. d. Berl. Akad., Jan. 19, 1888. PLATE V ELECTROMAGNETIC AFFECT OF COXVECTIOX-CURREXTS 253 the iield will be more irregular, and so make accurate measurements more difficult. In the present apparatus a uniform field is secured by using two vertical disks rotating about horizontal axes in the same line; the needle sy.-tcin is placed between the disks, opposite their centres. The disk? are in the meridian; they are gilded on the faces turned towards the needle. Between the disks are placed two glass condenser-plates gilded on the surfaces near the disk; and between these glasses is the needle. The whole apparatus is symmetrical about the lower needle of the astatic system. Each disk is surrounded by a gilded hard rubber guard-plate in order to keep the density of the charge uniform at the edges. The guard- plates are provided with adjusting-screws to enable them to be put accurately in the plane of the disks; and the glass plates in turn have adjusting-screws for securing parallelism with the guard-plates. The glass was carefully chosen as being nearly plane. Disks, glass plates, and guard-plates all have radial scratches, to prevent conduction-cur- rents from circulating around the coatings. In the periphery of the disk are set eight brass studs which pene- trate radially for about 5 centim., then turning off at a right angle run parallel to the axis until they come out on the surface of the disks. They there make contact with the gold foil. Metal brushes set in the guard-plate bear on these studs, and in this way the disks are electrified. The figure (PI. V, Fig. 1) gives a vertical projection of the entire disk-apparatus : D D are the disks ; G G G G the guard-rings ; Y Y Y Y the condenser-plates ; R R R R hard rubber rings fitting on the should- ers A A; X X X X bearing-boxes for the axle; P P P P supporting- standards ; E E metal bases sliding in the bed B B, and held in any position by screws Z ; F F the bases carrying the glass plates, sliding in the same way as the others. S S S 8 are the adjusting-screws for the guard-plates, and 1 1 for the glass plates. L L L L are collars for catch- ing the oil from the bearings; C C, C' C' are speed-counters, C C gear with the axle, and C' C' with C C in the manner shown; each has 200 teeth, and speed-reading is taken every 40,000 revolutions. The needle system is enclosed in the brass tube T, ending in the larger cylindrical box in which are the mirror and upper needle. This is closed in by the conical mouth-piece Q, across the opening of which is ] daced a wire grating. The mirror is shown at M, the upper needle at y and the lower at N. The system is hung by a fibre-suspension about 30 "> part of the room. To determine H at the sine-galvanometer a metre brass circle is put around the sine-galvanometer, and the needle of the latter used as the needle of the tangent-galvanometer thus made. I- ing this tangent-glavanometer in connection with a Weber electro- dynamometer, H at the sine-galvanometer is measured. The charging was by a Holtz machine connected to a battery of six gallon Leyden jars. These latter are in circuit with a reversing-key, an electrostatic gauge, and the disks. The potential was measured by a large absolute electrometer; all previous observers have used spark-length between balls, with Thom- son's formula. Greater accuracy is claimed for this work, largely on this account. In this instrument the movable plate is at one end of a balance-arm, from the other end of which hangs, on knife-edges, a balance-pan. This movable plate is surrounded by a guard-ring. The lower plate is fixed by an insulating rod to a metal stem, which slides up and down in guides. The distances are read off on a scale on the metal stem. The zero reading is got by inserting a piece of plane parallel glass whose thickness has been measured. The lower plate and = Angle of deflexion of sine-galvanometer. 8 = Angle of deflexion of tangent-galvanometer. J = Change of zero-point on electrifying the disks = half the charge on reversing. * = Scale-reading for disk-galvanometer. w = Weight on pan of electrometer. D = Distance of glass plates and disks. ^ = Electrometer reading, z = Condenser distance. Force, in the direction of the axis, due to a circular current of radius c, at a distance x on the axis Strength of convection-current NT .'. total force due to the disk of radius c _ 4 ^ _ _- ~ ~V and for the two disks acting in the same direction, total force T_Q_2 Na A V A ' This gives the force on the lower needle. ELECTROMAGNETIC EFFECT OF CONVECTION-CURRENTS 257 Correction for the upper needle : Potential at any point due to a circular current, V'= Cldw, equals the solid angle subtended at the point by the circle Substituting the value of /, we have as the potential of the disk '* * a. 4.. .81 1M /_v 1.3...(2i-l) p /c\"l ( ; a.4...2Ha*+2) W J But and 8 p _' & ft .'. The force f _atc". \ ~^^ and for the two, where the sign of the entire expression has been changed, since the poles of the upper and lower needles are opposite. Or X_Q_ * Z? i or. ^. 17 258 HENRY A. KOWLAND Needle constant. The disk-galvanometer windings have in the same way, for the lower needle, the force due to current I in one turn For the four turns, X'=8-/<7. Upper needle. The force is got in the same way as for the disk, omit- ting the integration, i. e. we must multiply the general term of B by _ an d replace 2* by /. This gives CL V yfil.3...(a-l)2Y\ M p 1. " 2.4 ... at 7 W ^ / ' a replacing c, and p, r. For the total force, ,_8^/r p /av_ 3p /Y n l - - r 1 \~ \ J- f ^4 I ~ I T. p L w \^/ J or Forces acting on the needle system: Let M = moment of lower needle, Let M' = moment of upper needle, then Couple on lower needle due to field = H M sin 6, Couple on upper needle due to field = H'M' sintf. Total couple = (EM H'M') sin 6. Due to disk-galvanometer: Couple on lower needle = MX' cos 6, Couple on upper needle = M' X^' cos#. Total couple = { MX' + M'XJ }cos 6, = S7iI\MC + M'D \cos0. .: for equilibrium, S-I\MO + M'D\ cos 6 = \HM- H'M'} sin fl, or __ (HM- H'M'} tan e ELECTROMAGNETIC EFFECT OF CONVECTION-CURRENTS 259 n ]u-t But =, = 0-03 nearly, and -^ is approximately unity. . . I== (HM-H'_M^^ 8nM(C + Z>) or -f '- =. - 1 1 3 (say) . M tan o Similarly, for the revolving disks, = /? tan J. 8 , ^ ^ ^_ O'<- T^~ ' - < F /?. J For the sine-galvanometer: TT I = sin .: :-;^- : :. ;-;- ;- ->.-: ..._. ,' i -. | .,. i .. ,_ : ..-.-..^ -'--.; --.J.--.-7 I"' -> -;. -.- .-_; _- -.; . -. : ,. ,- [ogfid .'-. - ".- r ;.":-? ::". " . " " "r i~ -iriil " " : ; ~". "" !oin.bine<3 weigiit^ tnd dEctvartalK fontty it ins fbvnd Dest to limit its swing' to a -fa nna. OB. cadk aide of its normal posrtiwm. The mean of two meadin^R of the :;--,i- :-. - r -.: r.: ".:- -'-. - >..i:r ;omp up md the >ther lown. ---.- ;-.-: one r The ad justm - :~ ~ - :' the plates parallel to each 0>ther ami o^f the nwiainle vlate in the Diane of the ne knfflorw baiL vezy acennateljr ttnmeii and nickel pW**^ in which two bolls .-: : ---.-... ,.'-;-._-"--,- , - : /.-..- '-;;;.- -:'_ i be - ?rv IT - ;i . ,. r . .:._..: . .-. ., :'-"-.'- -.- -.-. - ,-^-.\ - wus made ITT two wires aftMrat -J^T ^^ dBanwteTy one of which was protruded -- . _-:- - -.., '-., .-. - - .'-,.: - .-- ,-. -- , --- . .-;-.-. - r .--:: - mm Bam niftaVav- -. : -':- -.-: :~- tntrodiBBBJ ri aaiitan nlni in iffiit Iftn iHimliii^i Tins eonld be efiected five times ^- - - . . - - : 7~- , ; . - -. ---.".;.'- -. - -.-,--.-.-. -. .;-.-,,;-; -^--. ini d py ^aiing in water, and the ckilioafadie capacities fiwmd to be 50-00 and 29-556 e-g. SL mniteiw :- .- V.~ 7 -i - : >;-:. 268 HENRY A. KOWLAND Galvanometer for Electrical Discharges. This was very carefully m- sulated by paper and then put in hot wax in a vacuum to extract the moisture and fill the spaces with wax. It had two coils, each of about 70 layers of 80 turns each of No. 36 silk covered copper wire. They were half again as large as the ordinary coils of a Thomson galvano- meter. The two coils were fixed on the two sides of a piece of vulcanite and the needle was surrounded on all sides by a metal box to protect it from the electrostatic action of the coils. A metal cone was attached to view the mirror through. The insulation was perfect with the quickest discharge. The constant was determined by comparison with the galvanometer described in this Journal, vol. xv, p. 334. The constant then given has recently been slightly altered. The values of its constant are By measurement of its coils 1832-24 By comparison with coils of electrodynamometer. . . . 1833-67 By comparison with single circle 1832-56 Giving these all equal weights, we have 1832-82 instead of 1833-19 as used before. The ratio of the new galvanometer constant to this old one was found by two comparisons to be 10-4167 10-4115 Mean, 10-4141 Hence we have G = 19087. Electrodynamometer. This was almost an exact copy of the instru- ment described in Maxwell's treatise on electricity except on a smaller scale. It was made very accurately of brass and was able to give very good results when carefully used. The strength of current is given by the formula - T ysin a where K is the moment of inertia of the suspended coil, t its time of vibration, a the reading of the head, and C a constant depending on the number of coils and their form. RATIO OF ELECTROMAGNETIC TO ELECTROSTATIC UNIT 269 LARGE COILS. Total number of windings 240 Depth of groove -84 cm. Width of groove -76 cm. Mean radius of coils 13-741 cm. Mean distance apart of coils 13-786 cm. SUSPENDED COILS. Total numher of windings 126 Depth of groove -41 cm. Width of groove -38 cm. Mean radius 2-760 cm. Mean distance apart 2-707 cm. These data give, by Maxwell's formulae, (7 = 0-006457. In order to be sure of this constant, I constructed a large tangent galvanometer with a circle 80 cm. diameter and the earth's magnetism was determined many times by passing the current from the electro- dynamometer through this instrument and also by means of the ordi- nary method with magnets. In this way the following values were found. Magnetic Electrical method. method. December 16, 1879 -19921 -19934 January 3, 1879 -19940 -19942 February 25, 1879 -19887 -19948 February 28, 1879 -19903 -19910 March 1, 1879 -19912 -19928 Mean -19912 -19933 which differ only about 1 in 1000 from each other. Hence we have for C: From calculation from coils -006457 From tangent galvanometer -006451 Mean -006454 c. g. s. units. The suspension was bifilar and no correction was found necessary for the torsion of the wire at the small angles used. 270 HENRY A. EOWLAND The method adopted for determining the moment of inertia of the suspended coil was that of passing a tube through its centre and placing weights at different distances along it. In this way was found K = 82Q-Q c. g. s. units. The use of the electrodynamometer in the experiment was to determine the horizontal intensity of the earth's magnetism at any instant in the position of the ballistic galvanometer. This method was necessary on account of the rapid changes of this quantity in an ordinary building 1 and also because a damping magnet, reducing the earth's field to about J its normal value, was used. For this purpose the ballistic galvano- meter was set up inside the large circle of 80 cm. diameter with one turn of wire and simultaneous readings of the electrodynamometer and needle of ballistic galvanometer were made. THEORY OF EXPERIMENT. We have for the potential v 8*? , , , /-[", , -00021 - * d ^w -- ed V w\ 1 H g For the magnetic intensity acting on the needle TT__ 2xnp"-c V 1C sin a *(p 2 + J 2 )itan? For the condenser charge Whence _ eGC (p^ + b^Z Nt i*l wd tan? P.. >* '"*V TV sin a 2 sin 0[_ ~ 2 but and 2 sin $0 = I * |~1 i f * Y ~| nearly. ML \ us J " So that finally = eGC _.__ - __ A=0; -0011; -0030; -0056; -0090 for 1, 2, 3, 4, 5 discharges as inves- tigated below. 1 This experiment was completed before the new physical laboratory was finished. EATIO or ELECTROMAGNETIC TO ELECTROSTATIC UNIT 271 -0002 .Frrrz -0013 for first ball of condenser and -0008 for other, as investi- gated below. I = correction for torsion of fibre = as it is eliminated. e = constant of electrometer = 17-221. Q = constant of ballistic galvanometer = 19087. p = radius of large circle = 42-105 cm. w = number of coils on circle = 1. c = constant of electrodynamometer = -006454. K =. moment of inertia of coil of electrodynamometer = 826 -6. b = distance of plane of large circle from needle 1-27. C = capacity of condenser = 50-069 or 29-556. D = distance of mirror from scale = 170-18 cm. w = weight in pan of balance. t = time of vibration of suspended coil. 7*= time of vibration of needle of ballistic galvanometer. ,3 = deflection of needle on scale when constant current is passed. a = reading of head of electrodynamometer when constant current is passed. o = swing caused by discharge of condenser. A = distance of plates of electrometer. IV = number of discharges from condenser. X = logarithmic decrement of needle. A = correction due to discharges not taking place in an instant. The principal correction, requiring investigation is A. Let the posi- tion and velocity of the needle be represented by x = v sin U and v = f b cos bt, where b = / 1. At equal periods of time t t , 2/ r 3t t , etc., let new impulses be given to the needle so that the velocity is increased by v at each of these times. The equations which will represent the position and velocity of the needle at any time are, then, 272 HENRY A. EOWLAND between and t t x =. a sin bt v = a b cos bt " t t and 2t t x = a' sin b(t + t'} v = a'b cos b(t + /') " 2^ and 3*, x = a" sin b(t + I") v = a"b cos b(t + t") At the times 0, t t , 2t,, etc., we must have x = v = a b a sin W, = a' sin *(*, + *') v + a b cos W, = a'b cos (/, + t ) a' sin &(2f, + t'} = a" sin b(2t, + t") v.a'b cos b(2t, + t") etc. = a"b cos *(3f, + J") etc. Whence we have the following series of equations to determine a', a", etc., and t', t", etc. a fi b* = 2 i 2 + v* + 2r a b cos U t \ sin b(t t + t'} = |? sinW, " 2 * 2 = a' 2 5 2 4- Vo 2 + 2y a'i cos b(2t, - t') ; sin b(2t t + t") = ^sin i(2/, + /') S^ + i!"); sin 4(3^ + /'")= sin J(3/ 4 + r') etc. etc. "When t, is small compared with the time of vibration of the magnet, we have very nearly t' \t t \ t" = i fl t'" = f t fl etc. a" = 2a \l + cos bt t ) = 4<(1 - t (W,) 2 ) fl'" -9a 2 (l-f(^) 2 ) a'"* = 16a \l-$(bt t y) a iv2 = 25a 2 (l 2 (&,)*) T2 = Whence a' = 2a (l - 4 (&,)') a" =3-/ (l -*(,)') a'" =K(1-|(*O*). a iT =5fl (l- (d/,)) Now a , a', a", a'" and a" are the values of 3 with 1, 2, 3, 4 and 5 discharges and a , 2a , 3a , 4a and 5a are the values provided the discharges were simultaneous. This correction is quite uncertain as the time, ,, is uncertain. In assuming that the impulses were equal we have not taken account of the angle at which the needle stands at the second and subsequent discharges, nor the magnetism induced in the needle under the same circumstances. One would diminish and the other would increase the EATIO OF ELECTROMAGNETIC TO ELECTROSTATIC UNIT 273 effect. I satisfied myself by suitable experiments that the error from this cause might be neglected. The method of experiment was as follows: The store of electricity was contained in a large battery of Leyden jars. This was attached to the electrometer. The reading of the potential was taken, the handle of the discharger was turned and the momentary swing observed and the potential again measured. The mean of the potentials ob- served, with a slight correction, was taken as the potential during the time of discharge. This correction came from the fact that the first reading was taken before the connection with the condenser was made. The first reading is thus too high by the ratio of the capacities of the condenser and battery and the mean reading by half as much. Hence we must multiply d by 1 F where F= -0013 for first ball of con- denser and -0008 for other. This will be the same for 1 or 5 dis- charges. From 10 to 20 observations of this sort constituted a set, and the mean value of -, which was calculated for each observation sepa- rately, was taken as the result of the series. Before and after each series the times of vibration, t and T, and the readings, /9 and a, were taken. The logarithmic decrement was ob- served almost daily. EE STILTS The table on the following page gives the results of all the observa- tions. These results can be separated according to the number of discharges as follows: 1. 300-59 300-17 296-72 297-84 298-90 298-57 299-05 300-80 296-56 2. 3. 4. 5. 298-37 295-73 296-43 296-50 298-61 296-40 297-24 296-37 297-43 298-75 301-82 297-38 297.78 298-66 295-02 296-87 300-19 296-75 295-22 296-31 298-80 298-48 297-26 29715 296-69 18 CO 1 fa to O . _ ^ O rH x2 CO to rH 1C t- "- 1 T*< to CO O5 t- CO T* . * ^" to X^ CQ ti t-s i- o * x"3 os t- t- ic >* co to co * os co os ..to * 00 O CO <* CO O */! O t- S CO O (M CO O I? CO OS to CO " rH O? w fa to ^ 00 xo CO K5 7J * 00 x tO 1C CO 1- O CO GO iC GOtor-i'rflt- Tj< COOt- x j CO t- rH . . . rH . . 35 IM i I CO O-^l GO to OS 1- . ._. *- -i . SJ SO rH 35 O 00 O CO T*< 1ft CO i lot- to O r-t ... . . . 35 O OJ * CO 2 -* OS 1C CO ___ffl t> * rH XO cc to co co o x to coosos :oos _ CNI 30torHT*ICO IM -*OOO ^J; 1C O -s 00 t- xlft OB CO 10 ifl CO X * ' * 35 S>1 O? CD OCO 35 to t- os o to o ^rH S ^ os to t- >o os t- CO CO 00 OS CO X> *.*- CO oo o ffi rti i i o ooco in oo ,-1 . . . . . . ^ . CO to COIMCO coco ._ ~* OOtolM-tlGO rH 1COOO ^J^ w w OS IM 0* CO 0-* O CO (M CO rH rH OS (M lO CO """' r-l * TjH CO t- XIC d 3 NIC *^ O x-v^ OS O I- 1C CO " O CO W K: Xi CO OS ^SJ 35 OOOS*-*-* Tj< <-iOCO rH O W CO CD 2 * OS 3 CD CO I- to 1C ^rH to cotoco coic i-_ t- coto -* O CO OS 35 CO CO . -< t- !M CO rH (35 IM t^ * X-JO ^ (M X.2 OS CO 00 * i-H O to co os os co co ^-<* ic OOl rH COOOO IM t- rH ... . . . 00 OS N 55 CD 31 * OS OOW-fr-i i-H COOCO rH to 1-1 o w co co |2 ^ os to co r ^ i i yt B fa S OS co Hl___S TK ^^ OS CO 00 -* CO Xu/5 (M CO CO O 00 CO CO X 00 t> OO5rt CO CO IM OO CO * ^CO -H ooo^Ttioo * rHot> to w . rH -^ , o O IM CO CO 2 * to co TO rl 8 ^ CO CO to 1C rH CO to CO O5 O5 CO rH ^.1 ** GOto-*-*rH (M IMOOO to CO rH ... . . . J^ OS 7 CO CO 2 M OS (M CO I__fi S C 1 CO ^_ O 00 >C ^ OS CO O 10 O t- CO CO 00 <*! 70 to .CD CO oo-*o wot- x N i-H ... . . . oo ON-* CO CI 2 OS to CO CQ * S *s co co ic to to o to co (M 35 ro w ^to oo OtoCO-*t- CD rHOOO CO O 0} . . . . -^ O 35 3 ) + A & sin (5 bt + ? s ) + and electromotive force E = B, sin bt + B 3 sin (3 bt + v'- 8 ) + B, sin ( 5 bt + *.',) + The energy transmitted is, then, per unit of time C'CE dt= r'cEd (bt) If n is the number of complete periods in the primary term, then b = 2;rn and the energy transmitted per second becomes \\.A 1 B 1 cos

, ^ = rR c In case the circuit r contains some self inductance, I, we can correct for it by the equation 302 HENRY A. EOWLAND 17. In methods 1 to 14 inclusive the concentric circles are the coils of the electro- dynamometer. Either one is the fixed coil and the other the hanging coil. Oblong figures are inductances and when near each other, are mutual inductances. A pair of cross lines is a condenser. ELECTRICAL MEASUREMENT BY ALTERNATING CURRENTS 303 Method 4- + fl,,)] [# ( R' R" Method 5. L, = [jy (r + R it ) + R"(R' A _ [fl, (^" c ' (R r + R") (R" + R Method 6. c O We can correct for self inductions, U, L" in the circuits R', R" by using the exact equation R'R"(r+R")(R+R')=--0 or approximately = (R+B) (R'^--^- -. + etc. Method 7. R,R 3 M 13 M l2 + b*\_L 3 M l2 -MrM [^J/ M - Jf.JfJ = For a coil containing three twisted wires, M 12 = M 1S = M 23 and the self inductions of the coils are also equal to each other and nearly equal to the mutual inductions. Put an extra self induction L 3 in R 3 and a capacity C 2 in R 2 . Replace L 3 by L -f- L 3 and L 2 by L and we 6 2 can write As L M is very small and can be readily known, the formula will give ^r When L M = we have Method 8. V M(M+ 1) = rR 2b* M* =~rR+(rR)' or V M(M L) = (rR)' 2b 2 LM rR (rR)' 304 HENRY A. EOWLAKD Placing a capacity in the circuit R, we have also b'M (M+ L) - %= rR In case the coil is wound with two or more twisted wires, M L is small and known. For two wires, M L is negative. For three wires, two in series against the third, M can be made nearly equal to 2L. Hence M, L and C can be determined absolutely, or C in terms of M or vice versa. To correct for the self induction, I, or r we have the exact equations If the condenser is put in r, we have T M or - = rR + VM(L-M} Method 9. MM-*, = R, or - VL'M + *=R I Making R" = co and r + R' = r we have - VL'M+ M or VUM- ^ t C Lr Taking two observations we can eliminate WL'M and we have Knowing L'M we can find C'. Throwing out C' (i. e., making it oo ) we can find WL'M in absolute measure : then put in C' and find its value as above. To correct for self induction in R /f we have for case R" = oo , the exact equation ELECTRICAL MEASUREMENT BY ALTERNATING CURRENTS 305 The correction, therefore, nearly vanishes for two twisted wires in a coil where U M = and C is taken out. Method 10. c c \_R,R" - R lt R'-\ \rlR' + R" + R,+ fl,,] + ( + R) (R" + ) \ This can be used in the same manner as 9 to which it readily reduces. But it is more general and always gives zero deflection when adjusted, however M is connected. To throw out (7 make it oo . Method 11. L M_ c L + M - M} (L- M} c For the upper equation the last term may be made small and the method may be useful for determining L M when c is known. Me'thod 8, however, is better for this. Method 12. L' = R+R' I ~ r Should the circuits R and r also have small self inductances, L and I, we can use the exact equation rR When L' and Z are approximately known, we can write the following, using the approximate value on the right side of the equation L'_ R+R'T, Lr L r , VLl , I ' r Taking out L' and putting a condenser, (7, in R we have For a condenser, R can be small or zero. 20 306 HENRY A,. BOWLAND Method 13. (A} \bL"- 1 ,,T - [R tl R'-R,R"'\ I [_ bC"_\ This determines capacities or self inductions in absolute value. As described above, mutual induction can also be determined by convert- ing it into self induction. Method Of course, in any of these equations, methods 13 or 14, L" is elimi- nated by making L" = or the condenser, C, is omitted by making C = oo. Method 15. / R'R- R'"R or ^- or - 5 2 Z 6 V/ R '" R '" R ~ R ' R " (^ " ' ~ '" '"-" C, L When ^ //; = oo we have A -fl'^y, (R" + R"') R"R l R" t _ ft, r> ^" r 7->"/ r> E>' E> T ^r/ - ^>/// ~ Ka> u ~f>rrt I 2i && **u\ b 2 L c" R^RtR'R,! ' R"R'" If we adjust by continuous current, we shall have R'"R I R'R tt = Q. For a condenser we can made R" = provided there is no electric absorption. In this case l} 2 L t C" is indeterminate and we can adjust to findw,. However, two simultaneous adjustments are required. But I have shown that the presence of electric absorption in a con- denser causes the same effect as a resistance in its circuit, the resist- ance, however, varying* with the period of the current. Hence R" must ELECTRICAL MEASUREMENT BY ALTERNATING CURRENTS 307 include this resistance. However, the value of R" will not affect the first adjustment much and so the method is easy to work. If it is sensitive enough it will be useful in measuring the electric absorption of condensers in terms of resistance. It has the advantage of being practically independent of the current period for ^ as it should be. For comparison of capacities the same simplification does not occur. Indeed the method is of very little value in this case, being sur- passed by 16. Method 16. (A) [R,R"-R l ,R'-\[W+r' + r"] + W[R l r"-r f RJ = t _ L, r C" ~ R,, + R tl ( W+ r'r + ") The first equation is satisfied by adjusting the Wheatstone bridge so as to make (R I R'R II R)=Q R/'-R l /=Q R l (R ll + r")-R ll (K + r')=Q That is R, -R' -^ R tl ~ ~R" ~ r" We can then adjust W with alternating currents. This is a very good method and easy of application but requires many resistances of known ratio. Many of these, however, may be equal without disad- vantage. A well known case is given by making r' and r" = 0. (B) By placing self inductions or condensers in R, and r" instead of the above we have the following or VL ,-" or L > - << L '' r '-" Wr + 1 or - or + VL 1"= FUP c" ") (Rfi'-RuR)* W(R/'-R ll r f ) W+R" Making R" = we have c" r " L , or - VLp" or -' = In case we adjust the bridge to R,W R'R /I = and a condenser 308 HENRY A. EOWLAJSTD is in r" so that we can make r" = 0, the value of l 2 L t c" will be inde- terminate and we can find J f by the adjustment of W alone. i C This is an excellent method, apparently, as only one adjustment is required. However, see the remarks on method 15. This present method r" = for is Anderson's with, however, alternating currents instead C of direct as in his. The other two values are imaginary in this case. Indeed the whole method, B, is only of special value for , as two adjustments are needed c for the others. Method 17. (A) TF=oo. 72=00 VML'= R t R" - R tl R L' By this method the self induction of the mutual induction coil is eliminated. But it is difficult to apply, as two resistances must be adjusted and the adjustment will only hold while the current period remains constant. The same remarks apply to B and C following. (B) R=>. ,+ R" + #] + (R + JB,) (R" M~ RW x> L' _ R (R + R, + R" + #) + (K + #,) (R" M~ RR tl Method 18. R t R" - R'R tl = L ' - i L R " a. R' + R" W'~ *"%, ~W^~ L' and M' belong to the same coil. By adjusting the Wheatstone bridge first, W can then be afterwards adjusted. ELECTRICAL MEASUREMENT BY ALTERNATING CURRENTS 309 To find the ratio for any other coil independent of the induction coil, TJ we can first find ^ as above. Then add L to the same circuit and we M L 4- L' can find ^, Whence we can get L. This seems a convenient jj method if it is sensitive enough, as the value of -jj, should be accurately jd known for the inductance standard. Method 19. 'l-M*} = S- [RR t -R"Rl L' _R' + RL'l-M*l ,,\_K + R. R'R^-R'R.jl , , ~ ~ ~~~ ~~ * M~ r r* \M This is useful in obtaining the constants of an induction standard. For twisted wires L'l M 2 should be nearly 0, depending, as it does, on the magnetic leakage between the coils, -^.is often known suffi- ciently nearly for substitution in the right hand member. It can, however, be found by reversing the inductance standard. Method 20. R'R tl - R'R, = W R L L' any value. In case of a standard inductance, M and L are known, especially when the wires are twisted. The method can then be used for determining any other inductance, L', and is very convenient for the purpose. R n and R t + R tl are first calculated from the inductance standard. The Wheatstone bridge is then adjusted and W varied until a balance is obtained. This balance is independent of the current period, as also in the next two methods. Method 21. R'R tl - R"R, = I _R' + R, L' _(K + Rp. L' _R + R ll ^M M -- ^^ ; Tt~ rR, T = ~^T~ This is Niven's method adapted to alternating currents. See re- marks to method 20. 310 HEXEY A. EOWLAXD Methods 20 and 21 are specially useful when one wishes to set up an apparatus for measuring self induction, as the resistances R', R", R t , R lt can be adjusted once for all in case of a given induction standard and only W or r need be varied afterwards. Method 22. L '1 = KA. M =R R"- ^ = R" (i This is Carey Foster's method adapted to alternating currents and changed by making R" finite instead of zero. The ratio of R' -f- R, to R t is computed from the known value of the induction standard. R" is then adjusted and C" obtained. In general the adjustment can be obtained by changing R t and R". The adjustment is independent of the current period. Method 23. "rJvA^r+s+n, m If we make R = we have tfmL' = rR t M^r+R' + R, m ~ r This method requires two simultaneous adjustments. M must also be greater than m. As M and L' belong to the same coil, we can con- sider this method as one for determining m in terms of the M and L' of some standard coil. The resistance, A, can be varied to test for, or even correct, the error due to electrostatic action between the wires of the induction standard. Method 2.L M t M'r" M'~r,( This is a good method for comparing standards. We first determine -^ for each coil by one of the previous methods. Then we can calcu- late ^ and adjust the other resistances to balance. It is independent of the period of the current and suitable for stand- ELECTRICAL MEASUREMENT BY ALTERNATING CURRENTS 311 ards of equal as well as of different values, as the mutual inductances can have any ratio to each other. For twisted wire coils r t = r' very nearly. See method 23 for the use of the resistance, A. Method 25. In Fig. 6 remove the shunt R' and self induction L. This method then depends upon the measurement of the angular deflection when a self induction or a capacity is put in the circuit of the small coil of the electrodynamometer and comparing this with the deflection, when the circuit only contains resistance. The resistance of the circuit, r, is supposed to be so great compared with R that the current in the main circuit remains practically un- altered during the change. There is also an error due to the mutual induction of the electro- dynamometer coils which vanishes when r is great. 'Z i r+R" L-j-- -grr-J These formulas assume that the deflection is proportional to 6. This assumption can be obviated by adjusting 6 = 6' when we have 1 W R" These can be further simplified by making R " R". The method thus becomes very easy to apply and capable of con- siderable accuracy. As the absolute determination depends on the current period, however, no great accuracy can be expected for absolute values except where this period is known and constant, a condition almost impossible to be obtained. The comparison of condensers or of inductances is, however, independent of the period and can be carried out, however variable the period, by means of a key to make the change instantaneously. Method 26. Similar results can be obtained by putting the condenser or induc- tance in R" instead of r, but the current through the electrodynamo- meter suspension is usually too great in this case unless r is enormous. We have in this case for equal deflections, 1 //r 7?" _ v 7?"\ ^ or PL'" = R" (R"+r) p r >'' where r, and R" are the resistances without condenser or self induction. 312 HENKY A. EOWLAND This is a very good method in many respects. For using 25 and 26, a key to make instantaneous change of connec- tions is almost necessary. To measure resistance by alternating currents, a Wheatstone bridge is often used with a telephone. I propose to increase the sensitiveness of the method by using my method of passing a strong current through the fixed coils of an electrodynamometer while the weaker testing current goes through the suspended system. Using non-inductive resistances, methods 10, 13 A, B, C, and 14 all reduce to proper ones. 10 or 14 is specially good and I have no doubt will be of great value for liquid resistances. The liquid resistances must, however, be properly designed to avoid polarization errors. The increase of accuracy over using the electrodynamometer in the usual manner is of the order of magnitude of 1000 times. Since writing the above I have tried some of the methods, especially 6 and 12, with much satisfaction. By the method 12, results to 1 in 1000 can be obtained. Eeplacing U by an equal coil, the ratio of the two, all other errors being eliminated, can be obtained to 1 in 10,000, or even more accurately. The main error to be guarded against in method 12, or any other where large inductances or resistances are included, arises from twist- ing the wires leading to these. The electrostatic action of the leads, or the twisted wire coils of an ordinary resistance box, may cause errors of several per cent. Using short small wire leads far apart, the error becomes very small. Method 6 is also very accurate, but the electric absorption of the condensers makes much accuracy impossible unless a series of experi- ments is made to determine the apparent resistance due to this cause. In method 12 I have not yet detected any error due to twisting the wires of coils I. However, the electrostatic action of twisted wire coils is immense and the warning against their use which I have given above has been well substantiated by experiment. Only in case of low resist- ances and low inductances or in cases like that just mentioned is it to be tolerated for a moment. Connecting two twisted wires in a coil in series with a resistance between them, I have almost neutralized the self induction, which was one henry for each coil or four henrys for them in series;! Altogether the results of experiment justify me in claiming that ELECTRICAL MEASUREMENT BY ALTERNATING CURRENTS 313 these methods will take a prominent place in electrical measurement, especially where fluid resistances, inductances and capacities are to be measured. They also seem to me to settle the question as to standard inductances or capacities, as inductances have a real constant which can now be compared to 1 in 10,000, at least. The new method of measuring liquid resistances with alternating currents allows a tube of quite pure water a meter long and 6 Tnm. diameter having a resistance of 10,000,000 ohms to be determined to 1 in 1000 or even 1 in 10,000. The current passing through the water is very small, being at least 500 times less than that required when the bridge is used in the ordinary way. Hence polarization scarcely enters at all. It is to be noted that all the methods 15 to 24 can be modified by passing the main current through one coil of the electrodynamometer and the branch current through the other. The deflection will then be zero for a more complicated relation than the ones given. If, however, one adjustment is known and made, the method gives the other equa- tion. Thus method 18 requires R t E" R'R II = Q. Hence, when this is satisfied we must have the other condition alone to be satisfied. Also in method 22, when we know the ratio of the self and mutual inductances in the coil, the resistances can be adjusted to satisfy one equation while the experiment will give the other and hence the capacity in terms of the inductances. Again, pass a current whose phase can be varied through one coil of the electrodynamometer, and the circuit to be tested through the other. Vary the adjustments of resistances until the deflection is zero, how- ever the phase of current through the first coil may be varied. The best methods to apply the first modification to are 15 A, 16 A and B, 18, 20, 21, 22 and 24. In these, either a Wheatstone bridge can be adjusted or the ratio of the self and mutual inductances in a given coil can be assumed as known and the resistances adjusted thereby. The value of this addition is in the increased accuracy and sensitive- ness of the method, an increase of more than one hundred fold being assured. As a standard I recommend two or three coils laid together with their inductances determined and not a condenser, even an air condenser. 62 ELECTEICAL MEASUREMENTS BT HENRY A. ROWLAND AND THOMAS DOBBIN PENNIMAN [American Journal of Science [4], VIII, 35-57, 1899] In a previous article * mention was made of some work then being carried on at the Johns Hopkins University to test the methods for the measurement and comparison of self -inductance, mutual inductance, and capacity there described. In the present paper, there will be given an account of the experi- ments performed with some of the methods described in the previous article, together with a method for the direct measurement of the effect of electric absorption in terms of resistance. The methods that were tried were 25, 26, 9, 3, 12 and 6. Description of the Electrodynamometer, Dynamos, Coils, Condensers, Resistances and Connections used in the Experiments Electrodynamometer. The electrodynamometer was one constructed at the University, having a sensitiveness, with the coils in series, of 1 scale division deflected for -0007 ampere. The hanging coil was made up of 240 turns of No. 34 copper wire B and S gauge. The coil was suspended by a bronze wire connected with one terminal of the coil. The other terminal of the coil was a loop of wire hanging from the bottom of the coil and attached to the side of the case; both the suspension and the loop were brought out to binding posts. The resistance of the coil with suspension was 21-7 ohms. The fixed coils were made up of 300 turns each of No. 30 B and S gauge copper wire. The coils were wound on cup-shaped metal forms and soaked in a preparation of wax. The form was then removed and the coils placed a radius apart as in the arrangement of Helmholtz. Dynamos. There were two dynamos used, a Westinghouse alter- nator, and a small alternating dynamo constructed at the University. Journal, iv, p. 429, December, 1897; Philosophical Magazine, January, 1898. ELECTRICAL MEASUREMENTS 315 The Westinghouse dynamo was one having 10 poles so that each revo- lution of the armature produced 5 complete periods. The period of this dynamo was determined by taking the time of 1000 revolutions of the armature. This was accomplished by having the armature make an electric connection with a bell every 200 revolutions and taking the time of 5 of these. The taking of the speed during every experiment gave more regular results, as the speed was constantly changing, the dynamo being run by the engine in the University power-house when it was subject to great change of load. This dynamo had a period of about 132 complete periods per second. For the production of a current of less period than that of the West- inghouse, the small alternator constructed at the University was used. This dynamo was run by a small continuous Sprague motor. The arma- ture of the small alternator consisted of 8 coils, which coils were fas- tened flat on a German silver plate, the plate revolving between 8 field pieces producing 4 poles. The object of having the coils of the arma- ture on a metal plate was to secure a nearly constant speed. The metal plate produced a load that varied as the velocity and due to induced currents in the plate. The varying load, depending on the velocity of the moving plate, produced a nearly constant speed, which rendered unnecessary the constant taking of the speed. When this dynamo was used, the speed was only determined two or three times during a series of readings or experiments. The average of these determinations was taken as the speed during the whole series of experiments under con- sideration. Coils. The coils whose inductances were determined were all made in the same way, being wound on a metal form and soaked in a prepa- ration of wax. When the wax was hard the metal form was removed. This enabled the coils to be placed close together, as their sides were flat and smooth. The coils all had the same internal and external diameter, but their width varied, that being determined by the number of turns that were desired. Coils. P v External diameter 35-46 cm., internal diameter 23-8 cm., was made up of about 1200 turns of No. 16 B and 8 gauge single covered cotton copper wire, roughly wound; the turns were not smooth; self-inductance as finally determined -566 henry. P 2 ., Same dimensions. Turns were put on evenly. The number of turns was 1300 of No. 16 B and 8 single covered cotton copper wire. Self-inductance -724 henry. A. Same internal and external diameters as P, but the width was 316 HENKY A. EOWLAND 4-3 cm. Number of turns 3700 No. 20 B and 8 gauge single covered cotton copper wire. Self -inductance as determined 5-30 henrys. BI B 2 . This coil was made by winding two wires in parallel and all four of the terminals brought out to binding posts. Thus the coils could be used as two single coils, when the coils will be denoted by the symbols B^ and B 2 as the case may be, or as a single coil, the coils 5 1 and B 2 being joined up in series or in parallel. The dimensions of the coils BI B 2 were the same as A. Each of the coils B^ and B 2 were made up of 1600 turns of No. 22 B and 8 single covered cotton copper wire. The self-inductance of these coils taken separately when com- pared with P, which was determined absolutely, was nearly 1 henry. On this account B was taken as being 1 henry, and the other coils were compared with it as a standard. C. Same dimensions as P 2 . Number of turns 1747 of No. 22 B and 8 single covered cotton copper wire. Self-inductance as determined 1-30 henrys. Condensers. 2 and 3. Two paraffined paper condensers that had a capacity of 2 and 3 microfarads respectively. Jd Troy. A -Jd microfarad standard mica condenser built by the Troy Electric Co. Jd Elliott. A -Jd microfarad standard mica condenser built by Elliott Bros. Resistances. The resistances used in the experiments were of two kinds, those wound with double wire so as to have no self-inductance, as the ordinary resistance box, and those wound on frames or cards which had some small self-inductance, but almost no electrostatic capacity. The resistances which had self-inductance are called open resistances to distinguish them from resistance boxes, and were of different kinds and dimensions. Sources of Error and Experimental Difficulties In all work with alternating currents there are two great sources of error that have to be guarded against. These are the errors that may arise from the inductance of one part of the apparatus on another, as, for example, the direct induction of a coil in the circuit on the coils of -the electrodynamometer, and the effect of the electrostatic capacity of the leads and connections. In connecting the coils great care had to be taken to avoid the effect of electrostatic action of the leads and connections. For if there was a current of very considerable magni- ELECTEICAL MEASUREMENTS 317 tude, the difference of potential between the terminals of the coil might be great. If the connections under these circumstances were made with double wire, as is customary, a great error was introduced due to the electrostatic capacity of the leads. The error was sometimes as much as 7 per cent (see method 24). This error could be shown to be due to the electrostatic action of the leads by shifting a resistance in circuit with the coil in question from one end of the double wire to the other . The effect of this was to still further increase the difference of potential between the leads, and this increased the error. Experi- ments of this character showed the necessity of using open leads and open resistances having little or no capacity in all cases in which the coils experimented on and the resistance boxes used in their determina- tion have a current of any considerable magnitude passing through them. In several of the following methods constancy of current was necessary. This was accomplished by various means that will be de- scribed in their actual application. METHODS The methods that were tried were 25, 26, 9, 3, 12 and 6 described in this Journal, December, 1897. 2 Method 25. Method of equal deflections. Absolute method for the determination of self-inductance or capacity in terms of electromagnetic units. In this method the hanging coil is shunted off the fixed coils circuit, and this with a non-inductive resistance in circuit with the hanging coils is made the same as that of a certain inductive resistance in cir- cuit with the hanging coil. The connections are made as in the Figs. 1, 2, where C e ibt , C r 1 e*' M +*i), C^^+W are currents. R, R', r, resist- ances. They represent the entire resistance of their respective branches. L represents self-inductance of the coil by which it is placed. The outer circle in Fig. 1 represents the fixed coils and the small circle the hanging coil of the electrodynamometer. In Fig. 2 the terminals of the fixed and hanging coils are represented by F and H. D is a revers- ing commutator. K is a key to send the current first through the inductive and then through the non-inductive resistance. & = Z-xn, n = complete alternations per sec. This is the general notation adopted throughout the article. 2 Phil. Mag., January, 1898. 318 HENEY A. ROWLAND The quantity to be found is C C^ cos^, which is proportional to the deflection of the hanging coil in the two positions of K. In one position FIG. 2. Therefore In the other position of K Therefore ELECTRICAL MEASUREMENTS 319 0=0, as is an angle whose tangent is , and (7 = nearly. In the case of equal deflection D = D' and therefore VD=(R'-R) (R+r} If capacity had been used in the place of self-inductance the formula would be If self-inductance and capacity were used in series The application of this formula to the measurement of self-induc- tance gave results that agreed to within the accuracy with which the period of the alternations could be determined. That is, the results agreed to within about 1 per cent. In the determination of L the resistance in circuit R was varied from the least possible resistance as determined by the coils up to 1000 ohms and more, and the self- inductance was determined under these various conditions. These results agreed among themselves, and were apparently independent of the resistance in circuit with it. In the application of this method to the determination of capacity, however, great trouble was encountered, as the capacity apparently varied both with the resistance in circuit with it and with the period. This variation was regular for each period, the value derived depending on the resistance in circuit. This irregu- larity of derived value of the capacity led to the investigation and development of Maxwell's formula on the effect of absorption, a neces- sary characteristic of heterogeneous substances. When the formula was deduced, as may be seen in the article already referred to, the absorption comes in as an added resistance, the resist- ance being constant for a given period. By an inspection of the results this was found to be the case. The finding of the resistance due to absorption in this method is one of approximation, but the values deduced compare very favorably with those determined by direct meas- urement, as will be seen later when various results are collected. In the actual experiments the condensers used were two paraffined paper condensers of about 2 and 3 microfarads. The currents used had different periods, as seen in the table following, where n = 133, 53-3, 31 -9 and 14. The process was to place in the condenser circuit a resistance R, and 320 HENEY A. EOWLAND then to move the key K back and forth until R' was found that gave the same deflection. D, Fig. 2, was now reversed and the process repeated. This was repeated with different values of R and n and the apparent capacity. This gave great variation of apparent capacity with different values of R, which should not be the case, and, therefore, gave a means of finding the resistance due to absorption or absorption resistance, as we will designate, by approximation. As the effect of absorption is a resistance it is possible to find what resistance, if added to R, will make all the values of the capacity as determined for the different values of R the same. Therefore it should be the same for any two values of R. Calling the two values of R in the two cases R % and J? 2 respectively and the two corresponding values of R', R^', and R%, and let A be the added resistance due to absorption, the capacity should be the same in the two cases, or + r) - (#- A _ - From this A is found for the period used. By doing this for a number of different values of R, the true value of A is approximated. A was thus found for the condensers 2 and 3 microfarads with different values of n. The calculations were again performed adding to the different values of R a constant resistance A. The capacity that was found when A is added to R is called the corrected capacity. In the table below are collected the corrected values of the capacities together with n and the resistance A. Capacity 4-94 4-96 4-96 4-64 microfarads. n 131-1 53-3 31-98 14- complete alternations. A '5-19 20-5 34-09 139-62 absorption resistance in ohms. The last value of the capacity seems 'to be an error, possibly one of calculation. However, the results seem to show a nearly constant capacity, but a resistance increasing rapidly with decrease of period, as Maxwell's formula shows. The constant value of the capacity remains to be explained. But in the above, determinations of absorption resistance are by approximation. Professor Eowland has, therefore, devised a method by which it can be measured directly. This method, with the results that have been derived by it, will now be given. ELECTEICAL MEASUBEMENTS 321 Method for the Direct Measurement of Absorption Resistance In a Wheatstone bridge (Fig. 3) let the resistance of the different arms be denoted by R,, R', R tl , R" and r. Let J^have in circuit a self-inductance L t and let r have in circuit with it a self-inductance. Let C, ibt be the current through R, and C ** + *) be the current through r when a periodic electromotive force is applied to a and d in the figure. Let C' be the current through R t , and C" be the current through r when there is a constant difference of potential between a and d. The ratio of the current in this case is c' R"R-R'R R (R" _ r(R' + R"} i i FIG. 3. R, \ R' b / n SA ,_ Kn a a v J r c / R" FIG. 4. When a periodic electromotive force is applied to a and d, the ratio of the currents in this case is __ C 1 ~ R (R >r +RJ + r (R~+~R') + ibl (R + R") Separating the real and imaginary parts o ,_ (R"R If now the fixed coils of the electrodynamometer are placed in the R, arm of the bridge, and the hanging coil is placed in cross connection of the bridge, as in Fig. 4, the different resistances may be adjusted 21 322 HENRY A. KOWLAXD until there is no deflection, in which case = 90 or cos<= 0, therefore (R"R t - RRJ [#' (R" + RJ + r (R' + R"}-] + VILfl' (R' + R"} = , R" (R + R") .'. R'R. = R'R.. - VIL. I J? f ( J?" i J? \ i /. / V i ZP"\ ' K \t T -tv.) -\- T (^JV + JK ) If in connection with L' a capacity C is added, the formula becomes, substituting for L /t L t j~- . (R'R' + .R") c J R' (R" + ) - r (R + R"} ' In most cases since I and L, are generally the self-inductances of the instruments the term & 2 1 L t can be neglected in comparison with - C and the equation becomes Tftt T> T>t -p , I R" (R 1 + R ) * - * + ~ FIG. 5. In this equation R, includes both the ohmic and the absorption resist- ance. The value of R, is determined in terms of known quantities, that is the resistance and 2 and C. It was not necessary that I and C should be exactly known as the last term in the equation above plays the part of a correction term, and is in all cases below small and in some cases negligible. The capacities that were used in the experi- ments were the 2 and 3 microfarads, the ^ microfarad Elliott condenser, and the microfarad Troy condenser. Experiments. The process of experimenting was to apply a periodic electromotive force to a and d, and to adjust the different resistances until there was no deflection of the coil in the same way as in the ordinary measurement of resistance on a Wheatstone bridge. The different resistances R', R", R n and r being known, the apparent value of the resistance R, was found, and knowing the ohmic resistance of the R, circuit, the absorption resistance appears as the difference. ELECTBICAL MEASUBEMENTS 323 Some interest lies not alone in that the method is applicable, but that it confirmed the supposition that absorption resistance acts as an ordi- nary ohmic resistance in series in the circuit. This was confirmed by the fact that when condensers were in series and in parallel, their absorption resistances acted under these conditions like ohmic resist- ances, being increased in the one case and decreased in the other, and in the right ratio. This agreement was not exact, as the absorption resistance was extremely sensitive both to change of period and change of temperature. The great sensitiveness to change of temperature was shown either by letting the current go through the condensers for a little time, or placing the condensers before a hot air flue; in either case after cooling, the absorption resistance returned to its original value. The cooling was very slow, as there was very little radiation from the condensers inclosed in wooden boxes. The results are now given for the condensers 2 and 3 microfarads. In the calculation of the results the last term of the equation, that is 7 ry> f nr , , , ^- - - condensers 2 and 3 microfarads were used. has been left out, as it was very small when CONDENSERS 2 AND 3 MICROFARADS IN PARALLEL. =134, Z=-0007 .-. last term negligible. R" R y/ r R' R/ Resis. of R' circuit in ohms. Resistance due to absorption. 422- 6 488-6 5457-3 347 9 39-29 33 77 5-30 1488- 6 488-2 123 4 40-50 6-73 984- 1 82 1 40-72 33 81 6-91 2671- 6 22 5 41-116 | 7-30 423- 357 3 41-237 7-42 5474- 3 464 5 41-42 i 7-61 6734- 374 9 41-67 7-86 1 ohm in R"=f scale divisi n. i 7486- 638 6 41-64 i 7-83 9466- 81 15 41-85 i 8-04 Condensers 2 and 3 placed before the register and heated for 1 hour : 7489-7 488-27 713-8 46-534 34-33 12-20 After standing 1 hours in air at temperature of 12 -2 C. condenser has been open so that resistances have been cooled: 1240-5 487-8 109- 42-86 34- 8-86 After standing some little time: 7482-5 487-8 " 651-6 42-47 34- 8-49 The above table shows conclusively the heating of the condenser by the current, and the dependence of the absorption upon the temper- ature. K" R// R, r R, 348-5 488-6 396-3 11020-7 55-61 7488- it 849-2 u 55-41 (i (i 844-1 4026- 55-07 3485- u 396-1 u 55-58 324 HENRY A. ROWLAND CONDENSERS 2 AND 3 IN PARALLEL. N=57-6. R, in ohms. A. 33-77 21-84 " 21-64 21-30 21-81 Average, 21-63 N=56-6 per second. 3485- 200-24 976-7 4026- 56-00 22-23 Comparing these values with those found in the use of method 25 the agreement is at once apparent. N= _ 134- 131- _ 57-6 _ 56-6 _ 53- Method 25 _ 5-19 20-5 Direct measure- 5-30 cold 21-63 22-23 ment. 7-00 warm It should be remembered, in comparing the results, that the values obtained by method 25 would naturally be smaller than those found by direct measurement, as in method 25 the current going through the condensers was extremely small; there was therefore practically no heating. The experiments that confirm the mathematical theory that the absorption resistance could be treated as ordinary ohmic resistance were performed with the two condensers, ^ Troy and ^ Elliott microfarad condensers. These are next given. In these results it was necessary to take into account, in the calcula- tion of the apparent value of R,, the last term of the equation, that is L R" (R' + R"} c R' $ Troy and ^ Elliott in series, 1 o'clock. Apparent Ohmic resist- Absorption value ance resistance R" R/, R' r ofR, of R, A. 4751-8 499-9 404-8 4754- 43-141 34-143 8-998 ^ Troy, 2 o'clock. 4750- 497 75 352-4 37-288 34-144 3-144 i Elliott, 2.45 o'clock. 4749-3 497-67 390-3 " 41-260 " 7-116 Troy and ^ Elliott in parallel, 4 o'clock. 4749-3 497-6 350-23 " 36-94 34-15 2-79 Troy and Elliott in series. 4748-5 497-55 418-15 " 44-612 34-12 10-492 ELECTRICAL MEASUREMENTS 325 Calculating what the absorption resistance should be for Troy and ^ Elliott in series, from the absorption resistances of the two con- densers when determined separately, it is equal to 10-26 ohms, which is greater than the first and less than the last value above, showing that the condensers were heating during the experiments. Calculating the absorption resistance of Troy and -J Elliott in parallel in the same way, it is equal to 2-209 ohms, which is less than the value afterwards obtained by experiment for the same reason. The method was shown not to be based on any false supposition, by substituting in place of the condenser a coil of known self-inductance. When this was done the value of R^ as calculated from the other resist- ances and the self-inductances should be the same as the actual ohmic resistance of the circuit. This was tried with two coils P 2 and A and the agreement was re- markably close, as seen in the next table. Coil P used in place of condenser in the E t circuit: Deduced value Actual value R" R,, R' r ofR, of R, 474-9 487-8 758-2 5457- 77-86 77-8 Coil A in place of condenser in the R, circuit: 474-9 487-8 218-3 " 224-12 223-9 In these experiments great care was taken that the measurements of the resistances were performed immediately after the adjustment. In this way the actual resistances at the time of the experiment were obtained, and so the effect of the heating by the current was some- what eliminated. Methods 26, 9 and 3 give good results, but the methods that gave the most satisfaction were methods 12 and 6, method 12 being for the comparison of two self-inductances and method 6 for the comparison of a self-inductance with a capacity. These give some remarkable results, the theory and deductions of the methods being as follows : Method 12. Zero Method for the Comparison of two 8 elf -Inductances Let the connections be made as in the figure where the hanging coil and the fixed coils are in two distinct circuits. Let CH + ibL" The current in the E circuit is = (7 e t. Substituting the value of C" e fbt in equation (1) and simplifying, it becomes "r ibL"r FIG. 6. Therefore the deflection is proportional to cos ($, 0,) = (7|~ and the condition for zero deflection is - VLMR'r + VL"Mr(R+r) = 0, L _R+r The condition therefore of zero deflection is independent of M . But M is one of the factors of the electromotive force in the R" circuit, and on it therefore depends the sensitiveness, as it determines the current through the R" circuit. In the first figures of this method the fixed coils are in the R" circuit, and the hanging coil in the R circuit, but this is not necessary, as the fixed and hanging coils can be reversed. The choice of which of the above arrangements should be used depends ELECTEICAL MEASUREMENTS 327 on the impedances of the two circuits, as other things being equal the smaller current should go through the hanging coil. Experiments. The coils used in the experiments were coils P lf P 2 , C, B 1} B 2 , and A, which coils are described on page 315. From the dimensions of P 2 and its self-inductance as found by method 25, B t was designed to have a self-inductance of one henry. This will be shown to be nearly the case. For ease of comparison B 1 has been taken in the calculations of the results as being equal to one henry, and the other coils were compared with this coil as a standard. In these experiments the connections were made as in the figure 7, the coil BI that was taken as the standard being placed in circuit with the fixed coils of the electrodynamometer as L" and the resistance of this circuit was unaltered during the experiments in any particular series. The coils whose self-inductances were to be determined were placed in the hanging coil circuit and the resistance R was changed until there was no deflection. The resistance of the two circuits, R" and R -{- r were then measured by a Wheatstone bridge. The resistance r was in all cases small in order that (7 ibt should be large, and therefore by induction <7 1 *< M +*> the current through the fixed coils was made large and the instrument sensitive. The method 328 HENRY A. KOWLAND being very accurate, as will be seen later, great care had to be used to eliminate all sources of error, as for example, electrostatic action. In the first trial of the method small differences were noticed in the ratio of two self-inductances, depending both on the resistances used, and also on the connections of the coils, whether the leads were double, single, long or short. The same variation was noticed when several coils were joined in series and compared with another coil, and when these coils were compared separately and their sum taken. This irregularity led to an investigation of the effects of various resistances and connections in one of the circuits, the other circuit being unaltered. A little farther on, the variation in the deduced value of the self -inductance of one of the coils, when different resistances and leads were used, will be given, which variation was caused by the electrostatic action of the connections, etc. (Page 316.) The necessity of eliminating electrostatic action made obligatory the use of open resistances which had small self-inductances. These re- sistances were of three kinds resistances in the form of spirals, resist- ances wound on thin strips of micanite or paper, and those wound on open frames; see page 316. The self-inductance of the first and second classes of resistances was very small, as in one case there were only a few turns, and in the other the cross-section was very small. The third class were those wound on frames whose self-inductances were calculated. There were several resistances of 2000 ohms each, whose self -inductances were -0000436 henry, which would hardly affect the phase of the current or the impedance of the circuit. These coils were subdivided into resistances of various amounts. Another frame resistance used was of 7463 ohms divided into parts of about 250 ohms each. The self-inductance of the entire 7463 ohms was -000105 henry. As the open resistances were not divided into small amounts it was necessary to use resistance boxes for adjustment; as few ohms as possi- ble were used in each case. From the fact that the coils of the electrodynamometer had self- inductance a correction was introduced in order that the ratio of the resistances should give the ratio of the self-inductances of the coils direct. The value of this correction in ohms was calculated as follows: ELECTRICAL MEASUREMENTS 329 Calculation of Correction Due to Fixed and Hanging Coils Self-inductance of fixed coils =f= *0164 henry " " " hanging coil h = -0007 " Correction due to fixed coils. From an inspection of the tables it is seen that L R+r L R + r 01 B,+f~ R" 1.0164 ~~~90T' rhere L is the self -inductance of some coil and R -\- r is the corre- sponding resistance. B, is taken as equal to 1 henry L R + r~ 902 ' But the comparison of L with B^ = 1 is wanted, therefore both numer- ator and denominator of ~ ~ are divided by 1-0164 or yo . L \=B R+r 887-45 ' . L_ R + r B ~ 887-45 ' That is, the self-inductance of -0164 henry of the fixed coils produced a correction of 887-45 902 = 14-55 ohms, which must be applied to the R" circuit if the self-inductance of that circuit is to be considered as 1 henry. Correction due to hanging coil. The self-inductance = -0164 henry of the fixed coils gives a correction of * 14-55 ohms, therefore the self- inductance -0007 henry of the hanging coil gives a correction of -62 ohms to the R -\- r circuit. Applying these corrections, the results obtained for the several coils under various conditions are given below. The results are given in the following order. First. The values are calculated using double leads in the circuits but open resistances as far as possible. Second. The variation of the apparent value of the self-inductance of one of the coils with different positions of the coil, resistances, and different kinds of leads. Third. Short leads separated about 6 inches and crossed, used with all the coils except B^. Fourth. Open leads aad open resistances in the determinations. In the table R" was open resistance plus the resistance of coil B^ and fixed coils of instrument. R + r was made up of the small coil and open resistance plus the amount in the Queen ordinary resistance box. 330 HENRY A. KOWLAXD After all the inductive effect of the leads was removed and the ordi- nary resistance box used as little as possible, there was a different value obtained for the ratio of the self -inductances dependent on the position of the reversing commutator A'. With all the coils used the greater value occurred with the same position of A'. This was due to the electrostatic action between the coils B^ and B 2 , for if the terminals of the coil B 2 and the commutator A' were reversed at the same time, there was no change in the value of the ratio of the inductances. This showed that it was dependent on the coil itself and not on the leads and it could therefore not be eliminated. It is to be noticed that the values obtained for the lower number of alternations are always greater than those found with the higher number of alternations. This was caused by the electrostatic action of the turns of the coil on each other. In the case of the coil P 2 this effect would be caused by supposing a capacity of -0007 microfarads shunted across the terminals. The results are now given comparing the different coils with B^ as a standard and equal to 1 henry. DOUBLE LEADS OF BELL WIRE AND OPEN RESISTANCE r = 106 ohms, n = 45 complete periods per second. ". Correc. Coils. + C 901-6 -14-55 901-7 Cor- Aver- Com. Queen. R+r. rec. age. A'. Ratio. 887-05 292 2300 2 -62 2304-9 1 2-5983 310 2311 2 19 1158 3 1159-0 1 1-3099 22 1161 2 2 103 1659 1661-2 1 1-8727 109 1664 8 2 92 1800 2 1802-6 1 2-0288 99 1806 5 2 887-15 149 4776 5 4786-5 1 5-3956 196 4818 2 Current increased about 2 times. A + C 901 902 P, 141 4787 4781 3 1 5-3898 184 4807 2 887 05 211 5936 5958 3 1 6-7170 264 5982 2 51 6575 5 6602 5 1 7-4430 104 6631 2 887 45 158 4778 9 4795 25 1 5-4036 192 4813 2 183 1146 5 1146 7 1 1-9922 186 1148 5 2 7 643 15 642 67 1 7242 8 643 6 2 91 502 5 502 16 1 5658 503 1 2 ELECTRICAL MEASUREMENTS 331 DOUBLE LEADS. n=about 133 complete alternations per sec. Coils. R" Correc. Queen. R+r. P, 901-9 14-55 887-85 90 + s 500-4 u < 500-23 P., " 3 639-35 u " 4 639-6 A 901-87 887-32 ? 4742-2 " 133 4760-0 C 901-9 887-35 44 1151-4 44 1151-4 Cor- Aver- Coi rec. age. A' f-62 499-69 1 2 638-85 1 2 4750-48 1 2 1150-94 1 8 Ratio. 5631 7198 5-3537 1-2970 In the above determinations the coils were arranged in the way as indicated in the figure having leads of double bell wire. A SERIES OF DETERMINATIONS OF A UNDER VARIOUS CONDITIONS. Open resistance R on table (original position). Cor- Coils. R" Correc. Queen. R+r. rec. A 902-0 14-55 887-45 149 + s 4776-5 -62 " " " " 196 + s 4818- " " 901-95 " 887-4 ? 4783-5 " " " " " 190 + s 4808-5 " Open resistance E moved up to coil A (b^). Aver- Com. age. A'. Ratio. 4786-58 1 5-3936 2 4795-38 1 5-403 2 u " ? 4518- " 4517-38 2 5-0905 Open resistance E moved to the other side of A (& 2 ). 144 + s 4518- " 4518-88 1 5-0922 <( u u u ci 4521- " 2 Coil A placed in P x position and open resistance E restored to its position, and 159' of double wire added to the circuit. Cor- Aver- Com. Coils. R". Correc. Queen. R+r. rec. age. A'. Ratio. A 901-95 14-55 887-4 547- + 4129 -62 547 " 1 4676 583 + 4129 583 4712 4693-38 2 5-2888 Coil A at end of double wire 69' + 159' = 228' long. 607 + 4129 607 4736 634 + 4129 634 4763 New leads placed in B circuit, the wires were about 6" from each other. 332 HENRY A. EOWLAND Coils. R". Correc. Queen. R+7-, A 902-6 14-55 888-05 569+4129 " " 569 4698 594 + 4129 594 Open resistance placed next Coil A. 4723 663 + 4129 663 4292 Cor- Com. rec. Average. A'. Ratio. 4709-88 1 5-3088 2 4791-3 1 5-3956 4292- 2 7 0-6 In the following all connections were made with open leads, and open resistances were used. Pe- Cor- Aver- Com. riod. Coils. R" Correc. Queen. R+r. rec. age. A'. Ratio. 40 P, 902- -14-55 887- 46 90 + s 503 07 -62 502 71 1 5664 'i it it u u 90+s 503 6 M 2 133 it it u it 88 + s 522 53 ti 1 n 11 ti it u 88 + 8 502 15 501 72 2 5653 40 P Q 902 55 888 17 + s 644 3 u 1 M u it u u 18 + s 644 76 " 643 91 7251 133 it it 11 u 17+s 643 05 M 1 u it ii u 11 17 + s 643 1 " 642 45 2 7234 40 C 902-4 " 887- So 28 + s 1159 6 ti 1 it u " it ti 28 + s 1159 1 1158- 73 2 1-3050 133 ti it it u 24 + 8 1157 ii 1 ii tt M it it 26 + s 1158 8 " 1157 28 2 1-3034 40 C + PI 902- ' 887 45 105 + s 1658 8 it 1 ii it it I 11 110 + s 1664 1 1660 77 2 1-8713 133 it u 1 If 101+8 1656 7 ti 1 M it f- t II 106 + s 1660 3 " 1657 96 2 1 8683 40 C + P a 902-5 ' 887- 95 10 + 8 1803 u 1 'i tf it u u 12+8 1805 " 1803 3 2 2-0261 133 II it ti i< 8+8 1800 5 n 1 ii II 11 It 11 8 + 8 1800 2 " 1799 65 2 2-0221 40 PI + PS 902-4 " 887- 85 60 + s 2306 3 2307 98 1 2-5995 + c u 11 u u u I 2310 9 u 2 133 11 ii 11 11 56 + s 2304 1 2304 13 1 2-5951 ii II it tt u 57 + s 2305 4 tt 2 40 A 902-43 " 887- 88 85 + s 4703 ti 1 n it u II 11 106 + s 4724 2 " 4712 98 2 5-3080 133 it 902-4 " 887- 85 82 + 8 4704 2 it 1 u ti it 11 It 85 + s 4707 ii 4704 98 2 5-2991 40 A + C 902-35 887- 8 1146+s 9149 5 " 1 2M it 11 u u u 1227 + 8 9233 5 " 9190 88 2 10-3515 133 u 902-4 887- 85 1170 + s 9171 7 it 1 11 ti 11 u u 1194 + s 9191 7 9181 08 2 10-3395 40 A + C 902 35 " 887- 8 111+s 2550 9 ii 1 + 2M n u u it it 146 + 8 2556 4 2553 03 2 2-8716 133 u u u u 38+s 2548 7 u 1 11 u u u it 38 + s 2548 7 " 2548 08 2 2-8701 40 A + C 902 6 888-05 123 5852 ii 1 u 11 u ii if 169 5898 " 5880 13 2 6-6225 133 it u u u 134 5863 5 u 1 u it ii u u 140 5869 " 5865 63 2 6-6054 ELECTRICAL MEASUREMENTS 333 The above results show to what accuracy self-inductances of different values can be compared to each other, or to one of the self-inductances taken as a standard. The reason that the agreement between the different determinations is not greater than it is, even though the elec- trodynamometer was sensitive to a change of 1 part in 10000 in R -\- r, is that there was always some little heating of the resistances, and although they were measured in each determination on a Wheatstone bridge, still it was impossible to determine the exact resistance at the time that the experiment was made. This slight effect of the heating of the resistance would not enter in the comparison of two nearly equal self-inductances, that is the comparison of a coil with a standard. The accuracy of this comparison can be made to depend on the accuracy with which R -j- r can be determined for zero deflection, and this can be done to about 1 part in 10000. To do this, first the standard coil and the coil to be compared are substituted in turn in place of L in figure; they are thus compared separately to a third coil. But as the standard and the coil to be compared are nearly equal in self-inductance, the difference or self-inductance can be determined by the amount necessary to change R -\- r, and this change will be nearly independent of the slight heating of the resistances. To make a coil of the same self -inductance as the standard, the standard is placed in the R -\- r circuit and the value of R -\- r is found that produces no deflection. The coil to be compared is then substituted in place of the standard keeping R -)- r fixed, and the self-inductance of this coil is changed until there is no deflection, as in the case of the standard. The accuracy with which this can be done depends on the accuracy with which R -f- r can be set or 1 part in 10000. The method therefore gives a means of comparing and constructing coils to agree in self- inductance to within 1 part in 10000 with a standard. Method 6. Zero Method for the Comparison of 8 elf -Inductance with Capacity This method resembles method 12 and the connections are made as in the figures when both the hanging coil and fixed coils of the electro- dynamometer are shunted off the main circuit. Let the currents be denoted by C>>*, C^+M, (7 2 e*(W+W, O.eW+fc), and (7 4 itbt+ ~P O6, ). 1 + at + pt + + ^o) ^100 HQ + h lw A As the height of the barometer varies only very slightly during an experiment, the value of this expression is very nearly "100 "0 which does not depend on the absolute value of the scale divisions. But the best manner of testing a cathetometer is to take readings upon an accurate scale placed near the mercury columns to be meas- ured. I tried this with my instrument, and found that it agreed with the scale to within two or three one-hundredths of a millimeter, which was as near as I could read on such an object. In conclusion, every care was taken to eliminate the errors of this instrument, as the possibility of such errors was constantly present in my mind; and it is supposed that the instrumental errors did not amount to more than one or two one-hundredths of a millimeter on the mercury column. The proof of this will be shown in the results obtained. The Barometer This was of the form designed by Fortin, and was made by James Green of New York. The tube was 2-0 cm. diameter nearly on the outside, and about 1-7 cm. on the inside. The correction for capillarity is therefore almost inappreciable, especially as, when it remains con- 6 These amounted to less than -016mm. at any part. Ox THE MECHAXICAL EQUIVALENT OF HEAT 3f>3 stant, it is exactly eliminated from the equation. The depression for this diameter is about -08 mm., but depends upon the height of the meniscus. The height of the meniscus was generally about 1-3 mm.; but according as it was a rising or falling meniscus, it varied from 1-4 to 1-2 mm. These are the practical values of the variation, and would have been greater if the barometer had not been attached to the wall a little loosely, so as to have a slight motion when handled. Also in use the instrument was slightly tapped before reading. The varia- tion of the height of the meniscus from 1-2 to 1-4 mm. would affect the reading only to the extent of -01 to -02 mm. The only case where any correction for capillarity is needed is in finding the temperatures of the steam at the 100 point, and will then affect that temperature only to the extent of about 0-005. The scale of the instrument was very nearly standard at C., and was on brass. At the centre of the brass tube which surrounded the barometer, a thermometer was fixed, the bulb being surrounded by brass, and there- fore indicating the temperature of the brass tube. In order that it should also indicate the temperature of the barome- ter, the whole tube and thermometer were wrapped in cloth until a thickness of about 5 or 6 cm. was laid over the tube, a portion being displaced to read the thermometers. This wrapping of the barometer was very important, and only poor results were obtained before its use; and this is seen from the fact that 1 on the thermometer indi- cates a correction of -12 mm. on the barometer, and hence makes a difference of 0-04 on the air thermometer. As this is one of the most important sources of error, I have now devised means of almost entirely eliminating it, and making continual reading of the barometer unnecessary. This I intend doing by an artificial atmosphere, consisting of a large vessel of air in ice, and attached to the open tube of the manometer of the air thermometer. The Thermometers The standard thermometers used in my experiments are given in the following table on the next page. The calibration of the first four thermometers has been described. The calibration of the Kew standard was almost perfect, and no cor- rection was thought necessary. The scale divided on the tube was to half-degrees Fahrenheit; but as the 32 and 212 points were not cor- rect, it was in practice used as a thermometer with arbitrary divisions. 364 HEXKY A. EOWLAND "3 ^r >w rA t^, >.-^ S ^ ^ 00 Owner or Lender. Physical Laboratory, ohns Hopkins Universil 11 ii u u 11 II Prof. Barker, Univ. of Pennsylvania Chemical Laboratory, ohns Hopkins Universit rof. Gibbs, Harvard Co 11 11 Prof. Pickering, Harvard Observatory. Prof. Trowbridge, Harvard College. Physical Laboratory, ohns Hopkins Universit , W. Holman, Mass. Ins of Technology. pell calibrated, and sev OJ 03 13 B "3 3 J o ^ "** O> d CO S fl 03 pC] 'So h CO ^ *i ^ PH >-5 03 f- ffl .rH , " v ' r~- " v ' ^r~ 1 ^s 1 o a g *- ^A-a. ~\ d ,0 s a 03 o o] 8 2 , = CO CO rH ui t a o : , -^ CO rH ^ a > .2 " r r fl O w S A rH "5 i 1 ^ n } CJ " CJ E ( n HS u *w -*"V** i O ** rl V r d ^ If 8 ja A 03 s' vg * a | CO 1 S JM 4 ^ CO *^ ^ ci? ** TJ -* SH W ** 83 i m 1 'S O 03 CO 03 03 n 1 I a 1 filo bffto a *- Oi CO CO rH CO C35 O5 ^ >-H r*< DO * g . M 5 ^H * CO CO CO rH JO 4i -* o * W H) 0.0 ^H rH ^_ ^t rM O o> 03 ** 2 d *~ fc _.-.^-. T3 s ^ "3 o "S O 4? *~^ O t. Q ^5 pL| O ? t oi d d d ^ d OJ | a = 3 : w rH .t * - M S 2 3 j' ^ S d T-* o" o o' o* z * > U Y^ _2 *> M S r-**~-*-~- m 8*5 H O ft 000 O O O o o o O O CO H CO O O O ^ o rt a} ^ o ^* o * co CO O o O O rH r- 1 5 t -u ai "2 d ^i ^> j _l_ ^ ^ s > CQ bo fl O i "i o* O o o "p Q EC 1 M O o o 1 1 o * * Q 0> 1- M 1-1 O CO CO 75 rH CO (M rH O CO WO CO CM CO rH 4} P gj ^ 1 1 1 1 , ' <~ 1 1 ^ * ~ ** 1^ CD ~*~ E jf-o" ; S !fl"i -4-3 J2 "o & P-f d 2MB 03 woo tO tn in O CO JO CO 5 00 CO O O * rH rH CO CO *i V [O tj; *- J3 o ^.2 &3 ' -^ a _g PH ff 'S t- co in D CO CD g I h co co CO t- iO CO CO !> CO -* rH CO 0> 'S i^. a a S"S a os a 3 CO CO co 1-1 te D ^ CO CO 01 CO JO CO o ^ P< 03 9 0> CO W O '?^ 3 ON THE MECHANICAL EQUIVALENT OF HEAT 365 The interval between the and 100 points, as Welsh found it, was 180 -12, usinff barometer at 30 inches, or 180 -05 as corrected to 760 mm. of mercury. 8 At the present time it is 179 -68,* showing a change of 1 part in 486 in twenty-five years. This fact shows that the ordinary method of correcting for change of zero is not correct, and that the coefficient of expansion of glass changes with time. 10 I have not been able to find any reference to the kind of glass used in this thermometer. But in a report by Mr. Welsh we find a com- TABLE VI. COMPARISON BY WELSH, 1852. Mean of Kew Standards Nos. 4 and 14. Fastr6 231, Regnault. J Kew. Troughton and Simms (Royal Society). A Kew. 3200 3200 3200 38-71 38-72 +-01 38-70 01 45-04 45-03 01 45-03 01 49-96 49-96 00 49-96 00 55-34 55-37 + 03 55-34 00 60-07 60-05 02 60-06 01 65-39 65-41 + 02 65-36 03 69-93 69-95 + 02 69-93 00 74-69 74-69 | -00 74-72 + 03 80-05 80-06 + 01 80-14 + 09 85-30 85-33 + 03 85-44 + 14 90-50 90-51 + 01 90-56 + 06 95-26 95-24 02 95-40 + 14 101-77 101-77 00 101-94 + 15 109-16 109-15 -01 109-25 + 08 212-00 212-00 00 212-00 00 parison, made on March 19, 1852, of some of his thermometers with two other thermometers, one by Fastre, examined and approved by Eegnault, and the other by Troughton and Simms. The thermometer which I used was made a little more than a year after this; and it is 8 Boiling point, "Welsh, Aug. 17, 1853, 212 -17; barometer 30 in. Freezing point, " " " 32 -05. Boiling point, Rowland, June 22, 1878, 212 -46; barometer 760 mm. Freezing point, " " 32-78. The freezing point was taken before the boiling point in either case. 9 179 -70, as determined again in January, 1879. 10 The increase shown here is 1 in 80 nearly ! It is evidently connected with the change of zero ; for when glass has been heated to 100, the mean coefficient of ex- pansion between and 100 often changes as much as 1 in 50. Hence it is not strange that it should change 1 in 80 in twenty-five years. I believe this fact has been noticed in the case of standards of length. 366 HENRY A. ROWLAND reasonable to suppose that the glass was from the same source as the standards Nos. 4 and 14 there used. We also know that Regnault was consulted as to the methods, and that the apparatus for calibration was obtained under his direction. I reproduce the table on preceding page with some alterations, the principal one of which is the correction of the Troughton and Simms thermometers, so as to read correctly at 32 and 212, the calibration being assumed correct, but the divisions arbitrary. It is seen that the Kew standards and the Fastre agree perfectly, but that the Troughton and Simms standard stands above the Kew ther- mometers at 100 F. The Geissler standard was made by Geissler of Bonn, and its scale was on a piece of milk glass, enclosed in a tube with the stem. The calibration was fair, the greatest error being about 0-015 C., at 50 C.; but no correction for calibration was made, as the instrument was only used as a check for the other thermometers. 3. EESULTS OF COMPARISON Calculation of Air Thermometw This has already been described, and it only remains to discuss the formula and constants, and the accuracy with which the different, quantities must be known. The well-known formula for the air thermometer is ff-ft+4 m _J * V i - fl V\ 'l + a? "1 + 0* J Solving with reference 1 to T, and placing in a more convenient form, we have H-h' + *H-., T= - - _ nearlv, a A' _L_ __*_ v where ' and r = a = -00364. For the first bulb, v For the second bulb, v_ V ON THE MECHANICAL EQUIVALENT OF HEAT 367 To discuss the error of T due to errors in the constants, we must replace by its experimental value, seeing that it was determined with the same apparatus as that by which T was found. As it does not change very much, we may write approximately ^=100 H h I /H loo H\_b m H lw -bH\ ~m- r t\ From this formula we can obtain by differentiation the error in each of the quantities, which would make an error of one-tenth of one per cent in T. The values are for T = 40 nearly; = 20; H wo h = 270 mm. ; and h = 750 mm. If x is the variable, , dx *rp dx T _ 04 dx ~~dT ~oTT 1000 ~ ~dT ' TABLE VII. ERRORS PRODUCING AN ERROR IN T OF 1 IN 1000 AT 40 C. foinn ft bioo bioo-b H. f/ioo or h. JL a a a a ' 7> Jhnn i . OinnrO _ 4 , A bioo a a sani. a Absolute value, llmm. 27 mm. 005 00074 00087 0047 00087 Ax Relative value, 0-9 10 12 62 Ax X From this table it would seem that there should be no difficulty in determining the 40 point on the air thermometer to at least 1 in 2000; and experience has justified this result. The principal difficulty is in the determination of H, seeing that this includes errors in reading the barometer as well as the cathetometer. For this reason, as mentioned before, I have designed another instrument for future use, in which the barometer is nearly dispensed with by use of an artificial atmos- phere of constant pressure. The value of -^.does not seem to affect the result to any great extent; and if it was omitted altogether, the error would be only about 1 in 1000, assuming that the temperature t was the same at the determina- tion of the zero point, the 40 point, and the 100 point. It seldom varied much. The coefficient of expansion of the glass influences the result very slightly, especially if we know the difference of the mean coefficients 368 HENRY A. ROWLAND between and 100, and say 10 and -f 10. This difference I at first determined from Regnault's tables, but afterwards made a deter- mination of it, and have applied the correction. 11 The table given by Regnault is for one specimen of glass only; and I sought to better it by taking the expansion at 100 from the mean of the five specimens given by Regnault on p. 231 of the first volume of his Relation des Experiences, and reducing the numbers on page 237 in the same proportion. I thus found the values given in the second column of the following table. TABLE VIII. COEFFICIENT OF EXPANSION OF THE GLASS OF THE AIR THER- MOMETER, ACCORDING TO THE AIR THERMOMETER. Tempera- ture ac- cording to Air Ther- mometer. Values of b used for a first Calculation. b from Regnault's Table, Glass No. 5. Experimental Results. Apparent Coefficient of Expansion of Mercury. 5, using Regnault's Value for Mercury. 12 ft, using Recknagel's Value for Mercury. 13 b, using Wttllner's Value for Mercury. 14 20 40 60 80 100 0000252 0000253 0000256 0000259 0000262 0000264 0000263 0000264 0000267 0000270 0000273 0000276 00015410 00015395 00015391 0000254 0000258 0000261 .0000264 0000266 0000267 0000273 0000276 0000278 00015381 0000277 .0000277 0000287 The second column contains the values which I have used, and one of the last three columns contains my experimental results, the last being probably the best. The errors by the use of the second column compared with the last are as follows: TT i inr from using & 100 6 40 = -0000008 instead of -0000011; TD 3 r j r from using & 100 = -0000264 instead of -0000287; or, ^Vrr for both together. As the error is so small, I have not thought it worth while to entirely recalculate the tables, but have calculated a table of corrections (see opposite page), and have so corrected them. 11 This was determined by means of a large weight thermometer in which the mer- cury had been carefully boiled. The glass was from the same tube as that of the air thermometer, and they were cut from it within a few inches of each other. 12 Relations des Experiences, i, 328. 13 Fogg. Ann., cxiii, 135. "Experimental Physik, Wiillner, i, 67. ON THE MECHANICAL EQUIVALENT OF HEAT 369 T= T {1 + 373 (b( w - M - (273+ T}(V - b)\, T= T' {I .000858 + (273+7 v )(& b')\ t T= -99975 T approximately between and 40. The last is true within less than -j-gVir f a degree. The two bulbs of the air thermometer used were from the same piece of glass tubing, and consequently had nearly, if not quite, the same coefficient of expansion. In the reduction of the barometer and other mercurial columns to zero, the coefficient -000162 was used, seeing that all the scales were of brass. In the tables the readings of the thermometers are reduced to volumes of the tube from the tables of calibration, and they are cor- rected for the pressure of water, which increased their reading, except at 0, by about 0-01C. TABLE IX. TABLE OF CORRECTIONS. T T Correction. Calculated Temperature. Corrected Temperature. 10 9-9971 0029 20 19-9946 0054 30 29-9924 0076 40 39-9907 0093 50 49-9894 0106 60 59-9865 0135 80 79-9880 0120 100 100- The order of the readings was as follows in each observation: 1st, barometer; 2d, cathetometer; 3d, thermometers forward and backward; 4th, cathetometer; 5th, barometer, &c., repeating the same once or twice at each temperature. In the later observations, two series like the above were taken, and the water stirred between them. The following results were obtained at various times for the value of a with the first bulb : 0036664 0036670 0036658 0036664 0036676 Mean a = -00366664 24 370 HEXRY A. KOWLAXD obtained by using the coefficient- of expansion of glass -0000264: at 100, or a -0036698, using the coefficient -0000287. The thermometers Nos. 6163, 6165, 6166, were always taken out of the bath when the temperature of 40 was reached, except on Novem- ber 14, when they remained in throughout the whole experiment. The thermometer readings are reduced to volumes by the tables of calibration. TABLE X. IST SERIES, Nov. 14, 1877. Relative Weight. Air Thermometer. V 6163. V 6166. V 6167. Temperature by 6167. J 4 115-33 21-25 6-147 4 17 -1425 422-84 255-80 15-685 17-661 236 4 23 -793 534-71 341 05 19-157 24 -089 296 5 30 -582 653-49 431-71 22-833 30 896 314 2 38 -569 793 1 8 47-175 3 8 -93 5 366 2 51 -040 33-864 51 -320 280 4 59 -137 38-256 59 -452 315 The first four series, Tables X to XIII, were made with one bulb to the air thermometer. A new bulb was now made, whose capacity was 192-0 c. cm., that of the old being 201-98 c. cm. The value of L. for the new bulb was -0058. follows : June 8th June 22d June 25th ]\Iean The values of li' and a were obtained as 00366790 00366977 00366779 0036685 ft' 753-876 753-805 753-837 753-84 This value of is calculated with the old coefficient for glass. The new would have given -0036717. It now remains to determine from these experiments the most prob- able values of the constants in the formula, comparing the air with the mercurial thermometer. The formula is, as we have found, but I have generally used it in the following form: t=CV-f mt (100 /) (1 n (100 -f #)) , Ox THE MECHANICAL EQUIVALENT OF HEAT 371 N CO oo CO CO o; t- CO CD 71 CD OS OS CO I- OS CO CO rH 1C *3* 3 CO CO fij o CD o l> O O 00 rH O 00 rH CO O O CO -rfl t- 00 o >* oo o OS OS OS OO 1C OS CO CO OS 1C oo os CO 71 1 rH CO 00 05 OS CO O CO CD t- 1C * OS o CO 00 S : CO 6 -3 E o t- CO rH o I- CM OO rH o o 00 rH Tf< 1C o CO CO T>< I- 00 o 00 o OS OS o OS OS _o CM 1C r-i 00 t- rH CO O 1C CO 71 rH I- O rH t- rH CO O TjH CO CO CO 77 OS I '3 O O OO CO 00 OS rH CM * rH OS CM T* 1C CO CO "*1< t- 00 00 s ^g OO 7* 7* OO rH SM CO 00 OS to 77 -J} ~ 71 CO OS 1C CO 30 ^H O 1C 71 CO o o t- CO CO 00 t- t- CO o rH to CO rH rH iH rH OO 71 CM 00 71 * CO CO 1C rH 2 -,r -r -f . . |j OO CO CM t- OS o X CO Tt< CO rH CD l> CO o O ^JH * CO CO CO CO O Tjl O CO - 11 o' o CO rH o CM o o 00 rH o o o o OO rH * 1C o CO o o CO ^ l> 00 o 00 o OS OS OS O H OS O - ^ ! CO -* 00 CO OS t~ CO OS i rH o <* CO t- n w 1C .c 1C 1C 1C CO CD CO CO CO to t- ^ : ii o OS o 77 1C CO o ^* CO 1C CO 1C 30 O CO t- t- 00 3D 77 OS rH 77 rH (M CO *; CO ki < * * .C 1C 1C *_ OS CO 00 OS OS t- t- t- t- 71 CO O CO OS CO OS OS OS CO CO CO rH CO rH OS CO o 71 CD t- IC o t- iC 77 CO 00 CO rH CO 77 OS 77 rH 77 1 CO 77 CO CO CO o 1C OS CO * OS CO OS CO CO O rH CO rH O CO CO CD CO O o CO 00 ti CO CO t- OS 00 o 71 CO 71 CO 71 iC 00 30 1C 1C 00 CO 1C t- 00 00 00 00 rH OS CO 77 *f t* OS OS t- OS o 77 -H s III 00 -* 77 CO f- t- 1C t- 71 rH 1C o 00 00 O l- OO CO t- CM ID fl OS 1C o rH rH iff j> co 7 i CO rH 00 o * 1C 00 CO 00 O rn rH rH CO rfi rH rH t- O rH . 71 H O 77 CO 1 i |i? o o 2 CO 77 SM CO ^ 1C CO 77 CO OS CO 71 r- o O OS t- I life i- 7* I- I- ?i ^ 77 ! gl ?! - 1 O O 5 B-J5 "" it 77 CO 71 71 rH CO 77 77 - CO CO CO O o 372 HENKY A. EOWLAND 8^ s CD 00 CM 00 CD OS !! 10 00 90 OS IO HJa O 0> o o o o BcB o 00 CO OS 00 00 a^ rH CM CO CO 8 o rH O CO OS CO - CO IO OS IS 00 o rH OS CO OS OS 00 'S rH rH CM CO CO o T* -* t- l- CO o 00 CO ^ CO CO I 1 i 1 t" OS rWjB rH O OS cxt rH CM o to OS OS CO l- t- rH rH c\-> w * ; g 00 CO OS rH IO t- 1O 30 CO CO HI IO IO CO OS CO CO CO * K, S rH O rH OS ^ t- CM OS CO *fl( 1O CO t- t CO t> 00 , . rH fl CD ^ IO ^ 00 J-^ f^ co 00 IO~ el O rH 00 10 CM CO o IO o o t- oo CXI ^t SI oa O IO IO o o 00 rH o CO CM o OS o 00 CO o 00 CO ^ p fc 1 ?* OS 1-H rH OS IO CM CO CXI -4 rQ 1 CS rH CXI CO CD l- OS OS i-s N^ IO IO IO IO IO IO IO IO oT w w H i H ? CO * + o5 OS O OS O o 00 rH OS o CO CO ca P ^ CO CO ->TI i TtH * * "* * 3 !> H 1 I-H ^ rH T t- OS II OS HH OS OS CO ^ 00 CO M ft OS rH i CO CD -* o OS W rH ext CD * o rH OS i-5 OS pa < IO O CO CO oo rH OS CD CO 8 o -H 00 OS H 3 CO O CXt rfl CO t> 10 rH OS Ttl CO CO t- OS rH IO t- t- t- t- t- 00 00 00 00 o a> g-*^ 3 OS CO CD O5 t- OS 2> o S!D CO OS o Tt< rH CM S o J^. CXI O ^ -t! UH CM CO t- |3f rH 1 1 1 rH CO IO CD CO CO *H O II OJTJ CO rH OS CO o o 00 00 OS CO O5 00 CO 00 CO a 9 4* CO CO CM CM ct n CM CM 25 CO CO CD CD CO CD CO CO CO 11 g* _> jg 5 '3 ON THE MECHANICAL EQUIVALENT OF HEAT 373 1 , ; ; TH o OS CO to oo CNJ H OS o 00 00 a SB o o 00 TH o CO TH o IO o CO OS 04 o 00 CO o OS OS j> : ; to 10 iH CO TH TH t- IS IO CO TH CO >H oo + O 00 CO TH OS TH IO o CO o CO OS CO Os OS a o o IO O CO CO t- 00 00 CO o OS CO 1 1 t- OS TH OS F to 04 3* i fc-1 CO TH to 04 I- CO TH -H 1 10 t- co CO Os CO 1O 10 o -# to to CO to TH OS z> o "3 O t^5 * tO TH CO 50 I- IO to 5 CO Os l- TH 00 OS 04 iH 00 CO 2 CO ^ CO ^ TH rH e CO O4 co CO to o to TH l- ? ja TH 04 04 CO I- OS 04 Os O4 t- o O4 to 00 co TH to 00 Frt "a 1 ^ TH g o* t- iH O4 t- TH o Os TH 00 to O4 to 10 CO TH 04 00 TH : s ^ a "*" ? in" oo 4i Q> OS IO 00 0* * oo TH 04 IO O4 OS CO to IO o to IO oo o I IO o oo 00 O ft . M >? qj 03 - ^ ^ E^ fl n H W *H g O 3fl CO CO o t- t- O4 TH 00 TH o IO OS OS o CO CO OS O OS | y> *5 a o3 si T1 " rQ to 04 IO tO TH TH OS CO 04 to t- 1O CO Os l> OS o to CO CO I- 10 CO t- OS d OS TH CO o5 5 o hi - IO IO 10 IO IO IO 10 IO 10 10 t- o o o ^ * TX ^ * * * <* * TH <* < to -4* 1 o 2 oj oj "S 10 fe t- 00 ^1 CO CO 10 t- TH o l- 00 CO t- 10 i CO o to OS OS 04 t- o a to * s 1 co 1 o to to IH t- o CO 1O CO to t- CO t> o o TH 1 T 6 S CO o IO ;O CO H/l O OS Os CO OS 04 o oo 10 00 iO CO to 04 CO co CO CO to 00 TH CO SS 5 CO CO II II ^. Q ^ to s to to IO IO t- t- to to t- oo to o g to OS t- TH 00 CO to 04 00 CO 10 to o t- TH si g 10 iO t- t- IO t- t- IO IO t- o IO I- IO IO t- IO IO t- IO 10 IO IO t- IO IO IO IO t- z> 'S.SP M S en II CO 04 eo co * - . co CO . IO CO 374 HENRY A. ROWLAND ^S a" 1 o ' CM to O! iM CM CO 1C CO O5 to 1 : :+ + + + + + + + : fe" o i o o i o c O ; o CM o 1C o o Ifsjs o tf. to CO SB GO CO I- 55 o I- 1C I- o t- rH o o to CO o OS CO o O5 1C iffP o o o CM o CO cS iC 1C S to -f o o 00 o rH o o t- o o to CM 1-H CO O5 eo o S o 35 1C <*> . to t. iS o 1C CM rH o o 1C CM rH o CO CV c-. 35 1C GO CM j CM CO OS CO "C 35 1C "ill oo t- to 1-H 1C S rH 00 1C 0? to to o 2 00 00 to CO CO CO 1C CO l|s R CO CM ^ 00 Oi O CO iC 1C O5 5 1- 00 CO 5 CM 1C S to S o 00 05 00 CO o ct T? OS eo 5 O5 1-H CO 1C CM CM 05 CO 1-H o to 1C rH c CM CM CO CO CM CM 00 1C t- to to i-H 00 1 S 1C OS CO 1C 5 0) to o o l~ o CO OS c CO '. t- CM rH CO GO CO 1C 1C to 1C t- (H *H ^ rH o CO OS o to Oi CM to 1C d rH * GO oo o t- o ~f l- 00 iC 1C o o 00 o 1-H o 1-H o I- rH o o M o CO o 35 CO o c 1- o o 35 Ci rO Q 1 1 GO CM CO CO o CO GO w eo 1C o GO to 1C oo l- to O5 CM ^ to CO 1C 1C 1C 1C 1C 1C to to t - *i i * GO o eo 1C CO Oi CM It CO 00 GO to t- 35 30 0? to 3k 1 1C B t- S CO CO CO o* GO GO O5 o o o IN to 00 OS X CM CM to o i l- 1 1 to CM CO CO GO to 00 rH o CM 1C 1C to o* ta 1C 1-H GO rH to t- eo to 1C o GO 00 1C GO o CM oo oo 1C CM to CM o 3i I- 1-H r- t- o 00 l- Oi CO I- t- O5 2 00 00 1C CO 00 1C 1C 00 to X 00 rH rH OS 00 o ||||o S o o OS to o GO GO O5 00 o o o CO to I- S S i o rH 1-H t- t- to I- to I- ~i i A h . - * et 1-H - CM CM - rH OJ at 0? Ox THE MECHANICAL EQUIVALENT OF HEAT 375 J- fjg O + (M + CO + * CO + 00 (JJ + l~ + * + l- O + + 01 O 1 Iff S O CO O <* CO t- co O O t- * 00 O CO e- CC OS 1ft CO CO to O i E- 2 *^ H5|S 0.0 O O I-( O l- OS t- o CO CO O O * CO CO O O OS rH -* CO t- n O O t- l> I- O 00 t- Iff 30 Iff 00 00 CO O OS 9. i 5* e G~ O O O + l- t- ,-H CO - oo O Iff 1ft 1ft * CO 1ft Iff Iff g t- OS 00 > CO 30 00 CO i k g CO Ol CO O5 * 07 (?} O CO CO ^ 1 *3 s"^ *l 1 t- (M OS CO ** CO CC CO O 00 CO CO OS S CO e CO 1ft O 00 * CO OS 1ft so * l> so O t- 00 00 00 *-H rH (M *4 CO 00 Iff CO CO iO * S B CO CO CO OS 1 1 CO 1 Ml CO O * O t~ CO CO 1 1 * * ^-1 O * l- JI y o i-H O O O t- I 1 ff t- o O CO CO 00 O O O * OS 0* O ^ 1-H O *# CO O CO 1- w OS Iff CO O t- OS OS A|Q * CO b- * O * t> t- Iff CO 00 OS Iff (M 1 1 1ft so t- -I as as * i> iff CO CO OS c Iff CO CO 00 t- t- lO op Iff CO ^ 00 rH CO 8 CO T-H CO CO (M OS OS CO O O * OS CO ? CO CO OS OS CO so CO OS CO 1ft Tfl OS >**a'S Is III sggl- 00 o* CO O OS CO 1C < o CO OS- S t- o * 00 O t- ot CO CO CO CO <** CO t- rH Ift ? O OS 1 1 so * * w CO *< Tjt i-H so O I- S t- * I 1 OS OS * CM t- Tfl OS OS OS * t- CO 1ft CO O Ift t- CO OS O 1ft t- & O CO 1-H Ift I- 65 SS "Si tt * 376 HENET A. EOWLAND And the following relations hold among the constants : C = G' (1 + m (60 8400 )) , nearly , a = mn, b = ~ 100, n T=CVt 9 , i t *t l o n' ' In these formulae t is the temperature on the air thermometer; V is the volume of the stem of the mercurial thermometer, as determined from the calibration and measured from any arbitrary point; and C", f , m, and n are constants to be determined. The best way of finding these is by the method of least squares. C" must be found very exactly; t is only to be eliminated from the equations; m must be found within say ten per cent, and n need only be determined roughly. To find them only within these limits is a very difficult matter. Determination of n As this constant needs a wide range of temperatures to produce much effect, it can only be determined from thermometer No. 6167, which was of the same glass as 6163, 6165, and 6166. It is unfortunate that it was broken on November 21, and so we only have the experiments of the first and second series. From these I have found w = -003 nearly. This makes b = 233, which is not very far from the values found before from experiments above 100 by Eegnault on ordinary glass." Determination of C and m I shall first discuss the determination of these for thermometers Nos. 6163, 6165, and 6166, as these were the principal ones used. As No. 6163 extended from to 40, and the others only from to 30, it was thought best to determine the constants for this one first, and then find those for 6165 and 6166 by comparison. As this comparison is deduced from the same experiments as those from which we determine the constants of 6163, very nearly the same result is 15 Some experiments with Baudin thermometers at high temperatures have given me about 240, a remarkable agreement, as the point must be uncertain to 10 or more. ON THE MECHANICAL EQUIVALENT OF HEAT 377 found as if we obtained the constants directly by comparison with the air thermometer. The constants of 6163 can be found either by comparison with 6167, or by direct comparison with the air thermometer. I shall first deter- mine the constants for No. 6167. The constants C and t for this thermometer were found directly by observation of the and 100 points; and we might assume these, and so seek only for m. In other words, we might seek only to ex- press the difference of the thermometers from the air thermometer by a formula. But this is evidently incorrect, seeing that we thus give an infinite weight to the observations at the and 100 points. The true way is obviously to form an equation for each temperature, giving each its proper weight. Thus from the first series we find for No. 6167, Weight. Equations of Condition. 4 = 6-147 C t , 4 17 -427 = 15-685 C 1 930m, 4 23-793 = 19-157 C t 1140m, &c. &c. &c. 5 100 =60-156 C t , which can be solved by the method of least squares. As t is unim- portant, we simply eliminate it from the equations. I have thus found, Weight. 1 Nov. 14 (7 = 1-85171 m= -000217 2 Nov. 20, 21 (7 = 1-85127 m= -000172 Mean = 1-85142 m= -000187 The difference in the values of m is due to the observations not being so good as were afterwards obtained. However, the difference only signifies about 0-03 difference from the mean at the 50 point. After November 20 the errors are seldom half of this, on account of the greater experience gained in observation. The ratio of C for 6167 and 6163 is found in the same way. Weight. 1 Nov. 14 -0310091 2 Nov. 20 -0309846 Mean -0309928 378 HENRY A. BOWLAND Hence for 6163 we have in this way C = -057381 C" = -056995 m = -000187. By direct comparison of No. 6163 with the air thermometer., we find the following: m. 000239 000166 000226 000155 000071 .000115 Date. Weight. C'. Nov. 14 1 056920 Nov. 20 2 056985 Jan. 25 3 056986 Feb. 11 4 056997 June 8 3 056961 June 22 2 056959 Mean -056976 -000004 -000154 -000010 The values of C" agree with each other with great exactness, and the probable error is only 0-003 C. at the 40 point. The great differences in the values of m, when we estimate exactly what they mean in degrees, also show great exactness in the experi- ments. The mean value of m indicates a difference of only 0-05 between the mercurial and air thermometer at the 20 point, the and 40 points coinciding. The probable error of m in degrees is only 0.003C. There is one more method of finding m from these experiments; and that is by comparing the values of C' with No. 6167, the glass of 6167 being supposed to be the same as that of 6163. We have the formula C = C"(l + 34-8??i). Hence CC' m = 3i-SC' We thus obtain the following results: Date. Weight. Value of m Nov. 14 1 000236 Nov. 20 2 000218 Jan. 25 3 000217 Feb. 11 4 000197 June 8 3 000215 June 22 2 000216 Mean -000213 Ox THE MECHANICAL EQUIVALENT OF HEAT 379 The results for m are then as follows : From direct comparison of Xo. 6167 with the air thermometer -000187 From direct comparison of Xo. G163 with the air thermometer -000154 From comparison of Xo. 6163 with Xo. 6167 -000213 The first and last are undoubtedly the most exact numerically, but they apply to Xo. 6167, and are also, especially the first, derived from somewhat higher temperatures than the 20 point, where the correc- tion is the most important. The value of m, as determined in either of these ways, depends upon the determination of a difference of tem- perature amounting to 0-30, and hence should be quite exact. The value of m, as obtained from the direct comparison of Xo. 6163 with the air thermometer, depends upon the determination of a differ- ence of about 0-05 between the mercurial and the air thermometer. At the same time, the comparison is direct, the temperatures are the same as we wish to use, and the glass is the same. I have combined the results as follows: m from Xo. 6167 -000200 m from Xo. 6163 -000154 Mean 00018 1 It now remains to deduce from the tables the ratios of the constants for the different thermometers. The proper method of forming the equations of condition are as follows, applying the method to the first series : Weight. 4 21-25 C llt = 115-33 C l i\ 4 255-80 C llt = 422-84 C, r, 4 34 1 -05 C llt = 534-71 C t r. 5 431-71 C llt = 653-49 C t i\ where (?, is the constant for Xo. 6166, C, is that for Xo. 6163, and r is a constant to be eliminated. Dividing by C lt the equations can be solved for jw. The following table gives the results : "t 16 See Appendix to Thermometry, where it is finally thought best to reject the value from No. 6167 altogether. 380 HENEY A. EOWLAND TABLE XVI. RATIOS OF CONSTANTS. Date. Weight. 6163 6167 6166 6167 6166 6163 6165 6163 6165 6166 Nov. 14 Nov. 20 Jan. 25 Feb. 11 June 8 June 22 1 2 3 4 3 2 031009 030985 040658 040670 1-3111 1-3128 1-3122 1-3115 1-3108 1-3122 8-0588 8-0605 8-0588 6-1449 6-1469 6-1428 Mean .030993 .00005 .040666 000003 1.31175 -0004 8 . 0594 .0002 6.1451 .0004 From these we have the following, as the final most probable results : C n = 8-0601 C lt <7,,, = 1-31175 0,, C, = -031003 <7 iv , = -24991 <7 iv , 0,,,= -040661 IT , of which the last three are only used to calculate the temperatures on the mercurial thermometer, and hence are of little importance in the remainder of this paper. The value of C' which we have found for the old value of the coeffi- cient of expansion of glass was C' = -056976; and hence, corrected to the new coefficient, it is, as I have shown, C, =.056962. Hence, G n = '45912 , <7 y// = -074720. And we have finally the three following equations to reduce the ther- mometers to temperatures on the air thermometer: Thermometer No. 5163: T = -056962 V 1' -00018 T (40 T) (1 -003 (T -f 40)). Thermometer "No. 6165: T= -45912 V" V -00018 T (T 40) (1 -003 (T + 40)). Thermometer No. 6166: T= -074720 V'" V" ' 00018 T (T 40) (1 -003 (T+40)); where V, V" ', and V" are the volumes of the tube obtained by cali- bration; t ', t ", and t " f are constants depending on the zero point, and ON THE MECHANICAL EQUIVALENT OF HEAT 381 of little importance where a difference of temperature is to be meas- ured; and T is the temperature on the air thermometer. On the mercurial thermometer, using the and 100 points as fixed, we have the following by comparison with No. 6167: Thermometer No. 6163; = -057400 V t ; Thermometer No. 6165; = -46265 V 1 ; Thermometer No. 6166; = -075281 V 1 . The Kew Standard The Kew standard must be treated separately from the above, as the glass is not the same. This thermometer has been treated as if its scale was arbitrary. In order to have variety, I have merely plotted all the results with this thermometer, including those given in the Appendix, and drawn a curve through them. Owing to the thermometer being only divided to -J F., the readings could not be taken with great accuracy, and so the results are not very accordant; but I have done the best I could, and the result probably represents the correction to at least 0-02 or 0-03 at every point. (d) Reduction to the Absolute Scale The correction to the air thermometer to reduce to the absolute scale has been given by Joule and Thomson, in the Philosophical Transactions for 1854; but as the formula there used is not correct, I have recalculated a table from the new formula used by them in their paper of 1862. That equation, which originated with Rankine, can be placed in the form where p, v, and /j. are the pressure, volume, and absolute temperature of a given weight of the air; D is its density referred to air at C. and 760 mm. pressure; fa is the absolute temperature of the freezing point; and m is a constant which for air is 0-33 C. For the air thermometer with constant volume T = 100 P'~P or, since D = 1, tt - /,, = T- -00088 T from which I have calculated the following table of corrections: 382 HENRY A". ROWLAND TABLE XVII. REDUCTION OF AIR THERMOMETER TO ABSOLUTE SCALE. T Air Thermometer. M ("0 Absolute Temperature. A or Correction to Air Thermometer. 10 9-9972 0028 20 19-9952 0048 30 29-9939 0061 40 39-9933 0067 50 49-9932 0068 60 59-9937 0063 70 69-9946 0054 80 79-9956 0044 90 89-9978 0022 100 100-000 200 200-037 + -037 300 300-092 + -092 400 400-157 -1- -157 500 500-228 + -228 It is a curious circumstance, that the point of maximum difference occurs at about the same point as in the comparison of the mercurial and air thermometers. From the previous formula, and from this table of corrections, the following tables were constructed. TABLE XVIII. THERMOMETER No. 6163. Reading In Millimeters on Stem. Temperature on Mercurial Thermometer, and 100 fixed. Temperature on Mercurial Thermometer and 40 fixed by Air Thermom. Temperature on Air Ther- mometer. Temperature on Absolute Scale from C. Reading In Millimeters on Stem. Temperature ou Mercurial Thermometer, 0andlOUnxed. Temperature on Mercurial Thermom., and 40 fixed by Air Thermom. Temperature ou Air Ther- mometer. Temperature on Absolute Scale fromOC. 50 923 - 917 _911 -911 240 20-557 20-409 20-350 20345 58-1 250 21-670 21.515 21-457 21-452 60 + -217 + -215 + -214 + 214 260 22-776 22-616 22 559 22 554 70 1-356 1-336 1-328 1 328 270 23-884 23-713 23-657 23.652 80 2-494 2-475 2-461 2-460 280 24-989 24-810 24-755 24-750 90 3-631 3-604 3-584 3-583 290 26-093 25-907 25-854 25 848 100 4-767 4-733 4-707 4-706 300 27-200 27-006 26-956 26-950 110 5-903 5-860 5-829 5-827 310 28-311 28-108 28-060 28 056 120 7-036 6-986 6-950 6-948 320 29-425 29-214 29-169 39-163 130 8-170 8-111 8-071 8-069 330 30-541 30-324 30-282 30 -276 140 9-304 9-237 9-193 9-190 340 31-662 31-436 31-398 31-392 150 10-436 10.361 10-314 10-311 350 32.782 32-548 32,- 51 4 32-508 160 11-568 11-485 11-435 11-432 360 33-903 33-660 33-630 33-624 170 12-700 12-608 12-556 12-553 370 35-023 34-773 34-748 34-742 180 13-829 13-730 13-676 13-672 380 36-143 35-884 35-864 35-857 190 14-957 14-850 14-794 14-790 390 37-261 36-994 36-979 36-972 200 16-081 15-966 15-909 15-905 400 38-377 38-103 38-094 38-087 210 17-203 17-080 17-022 17-018 410 89-493 39-210 39-206 39 199 220 18-322 18-191 18-132 18-127 420 40-604 40-314 40-316 40-309 230 19-440 19-301 19-242 19-237 TABLE XIX. THERMOMETER No. 6165. Reading In Millimeters on Htom. Temperature on Mercurial, Thermometer, 0* and 100 fixed. Temperature on Mercurial Thermom., and 40 fixed by Air Thermom. O 1 S) m ^ U u . U. * o S*2 HI tH fc- ^ S I* 03 O b 0> .Q *-t o, o a<*~ 1 o a 5 fl< 3 H o H 0$ Reading In Millimeters on Stem. Temperature on Mercurial Thermometer, and 10U fixed. Temperature on Mercurial Thermom., and 40 fixed by Air Thermom. Temperature on Air Ther- mometer. Temperature on Absolute Scale from C. 30 464 460 o o .457 -457 230 17-198 17-067 17-009 17-005 35 240 18-056 17-920 17-861 17-8.57 40 + 463 + -460 + 457 +-457 250 18-917 18-773 18-714 18-709 50 1-387 1-376 1-368 1-368 260 19-771 19-621 j 19-562 19-557 60 2-307 2-290 2-276 2-275 270 20-621 20-465 ! 20-406 20-401 70 3-216 3-192 3-174 3-173 280 21-469 21-306 1 21-247 21-242 80 4-122 4-092 4-069 4-068 290 22-308 22-139 22-081 22-076 90 5-022 4-984 4-957 4-955 300 23-144 22-969 22-912 22-907 100 5-916 5-872 5 841 5 839 310 23-974 23-792 23-736 23-731 110 6-804 6-753 6-714 6.712 320 24 796 24-607 24.552 24-547 120 7-685 7-628 7-590 7-588 330 25-618 25-424 25-370 25-365 130 8-564 8-500 8-459 8.456 340 26-433 26-232 26-180 26-174 140 9-439 9.368 9-324 9-321 350 27-245 27-038 26-987 26-981 150 10-309 10-232 10-186 10-183 360 28-049 27-837 27-788 27-782 160 11-174 11-091 11-042 11-039 370 28-856 28-637 28-590 28 584 170 12-038 11.947 11-896 11-893 380 29-651 29-426 29-382 29-376 180 12-900 12-802 12.749 12.746 390 30-449 30-218 30-176 30-170 190 13-760 13-655 13-601 13-598 400 31-249 31-011 ; 30-971 30-965 200 14-619 14-508 14-453 14-450 410 32-073 31-829 31-782 31-786 210 15-479 15-362 15-305 15-302 420 32-861 32-611 32-577 32-581 220 16-340 16-215 16-157 16-153 TABLE XX. THERMOMETER No. 6166. a in iT 1 ? -6 m i a --o ffi _ .--d > _ d Reading In Millimeters c Stem. Temperatun ou Mercurla Thermomete] 0aud 100 flxe Temperature on Mercurla Thermometel and 40 flxe Temperatun on Air Ther- mometer. Temperaturi on Absolute Scale from Reading In Millimeters o Stem. Temperatur on Mercurla Thermomete and 100 flxe Temperatur on Mercurla Thermomete and 40 flxe Temperatur on Air Ther mometer. Temperatur on Absolute Scale from t> 20 036 036 034 034 230 16-478 16-356 16-298 16-294 30 + 770 + 764 + 759 + 759 240 17-259 17-132 17-074 17-070 40 1-574 1-562 1-553 1-553 250 18-042 17-908 17-849 17-845 50 2 368 2-350 2-336 2-335 260 18-825 18-686 18-627 18-622 60 3-156 3-133 3-115 3-114 270 19-609 19-464 19-405 19-400 70 3-941 3-911 3 889 3-888 280 20-392 20-241 20-182 20-177 80 4-726 4-691 4-665 4-664 290 21-176 21-019 20-960 20-955 90 5 509 5-468 5-438 5-436 300 21 735 21-793 21-735 21 730 100 6-293 6-246 6-212 6-210 j 310 22-511 22 569 22-511 22-506 110 7-076 7-024 6 -988 6-986 320 23-292 23-349 23-292 23-287 120 7-862 7-804 7 765 7-763 330 24-075 24-131 24 075 24-070 130 8-649 8-585 8-544 8-542 340 24-855 24-910 24-855 24-850 140 9-437 9-367 9 323 9-321 350 25-634 25-687 25 634 25-628 150 10-228 10-151 10-105 10-102 360 26-415 26-466 26-412 26-406 160 11-017 10-935 10-887 10-884 370 27-441 27-245 27-195 27-189 170 11-805 11-717 11-667 11-664 380 28 240 28-030 27-982 27-976 180 12-589 12-496 12-444 12-441 390 29-030 28-814 28-768 28-762 190 13-370 13-271 13-217 13-214 400 29-819 29-597 29-550 29-544 200 14-148 14-043 13-988 13-984 410 30-608 30-381 30-339 30-333 210 14-923 14-812 14-756 14-753 420 31-396 31-162 31-123 31-117 220 15- 699 15 583 15-526 15-522 430 32-189 31-950 31-914 31-908 384 HENRY A. BOWLAND In using these tables a correction is of course to be made should the zero point change. TABLE XXI. CORRECTION OF KEW STANDARD TO THE ABSOLUTE SCALE. Temperature C. Correction in degrees C. 10 03 20 05 30 06 40 07 50 07 60 06 70 04 80 02 90 01 100 Appendix to Thermometry The last of January, 1879, Mr. S. W. Holman, of the Massachusetts Institute of Technology, came to Baltimore to compare some thermom- eters with the air thermometer; and by his kindness I will give here the results of the comparison which we then made together. As in this comparison some thermometers made by Fastre in 1851 were used, the results are of the greatest interest. The tables are calculated with the newest value for the coefficient of expansion of glass. The calibration of all the thermometers, except the two by Casella, has been examined, and found good. The Casella thermometers had no reservoir at the top, and could not thus be readily calibrated after being made. The G-eissler also had none, but I suc- ceeded in separating a column. The absence of a reservoir at the top should immediately condemn a standard, for there is no certainty in the work done with it. From these tables we would draw the inference that No. 6163 repre- sents the air thermometer with considerable accuracy. At the same time, both tables would give a smaller value of ra than I have used, and not very far from the value found before by direct comparison, namely, -00015. The difference from using m= -00018 would be a little over 0-01 C. at the 20 point. All the other thermometers stand above the air thermometer, between and 100, by amounts ranging between about 0-05 and 0-35C., . 385 TABLE XXII. SEVENTH SERIES. Air Ther- mome- ter. Original Readings. Reduced Readings. 6163. 7334 Baudln. Kew Stand- ard No. 104. 32374 Casella. Gelss- ler. 6163 Reduced to Air Ther- mome- ter. 7334 Baudln. Kew Stand- ard No. 104. 32374 Casella. Gelss- ler. 6 is-43 6-08 12-68 20-49 24-55 29-51 39-45 39-15 51-17 61-12 70-74 80-09 80-39 89-95 89-92 100-00 "58-83 63-5 113-0 171-55 242-0 278-8 323-9 413-1 410-7 11 32-68 33-60 43-65 55-47 69-55 76-90 85-88 103-72 103-23 124-84 142-73 159-87 176-50 177-23 194-35 194-22 212-37 + 20 71 6-33 12-91 20-77 24-80 29-80 39-76 39-48 51-49 61-47 71-00 80-31 80-74 90-22 90-18 100-06 + 69 13-42 21-29 25-33 30-32 40-22 39-98 51-83 61-69 71-14 80-25 80-66 90-11 90-06 99-32 8 52 6-08 12-65 20-49 24-54 29 52 39-47 39-20 8 o 52 6-11 12-68 20-57 24-61 29-61 39-53 39-26 51-29 61-24 70-78 80-04 80-44 89-97 89-90 100-00 8 51 6-13 12-70 20-56 24-59 29-58 39-54 39-26 51-26 61-23 70-76 80-06 80-49 89-97 89-93 100-00 8 12-73 20-63 24-66 29-66 39-62 39-34 51-32 61-29 70-83 80-02 80-43 89-93 89-89 100-00 12-59 20-48 24-50 29-49 39-43 39-15 51-10 61-05 70-57 79-74 80-15 89-63 89-59 99-69 12-82 20-74 24-81 29-83 39-80 39-56 51-49 61-41 70-92 80-10 80-51 90-03 89-98 100-00 TABLE XXIII. EIGHTH SERIES. Air Ther- mome- ter. Original Readings. Reduced Readings. 6163. 378 Fastre. 7316 Baudln. 368 Fastr6. 3235 Casella. 6163 Reduced to Air Ther- mome- ter. 376 Fastrfi. 7316 Baudln. 368 Fastre. 3236 Casella. 6 3.67 11-55 20-72 32-19 39-36 50-71 60-10 73-82 86-50 " 58 60 90-7 161-6 243-7 347-4 411-85 111-3 130-0 170-9 217-9 276-9 313-85 372-0 420-0 490-6 555-25 550-2 624-93 23 11-40 20-59 32-09 39-26 50-57 59-92 73-59 86-16 85-21 99-70 87-6 106-25 147-2 194-2 253-2 290-1 248-2 396-45 466-85 531-22 525-95 600-58 32-80 39-35 53-70 70-15 90-80 103-68 123-65 140-80 165-68 188-20 186-42 212-45 o 3-61 11-56 20-70 32-17 39-36 o 3-64 11-60 20-75 32-24 39-43 50-75 60-10 73-84 86-48 86-45 100-00 8 3-64 11-62 20-80 32-28 39-48 50-80 60-21 73-93 86-56 85-45 100-00 8 3-65 11-63 20-79 32-29 39-45 50-57 60-12 73-97 86-56 85-51 100-00 11-64 20-84 32-34 39-52 50-84 60-19 73-87 86-51 85-50 100-00 100-00 none standing below. Indeed, no table has ever been published show- ing any thermometer standing below the air thermometer between 17 The original readings in ice were 58-68 and 58-45, to which -15 was added to allow for the pressure of water in the comparator. This, of course, gives the same final result as if -15 were subtracted from each of the other temperatures. No cor- rection was made to the others. 18 Probably some error of reading. 25 386 HENEY A. ROWLAND and 100. By inference from experiments above 100 on crystal glass by Regnault, thermometers of this glass should stand below, but it never seems to have been proved by direct experiment. The Fastre thermometers are probably made of this glass, and my Baudin's cer- tainly contain lead; and yet these stand above, though only to a small amount, in the case of the Fastre's. The Geissler still seems to retain its pre-eminence as having the greatest error of the lot. The Baudin thermometers agree well together, but are evidently made from another lot of glass from the No. 6167 used before. These last two depart less from the air thermometer. The explanation is plain, as Baudin had manufactured more than one thousand ther- mometers between the two, and so had probably used up the first stock of glass. And even glass of the same lot differs, especially as Regnault has shown that the method of working it before the blow-pipe affects it very greatly. It is very easy to test whether the calorimeter thermometers are of the same glass as any of the others, by testing whether they agree with No. 6163 throughout the whole range of 40. The difference in the values of m for the two kinds of glass will then be about -003 of the difference between them at 20, the and 40 points agreeing. The only difficulty is in calibrating or reading the 100 thermometers accur- ately enough. The Baudin thermometers were very well calibrated, and were graduated to ^ C., and so were best adapted to this kind of work. Hence I have constructed the following tables, making the and 40 points agree. TABLE XXIV. COMPARISON OF 6163 AND THE BATJDIN STANDARDS. 6163 Mercurial and 40 fixed. 7334.19 Difference. 6163 Mercurial and 40 fixed. 7316. 19 Difference. 12-699 12-673 + 026 11-609 11-584 + 025 20-547 20-553 006 20-762 20-746 + 016 24-604 24-567 + 037 32-203 32-211 008 29-564 29-550 + 014 39-358 39-358 39-337 39-337 19 A correction of 0-01 was made to the zero points of these thermometers on ac- count of the pressure of the water. Ox THE MECHANICAL EQUIVALENT OF HEAT 387 Taking the average of the two, it would seem that No. 6163 stood about -015 higher than the mean of 7334 and 7316 at the 20 point, or 6163 has a higher value of ra by -000045 than the others. These differ about -17 from the air thermometer at 40, which gives the value of m about -000104. Whence m for 6163 is -00015, as we have found before by direct comparison with the air thermometer. I am inclined to think that the former value, -00018, is too large, and to take -00015, which is the value found by direct comparison, as the true value. As the change, however, only makes at most a differ- ence of 0-01 at any one point, and as I have already used the previous value in all calculations, I have not thought it worth while to go over all my work again, but will 'refer to the matter again in the final results, and then reduce the final results to this value. m. CALOKIMETKY (a) Specific Heat of Water The first observers on the specific heat of water, such as De Luc, completed the experiment with a view of testing the thermometer; and it is curious to note that both De Luc and Flaugergues found th tem- perature of the mixture less than the mean of the two equal portions of which it was composed, and hence the specific heat of cold water higher than that of warm. The experiments of Flaugergues were apparently the best, and he found as follows : " 3 parts of water at and 1 part at 80 R. gave 19 -86 K. 2 parts of water at and 2 parts at 80 R. gave 39 -81 R. 1 part of water at and 3 parts at 80 R. gave 59 -87 R. But it is not at all certain that any correction was made for the specific heat of the vessel, or whether the loss by evaporation or radia- tion was guarded against. The first experiments of any accuracy on this subject seem to have been made by F. E. Neumann in 1831. 21 He finds that the specific heat of water at the boiling point is 1-0127 times that at about 28 C. (22 R.). The next observer seems to have been Regnault, 22 who, in 1840, M Gehler, Phys. Worterbuch, i, 641. "Pogg. Ann., xxiii, 40. 22 Ibid., li, 72. 388 HENRY A. EOWLAND found the mean specific heat between 100 C. and 16 C. to be 1-00709 and 1-00890 times that at about 14. But the principal experiments on the subject were published by Eegnault in 1850, 23 and these have been accepted to the present time. It is unfortunate that these experiments were all made by mixing water above 100 with water at ordinary temperatures, it being assumed that water at ordinary temperatures changes little, if any. An interpolation formula was then found to represent the results; and it was assumed that the same formula held at ordinary temperature, or even as low as C. It is true that Eegnault experimented on the subject at points around 4 C. by determining the specific heat of lead in water at various temperatures; but the results were not of sufficient accuracy to warrant any conclusions except that the variation was not great. Boscha has attempted to correct Eegnault's results so as to reduce them to the air thermometer; but Eegnault, in Comptes Rendus, has not accepted the correction, as the results were already reduced to the air thermometer. Him (Comptes Rendus, Ixx, 592, 831) has given the results of some experiments on the specific heat of water at low temperatures, which give the absurd result that the specific heat of water increases about six or seven per cent between zero and 13! The method of experi- ment was to immerse the bulb of a water thermometer in the water of the calorimeter, until the water had contracted just so much, when it was withdrawn. The idea of thus giving equal quantities of heat to the water was excellent, but could not be carried into execution without a great amount of error. Indeed, experiments so full of error only confuse the physicist, and are worse than useless. The experiments of Jamin and Amaury, by the heating of water by electricity, were better in principle, and, if carried out with care, would doubtless give good results. But no particular care seems to have been taken to determine the variation of the resistance of the wire with accuracy, and the measurement of the temperature is passed over as if it were a very simple, instead of an immensely difficult matter. Their results are thus to be rejected; and, indeed, Eegnault does not accept them, but believes there is very little change between 5 and 25. In PoggendorfFs Annalen for 1870 a paper by Pfaundler and Platter appeared, giving the results of experiments around 4 C., and deducing the remarkable result that water from to 10 C. varied as much as "Pogg. Ann., Ixxix, 241; also, Rel. d. Exp., i, 729. Ox THE MECHANICAL EQUIVALENT OF HEAT 389 twenty per cent in specific heat, and in a very irregular manner, first decreasing, then increasing, and again decreasing. But soon after an- other paper appeared, showing that the results of the previous experi- ments were entirely erroneous. The new experiments, which extended up to 13 C., seemed to give an increase of specific heat up to about 6, after which there was appar- ently a decrease. It is to be noted that Geissler's thermometers were used, which I have found to depart more than any other from the air thermometer. But as the range of temperature is very small, the reduction to the air thermometer will not affect the results very much, though it will somewhat decrease the apparent change of specific heat. In the Journal de Physique for November, 1878, there is a notice of some experiments of M. von Miinchausen on the specific heat of water. The method was that of mixture in an open vessel, where evaporation might interfere very much with the experiment. No reference is made to the thermometer, but it seems not improbable that it was one from Geissler; in which case the error would be very great, as the range was large, and reached even up to 70 C. The error of the Geissler would be in the direction of making the specific heat increase more rapidly than it should. The formula he gives for the specific heat of water at the temperature t is 1 -f -000302 i. Assuming that the thermometer was from Geissler, the formula, re- duced to the air thermometer, would become approximately 1 -00009 t+ -0000015 t 2 . Had the thermometer been similar to that of Kecknagel, it would have been 1 -f -000045 t -f -000001 t 2 . It is to be noted that the first formula would actually give a decrease of specific heat at first, and then an increase. As all these results vary so very much from each other, we can hardly say that we know anything about the specific heat of water between and 100, though Kegnault's results above that temperature are probably very nearly correct. It seems to me probable that my results with the mechanical equiv- alent apparatus give the variation of the specific heat of water with considerable accuracy; indeed, far surpassing any results which we can obtain by the method of mixture. It is a curious result of those experiments, that at low temperatures, or up to about 30 C., the spe- 390 HENKY A. EOWLAXD cific heat of water is about constant on the mercurial thermometer made by Baudin, but decreases to a minimum at about 30 when the reduction is made to the air thermometer or the absolute scale, or, indeed, the Kew standard. As this curious and interesting result depends upon the accurate comparison of the mercurial with the air thermometer, I have spent the greater part of a year in the study of the comparison, but have not been able to find any error, and am now thoroughly convinced of the truth of this decrease of the specific heat. But to make certain, I have instituted the following independent series of investigations on the specific heat of water, using, however, the same thermometers. The apparatus is shown in Fig. 4. A copper vessel, A, about 20 cm. in diameter and 23 cm. high, rests upon a tripod. In its interior is a three-way stopcock, communicating with the small interior vessel B, the vessel A, and the vulcanite spout C. By turning it, the vessel B could be filled with water, and its temperature measured by the ther- mometer D, after which it could be delivered through the spout into the calorimeter. As the vessel B, the stopcock, and most of the spout, were within the vessel A, and thus surrounded by water, and as the vulcanite tube was very thin, the water could be delivered into the calorimeter without appreciable change of temperature. The proof of this will follow later. The calorimeter, E, was of very thin copper, nickel-plated very thinly. A hole in the back at F allowed the delivery spout to enter, and two openings on top admitted the thermometers. A wire attached to a stirrer also passed through the top. The calorimeter had a capac- ity of about three litres, and weighed complete about 388-3 grammes. Its calorific capacity was estimated at 35-4 grammes. It rested on three vulcanite pieces, to prevent conduction to the jacket. Around the calorimeter on all sides was a water-jacket, nickel-plated on its interior, to make the radiation perfectly definite. The calorific capacity of the thermometers, including the immersed stem and the mercury of the bulb, was estimated as follows : 14 cm. of stem weighed about 3-8 gr., and had a capacity of -8 gr.; 10 gr. of mercury had a capacity of -3 gr.; total, 1-1 gr. Often the vessel B was removed, and the water allowed to flow directly into the calorimeter. The following is the process followed during one experiment at low temperatures. The vessel A was filled with clean broken ice, the open- ing into the stopcock being covered with fine gauze to prevent any ON THE MECHANICAL EQUIVALENT OF HEAT 391 small particles of ice from flowing out. The whole was then covered with cloth, to prevent melting. The vessel was then filled with water, and the two thermometers immersed to get the zero points. The calorimeter being about two-thirds filled with water, and having been weighed, was then put in position, the holes corked up, and one ther- mometer placed in it, the other being in the melting ice. An obser- vation of its temperature was then taken every minute, it being fre- quently stirred. FIG. 4. When enough observations had been obtained in this way, the cork was taken out of the aperture F and the spout inserted, and the water allowed to run for a given time, or until the calorimeter was full. It was then removed, the cork replaced, and the second thermometer removed from the ice to the calorimeter. Observations were then taken as before, and the vessel again weighed. Two thermometers were used in the way specified, so that one might approach the final temperature from above and the other from below. But no regular difference was ever observed, and so some experiments 392 HENRY A. EOWLAND were made with both thermometers in the calorimeter during the whole experiment. The principal sources of error are as follows : 1st. Thermometers lag behind their true reading. This was not noticed, and would probably be greater in thermometers with very fine stems like Geissler's. At any rate, it was almost eliminated in the experiment by using two thermometers. 2d. The water may be changed in temperature in passing through the spout. This was eliminated by allowing the water to run some time before it went into the calorimeter. The spout being very thin, and made of vulcanite, covered on the outside with cloth, it is not thought that there was any appreciable error. It will be discussed more at length below, and an experiment given to prove this. 3d. The top of the calorimeter not being in contact with the water, its temperature may be uncertain. To eliminate this, the calorimeter was often at the temperature of the air to commence with. Also the water was sometimes violently agitated just before taking the final reading, previous to letting in the cold water. Even if the tempera- ture of this part was taken as that of the air, the error would scarcely ever be of sufficient importance to vitiate the conclusions. 4th. The specific heat of copper changes with the temperature. Unimportant. 5th. Some water might remain in the spout whose temperature might be different from the rest. This was guarded against. 6th. Evaporation. Impossible, as the calorimeter was closed. 7th. The introduction of cold water may cause dew to be deposited on the calorimeter. The experiments were rejected where this occurred. The corrections for the protruding thermometer stem, for radiation, &c., were made as usual, the radiation being estimated by a series of observations before and after the experiment, as is usual in determin- ing the specific heat of solids. June 14, 1878. First Experiment Time. Ther. 6163. Ther. 6166. Points. 41 296-75 6163, 57-9 Air, 21 C. 42 296-7 6165, 34-8 Jacket about 25 C. 43 296-7 6166, 20-5* 44 296-65 ON THE MECHANICAL EQUIVALENT OF HEAT 393 Time. Ther. 6163. Ther. 6166. 44i-44f Water running. 46* 218-7 251-7 47* 218-8 251-8 48* 218-9 252-0 Temperature before 296-6 Correction for + -2 296-8=26-597 Correction for stem + '019 Initial temperature of calorimeter 26-616 218-6 + -2 = 218-8 = 17-994 Correction for stem -006 Points. Calorimeter before 2043-0 " after 2853'3 Water at added 810-3 Thermometer 1-1 Total at 8114 Calorimeter before 2043'0 Weight of Vessel 388-3 Water 1654-7 Capacity of calorimeter 35-4 " thermometer 1*1 Total capacity 1691-2 251-6 - 1 = 251-5 = 17-962- Correction for stem -006 17-956 17-988 Mean temperature of mixture, 17 -972. Mean specific heat 18 _ 1691-2 X 8-644 _ Mean specific heat 18 27 ~~ 811-4 X 17'972 June lit. Second Experiment Calorimeter before 2016-3; temperature 361-4 by No. 6163. Calorimeter after 3047-0; temperature 244-5 and 288-7. Air, 21 C.; jacket about 27. 361-4+ -2 = 361-6 = 33-803, or 33-863 when corrected for stem. 244-5 -|_ -2 = 244-7 = 20-865; no correction for stem. 288-7 1 = 288-6 = 20 -846; no correction for stem. Mean, 20 -855. Mean specific heat between and 21 _ ^.QQgg Mean specific heat between 21 and 34 June l-'f. Third Experiment Calorimeter before 1961-8; temperature 293-6 by No. 6166. Calorimeter after 3044-6; temperature 243-7 and 213-0. Air and jacket, about 18 C. 394 HENET A. EOWLAND 393-6 -l = 393-5 = 29-036, or 29-077 when corrected for stem. 243-7 -1 = 243 -6 = 17 -349; no correction for stem. 213-0 + -2 = 213-2 = 17 -374; no correction for stem. Mean, 17 -361. Mean specific heat between and 17 1-0024 Mean specific heat between 17 and 29 ~ It is to he observed that thermometer No. 6166 in all cases gave temperatures about 0-02 or 0-03 below No. 6163. This difference is undoubtedly in the determination of the zero points, as on June 15 the zero points were found to be 20-4 and 58-0. As one has gone up and the other down, the mean of the temperatures needs no correction. June 15 Calorimeter before 2068-2; temperature 364-6 by No. 6166. Calorimeter after 2929-2; temperature 249-7 and 217-7. Air and jacket at about 22 C. 264-6 = 26-766, or 26-782 when corrected for stem. 249-7 = H -822, or 17-812 when corrected for stem. 217-7+ -l = 217-8=17-884, or 17-874 when corrected for stem. Bejected on account of great difference in final temperatures by the two thermometers, which was probably due to some error in reading. June 21 Calorimeter before 2002-7; temperature 330-3 by No. 6163. Calorimeter after 3075-2; temperature 221-9 and 256-6. Air and jacket, 21 C. 330-3 + -1 = 330-4 = 30-321, or 30-359 when corrected for stem. 221-9+ -1=222-0 = 18-349, or 18-343 when corrected for stem. 256-6+ -0 = 256-6 = 18-358, or 18-352 when corrected for stem. Mean, 18 -347. Specific heat between and 18 __ Specific heat between 18 and 30 ~~ June 21 Calorimeter before 2073-8; temperature 347-8 by No. 6166. Calorimeter after 2986-8: temperature 234-5 and 206-6. Air and jacket, about 21 C. ON THE MECHANICAL EQUIVALENT OF HEAT 395 347-8+ -0 = 347-8 = 25 -457, or 25-471 when corrected for stem. 234-5 + -0 = 234-5 = 16-643, or 16-636 when corrected for stem. 206-6 + -1 = 206-7 = 16-651, or 16-644 when corrected for stem. Mean, 16 -640. Specific heat between and 17 _ .99971 Specific heat between 17 and 25 ~~ Eejected because dew was formed on the calorimeter. A series was now tried with both thermometers in the calorimeter from the beginning. June 25 Calor. before 2220-3; temperat. 325-6 by No. 6166; 309-9 by No. 6165. Calor. after 3031-4; temperat. 233-4 by No. 6166; 224-6 by No. 6165. Air, 24 -2 C.; jacket, 23 -5. 325-6 + -0 = 325-6 = 23-725, or 23-726 when corrected for stem. 309-9 + -2 = 310-1 = 23-739, or 23-740 when corrected for stem. 233-4+ -0 = 233-4 = 16-558, or 16-545 when corrected for stem. 224-6+ -2 = 224-8 = 16-562, or 16-549 when corrected for stem. Means, 23 -733 and 16 -547. Specific heat between and l' _ Specific heat between 16 and 24 ~ June 25 Calor. before 2278-6; temperat. 340-35 by No. 6166; 324-1 by No. 6165. Calor. after 3130-2; temperat. 242-5 by No. 6166; 232-8 by No. 6165. Air, 23 -5 C.; jacket, 22 -5. 340-35 + -0 = 340-35 = 24 -877, or 24 -881 when corrected for stem. 324-1 +-2 = 324-3 = 24 -899, or 24 -903 when corrected for stem. 242-5 + -0 = 242-5 =17 -264, or 17 -253 when corrected for stem. 232-8 + -2 = 233-0 =17 -261, or 17 -250 when corrected for stem. Specific heat between and 17 _ i . Specific heat between 17 and 25 Calor. before 2316-35; temperat. 386-1 by No. 6166; 368-4 by No. 6165. Calor. after 2966-90; temperat. 295-4 by No. 6166; 281-7 by No. 6165. Air, 23-5C.; jacket, 22 -5. 396 HENKY A. KOWLAND 386-1+ -0 = 386-1 = 28-455, or 2S-465 when corrected for stem. 268-4+ -2 = 368-6 = 28-472, or 28-482 when corrected for stem. 295-4+ -0 = 295-4 = 21-374, or 21-368 when corrected for stem. 281-7 + -2 = 281-9 = 21-400, or 21-394 when corrected for stem. Means, 28 -473 and 21 -381. Specific heat between and 21 "~ _ -. ~ Specific heat between 2r"and~28" " Two experiments were made on June 23 with warm water in vessel A, readings being taken of the temperature of the water, as it flowed out, by one thermometer, which was then transferred to the calorimeter as before. June 23 Water in A while running, 314-15 by No. 6163. Calor. before 1530-9; temperat. 281-1 by No. 6166. Calor. after 2996-3; temperat. 328-4 by No. 6166; 272-7 by No. 6163. 314-15 + -1 = 314-25 = 28-526, or 28-552 when corrected for stem. 281-1 +-0 = 281-1 =20 -262, or 20 -258 when corrected for stem. 328-4 +-0 = 328-4 =23 -945, or 23 -950 when corrected for stem. 272-7 + -1 = 272-8 =23 -960, or 23 -966 when corrected for stem. Specific heat between 20 and 24 _ .QQDQ Specific heat between 24 and 29 ~ June 23 Water in A while running, 383-9 by No. 6163. Calor. before 1624-9; temperat. 286-75 by 6166. Calor. after 3048-2; temperat. 392-45 by 6166, and 318-1 by 6163. 383-9 + -1 = 384-0 =36-303, or 36-357 when corrected for stem. 286-75+ -0 = 286- 75 = 20 -702, or 20 -700 when corrected for stem. 392-45+ -0 = 392-45 = 28 -954, or 28 -980 when corrected for stem. 318-1 +-1 = 318-2 =28 -964, or 28 -992 when corrected for stem. Specific heat between 21 and 29 _ . Specific heat between 29 and 36 To test the apparatus, and also to check the estimated specific heat of the calorimeter, the water was almost entirely poured out of the calorimeter, and warm water placed in the vessel A, which was then allowed to flow into the calorimeter. ON THE MECHANICAL EQUIVALENT or HEAT 397 Water in A while running, 309-0 by No. 6163. Calor. before 391-3; temperat. 314-5 by 6166. Calor. after 3129-0; temperat. 308-3 by 6166, and 378-5 by 6163. Air about 21 C. Therefore, water lost 0-078, and calorimeter gained 5. Hence the capacity of the calorimeter is 39. Another experiment, more carefully made, in which the range was greater, gave 35. The close agreement of these with the estimated amount is, of course, only accidental, for they depend upon an estimation of only 0-08 and 0-12 respectively. But they at least show that the water is delivered into the calorimeter without much change of temperature. A few experiments were made as follows between ordinary tempera- tures and 100, seeing that this has already been determined by Reg- nault. Two thermometers were placed in the calorimeter, the temperature of which was about 5 below that of the atmosphere. The vessel B was then filled, and the water let into the calorimeter, by which the temperature was nearly brought to that of the atmosphere; the opera- tion was then immediately repeated, by which the temperature rose about 5 above the atmosphere. The temperature of the boiling water was given by a thermometer whose 100 was taken several times. As only the rise of temperature is needed, the zero points of the thermometers in the calorimeter are unnecessary, except to know that they are within 0-02 of correct. June 18 Temperature of boiling water, 99 -9. Calor. before 2684-7; temperat. 259-2 by 6166, and 248-3 by 6165. Calor. after 2993-2; temperat. 381-0 by 6166, and 363-4 by 6165. 259-3 = 18-568, or 18-555 when corrected for stem. 248- 3 = 18 -564, or 18 -551 when corrected for stem. 381-0 = 28-054, or 28-065 when corrected for stem. 363-4 = 28 -055, or 28 -066 when corrected for stem. Specific heat 28 100 _ , . Of)24 Specific heat 18 - 28 ~ Other experiments gave 1-0015 and 1-0060, the mean of all of which 398 HENEY A. EOWLAXD is 1-0033. Regnault's formula gives 1-005; but going directly to his experiments, we get about 1-004, the other quantity being for 110. The agreement is very satisfactory, though one would expect my small apparatus to lose more of the heat of the boiling water than Regnault's. Indeed, for high temperatures my apparatus is much inferior to Regnault's, and so I have not attempted any further experi- ments at high temperatures. My only object was to confirm by this method the results deduced from the experiments on the mechanical equivalent; and this I have done, for the experiments nearly all show that the specific heat of water decreases to about 30, after which it increases. But the mechanical equivalent experiments give by far the most accurate solution of the problem; and, indeed, give it with an accuracy hitherto unattempted in experiments of this nature. But whether water increases or decreases in specific heat from to 30 depends upon the determination of the reduction to the air ther- mometer. According to the mercurial thermometers Nos. 6163, 6165 and 6166, treating them only as mercurial thermometers, the specific heat of water up to 30 is nearly constant, ~bui by the air thermometer, or ~by the Kew standard or Fastre, it decreases. Full and complete tables of comparison are published, and from them any one can satisfy himself of the facts in the case. I am myself satisfied that I have obtained a very near approximation to absolute temperatures, and accept them as the standard. And by this standard the specific heat of water undoubtedly decreases from to about 30. To show that I have not arrived at this result rashly, I may mention that I fought against a conclusion so much at variance with my precon- ceived notions, but was forced at last to accept it, after studying it for more than a year, and making frequent comparisons of thermometers, and examinations of all other sources of error. However remarkable this fact may be, being the first instance of the decrease of the specific heat with rise of temperature, it is no more remarkable than the contraction of water to 4. Indeed, in both cases the water hardly seems to have recovered from freezing. The specific heat of melting ice is infinite. Why is it necessary that the specific heat should instantly fall, and then recover as the temperature rises? Is it not more natural to suppose that it continues to fall even after the ice is melted, and then to rise again as the specific heat approaches infin- ON THE MECHANICAL EQUIVALENT OF HEAT 399 ity at the boiling point? And of all the bodies which we should select as probably exhibiting this property, water is certainly the first. (&.) Heat Capacity of Calorimeter During the construction of the calorimeter, pieces of all the material were saved in order to obtain the specific heat. The calorimeter which Joule used was put together with screws, and with little or no solder. But in my calorimeter it was necessary to use solder, as it was of a much more complicated pattern. The total capacity of the solder used was only about -$fa of the total capacity including the water; and if we should neglect the whole, and call it copper, the error would be only about y-gVfr- Hence it was considered sufficient to weigh the solder before and after use, being careful to weigh the scraps. The error in the weight of solder could not possibly have been as great as ten per cent, which would affect the capacity only 1 part in 12,000. To determine the nickel used in plating, the calorimeter was weighed before and after plating; but it weighed less after than before, owing to the polishing of the copper. But I estimated the amount from the thickness of a loose portion of the plating. I thus found the approxi- mate weight of nickel, but as it was so small, I counted it as copper. The following are the constituents of the calorimeter: Thick sheet copper 25-1 per cent. Thin sheet copper 45-7 " Cast brass 17-9 " Boiled or drawn brass 5-7 " Solder 4-0 Steel 1-6 " 100-0 Mckel -3 " To determine the mean specific heat, the basket of a Regnault's apparatus was filled with the scraps in the above proportion, allowing the basket of brass gauze, which was very light, to count toward the drawn brass. The specific heat was then determined between 20 and 100, and between about 10 and 40. Between 20 and 100 the ordinary steam apparatus was used, but between 10 and 40 a special apparatus filled with water was used, the water being around the tube containing the basket, in the same manner as the steam is in the 400 HENRY A. EOWLAND original apparatus. In the calorimeter a stirrer was used, so that the basket and water should rapidly attain the same temperature. The water was weighed before and after the experiment, to allow for evaporation. A correction of about 1 part in 1000 was made, on account of the heat lost by the basket in passing from the apparatus to the calorimeter, in the 100 series, but no correction was made in the other series. The thermometers in the calorimeter were Nos. 6163 and 6166 in the dif- ferent experiments. The principal difficulty in the determination is in the correction for radiation, and for the heat which still remains in the basket after some time. After the basket has descended into the water, it commences to give out heat to the water; this, in turn, radiates heat; and the tempera- ture we measure is dependent upon both these quantities. Let T = temperature of the basket at the time t i( IT" _ (I (( JW <- " " " water t Ql __ Q (I Q'l __ ( (( (( QO 6" = T". We may then put approximately TT" = (T - T")e-~z, where c is a constant. But rpl rpn rpi rp 0" 0' ' ' Q tf ' hence To find c we have 1 0" 0' t 3 ff' where 6" can be estimated sufficiently accurately to find C" approxi- mately. These formulae apply when there is no radiation. When radiation takes place, we may write, therefore, when t is not too small, 00' = (0" #')(! - e-~T) where is a coefficient of radiation, and t is a quantity which must be subtracted from t, as the temperature of the calorimeter does not rise Ox THE MECHANICAL EQUIVALENT OF HEAT 401 instantaneously. To estimate t , T a being the temperature of the air, we have, according to Newton's law of cooling, t C(t- Q = _ T C(0 T a } dt nearly, ~ a / 0" 0' t = c tf , _ T nearly, ri where it is to be noted that -,, _ is nearly a constant for all values of " *- a 0" T a according to Newton's law of cooling. The temperature reaches a maximum nearly at the time 0"o' t and if 6 m is the maximum temperature, we have the value of 0" as follows : 0" = T" = 0^ + C(t m + cL): \. m ' v/ 7 and this is the final temperature provided there was no loss of heat. When the final temperature of the water is nearly equal to that of the air, C will be small, but the time i m of reaching the maximum will be great. If a is a constant, we can put C = a (6" T a ), and G(t n + c ) will be a minimum, when or a = - ac That is, the temperature of the air must be lower than the tempera- ture of the water, so that T a = 6" as nearly as possible ; but the for- mula shows that this method makes the corrections greater than if we make T a = d', the reason being that the maximum temperature is not reached until after an infinite time. It will in practice, however, be found best to make the temperature of the water at the beginning about that of the air. It is by far the best and easiest method to make all the corrections graphically, and I have constructed the follow- ing graphical method from the formula?. First make a series of measurements of the temperature of the water of the calorimeter, before and after the basket is dipped, together with the times. Then plot them on a piece of paper as in Fig. 5, making the scale sufficiently large to insure accuracy. Five or ten centimeters to a degree are sufficient. nab c d is the plot of the temperature of the water of the calori- 26 402 HENRY A. EOWLAND meter, the time being indicated by the horizontal line. Continue the line d c until it meets the line I a. Draw a horizontal line through the point I. At any point, &, of the curve, draw a tangent and also a vertical line bg; the distance eg will be nearly the value of the con- stant c in the formula?. Lay off I f equal to c, and draw the line fJiTc through the point h, which indicates the temperature of the atmos- phere or of the vessel surrounding the calorimeter. Draw a vertical line, j Ic, through the point Tc. From the point of maximum, c, draw a line, j c, parallel to d m, and where it meets Ic j will be the required point, and will give the value of 6". Hence, the rise of temperature, corrected for all errors, will be Ic j. This method, of course, only applies to cases where the final tem- perature of the calorimeter is greater than that of the air; otherwise there will be no maximum. FIG. 5. In practice, the line d m is not straight, but becomes more and more nearly parallel to the base line. This is partly due to the constant decrease of the difference of temperature between the calorimeter and the air, but is too great for that to account for it. I have traced it to the thin metal jacket surrounding the calorimeter, and I must condemn, in 'the strongest possible manner, all such arrangements of calorimeters as have such a thin metal jacket around them. The jacket is of an uncertain temperature, between that of the calorimeter and the air. When the calorimeter changes in temperature, the jacket follows it but only after some time; hence, the heat lost in radiation is uncertain. The true method is to have a water jacket of constant temperature, and then the rate of decrease of temperature will be nearly constant for a long time. The following results have been obtained by Mr. Jacques, Fellow of the University, though the first was obtained by myself. Corrections were, of course, made for the amount of thermometer stem in the air. ON THE MECHANICAL EQUIVALENT OF HEAT 403 Temperature. Mean Specific Heat. 24 to 100 -0915 26 to 100 -0915 25 to 100 -0896 13 to 39 -0895 14 to 38 -0885 9 to 41 -0910 To reduce these to the mean temperature of to 40, I have used the rate of increase found by Bede for copper. They then become, for the mean from to 40, 0897 0897 0878 0893 0883 0906 Mean -0892 -00027 As the capacity of the calorimeter is about four per cent of that of the total capacity, including the water, this probable error is about -g-oW of the total capacity, and may thus be considered as satisfactory. I have also computed the mean specific heat as follows, from other observers : Copper between 20 and 100 nearly. 0949 Dulong. 0935 Eegnault. 0952 Eegnault. 0933 Bede. 0930 Kopp. 0940 This reduced to between and 40 by Bede's formula gives -0922. Hence we have the following for the calorimeter: 2 * 24 The cast brass was composed of 28 parts of copper, 2 of tin, 1 of zinc, and 1 of lead. The rolled brass was assumed to have the same composition. The solder was assumed to be made of equal parts of tin and lead. 404 HEXRY A. ROWLAND Per cent. Specific Heat between and 40 C. Copper 91-4 -0922 Zinc -7 -0896 Tin 3-6 -0550 Lead 2-7 -0310 Steel 1-6 -1110 Mean -0895 The close agreement of this number with the experimental result can only be accidental, as the reduction to the air thermometer would decrease it somewhat, and so make it even lower than mine. However, the difference could not at most amount to more than 0-5 per cent, which is very satisfactory. The total capacity of the calorimeter is reckoned as follows : Weight of calorimeter 3-8712 kilogrammes. Weight of screws . . . . -0016 kilogrammes. Weight of part of suspending wires. . -0052 kilogrammes. Total weight 3-8780 kilogrammes. Capacity = 3-878 X '0892 = -3459 kilogrammes. To this must be added the capacity of the thermometer bulb and several inches of the stem, and of a tube used as a safety valve, and we must subtract the capacity of a part of the shaft which was joined to -the shaft turning the paddles. Hence, 3459 -f- -0011 4- -0010 0010 Capacity =-3470 As this is only about four per cent of the total capacity, it is not necessary to consider the variation of this quantity with the tempera- ture through the range from to 40 which I have used. IV. DETERMINATION OF EQUIVALENT (o.) Historical Remarks The history of the determination of the mechanical equivalent of heat is that of thermodynamics, and as such it is impossible to give it at length here. ON THE MECHANICAL EQUIVALENT OF HEAT 405 I shall simply refer to the few experiments which a priori seem to possess the greatest value, and which have been made rather for the determination of the quantity than for the illustration of a method, and shall criticise them to the best of my ability, to find, if possible, the cause of the great discrepancies. 1. GENERAL REVIEW OF METHODS Whenever heat and mechanical energy are converted the one into the other, we are able by measuring the amounts of each to obtain the ratio. Every equation of thermodynamics proper is an equation between mechanical energy and heat, and so should be able to give us the mechanical equivalent. Besides this, we are able to measure a certain amount of electrical energy in both mechanical and heat units, and thus to also get the ratio. Chemical energy can be measured in heat units, and can also be made to produce an electric current of known mechanical energy. Indeed, we may sum up as follows the different kinds of energy whose conversion into one another may furnish us with the mechanical equivalent of heat.' And the problem in general would be the ratio by which each kind of energy may be converted into each of the others, or into mechanical or absolute units. a. Mechanical energy. 6. Heat. c. Electrical energy. d. Magnetic energy. e. Gravitation energy. f. Radiant energy. g. Chemical energy. h. Capillary energy. Of these different kinds of energy, only the first five can be measured other than by their conversion into other forms of energy, although Sir William Thomson, by the introduction of such terms as " cubic mile of sunlight," has made some progress in the case of radiation. Hence for these five only can the ratio be known. Mechanical energy is measured by the force multiplied by the dis- tance through which the force acts, and also by the mass of a body multi- plied by half the square of its velocity. Heat is usually referred to the quantity required to raise a certain amount of water so many degrees, though hitherto the temperature of the water and the reduction to the air thermometer have been almost neglected. 406 HENRY A. ROWLAND The energy of electricity at rest is the quantity multiplied by half the potential ; or of a current, it is the strength of current multiplied by the electro-motive force, and by the time ; or for all attractive forces varying inversely as the square of the distance, Sir William Thomson has given the expression TF/**' where R is the resultant force at any point in space, and the integral is taken throughout space. These last three kinds of energy are already measured in absolute measure and hence their ratios are accurately known. The only ratio, then, that remains is that of heat to one of the others, and this must be determined by experiment alone. But although we cannot measure f, g, h in general, yet we can often measure off equal amounts of energy of these kinds. Thus, although we cannot predict what quantities of heat are produced when two atoms of different substances unite, yet, when the same quantities of the same . substances unite to produce the same compound, we are safe in assuming that the same quantity of chemical energy comes into play. According to these principles, I have divided the methods into direct and indirect. Direct methods are those where & is converted directly or indirectly into a, c, d, or e, or vice versa. Indirect methods are those where some kind of energy, as g, is con- verted into &, and also into a, c, d, or e. In this classification I have made the arrangement with respect to the kinds of energy which are measured, and not to the intermediate steps. Thus Joule's method with the magneto-electric machine would be classed as mechanical energy into heat, although it is first converted into electrical energy. The table does not pretend to be complete, but gives, as it were, a bird's-eye view of the subject. It could be extended by including more complicated transformations; and, indeed, the sym- metrical form in which it is placed suggests many other transformations. As it stands, however, it includes all methods so far used, besides many more. In the table of indirect methods, the kind of energy mentioned first is to be eliminated from the result by measuring it both in terms of heat and one of the other kindsof energy, whose value is known in absolute or mechanical units. ON THE MECHANICAL EQUIVALENT or HEAT 407 It is to be noted that, although it is theoretically possible to measure magnetic energy in absolute units, yet it cannot be done practically with any great accuracy, and is thus useless in the determination of the equivalent. It could be thus left out from the direct methods without harm, as also out of the next to last term in the indirect methods. TABLE XXV. SYNOPSIS OF METHODS FOR OBTAINING THE MECHANICAL EQUIVALENT OF HBAT. j Mechanical Energy J. Gravltatlon 4 ft. Heat, Electric Energy . y. Heat, Magnetic Energy 1. Reversible process I 2. Irreversible cess pro- l. Reversible process 2. Irreversible cess pro- f a. Expansion or compression ac- cording to adlabatlc curve. 6. Expansion or compression ac- cording to Isothermal curve. c. Expansion or compression ac- cording to any curve with re- generator. d. Electro-magnetic engine driven by thermo-electric pile In a circuit of no resistance. a. Friction, percussion, etc. 6. Heat from magneto-electric cur- rents, or electric machine. a. Thermo-electric currents. ft. Pyro-electric phenomena (prob- ably). a. Heating of wire by current, or heat produced by discharge of electric battery. ( a. Thermo-electric current mag- 1. Reversible process '. netizlng a magnet in a circuit of no resistance. 2. Irreversible pro- ( a. Heating of magnet when de- cess I magnetized. a. Radiant Energy, Heat (Radiant energy absorbed by blackened eurface.) 0. Chemical Energy, Heat (Combustion, etc.) y. Capillary energy, Heat (Heat produced when a liq- uid Is absorbed by a po- rous solid.) S. Electrical energy, Heat (Heat generated in a wire by an electrical current.) e. Magnetic Energy, Heat (Heat generated on demag- netizing a magnet.) Gravitation Energy, Heat (Heat generated by a tail- ing body.) Crooke's radiometer. Thermo-electric pile. Thermo-electric pile with electro- magnet In circuit. 1. Cannon. 2. Electro-magnet machine run by galv. battery. Current from battery. Electro-magnet magnetized by a battery current. a. Mechanical Energy. 5. Electrical " c. Magnetic " d. Gravitation " a. Mechanical Energy 6. Electrical " c. Magnetic " ? d. Gravitation " a. Mechanical Energy. Movement of liquid by capillarity. . _. j Electrical currents from capillary " *' { action at surface of mercury. c. Magnetic " d. Gravitation " Raising of liquid by capillarity. agneto-electric or electro-mag- netic machine. Electric at- traction. Electro-magnet. a. Mechanical Energy 6. Magnetic " c. Gravitation " j M a. Mechanical Energy 6. Electrical c. Gravitation Armature attracted by a perma- nent Magnet. Induced current on demagnetizing a magnet. a. Mechanical Energy. J Velocity Imparted to a falling 6. Electrical " I body. c. Magnetic 408 HENRY A. ROWLAND TABLE XXVI. HISTORICAL TABLE OF EXPERIMENTAL RESULTS. Method in General. Method in Particular. Observer. Date. Result. A A A A /: S a a a ft ;-' ft 1 2 9 '3 n b a b or c a b a 2 1 Compression of air Joule" Joule" 1845 443-8 1845 437-8 Expansion " Theory of gases (see below) . " vapors (see below) Experiments on steam-engine Hirn v " Hirn v " Edlund* 1 " Rumford ix Joule 1 " Joule lv Joule v Joule vi Joule vl Joule vi Him 1 Favre lx Him 1 " 1 Him'' 11 Hirn T Him* 11 Hirn T " Puluj* 1 " Joule Joule" 1 Vioile* Quintus Icilius* 1 also Weber Lenz, also Weber Joule* 1 " H. F. Weber* 1 ' Joule" 1 Favre IV Weber, Boscha, Favre, and Silbermann Joule Boscha* 11 1857 1860-1 1865 J 1798 1843 1845 1847 1850 1850 1850 1857 1858 1858 1858 1860-1 1860-1 1860-1 1876' 1878 1843 1870 J (.1857 J1859J 1867 1878 1843 1858 Il857 J1859 413-0 420-432 443-6 430-1 428-3 940ft.lbs. 424-6 488-3 428-9 423-9 424-7 425-2 371-6 413-2 400-450 425-0 432-0 432-0 425-0 426-6 423-9 460-0 435.2 434-9 435-8 437 '4 399-7 396-4 478-2 429-5 428-15 499-0 443-0 432-1 419-5 ti ti 11 Expansion and contraction of metals. . . Boring of cannon Friction of water in tubes " ' in calorimeter <* " in calorimeter " " in calorimeter Friction of mercury in calorimeter " plates of iron metals " metals in mercury calor. . . . " metals. . . Boring of metals . Water in balance afrottement Flow of liquids under strong pressure. . Crushing of lead Water in calorimeter Heating by magneto-electric currents. . . Heat generated in a disc between the ) poles of a magnet f Heat developed in wire of known ab- \ solute resistance ") Do. do. do. Do. do. do. Do. do. do. Diminishing of the heat produced in a 1 battery circuit when the current V produces work ) Do. do. do. Heat due to electrical current, electro- "| chemical equivalent of water = 009379, absolute resistance electro- i motive force of Daniell cell, heat [ developed by action of zinc on sul. | of copper J Heat developed in Daniell cell Electro-motive force of Daniell cell. . . . Ox THE MECHANICAL EQUIVALENT OF HEAT 409 2. KESULTS OF BEST DETERMINATIONS ' On the basis of this table of methods I have arranged the following table, showing the principal results so far obtained. In giving the indirect results, many persons have only measured one of the transformations required; and as it would lengthen out the table very much to give the complete calculation of the equivalent from these selected two by two, I have sometimes given tables of these parts. As the labor of looking up and reducing these is very great, it is very possible that there have been some omissions. I have taken the table published by the Physical Society of Berlin, 1 as the basis down to 1857, though many changes have been made even within this limit. I shall now take up some of the principal methods, and discuss them somewhat in detail. Method from Theory of Gases As the different constants used in this method have bf en obtained by many observers, I first shall give their results. TABLE XXVII. SPECIFIC HEAT OF GASES. Limit to Temperature. Approximate Temperature of Water. Temperature reduced to Specific Heat. Air , Mercurial i -2669 I Delaroche and 20 to 210 -iZ { Thermometer Air Thermometer y ( i 23751"' Berard. Regnault. 20 to 100 20 j Mercurial Thermometer j -2389"" E.Wiedemann. Hydrogen.. . . .j Mercurial \3-2936 -( Delaroche and 15 to 200 1 12-2 | Thermometer Air Thermometer / t 1 3 -4090" 1 Berard. Regnault. 21 to 100 21 | Mercurial Thermometer 13-410"" E.Wiedemann. 25 Taking mean results on page 101 of Rel. des Exp., torn, ii., 410 HENRY A. KOWLAND TABLE XXVIII. COEFFICIENT OF EXPANSION OF AlR UNDER CONSTANT VOLUME Taking Expansion of Mercury according- to Regnault. Taking Expansion of Mercury according to Wiillner's Re- calculation of Regnault's Experiments. Regnault 0036655 0036687 Magnus 0036678 0036710 Jolly 0036695 0036727 Rowland 0036675 0036707 Mean 0036676 0036708 TABLE XXIX. RATIO OF SPECIFIC HEATS OF AIR. Method. Observer. Date. Ratio of Specific Heats. Method of Clement & Desormes, ) globe 20 litres I Clement & | Desormes""' J 1812 Published in t 1-354 Never fully published Gay-Lussac et Welter 1 ' 1 . 1819 1-3748 Method of C16ment & Desormes. . Using Breguet thermometer Delaroche et Berard* 11 . . Favre & Silbermann""'. 1853 1-249 1-421 Clement & Desormes, globe 39 ) Masson" 1858 1-4196 Clement & Desormes Weisbach" 1 . . . . '. 1859 1 4025 C16ment & Desormes, globe 10 ) Hirn xxli 1861 1-3845 litres ) Passage of gas from one vessel ) Cazin" lv 1862 1-41 into another, globes 60 litres j Pressure in globe changed by ) 1863 aspirator, globe 25 litres. . . . ) Heating of gas by electric cur- ) Jamin & Richard 1 "" 1 . . . 1864 1-41 Clement & D6sormes Tresca et Laboulaye"' 1 . 1864 Barometer under air-pump re- ) Kohlrausch 1 "' 1869 1-302 ceiver of 6 litres ) Compression and expansion of ) Regnault 1871 J Results lost in the siege C16ment&D6sormes with metal- ) R6ntgen" v " I 1873 of Paris. 1-4053 lie manometer, globe 70 litres ) Compression of gas by piston. Amagat XXI 1874 1-397 ON THE MECHANICAL EQUIVALENT OF HEAT 411 fgsi so t- SO ^ CO H9 o 00 "3 Q." ''"'S CM CM CM nr> o CM CM ^^ . ^ o + S CO CO CO CM CO CO CO CO 8*6=1 CO CO CO ts CO CO ' CO CO ii-OflJS ; ; 00 s t- co rH t- -** 0*^ . CM CO rH CO CM O ^ M ^ O A -*S Q H S CO CO OO scaSri O o ts-S~" s O5 S t- s o 3 S s so CO s CO 35 o 0* CM rH CO CO eo CO CO CO CO 35 M M 53 CO 04 CO CO rg CO CM CO CO CO CO CO CO CO CO CO * 1 <* ? s s Md H - . . S o "3 t CO >A CM rH VI a o fe 13 ^3 a o i France Dussel -3 a i i 3 s 1 1 France Austri Hollan Hollan OQ o PH OQ France s 00 CO -i CM rH c CM ct CO 1A 4 CO 3 SO l> 00 CO CO CO CO H CO o* CO 00 CO r- ""I r '. S ,0 *> . H M M a L* P M M h a _, 5 a a a o so M M hi '. J3 2 S H M o =5 fl? oS o I o X S? I VI a oS " OQ O fa H o ,0 fl S9 bo a = 3 "P, 4 "3 09 | oJ a o G a o "o V b i "3 z b eS C8 2 & PQ PQ OQ * PH OQ PQ i i i - ^T CO -^ - -1* SO t- 00 35 O rH w - 6 412 HENRY A. KOWLAND References. (Tables XXVI to XXX.) j Physical Society of Berlin, Fort, tier Phys., 1858. " Joule, Phil. Mag., ser. 3, TO!, xxvi. See also Mec. Warmeaquivalent, Gesammelte Abhandlungen von J. P. Joule, Braunschweig, 1872. 111 Joule, Phil. Mag., ser. 3, vol. xxiii. See also 2 above. iv 2 y S *s S 1 *5 2 140 52-0 005 9-185 5-485 7 "iflQ 160 180 203 220 240 56-0 59-2 63-4 66-5 70-2 003 + 006 + 011 + 020 017 022 015 001 + 027 11-412 13-650 16-230 18-137 20-392 18-023 30-652 45-329 56-241 69-153 7-478 7-442 7-394 7-364 7. 3^4. 951 1906 3010 3825 4786 io 11 12 13 14 348 775 1202 1629 2056 5728 6155 6582 7009 7436 259 74-0 + 028 + 067 22-538 81-484 5702 15 2484 7864 289 80-0 + 045 + 161 25-943 101-214 7156 16 2912 8292 17 3340 8720 18 3767 9147 19 4193 9573 20 4619 9999 21 5048 10428 22 5472 10852 23 5899 11279 24 6326 11706 25 6753 12133 26 7180 12560 448 HENRY A. ROWLAND TABLE XXXVIII SECOND SERIES. Preliminary. March 7, 1878. Jacket 18.5 to 22. 5. Air about 21 C. Thermometer No. 6163. e R Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilo- gramme = 2 10-060 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 6812 S i f6 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 19-9 016 12-537 13-646 14-755 15-863 16-972 18-085 19-196 20-305 21-419 22 533 23-642 24-754 25-867 26-990 28-119 29-253 30-393 31 540 32-689 33-842 34-998 36-158 37-321 5-03 11-12 17-22 23-36 29-55 35-70 41-90 48-09 54-30 7-737 7-710 7.666 7-642 7-641 7.630 7.611- 7.600 7.596 7.582 7.552 7.547 7.576 7-611 7-604 7-611 7-617 7-602 7-592 7-576 7-550 7-550 474 947 1421 1897 2369 2845 3319 3794 4740 5213 5687 6164 6643 7125 7608 8097 8590 9081 9576 10071 10567 18 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 198 625 1052 1480 1909 2333 2761 3189 3615 4041 4467 4892 5318 5744 6168 6593 7017 7441 7867 8294 8722 9149 9577 10004 10430 7010 7437 7864 8292 8721 9145 9573 10001 10427 10853 11279 11704 12130 12556 12980 13405 13829 14253 14679 15106 15534 15961 16389 16816 17242 26-8 010 .036 33.8 + .003 036 66-69 72-92 79-16 85-42 91-67 97-98 104-28 110-67 117-12 123-54 130-04 136-56 143-08 40-8 + 0-20 001 47-8 + 044 + 073 51-4 55-0 + 072 + 184 58-7 + 588 + 261 TABLE XXXIX THIRD SERIES. Preliminary. March 12, 1878. Jacket 13-2 to 16-6. Air about 15 C. Thermometer No. 6166. S H Correction. Corrected Temperature. Revolutions of Chronograph 2n. 4(1 Mean Weight W. Work per Kilogramme = 2 9-9690 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 7599. S I i 205 210 220 230 28-0 28-6 29-9 31-1 + -002 14-368 14-754 15-529 16-307 3-156 5-334 9-770 14-184 U-5167 164 495 827 15 16 17 269 696 1122 7868 8295 8721 + 003 + 010 45 In the calculation of this column, more exact data were used than given in the other two columns, seeing that the original calculation was made every 5 mm. of the thermometer. Hence the last figure may not always agree with the rest of the data. 46 As this table was originally calculated for every 5 mm. on the thermometer, I have given the weights which were used to check the more exact calculation. ON THE MECHANICAL EQUIVALENT OF HEAT 449 TABLE XXXIX. Continued. Thermometer No. 6106. i EH Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilogramme = 2 9-690 TFn. Temperature. Work per Kilogramme. Work per Kilogramme + 7599. 1 I 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 32-4 33-6 34-9 36-2 37-4 38-7 39 9 41-2 42-5 43-7 45-0 46-3 47-6 48-9 50-1 51-4 52-7 54-0 55-3 17-090 17-875 18-662 19-452 20-242 21-029 21-825 22-619 23-418 24-220 25-023 28-825 26-628 27-438 28-253 29-069 29-884 30-703 31-519 18-642 23-080 27-550 32-014 36-474 40-924 45-424 49-838 54-302 58-844 63-366 67.874 72-403 76-987 81-550 86-100 90-720 95-316 99-920 (.7-5462 (.7 -5668 (.7-5875 V 7- 5763 (.7-5872 (.7-5801 1160 1495 1831 2167 2504 2840 3179 3514 3853 4194 4536 4876 5219 5565 5910 6255 6604 6951 7299 o 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1548 1975 2401 2828 3253 3676 4101 4526 4951 5378 5803 6226 6653 7078 9147 9574 10000 10427 10852 11275 11700 12125 12550 12977 13402 13825 14252 14677 + 009 + -021 + 014 + 038 + 019 + 055 + 024 + 089 + 030 + 120 + 038 + 159 + 047 + 202 + 056 + 251 + 066 + 304 TABLE XL. FOUBTH SERIES. Preliminary." March 24, 1878. Jacket 5-4 to 8 -2. Air about 6 C. Thermometer No. 6163. I B Correction. Corrected Temperature. Revolutions of Chronograph In. Mean Weight W. o.e y* ft|o LJ 03 T 1 * tHCO SH >s^ .2 & *|M *l Temperature. Work per Kilogramme. Work per Kilogramme + 4903. a 2 en 1 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 27 ; 4 29-2 31-0 32-9 34-7 36-6 38-4 40-3 42-2 44-2 46-1 + 002 8-071 9-204 10-340 11-480 12-620 13-763 14-908 16-054 17-202 18-350 19-504 42-364 48-898 55-438 62-066 68-669 75-330 81-973 88-597 95-264 101-941 108-588 7-471 7-446 7-442 7-405 7-390 7-398 7-431 7-429 7-437 7-433 V 7-4617 7-509 7-502 485 968 1458 1944 2433 2921 3410 3902 4395 4886 6855 7350 7844 O 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 -30 398 823 1252 1680 2107 2534 3960 3387 3815 4245 4672 5098 5524 5950 6376 6802 7228 7651 4872 5300 5725 6154 6582 7009 7436 8862 8289 8717 9147 9574 10000 10426 10852 11278 11704 12130 12553 + 010 + 019 + 017 + 050 + 025 + 093 + 034 + 150 + 046 + -222 .... 53-6 55-7 57-7 + 073 + 399 24-124 25-288 26-456 135-158 141-803 148-427 + 084 + 524 47 The first part of the experiments was lost, as the pen of the chronograph did not work. 29 450 HENRY A. EOWLAND TABLE XLI. FIFTH SERIES. Preliminary. March 24, 1878. Jacket 5-4 to 8-4. Air about 6C. Thermometer No. 6163. 1 H Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilogramme = 29-8816 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 2250. a i 02 d I w 75 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 810 0-9 1-7 3-4 5-1 6-8 8-5 10-2 12-0 13-7 15-5 17-2 19-0 20-8 22-6 24-3 26-1 27-9 29-6 003 1-891 2-451 3-569 4-690 5-810 6-936 8-060 9-190 10-323 11-459 12-600 13-742 14-882 16-025 17-170 18-316 19-467 20-615 3-154 6-118 12-174 18-172 24-212 30-397 36-621 42-854 49-068 55 398 61-707 68-036 74-358 80-716 87-064 93-402 99-677 105-950 8-1544 8-0900 8-0409 8-0074 7-9170 7-8973 7-8786 7-8512 7-8061 7-7799 7-7622 7-7643 7-7807 7-8419 7-8468 7-8579 7-8802 (.7-8980 7-9038 7-9091 7-8979 7-8974 239 723 1200 1677 2161 2647 3132 3614 4103 4588 5073 5558 6047 6539 7030 7518 8006 9482 9976 10474 10974 11481 o 2 3 4 5 6 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 46 477 906 1332 1759 2189 2621 3050 3477 3905 4333 4759 5183 5608 6036 6466 6895 7320 7745 8170 8597 9024 9451 9878 10305 10733 11160 2296 2727 3156 3582 4009 4439 4871 5300 5727 6155 6583 7009 7433 7858 8286 8716 9145 9570 9995 10420 10847 11274 11701 11128 12555 12983 13410 002 012 017 + 003 012 + 007 + 005 + 015 + 032 + 024 + 028 + 068 + 092 + 039 + 150 + 050 + 270 34-9 36-7 38-5 40-2 42-1 + 069 + 351 24-072 25-231 26-395 27-565 28-748 124-863 131-181 137-560 143-972 150-467 + 087 + 450 + 109 + 583 TABLE XLIL SIXTH SEEIES. May 14, 1878. Jacket 12-1 to 12-4. Air about 13 C. Thermometer No. 6165. I p Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W Work per Kilogramme = 2 9.9051 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 5433. a s 02 i 140 150 160 170 180 190 200 210 220 46-4 47-9 49-4 50-9 52-5 54-0 55-5 57-0 58-5 002 9-319 10-178 11-032 11-886 12-740 13-596 14-454 15-314 16-174 1-93 7-07 12-19 17-37 22-52 27-70 32-88 38-07 43-29 I 7- 2291 17-1608 i 7- 1500 I 7-1512 370 735 1102 1467 1835 2201 2568 2938 9 10 It 12 13 14 15 16 17 137 293 721 1151 1579 2007 2434 2863 3290 5296 5726 6154 6584 7012 7440 7867 8296 8723 000 007 + 002 008 + 006 002 + 010 + 011 ON THE MECHANICAL EQUIVALENT OF HEAT 451 TABLE XLII. Continued. Thermometer No. 6165. i H Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. gtl S.B~ O oos ^5" M| Temperature. Work per Kilogramme. Work per Kilogramme + 5433. a s 1 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 60-0 61-6 17037 17-093 48-50 53-70 jl.7-1446 ]. 7-1536 J. 7-1230 [7-1344 \. 7-1302 17-1117 I 7 -0958 1^7-1076 '. 7-1088 .7-1064 3306 3675 4778 5148 5514 5878 6240 6600 6962 7319 7680 8035 8396 8754 9115 9475 9833 10192 o 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 83 3716 4142 4567 4993 5420 5846 6271 6696 7121 7547 7973 8400 8829 9259 9678 10096 9149 9575 10000 10426 10853 11279 11704 12129 12554 12980 13406 13833 14262 14692 15111 15529 + 015 + 031 66-2 67-7 69-2 70-7 72-2 73-7 75-2 76-2 78-2 79-7 81-2 82-7 84-2 85-7 87-2 88-7 + 024 + 075 20-500 21-362 22-220 23-076 23-928 24-774 25-624 26-467 27-309 28-147 28-990 29-825 30-663 31 505 32-377 33-226 69-27 74-50 79-69 84-84 89-97 95-05 100-19 105-27 110-39 115-44 120-57 125-66 130-78 135-90 140-98 146-08 + 031 + 113 + 039 + 158 + 047 + 212 + 056 + 272 + 065 + -341 + 076 + 417 + 087 + 504 TABLE XLIII. SEVENTH SERIES. May 15, 1878. Jacket 11. 8 to 12. Air about 12 C. Thermometer No. 6163. S EH Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilogramme = 2 9.9387 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 5097. S 3 d * 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 30.9 32.2 33.6 35.0 36.3 37.6 38.9 40.2 41.5 42.8 44.2 45.5 46.9 48.3 49.6 50.9 52.3 .004 8.538 9.315 10.094 10.875 11.654 12.433 13.209 13.984 14.758 15.536 16.317 17.103 17.891 18.682 19.475 20.269 21.079 5.07 9.73 14.36 18.98 23.56 28.16 32.74 37.31 41.84 46.38 50.99 55.62 60.29 69.63 74.34 79.01 t 7. 2850 1.7. 3011 i 7.3165 i 7. 3460 17.3094 |^7.2846 J^7.2822 ^7.2610 335 668 1003 1335 1670 2003 2337 2667 2998 3332 3667 4005 4681 5021 5358 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 199 628 1056 1484 1913 2344 2770 3196 3623 4052 4478 4906 5324 5754 6179 6603 5296 5725 6153 6581 7010 7441 7867 8293 8720 9149 9575 10003 10421 10851 11276 11700 .002 .006 .010 + .003 .008 + .006 .000 + .010 + .013 + .014 + .032 + .019 + .056 + .025 + .090 452 HENRY A. ROWLAND TABLE XLIII. Continued. Thermometer No. 6163. 1 H Correction. Corrected Temperature. Revolutions of Chronograph 2. Mean Weight W. Work per Kilogramme = 2 9.9387 Wn. Temperature. Work per Kilogramme. Work per Kilogramme +5097. a 2 CD c 03 M 300 310 320 330 340 350 360 370 380 390 400 410 420 53.6 55.0 56.4 57.8 59.2 60.5 61.9 63.2 64.6 66.0 67.4 68.8 70.1 21.866 22.665 23.471 24.281 25.088 25.896 26 . 706 27.523 28.346 29.172 29.996 30.827 31.653 83.71 88.42 93.14 97.88 102.61 107.36 112.14 116.88 121.62 126.34 131.12 135.90 140.66 ) 7.2504 | 7.2893 | 7.3047 ) 7.3389 ) 7.4109 ) 7.4356 ' 7.4581 5697 6037 6379 6722 7065 7410 7759 8104 8454 8801 9155 9508 9861 25 26 27 28 29 30 31 32 7028 7454 7883 8307 8729 9157 9582 10009 12125 12551 12980 13404 13826 14254 14679 15106 + .032 + .039 + .127 + .172 + .046 + .222 + .055 + .279 + .065 + .345 + .075 + .080 + .419 + .456 TABLE XLIV EIGHTH SERIES. May 23, 1878. Jacket 16.2 to 16.5. Air about 20 C. Thermometer No. 6166. 1 H Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilogramme = 2 9.9075 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 8409. S GO d S 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 23.9 25.4 26.8 28.3 29.7 31.2 32.7 34.2 35.6 37.1 38.6 40.1 41.6 43.1 44.6 46.0 47.5 49.0 50.6 52.1 .007 16?287 17.063 39.120 43.982 6.9137 L 6. 9358 6.9007 6.9125 6.8878 6.8866 6.8594 6.8358 6.8748 6.9184 6.9444 6.9291 6.9338 6.9385 6.9444 6.9467 6.9314 333 1338 1673 2010 2346 2682 3020 3363 3702 4044 4385 4727 5074 5418 5766 6115 6464 o 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 306 735 1163 1592 2019 2446 2871 3298 3722 4150 4574 4999 5423 5851 6275 8715 9144 9572 10001 10428 10855 11280 11707 12131 12559 12983 13408 13832 14260 14684 .000 + .005 19.405 20.190 20.978 21.765 22.554 23.350 24.151 24.952 25.751 26.552 27.361 28.175 28.989 29.800 30.624 31.445 58.602 63.503 68.428 73.351 78.283 83.245 88.314 93.294 98.275 103.232 108.216 113.269 118.281 123.329 128.399 133.480 + !008 + .040 + .017 + .028 + .085 + .144 + .039 + .217 + .047 + .281 Ox THE MECHANICAL EQUIVALENT OF HEAT 453 TABLE XLV. NINTH SERIES. May 27, 1878. Jacket 19.6 to 20. Air about 23 C. Thermometer No. 6163. 1 B Correction. Corrected Temperature. Revolutions of Chronograph 2w. Mean Weight. W. Work per Kilogramme = 2 9.9077 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 8246. S 5 1 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 38.0 39.4 40.9 42.3 43.8 45.3 .015 15.890 17.000 18.106 19.219 .20.329 21.442 22.552 23.659 24.771 25.885 27.006 28.133 29.264 30.404 31.552 32.702 33.853 35.011 36.170 37.331 38.497 39.664 40.833 6.33 11.74 17.17 22.62 28.13 33.68 1 8. 8108 1 8. 7341 8.6030 ) 8.4800 ^8.4399 J ^8.4765 \ 8.4552 -I 8.4015 1 8.4222 I 8.4706 8.4316 473 946 1419 1895 2368 3785 4263 4737 5215 5697 6182 6669 7159 7652 8143 8638 9128 9626 10126 10620 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 47 473 901 1326 1754 2180 2606 3031 3457 3883 4312 4734 5159 5584 6010 6435 6860 7286 7714 8138 8565 8988 9414 9842 10268 10691 8293 8719 9147 9572 10000 10426 10852 11277 11703 12129 12558 12980 13405 13830 14256 14681 15106 15532 15960 16384 16811 17234 17660 18088 18514 18937 Oil .010 -.005 .011 + .002 .004 49.8 51.3 52.9 54.4 56.0 57.5 59.1 60.6 62.2 63.8 65.4 67.0 68.6 70.2 71.8 + .009 + .012 50.55 56.25 61.93 67.63 73.36 79.15 84.97 90.85 96.78 102.66 108.59 114.45 120.36 126.33 132.26 + .019 + .037 + .029 + .072 + .042 + .118 + .056 + .173 + .071 + .242 + .088 + .322 + .105 + .419 454 HENRY A. KOWLAND TABLE XLVL TENTH SERIES. June 3, 1878. Jacket 18. 1 to 18. 4. Air about 20 C. Thermometer No. 6166. 6 S B Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilogramme = 2 9.8878 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 9076. S as 1 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 4.1 7.0 9.9 12.8 15.7 18.7 21.6 24.5 27.5 30.5 33.6 36.6 39.6 42.7 45.8 48.9 52.0 -.007 !6o3 + .004 17.838 18.617 19.401 20.188 20.978 21.763 22.551 23.354 24. 162 24.970 25.780 26.593 27.415 28.246 29.079 29.911 30.754 7.82 23.19 30.95 38.70 46.41 54.21 62.04 69.92 77.92 85.89 93.94 102.05 110.34 118.49 126.66 134.89 | 4. 3899 1 4. 3919 J4.3912 1 4. 3907 | 4. 3624 J4.3542 1 4. 3362 i 4. 3978 667 1005 1341 1676 2014 2354 2696 3041 3385 3731 4081 4437 4786 5141 5499 18 19 20 21 22 23 24 25 26 27 28 29 30 31 69 496 925 1350 1778 2204 2627 3054 3479 3904 4332 4852 5179 5604 9145 9572 10001 10426 10854 11280 11703 12130 12555 12980 13408 13828 14255 14680 + .003 + .020 + .008 + 0.037 + .014 + .078 + .020 + .132 + .028 + .198 + .036 + .281 + .044 + .377 . . I TABLE XLVIL ELEVENTH SERIES. June 19, 1878. Jacket 19. 6 to 20. Air about 23 C. Thermometer No. 6163. 6 S B Correction. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilogramme = 2 9.8404 Wn. Temperature. Work per Kilogramme. Work per Kilogramme + 10620. S 5 -t-> 02 i W 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 .... .002 + .002 + .006 21?450 22.562 8.933 16.087 6.7572 I 6. 7678 476 o 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 -192 235 662 1087 1511 1939 2365 2789 3214 3638 4063 4488 4913 5337 5760 6187 6614 7040 7465 7891 8317 10428 10855 11282 11707 12131 12559 12985 13409 13834 14258 14683 15108 15533 15957 16380 16807 17234 17660 18085 18511 18937 .... + .010 + .029 24.789 25.907 27.032 28.168 29.307 30.456 31.612 32.774 33.939 35.110 36.280 37.456 38.637 39.821 41.010 30 281 37.439 44.655 51.848 59.098 66.390 73 . 724 81.153 88.462 95.734 103.093 110-560 118.121 125.693 133.250 i 6 . 7749 i 6. 7896 j. 6. 7973 i 6. 8188 I 6. 9165 j. 6. 7876 I 6. 7808 1421 1899 2379 2860 3344 3832 4323 4817 5311 5807 6307 6808 7311 7815 8321 + .019 + .063 .... + .031 + .113 + .043 + .177 + .058 + .257 + .072 + .351 + .087 + .463 + .106 + .595 ON THE MECHANICAL EQUIVALENT OF HEAT 455 '0961 + tuBJ jad JIJ cooo;i>t-oooooooioio 1 '- | 90iS8'6S 90iS8'6 eoo-*ooCMOcO'-it-O5iniftcoo t- wo JO . OOOOOOOOOOOOO500O5O5O:OiOOO5O OJ O t- 00 00 OS O5 O iH i-l *(< MI ^fi Tt< M< WlftW qdBJJSouoaqo JO SUOt?.niOA9}J jo oqnx MTV oo 10 10 o -oo O O o o : l' : + : + : & r-< if) O O 1 I *H co -N '8919 jo mooq 58 aqnx 00 O! m in to *t *< o '8919 'ON ^q J9J8UIIJOIBO JO .1.1 n nu.- ot-cOi-iyico'* 6919 ' 456 HENRY A. EOWLAND TABLE XLIX. THIRTEENTH SERIES. Dec. 19, 1878. Jacket 3.2 to 3.5. Air 4. 2 to 5.2 C. Thermometer No. 6163. Corrections. Corrected Temperature. Revolutions of Chronograph 2n. Mean Weight W. Work per Kilogramme 9.8938 X Wn. 2 9.8938 Wn. Temperature. Work per Kilogramme. Work + 1964. a 5 00 1 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 1?248 2.378 3.500 4.626 5.751 6.881 8.013 9.148 10.284 11.424 12.569 13.713 14.859 16.005 17.154 18.300 19.452 20.604 21.760 22.912 24.065 25.221 1.72 7.38 13.11 18.89 24.70 30.55 36.38 42.27 48.10 53.92 59.81 65.72 71.57 77.50 83.40 89.30 95.23 101.17 8.6610 8.5571 8.4325 8.3688 8.4155 8.4189 8.3953 8.4366 8.4484 8.4189 8.3988 8.4153 8.3811 8.3835 8.3976 8.4035 8.4460 1 5*8.4555 8.4602 8.4779 485.0 485.1 482.2 481.1 487.1 485.6 489.2 486.6 486.5 490.6 491.1 487.1 491.7 489.4 490.2 493.0 496.4 981.3 494.7 494.0 485.0 970.1 1452.3 1933.4 2420.5 2906.1 3395 . 3 3881.9 4368.4 4859.0 5350.1 5837.2 6328.9 6818.3 7308.5 7801.5 8297.9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 106 + 323 754 1184 1612 2041 2472 2901 3331 3760 4187 4615 5045 5472 5898 6327 6753 7180 7608 8038 8465 8891 9317 9746 10173 1858 2287 2718 3148 3576 4005 4436 4865 5295 5724 6151 6579 7009 7436 7862 8291 8717 9144 9572 10002 10429 10855 11281 11710 12137 .003 + .001 + .003 + .005 + .019 + .009 + .044 + .016 + .080 + .023 + .126 + .033 + .183 + .044 + .251 + .056 + .332 112.90 118.81 124.70 9279.2 9773.9 10267.9 + .069 + .424 ON THE MECHANICAL EQUIVALENT OF HEAT 457 TABLE L. FOURTEENTH SERIES. December 20, 1878. Jacket 1.5 to 1.9. Air about 3.4 C. Temperature by Kew Standard. 4 a H Corrections. Corrected Tem- perature Abso- lute Scale. Revolution of Chronograph 2n. Mean Weight W. k e 11^ Sfi 2 *s Temperature. Work per Kilogramme. Work per Kilogramme + 2210. Reduction to Absolute Scale. 1 i 36.0 38.5 41.0 43.5 46.0 48.5 51.0 53.5 56.0 58.5 61.0 63.5 66.0 68.5 71.0 73.5 76.0 78.5 56.0 58.4 .9 3.3 5.8 8.2 10.7 13.2 15.6 18.2 20.7 23.3 25.9 28.5 31.2 33.8 36.5 39.2 .00 182 3.23 4.62 6.02 7.43 8.84 10.26 11.68 13.12 14.56 16.01 17.46 18.92 20.39 21.86 23.34 24.84 26.33 8.03 16.37 24.78 33.19 41.48 49.81 58.18 66.56 74.95 83.56 92.27 100.99 109.95 118.84 127.83 136.75 145.78 154.80 7.3682 7.3458 7.3705 7.4012 7.4142 7.4177 7.4390 7.4107 7.3493 7.3269 7.2335 7.1603 7.2075 7.1839 7.2122 7.2252 7.2134 601 1206 1812 2412 3016 3624 4234 4842 5461 6085 6703 7330 7957 8589 9218 9857 10493 O 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 77 503 936 1370 1803 2226 2656 3084 3513 3942 4369 4790 5220 5650 6081 6507 6935 7364 7791 8219 8648 9074 9499 9925 10352 2287 2713 3146 3580 4013 4436 4866 5294 5723 6152 6579 7000 7430 7860 8291 8717 9145 9574 10001 10429 10858 11284 11709 12135 12562 -.01 .00 + .01 -.02 + .01 + .04 -.03 + .02 + .09 -.04 + .03 + .16 -.04 + .05 + .25 -.05 + .06 + .38 -.05 + .08 + .52 -.05 + .10 + .69 458 HENRY A. ROWLAND H O H O p O a H , O 5 H ^ O M S P HIOJJ ITB9J^ IBJ9U9Q OSOSOOSCSOOOOt-JOCM COrHiOt-OCOCOOSCMjO CM CM CO CO **& ^ TJ^ JO JO CO O t- JO CM O GO O CO CO OS CO 1> t- l> 00 n^ssrso GOOOOSCOOOt-COt-COCO OOrHT^l-OeOCOOSCMJO (Mt-rHJOO-^GOCMt-rH CM CM CO CO ^1 ^ ^ JO JO CO rH GO CO CO rH OO O CO CO OS JO O * 00 CM CO t- t- l> 00 S!Jin89}J IBUIJ JO UTS9J^ cojocoi-aot-cocojoco GOrHTj I> GO s^jn89}j A'.nuinm |,u,| jo UB9PI rH O J> JO CM OS CD CO -H CO O CO CD OS JO O * 00 CM CO t- I- t> 00 * JO JO CO unoq J9d fS i* 1-eOcDOCOCOCOTtHMCM GOrH^COrHCOCOOSCMJO CMt-rHJOO^GOCMt-rH O5 O O O rH I- O CO CO OS iO O * GO CM CO t Z> t~ OO jnoq J9d O gf '8919 '61 -09Q t-COOOCOJOCO'rtJO'^rH 00 -*t-OCOCOOSCMJO CM t rH JO O ^ 00 CM t~ rH OS OS CO CM rH t- O CO CD OS JO O ^ 00 CM CO t> t- t- 00 jnoq J9d O f8 a 'IJ31 2'i ^q3i9^ ^ aj '8919 Ml 'OSQ d* 3 ^ JO JO JO CD OS * t CO OOrHTflf-ocOCOOSCMJO CMt--^iOO-*OOCMt-rH O 3O JO CM t- co o :o oo JO O * 00 CM CO t- t- t- 00 gS -Jnoqj9d i8 5310 "8919 "61 9nnp * S g33 unoq J9d 9i; ^"2 "9919 "8 9unp T*$ $ "S u) unoq J9d O gf feS 'IW 9*8 WSfSM. 0 CO 00 r-t ^ CD OS JO O * GO CM CO t- t- t- 00 CM t- rH JO JO CO 1 unoq J9d O fg ^ '8919 "H ^BH * CM O I- CO OO i 1 *& CO OS IO O * CO CM O I t- t- GO CM l> -H JO JO CO unoq J9d 68 gg ^ '8919 "-S9IJ9S S COt-COCMOSOSrHOt-JO O5CMOCOOCOt-OCMJO CMl rHJOO^GOCOt-rH CMCMCOCO'^'tlTflJOiOCO CO OS CO OO CO 00 O CO IO CO JO O * 00 CM co r> t- i- oo ^S S unoqj9d 98 "?( '" '8919 '89IJ9S I CM OS CO CM OS 00 O SO CO GO JO O Tt< 00 C< CO l> t- I- 00 H A unoq J9d 88 S H 'IT 3 ! 9'i *q3t9M 5 o "9919 'SI qoJBJC MtH ^ jnoq J9d 88 2jj '8919 'i'JBH Q^S t- I- I- OO ^^ unoqj9d 98 "8919 "91 'UBf 00 'O O5 OS CO ^ CM GO o io ec os IO O * OO CM CO t- t- I- 00 t- rH JO CO 9Jn^BJ9din9x CM COrflJOCOt-OOOSOrH CM CO rt< iO CO ON THE MECHANICAL EQUIVALENT OF HEAT 459 p r 12 | i Hill lillllilllliil X x 5= S OS | o CO e CO a OS O O O COOOtOt-ICOO*OS'*r-lt-OtOCMt- k 1 g 3 1 s S 1 ililsiiliillii CO ~> 00 t- co os m o " * s s 2 s a t- **< t- c B X o X 00 O CO CO O) t- rH lO t- i- f -r >A o< c c r. o* "* 1.- i rH O t- (M l> -l X t- 1-1 C OS -! X (TJ t> ^H ; 00 cc Oi oo o iOCO-HCOSMO-<*-i**OCOTjit- JH -r f~ CJ 8 GO O CO 10 00 ~ g CO S CO O O W5 ^ O d t*- ^H iO C& r5 ~ 1- 5 ~ :7 Oi ^ Oi rf< O 30 g 2 i i rH T-H O^ d d 8 9 9 z * * J 2n 5 B OS 00 o> 01 o s | Ir s o -.c X 00 "*& C5 3O to 0. UP " 2 5 F^ 1 ^ X S t^ J - ^ - 1 3 s a a a ^_r^_^ L " :t F M OS * O O O iOOSCOO5gjJ WrHOOOtOiHOSl-COOO w < '61 '09Q O5OiOOOOCOOOl-t-t-l-l> H **** * ThTj<'*'* H~ . owoi-rH>t-^weo i 'il -09Q : : :SSwS H *-*"*Ttl- t- to O* d CO d eosococoininminin d d d d d d d d d inmininmininin dddddddd * OS CO d 5 t- i> _ * * * rH :::/::;:: d <* d d O o d d m M T-H O OS 00 OS rH rH CO ^ in m m d d d in^-^-^ininmin dddddddd *** ^ ^* CO CO Tf Tj< co m m in . inrHcooocoin^jn t-inco-^incoooco ; co co m in in in m in dddddddd ininoininminm dddddddd CO -^ O OS CO ' d d d d d '.'.'.'.'.'.'.'. CO OS ooooomrHrHcoin d d dddddddd t- ** dCOt-t-COdCOOOO d m CO d CO 00 CO d comininincocooin o os t- in :::::::: CO d *# 00 CO d 00 * t- in co in TH d o OS t" coMiccoi-Haoz>iCTt ' ' : SNwSct^N pJBpUB^g A192 . . .cooooeo^esoooas.ccocs.o wSwWWNCQWWWWWN J9I88I9Q .SilCCOOCJ^r-IOOOOO ' '. Icococoeocococococococococo Absolute Thermomet. Scale. Absolute C. G S. System. SUISR OOOOO>OSO5O5OiCOCOCOCO o __L____^LJ^!__L____J!!!!____ '81000' = I" -r-iooooosososajoscocooo Kilogr.- Metres at Baltimore. . . .^c*ot--*(MOOS?O^WOOO : : :SiwNNNNwwww "BS5- . . .1-^WOSCO^OJOt-iCCO^OS ! '. IOSCSCSOOOOGOOO co t~ z> t- t- o Work. 'WmraMVSd* OCO'^'l-t-OSOlO' (OOiCOt-tOlC'tiTH O'*DOOOCN(-#t-CT-<B89?,9 W - n Son 3 .98000'T s ^ B 3 *CiC5OT^ i ^COCN('--tOSlCCOOt^- 1 ^THOS OSCMlCOO-HTtOCSJ)CCOTHCO!OO5r-l Rc>-ino4ieoAci-iioOTfiaO'Mb< T-ilCO'tlOOi-liCO-*iCOCJt- Temperature. Approximate, Mercurial Thermom. w, T^ i ( O5 C^l CO CO CO ^ ^ ^ iC iC *C 1C 5O 5O oooooooooooooooo C^CO^lC5O?>OOC35Ot lO5CO^iC5Ot- f PL JO aso o (MCO-*COt-OOOSOT-liNCO-*iCI> Absolute Scalel QIOOO- = i OOOOOOOOOOOOOOr-lrH OO OOOOOOOOOOOOOOO WCO^io?ct-OOOSO'H(jjcO'*COl> '81000' = Smsn 0C501- Ox THE MECHANICAL EQUIVALENT or HEAT 463 ICCOCOi-HrHOSOSOOOOt-OCt-OOOOOSOSr-JrHOI lCiClClCiC'^'^''t < '^ 1 '^^* 1T **'^ l '^'^'^ | lClClC 01010101010101010101010101010101010101 COiCiC^TfiCOOIOIOIOICOCO^lCiCCOoOCiO . . . . O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1 " ' " " COt-COlC-*OlO1r-(OOOOSOOOrHO1O1CO CIC1^'C1CIC1C1C1C1C1C'<<1C1C1C1C1C1C1C " * * O1O1O1O1O1CMO1O1CMO1O1O1C OSOSOOOOOr-*OlOl^^COt~O5OOlTt'ic . . . ooiwco'co'coco'ccco'eoco'eo'eocoeoTi3'*M*i>t~*t t t t t-CO5OCOCOt~^l>t t-iC^OlrHOCsooi-cocococococet l-oooo ; ; cc'co'ococo'o'ic'icicicic'ic'ic'icic'ic'icic'ic O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1 t^lCrtiOlrHOSOOt COlClC^^^^^iClCiC COCO5O5O5OiClCiCiClClClCiClClCiClClc*C . . . OJO1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1O1 . . . coe*OGO5ocooioo5ooiascooiGooiot--*oi c 'oo'Coi 5OOOOrHCOlCt-COOOlCOiCl NB0 OOO1COlCC > -C3SOO1 1 ^ rHlCO*(t10OO1COOlCOSCOt*' |1CO^OOO15OO1COSCO CJSOSOOOr-lr-IOIOIOJCOCO^^lClClCCOCOt-t-l-CO t-^OCOO100^tlOO'*OSCOlCO1t-OO'*O5COOCOO1t Ol ^*l-OO11Ct OOllCt-OOJiCt-OSOlTtlt- OOllCt-O rHiCO^OOOIt-rHlCOS-^OOOIeOOiCOSCOCOOICOOlC OSOSOOOrHr-l04C1O1COCO^TtlC'CiCCOCOl-t-OOaO t-^O5OO1001COOlCOSTt(COCOOOOlCr-ICOO1CO^t*OSC *^.r*iroiCtoO1iCl>OO!lCt~OO1iCt~OO11Ct"*O t-r-iiCOS-^OOOlcOr-liCOSCOCOOICOOlCOS Oi- j <-HOioioicocoTjCOCOOOOO11COOOCOlCOOOCOOOrH rHlCCSTjtOOOICOr-llCOSCOaOOICOOlCOS i-HO101O1COCO-*-*lClCiCcoCOl->0000 COOOCOOOCIOOOOSOSOSOSOSOSOSOOOOOO OOOOOOOOOOOOOOOOOOi-jrHr-JrHrH adosorHWco'^'ioeo'^odosOrHoico^iccdt^odoso 1-1 IO!O1O1O1O1O1O1O1O1O1COCOCOCOCOeOCOCOCOCOTt< ooosorHoico^iccot^cdosOrHoieo'-^iccdt^coosc:) rHr-iOlO1O1O1OlOJCMO1O1O1SOCOCOeOCOCOCOCOCOCO-* jCiClCiCiCiCcOCOCOCOCOCOCOCO5Ob - l > *l > -t !> O O O O O C5 O O O O O O O O O O O O CD O O O O __ a6os'o^oicoTiiiccdt>odosorHOco''*iccdt-odo5Or-I a OJOioioioioiojesjoiojcocoeocoeocococoeoco-* 1 * o eoT*^^^^lftftee>^ttC3SOSOOr^*^rHO1OlO1C > 10 : l oioioicoeococococoeoeocococo -^ ooosot ioico^iC5Ot-odosO'-5oieo'Tjiic5oi-ooos~ r-l-jcoOIOlOIOIOIOIOlOIOICOCOCOCOCOCOCOCOCOCO 3 eoeo-} a <*> s . . S 8 "8 sga OCQ S 2 a>S->-U 8*3 s 25 302 s 2 a aJu2 &gs 11 5 00 . bc+^'-S Jv83 ll SS g ttf)'* J 4^* o p ~~ ( |o6 l"|l |||" H 2 K q S m hi ID g 2 = 5 w i 00000. 0000. o 00000. 0000. 2 2289 2443 22 10852 10835 426.1 4176 3 2720 2865 23 11278 11253 426.0 4175 4 3150 3286 24 11704 11670 425.9 4174 5 3580 3708 429.8 4212 25 12130 12088 425.8 4173 6 4009 4129 429.5 4209 26 12556 12505 425.7 4172 7 4439 4550 429.3 4207 27 12982 12922 425.6 4171 8 4868 4970 429.0 4204 28 13407 13339 425.6 4171 9 5297 5390 428.8 4202 29 13833 13756 425.5 4170 10 5726 5811 428.5 4200 30 14258 14173 425.6 4171 11 6154 6230 428.3 4198 31 14684 14950 425.6 4171 12 6582 6650 428.1 4196 32 15110 15008 425.6 4171 13 7010 7070 427.9 4194 33 15535 15425 425.7 4172 14 7438 7489 427.7 4192 34 15961 15842 425.7 4172 15 7865 7908 427.4 4189 35 16387 16259 425.8 4173 16 8293 8327 427.2 4187 36 16812 16676 425.8 4173 17 8720 8745 427.0 4185 37 17238 17094 18 9147 9164 426.8 4183 38 17664 17511 19 9574 9582 426.6 4181 39 18091 17930 20 10000 10000 426.4 4179 40 18517 18347 21 10426 10418 426.2 4177 41 18943 18765 TABLE LV. QUANTITY TO ADD TO THE EQUIVALENT AT BALTIMORE TO REDUCE TO ANT LATITUDE. Latitude. Addition in Kilogramme-Metres. + 0.89 10 + 0.82 20 + 0.63 30 + 0.34 40 + 0.08 50 0.41 60 0.77 70 -1.06 80 1.26 90 -1.33 Manchester 0.5 ; Paris 0.4 ; Berlin 0.5. ON THE MECHANICAL EQUIVALENT OF HEAT 465 V. CONCLUDING REMARKS, AND CRITICISM OF RESULTS AND METHODS On looking over the last four columns of Table LIII, which gives the results of the experiments as expressed in terms of the different mercurial thermometers, we cannot but be impressed with the unsatis- factory state of the science of thermometry at the present day, when nearly all physicists accept the mercurial thermometer as the standard between and 100. The wide discrepancy in the results of calori- metric experiments requires no further explanation, especially when physicists have taken no precaution with respect to the change of zero after the heating of the thermometer. They show that thermometry is an immensely difficult subject, and that the results of all physicists who have not made a special study of their thermometers, and a com- parison with the air thermometer, must be greatly in error, and should be rejected in many cases. And this is specially the case where Geissler thermometers have been used. The comparison of my own thermometers with the air thermometer is undoubtedly by far the best so far made, and I have no improvements to offer beyond those I have already mentioned in the ' Appendix to Ther- mometry/ And I now believe that, with the improvement to the air thermometer of an artificial atmosphere of constant pressure, we could be reasonably certain of obtaining the temperature at any point up to 50 C. within 0-01 C. from the mean of two or three observations. I believe that my own thermometers scarcely differ much more than that from the absolute scale at any point up to 40 C., but they represent the mean of eight observations. However, there is an uncertainty of 0-01 C. at the 20 point, owing to the uncertainty of the value of m. But taking m= -00015, I hardly think that the point is uncertain to more than that amount for the thermometers Nos. 6163, 6165, and 6166. As to the comparison of the other thermometers, it is evidently un- satisfactory, as they do not read accurately enough. However, the fig- ures given in Table LIII are probably very nearly correct. The study of the thermometers from the different makers introduces the question whether there are any thermometers which stand below the air thermometer between and 100. As far as I can find, nobody has ever published a table showing such a result, although Bosscha infers that thermometers of " Cristal de Choisy-le-Eoi " should stand below, and his inference has been accepted by Eegnault. But it does not seem to have been proved by direct experiment. My Baudin thermometers seem to contain lead as far as one can tell from the blackening in a gas 30 466 HENRY A. ROWLAND flame, but they stand very much above the air thermometer at 40. I have since tried some of the Baudin thermometers up to 300, and find that they stand Mow the air thermometer between 100 and 240 ; they coincide at about 240, and stand above between 240 and 300. This is very nearly what Eegnault found for " Verre Ordinaire." It is to be noted that the formula obtained from experiments below 100 makes them coincide at 233, which is remarkably close to the result of actual experiment, especially as it would require a long series of experiments to determine the point within 10. The comparison of thermometers also shows that all thermometers in accurate investigations should be used as thermometers with arbi- trary scales, neither the position of the zero point nor the interval be- tween the and 100 points being assumed correct. The text books only give the correction for the zero point, but my observations show that the interval between the and 100 points is also subject to a sec- ular change as well as to the temporary change due to heating. Of all the thermometers used, the Geissler is the worst in this as in other respects, except accuracy of calibration, in which it is equal to most of the others. The experiments on the specific heat of water show an undoubted decrease as the temperature rises, a fact which will undoubtedly sur- prise most physicists as much as it surprised me. Indeed, the dis- covery of this fact put back the completion of this paper many months, as I wished to make certain of it. There is now no doubt in my mind, and I put the fact forth as proved. The only way in which an error accounting for this decrease could have been made appears to me to be in the determination of ra in " Thermometry." The determination of m rests upon the determination of a difference of only 0-05 C. between the air thermometer and the mercurial, the and 40 points coincid- ing, and also upon the comparison of the thermometers with others whose value of m was known, as in the Appendix. Although the quan- tity to be measured is small, yet there can be no doubt at least that m is larger than zero; and if so, the specific heat of water certainly has a minimum at about 30. One point that might be made against the fact is that the Kew stand- ard, Table L, gives less change than the others. But the calibra- tion of the Kew standard, although excellent, could hardly be trusted to 0-02 or 0-03 C., as the graduation was only to F. In drawing the curve for the difference between the Kew standard and the air ther- mometers, I ignored small irregularities and drew a regular curve. On ON THE MECHANICAL EQUIVALENT OF HEAT 467 looking over the observations again, I see that, had I taken account of the small irregularities, it would have made the observations agree more nearly with the other thermometers. Hence the objection vanishes. However, I intend working up some observations which I have with the Kew standard at a higher temperature, and shall publish them at a future time. There is one other error that might produce an apparent decrease in the specific heat, and that is the slight decrease in the torsion weight from the beginning to the end of most of the experiments, probably due to the slowing of the engine. By this means the torsion circle might lag behind. I made quite an investigation to see if this source of error existed, and came to the conclusion that it produced no perceptible effect. An examination of the different experiments shows this also, for in some of them the weight increases instead of decreasing. See Tables XXXVII to L. The error from the formation of dew might also cause an apparent decrease; but I have convinced myself by experiment, and others can convince themselves from the tables, that this error is also inappre- ciable. The observations seem to settle the point with regard to the specific heat at the 4 point within reasonable limits. There does not seem to be a change to any great extent at that point, but the specific heat decreases continuously through that point. It would hardly be possible to arrive at this so accurately as I have done by any method of mixture, for Pfaundler and Platter, who examined this point, could not obtain results within one per cent, while mine show the fact within a fraction of one per cent. The point of minimum cannot be said to be known, though I have placed it provisionally between 30 and 35 C., but it may vary much from that. The method of obtaining the specific heat of the calorimeter seems to be good. The use of solder introduces an uncertainty, but it is too small to affect the result appreciably. The different determinations of the specific heat of the calorimeter do not agree so well as they might, but the error in the equivalent resulting from this error is very small, and, besides, the mean result agrees well with the calculated result. It may be regarded as satisfactory. The apparatus for determining the equivalent could scarcely be im- proved much, although perhaps the record of the torsion might be made automatic and continuous. The experiment, however, might be im- HENRY A. ROWLAND proved in two ways; first, by the use of a motive power more regular in its action; and, second, by a more exact determination of the loss due to radiation. The effect of the irregularity of the engine has been calcu- lated as about 1 in 4000, and I suppose that the error due to it cannot be as much as that after applying the correction. The error due to radiation is nearly neutralized, at least between and 30, by using the jacket at different temperatures. There may be an error of a small amount at that point (30) in the direction of making the mechanical equivalent too great, and the specific heat may keep on decreasing to even 40. Between the limits of 15 and 25 I feel almost certain that no sub- sequent experiments will change my values of the equivalent so much as two parts in one thousand, and even outside those limits, say be- tween 10 and 30, I doubt whether the figures will ever be changed much more than that amount. It is my intention to continue the experiments, as well as work up the remainder of the old ones. I shall also use some liquids in the calorimeter other than water, and so have the equivalent in terms of more than one fluid. Baltimore, 1878-79. FinisTied May 27, 1879. 21 APPENDIX TO PAPEE ON THE MECHANICAL EQUIVALENT OF HEAT, CONTAINING THE COMPARISON WITH DR. JOULE'S THERMOMETER [Proceedings of the American Academy of Arts and Sciences, XVI, 38-45, 1881] Presented, March, 1880 In the body of this paper I have given an estimate of the departure of Dr. Joule's thermometer from the air thermometer, based on the com- parison of thermometers of similar glass. But as it seemed important that the classical determinations of this physicist should be reduced to some exact standard, I took to England with me last summer one of my standards, Baudin, No. 6166, and sent it to Dr. Joule with a statement of the circumstances. He very kindly consented to make the comparison, and I now have the results before me. These confirm the estimate that I had previously made, and cause our values for the equivalent to agree with great accuracy. The following is the table of the comparison : Readings. Temperatures. By perfect Air Baudin, No. 6166. Joule. Thermometer according to By Joule's Thermometer. Difference. No. 6166. 21.88 22.62 8 8 o 41.930 59.410 1 . 590 1.578 .012 48.782 72.200 2.126 2.127 + .001 53.705 81.340 2.511 2.519 .008 58.916 90.877 2.918 2.928 .010 64.914 101.777 3.382 3.396 .014 73.374 117.291 4.039 4.061 .022 80.176 129.990 4.567 4.606 .039 85.268 139.255 4.961 5.003 .042 90.564 148.834 5.370 5.414 .044 94.243 155.460 5.654 5.698 .044 99.168 164.400 6.036 6.082 .046 104.030 173.140 6.413 6.457 .044 108.863 182.040 6.789 6.839 .050 113.706 190.885 7.165 7.218 .053 114.000 191.382 7.188 7.239 .051 '121.507 '219.497 '7.772 '8.445 1 Evidently a mistake in the readings. 470 HENBY A. ROWLAND Continued. Readings. Temperatures. Baudin, No. 6166. Joule. By perfect Air Thermometer according to No. 6166. By Joule's Thermometer. Difference. o o o 135.858 231.115 8.890 8.944 .054 140.467 239.939 9.249 9 . 309 .060 143.405 245.006 9.479 9.540 .061 146.445 250.566 9.717 9.778 .061 152.360 261.481 10.180 10.246 .066 158.770 273.239 10.681 10.751 070 164.635 283.957 11.138 11.211 .073 170.485 294 . 739 11 . 595 11.670 .075 175.436 303.682 11.979 12.057 .078 182.795 316.968 12.550 12.627 .077 188.705 327.746 13.008 13.089 .081 193.954 337.220 13.412 13.495 .083 199.558 347.294 13.844 13.928 .084 206.054 259.060 14.343 14.432 .089 211.528 368.953 14.764 14.857 .093 216.440 377.826 15.142 15.237 .095 221.858 387.562 15.560 15.655 .095 229.601 401.419 16.158 16.249 .091 235.598 412.367 16.623 16 . 719 .096 241.028 422.258 17.045 17.143 .098 247.436 433.800 17.541 17.638 .097 253.704 445.267 18.028 18.130 .102 259". 786 456.286 18.500 18.603 .103 266.086 467.817 19 . 991 19.097 .106 273 . 143 480.643 19.539 19.648 .109 280.176 493.442 20.086 20.197 .111 287.634 506.906 20.666 20.774 .108 294.927 520.052 21.232 21.338 .106 304.148 536.832 21.947 22.058 .111 310.397 548.152 22.432 22.544 .112 316.596 559.336 22.916 23.023 .107 321.271 568.051 23.282 23.397 .115 327.148 578.528 23.742 23.846 .104 333.661 590.661 24.251 24.367 .116 339.664 601.596 24.719 24.836 .117 346.557 614.004 25.254 25.369 .115 352.878 625.510 25.746 25.862 .116 359.986 638.526 26.299 26.421 .122 365.080 647 . 833 26.697 26.820 .123 371.811 660.071 27.225 27.345 .120 382.770 680.149 28.087 28.206 .119 We can discuss the comparison of these thermometers in two ways; either by direct comparison at the points we desire, or by the repre- sentation of the differences by a formula. Joule's result in 1850 was referred to water at about 14 C., and in 1878 to water at 16 -5 C. Taking intervals in the above table of from APPENDIX TO THE MECHANICAL EQUIVALENT OF HEAT 471 6 to 12, so that the mean shall be nearly 14 and 16 -5, I find the following for the ratios : 1-0044 1-0042 1-0042 1-0042 1-0049 1-0040 1-0047 1-0030 1-0047 1-0035 1-0052 1-0035 Mean, 1-0047 1-0037 So that we have the following for Joule's old and new values : Old. New. 423-9 423-9 Correction for thermometer 2-0 1-6 Correction for latitude -5 -5 Correction for sp. ht. of copper -7 427-1 426-0 My value 427-7 427-1 Difference -6 1-1 or 1 in 700 and 1 in 390, respectively. But the correction found in this way is subject to local irregulari- ties, and it is perhaps better in many respects to get the equation giving the temperature of Joule's thermometer on the air thermometer. Let T be the temperature by Joule's thermometer, and t that by the air thermometer. Then I have found t = 0-002 + 1-00125 T -00013 \ 100 T\ \ 1 -003 (100 -f T) \ The factor 1-00125 enters in the formula, probably because the ther- mometer which Joule used to get the value of the divisions of his ther- mometer was not of the same kind of glass as his standard. The rela- tive error at any point due to using the mercurial rather than the air thermometer will then be E = 1 $** = 00125 + -00000039 \ 23300 666 t + 3 f\ dT * 472 HENRY A. ROWLAND From this I have constructed the following table : Approximate Addition to Equivalent as measured on Joule's Thermometer. Temperature. Metric System. English System. .0078 3.3 6.0 5 .0066 2.8 5.1 10 .0054 2.3 4.2 15 .0042 1.8 3.2 20 .0031 1.8 2.4 25 .0021 .9 1.6 30 .0011 .5 .8 Corrected in this way we have, Joule's value Eeduction to air thermometer Reduction to latitude of Baltimore Correction for sp. ht. of copper My value Difference Old. 423-9 1-9 5 7 427-0 427-7 New. 423-9 1-7 5 426-1 427-1 1-0 or 1 in 600 and 1 in 426, respectively. But it is evident that all the other temperatures used in the experi- ment must also be corrected, and I have done this in the following man- ner. The principal other correction required is in the capacity of the calorimeter, and this amounts to considerable in the experiments on mercury and cast-iron, where no water is used. Dr. Joule informs me that the thermometer with which he compared mine was made in 1844, but does not give any mark by which to designate it, although it is evi- dently the thermometer called "A" by him. I shall commence with the experiments of 1847. The calorimeter was composed of the following substances, whose capacities I recompute according to what in my paper I have considered the most probable specific heats. wai-o-ht Capacity accord- Most probable Most probable ing to Joule. Specific Heat. Capacity. Water 77617 grains 77617 1-000 77617 Brass 24800 grains 2319 -0900 2232 Copper 11237 grains 1056 -0922 1036 Tin (?) 363 363 Total capacity 81355 81248 APPENDIX TO THE MECHANICAL EQUIVALENT OF HEAT 473 Equivalent found 781-5 at about 59 F. Correction for thermometer 3-3 Correction for capacity 1-3 Correction for latitude -9 Corrected value 787-0 or 442-8 at 15 C. on the air thermometer. The other experiment, on sperm oil, made at this time, is probably hardly worth reducing. The experiments of 1850 are of the highest importance and should be accurately reduced. In the experiments with water the capacity of the calorimeter is cor- rected as follows : Weight. Capacity used > by Joule. S [ost probable peciflc Heat. Most probable Capacity. Water 93229-7 93229-7 1-000 93229-7 ^ Copper 25541- 2430-2 092 2349-8 * Brass 18901- 1800-0 091 1720-0 Brass stopper 10-3 10-3 Total capacity 97470-2 97309-8 Therefore correction is -0016. Hence the result with water requires the following corrections : Joule's value 772-7 at 14 C. Correction for thermometer 3-2 Correction for latitude -9 Correction for capacity 1-2 778-0 or 426-8 on the air thermometer in the latitude of Baltimore at the temperature of 14 C., nearly. In the next experiment, with mercury, Joule determined the capacity of the apparatus by experiment. The mean of the experiments was that the apparatus lost 20 -33155 F. in heating 143430 grains of water 3 13305 F. To reduce these to the air thermometer we must divide respectively by 1-0042 and 1-0056. Therefore the capacity must be divided by 1-0014. Therefore the corrected values are: 772-8 at 9 C. 775-4 at 11 C. Correction for thermometer 4-4 4-0 Correction for capacity 1-1 1-1 Correction for latitude -9 -9 779-2 781-4 474 HENEY A. ROWLAND The reduction to the air thermometer was made for the temperatures of 9 C. and 11 C. respectively, but they both refer to the temperature of the water used when the capacity was determined; this was about 9 C. Hence these experiments gave 427-5 and 428-7 on the air ther- mometer, with the water at about 9 C. The next experiments, with cast-iron, can be corrected in the same manner, and thus become 776-0 773-9 Correction for thermometer 4-2 4-3 Correction for capacity 1*1 !! Correction for latitude -9 -9 782-2 780-2 and these are as before for water at 9. The determination by the heating of a wire, whose resistance was measured in ohms, can be thus reduced. The value found by Joule was 429-9 in the latitude of Baltimore at 18 -6 C. Using the capacity of the copper -0922, as I have done in my paper, this quantity will be increased to 430-3. But I have given reasons in my paper on the " Absolute Unit of Electrical Resistance " to show that there should be a correction to the B. A. Committee's experiments, which would make the ohm -993 earth quadrant -f- second, instead of 1-000 as it was meant to be, which nearly agrees with the quantity which I found, namely, -991. Taking my value -9911, Joule's result will reduce as follows : 429.9 at 18 -6 C. Correction for thermometer -|- 1-5 Correction for capacity -|- -4 Corrected for ohm 3-8 Corrected value 428-0 at 18 -6 C. The last determinations in the ' Philosophical Transactions ' of 1878 can be reduced as follows : The capacity of the calorimeter was determined by experiment, in- stead of calculated from the specific heat of copper given by Regnault, as in the older experiments. The value used, 4842-4 grains, corre- sponded to a specific heat of brass of about -090, which is almost exactly what I have considered right. The reduction to the air thermometer will decrease it somewhat, and the correction for the increase of the APPENDIX TO THE MECHANICAL EQUIVALENT OF HEAT 475 specific heat of brass and the decrease of the specific heat of water will also change it somewhat. In all, the amount will be about 1 in 200. Hence the reduction becomes as follows : Joule's values Correction for thermometer Correction for capacity Correction for latitude Correction to vacuum Corrected values 772-7 774-6 3-2 3-7 2 -2 9 -9 773-1 3-1 2 9 767-0 774-0 3-3 2-8 2 -2 9 -9 9 -9 776-1 778-5 776-4 770-5 777-0 at 14-7 atl2-7 at!2-5 at 14-5 at 17-3 To reduce the values in English measure to metres and the Centi- grade scale, I have simply taken the reducing factor 1-8 X -304794, although the barometer on the two systems is not exactly the same: for this is taken into account in the comparison of the thermometers. However, a barometer at 30 in. and 60 F. is equivalent to 759-86 mm. at C. which hardly makes a difference of 0-01 C. in the temperature of the hundred-degree point. Joule's Value re- duced to Air Ther- * and of the ellipse or hyperbola R + re = 2* or (i 2 a 2 ) x 3 + fry 2 = tf(V a' i ) in which c has disappeared. dx y y' - --- ON CONCAVE GRATINGS FOR OPTICAL PURPOSES 495 dzl (b z a 2 ) xPy ^^ } = b\W - (a? x x . - ,b " (V + y* + a 2 ) This equation gives us the proper distance of the rulings on the sur- face, and if we could get a dividing engine to rule according to this formula the problem of bringing the spectrum to a focus without tele- scopes would be solved. But an ordinary dividing engine rules equal spaces and so we shall further investigate the question whether there is any part of the circle where the spaces are equal. We can then write ds __ n db~ And the differential of this with regard to an arc of the circle must be zero. Differentiating and reducing by the equations dx _ _y y' . db _ p ~dy ~ x=2' ~dy ~ G (x a/)' we have P { 2xb (y y'} - 2yb (x x'}- - [6i a - (a? + y 1 + a 1 )] } It is more simple to express this result in terms of E, r, p and the angles between them. Let fi. be the angle between p and r, and v that between p and R. Let us also put Let /?, f and 3 also represent the angles made by r, R and p respec- tively with the line joining the source of light and focus, and let Then we have _ R cos f + r cos ,5 _ R sin f + r sin p _r cos /3 R cos y -I 2/ 9 9. " 496 HENKY A. ROWLAND (b* - a^(y -y'T + P (x - x'J = f ( 2 - 8 sin 2 3) , I 1 a* = Rr cos 2 a , R -\- r ir _ R simj = ^ sin a; cos -n = - cos a, 2a 2a = --, = -, T cos 7] sin r sin ft Rr . x=b - r ; v = a -. '- - - = r- sm in cos a , COS a Sin a COS a Vy (y -y'}+x (I* - a 2 ) (a; - aT) = (cos ,,. + cos 26 2 (V + */ 2 + O = #r, - x')= (sin n + sin v) sin /jt + sin v cos a sin e 2a cos 5 = r cos /j. R cos y , 2a sin 5 = r sin /* R sin v . . On substituting these values and reducing, we find 2 2Rr cos a cos e ~ r cos 2 y + R cos 2 n ' ds 2 A more simple solution is the following: _ mnst be constant in the direction do in which the dividing engine rules. If the dividing engine rules in the direction of the axis y, the differential of this with respect to y must be zero. But we can also take the reciprocal of this quantity and so we can write for the equation of condi- tion d d(R+ r) _ dy ds Taking a circle as our curve we can write (Z_X')2+ ( y yf)* = p* and (x x")* + (y y"V = -R 2 , (X - 2///)2 + (y - y'")1 = r 2 , + r)_ i ( ,j*-x" x-x>\_ { ^_^ly-y" + y-v"'\) ~~i\ (l/ y \2t - J \~~W~ ~r - j} (R + r) _ 1 r x x"x x'" , \~ x x")(y y"} dT~ ~yj~ R- ~T~ ~^~~ \ _ sin fi = p sin /./ cos 8' + R sin d' p cos // sin 8', sin /j. = sin // cos d' \ 1 + r J l A tan 8 f i , iOsmjH, y where * _ -. _ p cos ,u Developing the value of cos d' in terms of d, we have cos " = cos S { 1 + A [l + '' 8 "'"| ' As the cases we are to consider are those where A is small, it will be sufficient to write tan * : = Whence we have sin <,. = sin // cos d + ,5 3 + &c. \ - We can write the value of sin v from symmetry. But we have 2 -7- = sin fj. + sin v . as In this formula, db can be considered as a constant depending on wave-length of light, etc., and ds as the width apart of the lines on the grating. The dividing engine rules lines on the curved surface accord- ing to the formula 2 -7- = cos 8 (sin //,+ sin v ). CL8 But this is the second approximation to the true theoretical ruling. And this ruling will not only be approximately correct, but exact when 502 HENRY A. ROWLAND all the terms of the series except the first vanish. In the case where the slit and focus are on the circle of radius %p, as in the automatic arrange- ment described above, we have A = and the second and third terms of the series disappear, and we can write since we have TO r t = cos fJL and - cos v , P P n db / . \/i i sin >j. tan // + sin v tan * 3 \ 2 = cos d (sin ,u + sin > ) 1 J - r+ &c. . ds \ sm fj + sm > / But in the automatic arrangement we also have v = 0, and so the formula becomes 2 -j- = cos d (sin /; + sin K O ) { 1 J tan ^ ^ ! + &c. }. 6t5 To find the greatest departure from theoretical perfection, d must refer to the edge of the grating. In the gratings which I am now mak- ing, p is about 260 inches and the width of the grating about 5-4 inches. Hence d = - approximately and the series becomes Hence the greatest departure from the theoretical ruling, even when ta.nfji ( f=2, is 1 in 1,000,000. Now the distance apart of the compon- ents of the 1474 line is somewhat nearly one forty-thousandth of the wave-length and I scarcely suppose that any line has been divided by the best spectroscope in the world whose components are less than one- third of this distance apart. Hence we see that the departure of the ruling from theoretical perfection is of little consequence until we are able to divide lines twenty times as fine as the 1474 line. Even in that case, since the error of ruling varies as 3 s , the greater portion of the grating would be ruled correctly. The question now comes up as to whether there is any limit to the resolving power of a spectroscope. This evidently depends upon the magnifying power and the apparent width of the lines. The magnify- ing power can be varied at pleasure and so we have only to consider the width of the lines of the spectrum. The width of the lines evidently depends, in a perfect grating, upon three circumstances, the width of the slit, the number of lines in the grating and the true physical width of the line. The width of the slit can be varied at pleasure, the number of lines on the grating can be made very great (160,000 in one of mine), and hence we are only limited by the true physical width of the lines. Ox COXCAVE GRATINGS FOR OPTICAL PURPOSES 503 We have numerous cases of wide lines, such as the C line, the compon- ents of the D 3 and H lines and numerous others which are perfectly familiar to every spectroscopist. Hence we are free to suppose that all lines have some physical width, and we are limited by that width in the resolving power of our spectroscope. Indeed, from a theoretical stand- point, we should suppose this to be true : for the molecules only vibrate freely while swinging through their free path and in order to have the physical width one one-hundred-thousandth of the wave-length, the molecule must make somewhat nearly one hundred thousand vibrations in its free path: but this would require a free path of about sooVoo inch ! Hence it would be only the outermost solar atmosphere that could produce such fine lines and we could hardly expect to see much finer ones in the solar spectrum. Again * it is found impossible to obtain interference between two rays whose paths differ by much more than 50,000 wave-lengths. All the methods of determining the limits seem to point to about the 150,000th of the wave-length as the smallest distance at which the two lines can be separated in the solar spectrum by even a spectroscope of infinite power. As we can now nearly approach this limit I am strongly of the opinion that we have nearly reached the limit of resolving power, and that we can never hope to see very many more lines in the spectrum than can be seen at present, either by means of prisms or gratings. It is not to be supposed, however, that the average wave-length of the line is not more definite than this, for we can easily point the cross- hairs to the centre of the line to perhaps 1 in 1,000,000 of the wave- length. The most exact method of detecting the coincidences of a line of metal with one in the solar spectrum would thus be to take micro- metric measurements first on one and then on the other; but I suppose it would take several readings to make the determination to 1 in 1,000,000. Since writing the above I have greatly improved my apparatus and can now photograph 150 lines between the H and K lines, including many whose wave-length does not differ more than 1 in about 80,000. I have also photographed the 1474 and b 3 and & 4 , widely double, and also E just perceptibly double. With the eye much more can be seen, but I must say that I have not yet seen many signs of reaching a limit. The 3 1 have recently discovered that each component of the D line is double probably from the partial reversal of the line as we nearly always see it in the flame spectrum. *This method of determining the limit has been suggested to me by Prof. C. 8. Hastings, of this University. 504 HE^RY A. EOWLAND lines yet appear as fine and sharp as with a lower power. If my grat- ing is assumed to be perfect, in the third spectrum I should be able to divide lines whose wave-lengths differed, in about 150,000, though not to photograph them. The E line has components, about ^uwfrth of the wave-length apart. I believe I can resolve lines much closer than this, say 1 in 100,000 at least. Hence the idea of a limit has not yet been proved. However, as some of the lines of the spectrum are much wider than others we should not expect any definite limit, but a gradual falling off as we increase our power. At first, in the short wave-lengths at least, the number of lines is nearly proportional to the resolving power, but this law should fail as we approach the limit. 31 ON MR. GLAZEBROOK'S PAPER ON THE ABERRATION OF CONCAVE GRATINGS [American Journal of Science [3], XXVI, 214, 1883 ; Philosophical Magazine [5], XVI, 210, 1883] In the June number of the Philosophical Magazine., Mr. R. T. Glaze- brook has considered the aberration of the concave grating and arrives at the conclusion that the ones which I have hitherto made are too wide for their radius of curvature. As I had published nothing but a preliminary notice of the grating at that time, Mr. Glazebrook had not then seen my paper on the subject, of which I gave an abstract at the London Physical Society in November last. In this paper I arrive at the conclusion that there is practically no aberration and that in this respect there is nothing further to be desired. The reason of this discrepancy is not far to seek. Mr. Glazebrook assumes that the spaces are equal on the arc of the circle. But I do not rule them in this manner; but the equal spaces are equal along the chord of the arc. Again, the surface is not cylindrical, but spherical. These two errors entirely destroy the value of the paper as far as my gratings are concerned, for it only applies to a theoretical grating, ruled in an entirely different manner from my own, and on a different form of surface. I am very much surprised to see the method given near the end of the paper for constructing aplanatic gratings on any surface, for this is the method by which I discovered the concave grating originally, and the figure is the same as I put on the blackboard at the meeting of the Physical Society in November last. I say I am surprised, for Mr. Glaze- brook's paper was read at the Physical Society, where I had given the same method a few months before, and yet it passed without comment. Indeed, I have given the same method many times at various scientific societies of my own country. However, as Mr. Glazebrook was not present at the meeting referred to, he is entirely without blame in the matter. 33 SCEEW [Encyclopedia Britannica, Ninth Edition, Volume XXI \ The screw is the simplest instrument for converting a uniform motion of rotation into a uniform motion of translation (see ' Mechanics/ vol. xv, p. 754). Metal screws requiring no special accuracy are generally cut by taps and dies. A tap is a cylindrical piece of steel having a screw on its exterior with sharp cutting edges; by forcing this with a revolv- ing motion into a hole of the proper size, a screw is cut on its interior forming what is known as a nut or female screw. The die is a nut with sharp cutting edges used to screw upon the outside of round pieces of metal and thus produce male screws. More accurate screws are cut in a lathe by causing the carriage carrying the tool to move uniformly for- ward, thus a continuous spiral line is cut on the uniformly revolving cylinder fixed between the lathe centres. The cutting tool may be an ordinary form of lathe tool or a revolving saw-like disk (see ' Machine Tools/ vol. xv, p. 153). Errors of Screws. For scientific purposes the screw must be so regu- lar that it moves forward in its nut exactly the same distance for each given angular rotation around its axis. As the mountings of a screw introduce many errors, the final and exact test of its accuracy can only be made when it is finished and set up for use. A large screw can, how- ever, be roughly examined in the following manner: (1) See whether the surface of the threads has a perfect polish. The more it departs from this, and approaches the rough, torn surface as cut by the lathe tool, the worse it is. A perfect screw has a perfect polish. (2) Mount upon it between the centres of a lathe and the slip a short nut which fits perfectly. If the nut moves from end to end with equal friction, the screw is uniform in diameter. If the nut is long, unequal resist- ance may be due to either an error of run or a bend in the screw. (3) Fix a microscope on the lathe carriage and focus its single cross- hair on the edge of the screw and parallel to its axis. If the screw runs true at every point, its axis is straight. (4) Observe whether the short nut runs from end to end of the screw without a wabbling motion when the screw is turned and the nut kept from revolving. If it wabbles the SCREW 507 screw is said to be drunk. One can see this error better by fixing a long pointer to the nut, or by attaching to it a mirror and observing an image in it with a telescope. The following experiment will also detect this error: (5) Put upon the screw two well-fitting and rather short nuts, which are kept from revolving by arms bearing against a straight edge parallel to the axis of the screw. Let one nut carry an arm which supports a microscope focused on a line ruled on the other nut. Screw this combination to different parts of the screw. If during one revolu- tion the microscope remains in focus, the screw is not drunk; and if the cross-hairs bisect the lines in every position, there is no error of run. Making Accurate Screws. To .produce a screw of a foot or even a yard long with errors not exceeding -nnn^h of an inch is not difficult. Prof. Wm. A. Eogers, of Harvard Observatory, has invented a process in which the tool of the lathe while cutting the screw is moved so as to counteract the errors of the lathe screw. The screw is then partly ground to get rid of local errors. But, where the highest accuracy is needed, we must resort in the case of screws, as in all other cases, to grinding. A long, solid nut, tightly fitting the screw in one position, cannot be moved freely to another position unless the screw is very accu- rate. If grinding material is applied and the nut is constantly tight- ened, it will grind out all errors of run, drunkenness, crookedness, and irregularity of size. The condition is that the nut must be long, rigid and capable of being tightened as the grinding proceeds ; also the screw must be ground longer than it will finally be needed so that the imper- fect ends may be removed. The following process will produce a screw suitable for ruling grat- ings for optical purposes. Suppose it is our purpose to produce a screw which is finally to be 9 inches long, not including bearings, and 1-| in. in diameter. Select a bar of soft Bessemer steel, which has not the hard spots usually found in cast steel, and about If inches in diameter and 30 long. Put it between lathe centres and turn it down to one inch diameter everywhere, except about 12 inches in the centre, where it is left a little over 1 inches in diameter for cutting the screw. Now cut the screw with a triangular thread a little sharper than 60. Above all, avoid a fine screw, using about 20 threads to the inch. The grinding nut, about 11 inches long, has now to be made. Fig. 1 represents a section of the nut, which is made of brass, or better, of Bessemer steel. It consists of four segments, a, a, which can be drawn about the screw by two collars, &, &, and the screw c. Wedges between 508 HENEY A. ROWLAND the segments prevent too great pressure on the screw. The final clamp- ing is effected by the rings and screws, d, d, which enclose the flanges, e, of the segments. The screw is now placed in a lathe and surrounded by water whose temperature can be kept constant to 1 C., and the nut placed on it. In order that the weight of the nut may not make the ends too small, it must either be counterbalanced by weights hung from a rope passing over pulleys in the ceiling, or the screw must be vertical during the whole process. Emery and oil seem to be the only available grinding materials, though a softer silica powder might be used towards the end of the operation to clean off the emery and prevent future wear. Now grind the screw in the nut, making the nut pass backwards and forwards over the screw, its whole range being nearly 20 inches at first. FIG. 1. Section of Grinding Nut. Turn the nut end for end every ten minutes and continue for two weeks, finally making the range of the nut only about 10 inches, using finer washed emery and moving the lathe slower to avoid heating. Finish with a fine silica powder or rouge. During the process, if the thread becomes too blunt, recut the nut by a short tap so as not to change the pitch at any point. This must, of course, not be done less than five days before the finish. Now cut to the proper length; centre again in the lathe under a microscope, and turn the bearings. A screw so ground has less errors than from any other system of mounting. The periodic error especially will be too small to be discoverefl, though the mountings and graduation and centering of the head will introduce it; it must therefore finally be corrected. Mounting of Screws. The mounting must be devised most carefully, and is, indeed, more difficult to make without error than the screw itself. The principle which should be adopted is that no workmanship is per- fect; the design must make up for its imperfections. Thus the screw SCREW 509 can never be made to run true on its bearings, and hence the device of resting one end of the carriage on the nut must be rejected. Also all rigid connection between the nut and the carriage must be avoided, as the screw can never be adjusted parallel to the ways on which the car- riage rests. For many purposes, such as ruling optical gratings, the carriage must move accurately forward in a straight line as far as the horizontal plane is concerned, while a little curvature in the vertical plane produces very little effect. These conditions can be satisfied by making the ways Y-shaped and grinding with a grinder some- what shorter than the ways. By constant reversals and by lengthen- ing or shortening the stroke, they, will finally become nearly per- fect. The vertical curvature can be sufficiently tested by a short car- riage carrying a delicate spirit level. Another and very efficient form of ways is V-shaped with a flat top and nearly vertical sides. The carriage rests on the flat top and is held by springs against one of the nearly vertical sides. To determine with accuracy whether the ways are straight, fix a flat piece of glass on the carriage and rule a line on it by moving it under a diamond ; reverse and rule another line near the first, and measure the distance apart at the centre and at the two ends by a micrometer. If the centre measurement is equal to the mean of the two end ones, the line is straight. This is better than the method with a mirror mounted on the carriage and a telescope. The screw itself must rest in bearings, and the end motion be prevented by a point bear- ing against its flat end, which is protected by hardened steel or a flat diamond. Collar bearings introduce periodic errors. The secret of success is so to design- the nut and its connections as to eliminate all adjustments of the screw and indeed all imperfect workmanship. The connection must also be such as to give means of correcting any residual periodic errors or errors of run which may be introduced in the mount- ings or by the wear of the machine. The nut is shown in Fig 2. It is made in two halves, of wrought iron filled with boxwood or lignum vitae plugs, on which the screw is cut. To each half a long piece of sheet steel is fixed which bears against a guiding edge, to be described presently. The two halves are held to the screw by springs, so that each moves forward almost independently of the other. To join the nut to the carriage, a ring is attached to the latter, whose plane is vertical and which can turn round a vertical axis. The bars fixed midway on the two halves of the nut bear against this ring at points 90 distant from its axis. Hence each half does its share independently of the other in moving the carriage forward. Any want 510 HENRY A. ROWLAND of parallelism between the screws and the ways or eccentricity in the screw mountings thus scarcely affects the forward motion of the car- riage. The guide against which the steel pieces of the nut rest can be made of such form as to correct any small error of run due to wear of the screw. Also, by causing it to move backwards and forwards peri- odically, the periodic error of the head and mountings can be corrected. In making gratings for optical purposes the periodic error must be very perfectly eliminated, since the periodic displacement of the lines only one-millionth of an inch from their mean position will produce m FIG. 2. " ghosts " in the spectrum. 1 Indeed, this is the most sensitive method of detecting the existence of this error, and it is practically impossible to mount the most perfect of screws without introducing it. A very prac- tical method of determining this error is to rule a short grating with very long lines on a piece of common thin plate glass ; cut it in two with a diamond and superimpose the two halves with the rulings together and displaced sideways over each other one-half the pitch of the screw. On now looking at the plates in a proper light so as to have the spec- 1 In a machine made by the present writer for ruling gratings the periodic error is entirely due to the graduation and centering of the head. The uncorrected periodic error from this cause displaces the lines ^^fa^ih of an inch, which is sufficient to entirely ruin all gratings made without correcting it. SCREW 511 tral colors show through it, dark lines will appear, which are wavy if there is a periodic error and straight if there is none. By measuring the comparative amplitude of the waves and the distance apart of the two lines, the amount of the periodic error can be determined. The phase of the periodic error is best found by a series of trials after set- ting the corrector at the proper amplitude as determined above. A machine properly made as above and kept at a constant tempera- ture should be able to make a scale of 6 inches in length, with errors at no point exceeding nnnnnrth of an inch. When, however, a grating of that length is attempted at the rate of 14,000 lines to the inch, four days and nights are required, and the result is seldom perfect, possibly on account of the wear of the machine or changes of temperature. Grat- ings, however, less than 3 inches long are easy to make. 39 ON" THE RELATIVE WAVE-LENGTH OF THE LINES OF THE SOLAE SPECTRUM [American Journal of Science [3J, XXXIII, 182-190, 1887 ; Philosophical Magazine [5], XXIII, 257-265, 1887] For several years past I have been engaged in making a photographic map of the solar spectrum to replace the ordinary engraved maps and I have now finished the map from the extreme ultra violet, wave-length 3200, down to wave-length 5790. In order to place the scale correctly on this map, I have found it necessary to measure the relative wave- lengths of the spectrum and to reduce it to absolute wave-lengths by some more modern determination. I have not yet entirely finished the work, but as my map of the spectrum is now being published and as O all observers so far seem to accept the measures of Angstrom, I have decided that a table of my results would be of value. For as they stand now they have at least ten times the accuracy of any other determina- tion. This great accuracy arises from the use of the concave grating which reduces the problem of relative wave-lengths to the measure of the coincidences of the lines in the different spectra by a micrometer. The instrument which I have employed has concave gratings 5 or 6 in. diameter, having either 7200 or 14,400 lines to the inch and a radius of 21 ft. 6 in. By my method of mounting, the spectrum is normal where measured, and thus it is possible to use a micrometer with a range of 5 inches. The spectrum keeps in focus everywhere and the constant of the micrometer remains unchanged except for slight variations due to imperfections in the workmanship. The micrometer has no errors of run or period exceeding the -J^TTF inch. The probable error of a single setting on a good clear line is about ^nrVur ^ the wave-length. 1" of arc is about -0012 inch. The D line in the second spectrum is -17 inch or 4-4 mm. wide. Determinations of relative wave-length of good lines seldom differ 1 in 500,000 from each other and never exceed 1 in 100,000, even with different gratings. This is, of course, for the prin- cipal standard lines, and the chance of error is greater at the extremities of the spectrum. The interpolation of lines was made by running the micrometer over the whole spectrum, 5 inches at a time, and adding the KELATIVE WAVE-LENGTH OF LINES OF SOLAS SPECTEUM 513 readings together so as to include any distance, even the whole spec- trum. The wave-length is calculated for a fixed micrometer constant and then corrected so as to coincide everywhere very nearly with the standards. I suppose the probable error of the relative determinations with the weight 1 in my table to be not far from 1 in 500,000. Ang- strom thinks his standard lines have an accuracy of about 1 in 50,000 and ordinary lines much less. As to the absolute measure, it is now well determined that Angstrom's figures are too small by about 1 part in 6000. This rests: 1st, on the determination of Peirce made for the U. S. Coast Survey with Ruther- furd's gratings and not yet completely published; 2d, on an error made by Tresca in the length of the standard metre used by Angstrom 1 which increases his value by about 1 in 7700; 3d, on a result obtained in my laboratory with two of my gratings by Mr. Bell, which is published with this paper. Mr. C. S. Peirce has kindly placed his grating at our dis- posal and we have detected an error of ruling which affects his result and makes it nearly coincide with our own. The wave-length of the mean of the two E lines is Angstrom (atlas) 5269-12 -5 Angstrom (Corrected by Thalen) 5269-80 l Peirce 5270-16 Peirce (Corrected by Rowland and Bell) 5270-00 * Bell 5270-04 These results are for air at ordinary pressures and temperatures. The last is reduced to 20 C. and 760 mm. pressure. To reduce to a vacuum multiply by the following : Fraunhofer line A C E G H Correction factor. .1-000291 1-000292 1-000294 1-000297 1-000298 o The relation between my wave-lengths and those of Angstrom are O given by the following, Angstrom's value being from p. 31 of his memoir: A (edge) B (edge) C Angstrom 7597-5 6867-10 6717-16 6562-10 6264-31 Rowland . . 7593-97 6867-38 6717-83 6562-96 6265-27 Difference 3-5 -28 -67 -86 -96 1 Thal6n, Sur Spectre du Fer, Societe Royale des Sciences d'Upsal, September, 1884, p. 25. 2 From one grating only. 514 HENRY A. ROWLAND Da A Peirce's line Angstrom 5895-13 5889-12 5708-45 5623-36 5454-84 Eowland . 5896-08 5890-12 5709-56 5624-70 5455-68 Difference -95 1-00 1-11 1-34 -84 E E bi F Angstrom 5269-59 5268-67 5183-10 5138-78 4860-74 Rowland , . 5270-43 5269-65 5183-73 5139-47 4861-43 Difference -84 -98 -63 -69 -69 o Angstrom 4702-44 4307-25 Rowland , . 4703-11 4307-96 Difference -67 -71 * The greatest variation in these differences is evidently due to the poor definition of Angstrom's grating by which the numbers refer to groups of lines rather than to single ones. Selecting the best figures, we find that Angstrom's wave-lengths must be multiplied by 1-00016 to agree with Bell, while the correction for Angstrom's error of scale would be 1-000110. It is impossible for me to give at present all the data on which my determinations rest, but I have given in Table I many of the coinci- dences as observed with several gratings, the number of single readings being given in the parenthesis over each set. Table II gives the wave-lengths as interpolated by the micrometer. It is scarcely possible that any error will be found (except accidental errors) of more than -02, and from the agreement of the observations I scarcely expect to make any changes in the final table of more than 01, except in the extremities of the spectrum, where it may amount to -03 in the region of A and H lines. The wave-lengths of weight greater than 1 will probably be found more exact than this. The lines can be identified on my new photograph of the spectrum down to 5790. Below this there is little trouble in finding the right ones. All maps of the spectrum, especially above F, are so imperfect that it is almost impossible to identify my lines upon them. The lines can only be prop- erly identified by a power sufficient to clearly divide & 3 and & 4 . Some of them are double and most of these have been marked, but as the table has been made for my own use, I have not been very careful to examine each line. This will, however, be finally done. Micrometric measures KELATIVE WAVE-LENGTH OF LINES OF SOLAK SPECTRUM 515 have now been made of nearly all the lines below & with a view of mak- ing a map of this region. Table I gives the coincidences of the different orders of the spectra as observed with several concave gratings on both sides of the normal, the numbers in the brackets indicating the number of observations. The observations have been reduced as nearly as possible to what I consider the true wave-length, the small difference from the numbers given in Table II being the variation of the observations from the mean value. The true way of reducing these observations would be to form a linear equation for each series and reduce by the method of least squares. A simpler way was, however, used and the relative wave-length of the standard lines, marked S in Table II, was obtained; however, some other observations were also included. Table II gives the wave-lengths reduced to Bell's value for the abso- lute wave-length of the D line. These were obtained by micrometric measurement from the standards as described before. The weights are given in the first column and some of the lines, which were meas- ured double, have also been marked. But the series has not yet been carefully examined for doubles. The method is so much more accurate than by means of angular measurement that the latter has little or no weight in comparison. This table is to be used in connection with my photographic map of the normal spectrum to determine the error of the latter at any point. The map was made by placing the photograph in contact with the scale, which was the same for each order of spectrum, and enlarging the two together. In this way the map has no local irregularities, although the scale may be displaced slightly from its true position, and may be a little too long or short, although as far as I have tested it, it seems to have very little error of the latter sort. The scale was meant in all cases, except the ultra violet, to apply to Peirce's absolute value and so the correction is generally negative, as follows : Approximate correction to the photographic map of the normal spectrum to reduce to latest absolute value. Strip 3200 to 3330 Correction -05 " 3275 to 3530 " -05 " 3475 to 3730 " -02 " 3675 to 3930 <* -10 " 3875 to 4130 " -16 " 4075 to 4330.. " ...-04 516 HENRY A. KOWLAND Strip 4275 to 4530 Correction -08 " 4480 to 4735 -10 " 4685 to 4940 " -18 " 4875 to 5130 " -14 " 5075 to 5330 " -15 " 5215 to 5595 " about -05 " 5415 to 5795 " about -04 " 3710 to 3910 " -20 " 3810 to 4000 " -14 It is to be noted that the third spectrum of the map runs into the second, so that it must not be used beyond wave-length 3200, as it is mixed with the second in that region. [The tables are omitted.] 41 TABLE OF STANDAKD WAVE-LENGTHS [Johns Hopkins University Circulars, No. 73, p. 69, 1889 ; Philosophical Magazine [5], XXVII, 479-484, 1889] In the ' American Journal of Science ' for March, 1887, and the ' Lon- don, Dublin and Edinburgh Philosophical Magazine ' for the same month, I have published a preliminary list of standards as far as could be observed with the eye, with a few imperfectly observed by photog- raphy, the whole being reduced to Bell's and Peirce's values for absolute wave-lengths. Mr. Bell has continued his measurements and found a slightly greater value for the absolute wave-length of the D line, and I have reduced my standards to the new values. Nearly the whole list has been gone over again, especially at the ends around the A line and in the ultra violet. The wave-lengths of the ultra violet were obtained by photographing the coincidence with the lower wave-lengths, a method which gives them nearly equal weight with those of the visible spectrum. The full set of observations will be published hereafter, but the pres- ent series of standards can be relied on for relative wave-lengths to -02 division of Angstrom in most cases, though it is possible some of them may be out more than this amount, especially in the extreme red. As to the absolute wave-length, no further change will be necessary, provided spectroscopists can agree to use that of my table, as has been done by many of them. By the method of coincidences with the concave grating the wave- lengths have been interwoven with each other throughout the whole table so that no single figure could be changed without affecting many others in entirely different portions of the spectrum. The principal dif- ference from the preliminary table is in the reduction to the new abso- lute wave-length by which the wave-lengths are about 1 in 80,000 larger than the preliminary table. I hope this difference will not be felt by those who have used the old table because measurements to less than A- o division of Angstrom are rare, the position of the lines of many metals being unknown to a whole division of Angstrom. As the new map of the spectrum has been made according to this new table, I see no further reason for changing the table in the future. 518 HENRY A. ROWLAND No attempt has been made to reduce the figures to a vacuum as the index of refraction of air is imperfectly known, but this should be done where numerical relations of time period are desired. In the column giving the weight, the primary standards are marked 8 and the other numbers give the number of separate determination of the wave-length and thus, to some extent, the weight. Many of these standards are double lines and some of them have faint components near them, which makes the accuracy of setting smaller. This is specially the case when this component is an atmospheric line whose intensity changes with the altitude of the sun. The principal doubles are marked with d, but the examination has not been completed yet, especially at the red end of the spectrum. [A table of the standard wave-lengths is given on p. 78 J. H. U. Circ., but is omitted in this volume.] 42 A FEW NOTES ON THE USE OF GKATINGS [Johns Hopkins University Circulars, No. 73, pp. 73, 74, 1889] The ghosts are very weak in most of my gratings. They are scarcely visible in the lower orders of spectra, hut increase in intensity as com- pared with the principal line as the square of the order of the spectrum. Hence, to avoid them, obtain magnification by increasing the focal dis- tances instead of going to the higher orders. The distances from the principal line in my gratings are the same as the distances of the spectra from the image of the slit when using a grating of 20 lines to the inch. They are always symmetrical on the two sides, and about -^ inch for the violet and inch for the red in a grating of 21 ft. 6 in. radius in all orders of spectra. When the given line has the proper exposure on the photographic plate, the ghosts will not show, but over-exposure brings them out faintly in the third spectrum of a 20,000 grating or the 6th of a 10,000 one. They never cause any trouble, as they are easily recog- nized and never appear in the solar spectrum. In some cases the higher orders of ghosts are quite as apparent as those of the first order. The gratings with 10,000 lines to the inch often have better definition than those of 20,000, as they take half the time to rule, and they are quite as good for eye observation. They can also be used for photo- graphing the spectrum by absorbing the overlying spectra, but there are very few materials which let through the ultra violet and absorb the longer wave-lengths. The 10,000 gratings have the advantage, how- ever, in the measurement of wave-lengths by the overlapping spectra, although this method is unnecessary since the completion of my map of the spectrum. By far the best is to use a 20,000 grating and observe down to the D line by photography, using erythrosin plates from the F line down to D. Below D, cyanine plates can be used, although the time of exposure is from 10 to 60 minutes with a narrow slit. The solar spectrum extends to wave-lengths 3000, and the map has been contin- ued to this point. Beyond this, the coincidence with the solar spectrum cannot be used, but those of the 1st and 2d or 2d and 3d spectra can be. Some complaints have been made to me that one of my gratings has no spectrum beyond 3400. even of the electric arc. I have never found this the case, as the one I use gives w. 1. 2200, readily with 30 minutes exposure on slow plates, requiring 5 minutes for the most sensitive 520 HENRY A. KOWLAND part and using the electric arc. With sensitive plates, the time can be diminished to one-fifth of this. For eye observations, a very low power eye-piece of 1 or 2 in. focus is best. This, with a focus of 21 ft. 6 in. is equivalent to a plane grat- ing with a telescope of a power of 100 or 200. In measuring the spectra, an ordinary dividing engine with errors not greater than 10*00 inch can be used, going over the measurements twice with the plate reversed between the separate series. The plates are on so very large a scale that the microscope must have a very low power. The one I use has a 1 inch objective and a 2 inch eye-piece. The measured part of the plate is about a foot long, the plates being 19 in. long. All the spectrum photographs taken at different times coincide per- fectly, and this can be used for such problems as the determination of the atmospheric lines. For this purpose, negatives at high and low sun are compared by scraping the emulsion off from half the plates and clamping them together with the edges of the spectra in coincidence. The two spectra coincide exactly line for line except where the atmo- spheric lines occur. This method is specially valuable for picking out impurities in metal- lic spectra, using some standard impurity in all the substances to give a set of fiducial lines; or better, obtaining the coincidence of all the metals with some one metal, such as iron. Making the iron spectrum coincide on the two plates, the other spectra can be compared. This is specially possible because the focus of a properly set up concave grating need not be altered in years of use, for, when necessary, it can be ad- justed at the slit, keeping the distance of the grating from the slit con- stant. The spectrum of the carbon poles is generally too complicated for use with anything except the more pronounced lines of metals, there being, at a rough guess, 10,000 lines in its spectrum. However, in pho- tographing metallic spectra but few of these show on the plate, as they are mostly faint. The spark discharge gives very nebulous lines for the metals. Most gratings are ruled bright in the higher orders, but this is more or less difficult, as most diamond points give the first spectrum the brightest. Indeed, it is very easy to obtain ruling which is immensely bright in the first spectrum. Such gratings might be used for gaseous spectra. Short focus gratings of 5 ft. radius of curvature, very bright in the first order, require only a fraction of a second exposure for the solar spectrum and the spectrum of a gas can be obtained in less than an hour. 46 KEPOET OF PROGRESS IN SPECTKUM WORK [Johns Hopkins University Circulars, No. 85, pp. 41, 42, 1891 ; American Journal of Science [3], XLI, 243, 244, 1891 ; The Chemical News, LXIII, 133, 1891] During the past year or two a great deal of work has been done in the photography of the spectra of elements and the identification of the lines in the solar spectrum, which it will take a long time to work up, ready for publication. Hence, I have thought that a short account of what has been done up to the present time might be of interest to work- ers in the subject. In the prosecution of the work financial assistance has been received from the Rumford Fund of the American Academy of Arts and Sciences, as well as from the fund given by Miss Bruce to the Harvard Astronomical Observatory for the promotion of research in astronomical physics, and the advanced state of the work is due to such assistance. The work may be summed up under the following heads : 1st. The spectra of all known elements, with the exception of a few gaseous ones, or those too rare to be yet obtained, have been photo- graphed in connection with the solar spectrum, from the extreme ultra violet down to the D line, and eye observations have been made on many to the limit of the solar spectrum. 2d. A measuring engine has been constructed with a screw to fit the above photographs, which, being taken with the concave grating, are all normal spectra and to the same scale. This engine measures wave- 1-engtlis direct, so that no multiplication is necessary, but only a slight correction to get figures correct to y^g- of a division of Angstrom. 3d. A table of standard wave-lengths of the impurities in the car- bons, extending to wave-length 2000, has been constructed to measure wave-lengths beyond the limits of the solar spectrum. 4th. Maps of the spectra of some of the elements have been drawn on a large scale ready for publication. 5th. The greater part of the lines in the map of the solar spectrum have been identified and the substance producing them noted. 6th. The following rough table of the solar elements has been con- structed entirely according to my own observations, although, of course, most of them have been given by others. 522 HENEY A. ROWLAND I do not know which are the new ones, but call attention to Silicon, Vanadium, Scandium, Yttrium, Zirconium, Glucinum, Germanium and Erbium, as being possibly new. Silicon has lines on my map at wave-lengths 3905-7, 4103-1, 5708-7, 5772-3 and 5948-7. That at 3905-7 is the largest and most certain. That at 4103-1 is also claimed by Manganese. ELEMENTS IN THE SUN, ARRANGED ACCORDING TO THE INTENSITY AND THE NUMBER OF LINES IN THE SOLAR SPECTRUM. ACCOBDING TO INTENSITY. Calcium. Iron. Hydrogen. Sodium. Nickel. Magnesium. Cobalt. Silicon. Aluminium. Titanium. Chromium. Manganese. Strontium. Vanadium. Barium. Carbon. Scandium. Yttrium. Zirconium. Molybdenum. Lanthanum. Niobium. Palladium. Neodymium. Copper. Zinc. Cadmium. Cerium. Glucinum. Germanium. ACCORDING TO NUMBER. Iron (2000 or more). Nickel. Titanium. Manganese. Chromium. Cobalt. Carbon (200 or more). Vanadium. Zirconium. Cerium. Calcium (75 or more). Scandium. Neodymium. Lanthanum. Yttrium. Niobium. Molybdenum. Palladium. Magnesium (20 or more). Sodium (11). Silicon. Strontium. Barium. Aluminium (4). Cadmium. Rhodium. Erbium. Zinc. Copper (2). Silver (2). REPORT OF PROGRESS IN SPECTRUM WORK 523 ACCORDING TO INTENSITY. ACCORDING TO NUMBER. Rhodium. Glucinum (2). Silver. Germanium. Tin. Tin. Lead. Lead (1). Erbium. Potassium (1). Potassium. DOUBTFUL ELEMENTS. Iridium. Ruthenium. Tungsten. Osmium. Tantalum. Uranium. Platinum. Thorium. NOT IN SOLAR SPECTRUM. Antimony. Caesium. Rubidium. Arsenic. Gold. Selenium. Bismuth. Indium. Sulphur. Boron. Mercury. Thallium. Nitrogen (vacuum tube). Phosphorus. Praeseodymium. SUBSTANCES NOT YET TRIED. Bromine. Oxygen. Holmium. Chlorine. Tellurium. Thulium. Iodine. Gallium. Terbium, etc. Fluorine. These tables are to be accepted as preliminary only, especially the order in the first portion. However, being made with such a powerful instrument, and with such care in the determination of impurities, they must still have a weight superior to most others published. The substances under the head of "Not in Solar Spectrum" are often placed there because the elements have few strong lines or none at all in the limit of the solar spectrum when the arc spectrum, which I have used, is employed. Thus boron has only two strong lines at 2497. Again, the lines of bismuth are all compound and so too diffuse to ap- pear in the solar spectrum. Indeed, some good reason generally ap- pears for their absence from the solar spectrum. Of course, this is little evidence of their absence from the sun itself. Indeed, were the whole earth heated to the temperature of the sun, its spectrum would probably resemble that of the sun very closely. 524 HENRY A. ROWLAND With the high dispersion here used the "basic lines" of Lockyer are widely broken up and cease to exist. Indeed, it would be difficult to prove anything except accidental coincidences among the lines of the different elements. Accurate investigation generally reveals some slight difference of wave-length or a common impurity. Furthermore, the strength of the lines in the solar spectrum is gen- erally very nearly the same as that in the electric arc, with only a few exceptions, as for instance calcium. The cases mentioned by Lockyer are generally those where he mistakes groups of lines for single lines or even mistakes the character of the line entirely. Altogether there seems to be very little evidence of the breaking up of the elements in the sun as far as my experiments go. Even after comparing the solar spectrum with all known elements, there are still many important lines not accounted for. Some of these I have accounted for by silicon and there are probably many more. Of all known substances this is the most difficult to bring out the lines in the visible spectrum although it has a fine ultra-violet one. Possibly iron may account for many more, and all the elements at a higher tem- perature might develope more. Then, again, very rare elements like scandium, vanadium, etc., when they have a strong spectrum, may cause strong solar lines and thus we may look for new and even rare elements to account for very many more. Indeed, I find many lines accounted for by the rare elements in gadolinite, samarskite and fergusonite other than yttrium, erbium, scandium, praeseodymium, neodymium, lantha- num and cerium, which I cannot identify yet and which may be without a name. For this reason, and to discover rare elements, I intend finally to try unknown minerals, as my process gives me an easy method of detecting any new substance or analyzing minerals however many ele- ments they may contain. The research is much indebted to the faithful and careful work of Mr. L. E. Jewell who has acted as my assistant for several years. Preliminary publications of results will be made in the ' University Circulars.' Among the lastest results I may mention the spectroscopic separation of yttrium into three components, and the actual separation into two. 49 GRATINGS IN THEORY AND PRACTICE l [Philosophical Magazine [5], XXXV, 397-419, 1893 ; Astronomy and Astro -Physics, XII, 129-149, 1893] PART I 1 It is not my object to treat the theory of diffraction in general but only to apply the simplest ordinary theory to gratings made by ruling grooves with a diamond on glass or metal. This study I at first made with a view of guiding me in the construction of the dividing engine for the manufacture of gratings, and I have given the present theory for years in my lectures. As the subject is not generally understood in all its bearings I have written it for publication. Let p be the virtual distance reduced to vacuo through which a ray moves. Then the effect at any point will be found by the summation of the quantity A C08&O Vt) + Bsinb(p V) , o in which & = ~, I being the wave-length. V is the velocity reduced to L vacuo, and t is the time. Making 6 = tan" 1 - - we can write this sin [0 + b ( p The energy or intensity is proportional to (A 2 -f- B 2 ). Taking the expression (A +iB)g~ , a where I is the wave-length in vacuo. In case of the reflecting grating 1 = 1' and we can write A = I\coa

+ sin [ AX ny] /7 J J 528 HENRY A. ROWLAND CASE I. SIMPLE PERIODIC RULING Let the surface be divided up into equal parts in each of which one or more lines or grooves are ruled parallel to the axis of z. The integration over the surface will then resolve itself into an integration over one space and a summation with respect to the num- ber of spaces. For in this case we can replace y by na -\- y where a is the width of a space and the displacement becomes g-il)(R-Vt) v e + ibnan I I e +ib (Ax + Ml/) ds , but ~bnit. n-i - smw v 0+ibpan sin ba;i Bin -- Multiplying the disturbance by itself with i in place of -j- i we have for the light intensity I C e-n l * x + /> ds \ I /(.+ ib < Ax + *v) ds\ sm - The first term indicates spectral lines in positions given by the equation with intensities given by the last integral. The intensity of the spec- tral lines then depends on the form of the groove as given by the equa- tion x = f(y) and upon the angles of incidence and diffraction. The first factor has been often discussed and it is only necessary to call attention to a few of its properties. When bafjt*=%7rN, N being any whole number, the expression be- comes n 2 . On either side of this value the intensity decreases until ribdfj! '=2xN, wheniit becomes 0. The spectral line then has a width represented by// / M"=T 2^ nearly; on either side of this line smaller maxima exist too faintly to be ob- served. When two spectral lines are nearer together than half their width, they blend and form one line. The defining power of the spec- troscope can be expressed in terms of the quotient of the wave-length by the difference of wave-length of two lines that can just be seen as divided. The defining power is, then, 3 An expression of Lord Rayleigh's. GRATINGS ix THEORY AND PRACTICE 529 Now na is the width of the grating. Hence, using a grating at a given angle, the defining power is independent of the number of lines to the inch and only depends on the width of the grating and the wave- length. According to this, the only object of ruling many lines to the inch in a grating is to separate the spectra so that, with a given angle, the order of spectrum shall be less. Practically the gratings with few lines to the inch are much better than those with many, and hence have better definition at a given angle than the latter except that the spectra are more mixed up and more difficult to see. It is also to be observed that the defining power increases with shorter wave-lengths, so that it is three times as great in the ultra violet as in the red of the spectrum. This is of course the same with all optical instruments such as telescopes and microscopes. The second term which determines the strength of the spectral lines will, however, give us much that is new. First let us study the effect of the shape of the groove on the bright- ness. If N is the order of The spectrum and a the grating space we have Nl /j. = /(sin

+ ^ v) It is to be noted that this expression is not only a function of N but also of I, the wave-length. This shows that the intensity in general may vary throughout the spectrum according to the wave-length and that the sum of the light in any one spectrum is not always white light. This is a peculiarity often noticed in gratings. Thus one spectrum may be almost wanting in the green, while another may contain an excess of this color; again there may be very little blu^ in one spectrum while very often the similar spectrum on the other side may have its own share and that of the other one also. For this reason I have found it almost impossible to predict what the ultra red spectrum may be, for it is often weak even where the visible spectrum is strong. The integral may have almost any form although it will naturally tend to be such as to make the lower orders the brightest when the diamond rules a single and simple groove. When it rules several lines 34 530 HENRY A. KOWLAND or a compound groove, the higher orders may exceed the lower in brightness and it is mathematically possible to have the grooves of such a shape that, for given angles, all the light may be thrown into one spectrum. It is not uncommon, indeed, very easy, to rule gratings with im- mensely bright first spectra, and I have one grating where it seems as if half the light were in the first spectrum on one side. In this case there is no reflection of any account from the grating held perpendicu- larly: indeed to see one's face, the plate must be held at an angle, in which case the various features of the face are seen reflected almost as brightly as in a mirror but drawn out into spectra. In this case all the other spectra and the central image itself are very weak. In general it would be easy to prove from the equation that want of symmetry in the grooves produces want of symmetry in the spectra, a fact universally observed in all gratings and one which I generally utilize so that the light may be concentrated in a few spectra only. EXAMPLE 1 SQUARE GROOVES When the light falls nearly perpendicularly on the plate, we need not take the sides into account but only sum up the surface of the plate and the bottom of the groove. Let the depth "be X and the width equal to*. m The intensity then becomes proportional to 'N T S T ~rn r T" This vanishes when N = m , 2m , 3m, etc., or = 0, 1, 2, 3, etc. The intensity of the central light, for which N = 0, will be * - / * ]T\ rein(* T XJ. This can be made to vanish for only one angle for a given wave- length. Therefore, the central image will be colored and the color will change with the angle, an effect often observed in actual gratings. The color ought to change, also, on placing the grating in a liquid of different index of refraction since A contains 7, the index of refraction. It will be instructive to take a special case, such as light falling per- pendicularly on the plate. For this case GRATINGS IN THEORY AND PRACTICE 531 A77

+ cos -^- [(/* + c' A) (a w) w (// c/)] I . This expression is not symmetrical with respect to the normal to the grating, unless the groove is symmetrical, in which case c = c' and .=. In this case, as in the other, the colors of the spectrum are of vari- able intensity, and some of them may vanish as in the first example, but the distribution of intensity is in other respects quite different. CASE II. MULTIPLE PERIODIC RULING Instead of having only one groove ruled on the plate in this space a, let us now suppose that a series of similar lines are ruled. We have, then, to obtain the displacement by the same expression as before, that is sn 2 r I I e ib ^ x + *) ds, * except that the last integral will extend over the whole number of lines ruled within the space a. In the spaces a let a number of equal grooves be ruled commencing at the points y = 0, y lt y 2 , y z , etc., and extending to the points w, y l -f- w, y z -f- w, etc. The surface integral will then be divided into portions from w to y u from y l -f- w, to y z , etc., on the original surface of the plate for which x = 0, and from w to 0, from y -\- w to y u etc., for the grooves. The first series of integrals will be /e dv = 4 ( 6 a >i iW + efoMi fc^(i/i+>) + gib^ etc. tOft But, e ib ^ a = 1 since &/* = 2^-JV for any maximum, and thus the inte- gral becomes f < 1 4- fribnyi 4- gib^y^ -\- etc. GRATINGS IN THEORY AND PRACTICE' 533 The second series of integrals will be / The total integral will then be 8inw ^ri * sin^i L *&, ^ Jo 6 JL i As before, multiply this by the same with the sign of i changed to get the intensity. EXAMPLE 1. EQUAL DISTANCES The space, a, contains n' 1 equidistant grooves, so that y^ = y z y\ = etc., = -, n' metals with some one metal, such as iron. Malting the iron spectrum -. a v tt>n^ n Hence the displacement becomes bttu sin n . As the last term is simply the integral over the space -, in a different form from before, this is a return to the form we previously had except that it is for a grating of nn' lines instead of n lines, the grating space being . EXAMPLE 2. Two GROOVES But ba/jt = 2 ATT. Hence this becomes . v\_ y a The square of the last term is a factor in the intensity. Hence the spectrum will vanish when we have ~n~ ' 4 A theorem of Lord Rayleigh's. 534 HENRY A. ROWLAND or N _ la 3 a 5 a , " ~cT J ~~c\~ > TT" *"*" 2 y, 2 y, 2 y, Thus when = 2, the 1st, 3d, etc., spectra will disappear, making y\ a grating of twice the number of lines to the cm. When =4, the 2d, 6th, 10th, etc., spectra disappear. When y\ = 6, the 3d, 9th, etc., spectra disappear. y\ The case in which = 4, as Lord Rayleigh has shown, would be very y\ useful as the second spectrum disappears leaving the red of the first and the ultra violet of the third without contamination by the second. In this case two lines are ruled and two left out. This would be easy to do but the advantages would hardly pay for the trouble owing to the following reasons: Suppose the machine was ruling 20,000 lines to the inch. Leaving out two lines and ruling two would reduce the dispersion down to a grating with 5000 lines to the inch. Again, the above theory assumes that the grooves do not overlap. Now I believe that in nearly, if not all, gratings with 20,000 lines to the inch the whole surface is cut away and the grooves overlap. This would cause the second spectrum to appear again after all our trouble. Let the grooves be nearly equidistant, one being slightly displaced. In this case y t = ? -j- v - , Ny, I 7TJV i:Nv . nN ff cos 2 TT S3 = [ oos-s- cos - sin -4- am - a \ 2 a % For the even spectra this is very nearly unity, but for the odd it becomes Hence the grating has its principal spectra like a grating of space ^ but there are still the intermediate spectra due to the space a, and of intensities depending on the squares of the order of spectrum, and the squares of the relative displacement, a law which I shall show applies to the effect of all errors of the ruling. This particular effect was brought to my attention by trying to use a tangent screw on the head of my dividing engine to rule a grating with say 28,872 lines to the inch, when a single tooth gave only 14,436 to the inch. However carefully I ground the tangent screw I never was GRATINGS IN THEORY AND PRACTICE 535 able to entirely eliminate the intermediate spectra due to 14,436 lines, and make a pure spectrum due to 28,872 lines to the inch, although I could nearly succeed. EXAMPLE 3. ONE GROOVE IN m MISPLACED Let the space a contain m grooves equidistant except one which is displaced a distance v. The displacement is now proportional to Multiplying this by itself with i in place of -+- i, and adding the factors in the intensity, we have the whole expression for the intensity. One of the terms entering the expression will be sm sin^ sin** 2m 2 Now the first two terms have finite values only around the points _^= rw^Vrr, where mN is a whole number. But 2p m -\- 1 is also a 2 whole number, and hence the last term is zero at these points. Hence the term vanishes and leaves the intensity, omitting the groove factor, baa . . ba sin ~ sin* - 2 in 2 The first term gives the principal spectra as due to a grating space of and number of lines nm as if the grating were perfect. The last term gives entirely new spectra due to the grating space, a, and with lines of breadth due to a grating of n lines and intensities equal to Hence, when the tangent screw is used on my machine for 14,436 lines to the inch, there will still be present weak spectra due to the 14,436 spacing although I should rule say 400 lines to the mm. This I have practically observed also. The same law holds as before that the relative intensity in these 536 HENRY A. ROWLAND subsidiary spectra varies as the square of the order of the spectrum and the square of the deviation of the line, or lines from their true position. So sensitive is a dividing engine to periodic disturbances that all the belts driving the machine must never revolve in periods containing an aliquot number of lines of the grating; otherwise they are sure to make spectra due to their period. As a particular case of this section we have also to consider PERIODIC ERRORS OF RULING. THEORY OF " GHOSTS " In all dividing engines the errors are apt to be periodic due to " drunken " screws, eccentric heads, imperfect bearings, or other causes. We can then write y = a t n + a^ sin (e^ri) + a^ sin (e?n), + etc. The quantities e 1? e z) etc., give the periods, and a 1} a 2 , etc., the ampli- tudes of the errors. We can then divide the integral into two parts as before, an integral over the groove and spaces and a summation with respect to the numbers. ds . I I 'e~ ib < Ax + w) ds = le-tbw j " Vy 1 */0 It is possible to perform these operations exactly, but it is less com- plicated to make an approximation, and take y"- y r = a, a constant as it is very nearly in all gratings. Indeed the error introduced is vanishingly small. The integral which depends on tho shape of the groove, will then go outside the summation sign and we have to per- form the summation sine^ + o s sine 2 Let J n be a Bessel's function. Then cos (u sin ?) = 7 () + 2 [J" 2 (w) cos 2 y + J t (w) cos* ^ + etc.] sin (w sin ) = 2 [Ji (w) sin ^ + /, (w) sin 3 ^ + etc.] But e~ iu sin = cos (u sin ^ ) i sin (w sin ^>) . Hence the summation becomes X [Jo (^0 + 2 ( iJi (S/iOi) sin e^n + J t (ft/taj cos 'Ze^n etc.)] X [J (bvctt*) + 2 ( iJ t (b/jifty) sin e z n + J t (J//a 2 ) cos Zeji etc.)] X [/ (bra,*) + etc.] X [etc.] GRATINGS IN THEORY AND PRACTICE 537 CASE I. SINGLE PERIODIC ERROR In this case only a and a^ exist. We have the formula Hence the expression for the intensity becomes sn n sin n Mo e l } + etc. 2 J As n is large, this represents various very narrow spectral lines whose light does not overlap and thus the different terms are independent of each other. Indeed in obtaining this expression the products of quan- tities have been neglected for this reason because one or the other is zero at all points. These lines are all alike in relative distribution of light and their intensities and positions are given by the following table : Places. Intensities. Designations. Primary line Ghosts of 1st order. Ghosts of 2d order. Ghosts of 3d order, etc. etc. etc. = I* = ;*-E- 1 J.'QwJ Hence the light which would have gone into the primary line now goes to making the ghosts, so that the total light in the line and its ghosts is the same as in the original without ghosts. The relative intensities of the ghosts as compared with the primary line is 538 HENRY A. ROWLAND This for very weak ghosts of the first, second, third, etc., order, becomes The intensity of the ghosts of the first order varies as the square of the order of the spectrum and as the square of the relative displace- ment as compared with the grating space a . This is the same law as we before found for other errors of ruling, and it is easy to prove that it is general. Hence The effect of small errors of ruling is to produce diffused light around the spectral lines. This diffused light is subtracted from the light of the primary line, and its comparative amount varies as the square of the relative error of ruling and the square of the order of the spectrum. Thus the effect of the periodic error is to dimmish the intensity of the ordinary spectral lines (primary lines) from the intensity 1 to t7 2 (fy" a i)j and surround it with a symmetrical system of lines called ghosts, whose intensities are given above. When the ghosts are very near the primary line, as they nearly always are in ordinary gratings ruled on a dividing engine with a large number of teeth in the head of the screw, we shall have f- + A) + Jftai (f* j^} = IJfta^ nearly. oaj \ baj Hence the total light is by a known theorem, Thus, in all gratings, the intensity of the ghosts as well as the diffused light increases rapidly with the order of the spectrum. This is often marked in gratings showing too much crystalline structure. For the ruling brings out the structure and causes local difference of ruling which is equivalent to error of ruling as far as diffused light is concerned. For these reasons it is best to get defining power by using broad gratings and a low order of spectra although the increased perfection of the smaller gratings makes up for this defect in some respects. There is seldom advantage in making both the angle of incidence and diffraction more than 45, but, if the angle of incidence is 0, the other angle may be 60, or even 70, as in concave gratings. Both theory and practice agree in these statements. Ghosts are particularly objectionable in photographic plates, especi- GRATINGS IN THEORY AND PRACTICE 539 ally when they are exposed very long. In this case ghosts may be brought out which would be scarcely visible to the eye. As a special case, take the following numerical results: 1 2 3 1 1 1 1 1 1 1 1 1 25' 50 ' 100 25' 50' 100 25' 50' 100' 1 1 1 1 1 1 1 1 1 63 ' 252' 1008 16' 63' 252 7 ' 28' 102* In a grating with 20,000 lines to the inch, using the third spectrum, we may suppose that the ghosts corresponding to a i=~ will be visible a 50 and those for - 1 = -^ very troublesome. The first error is a, = T Tnrinnnr a 25 in. and the second a^ = 5 0*0 o o in. Hence a periodic displacement of one millionth of an inch will produce visible ghosts and one five hun- dred thousandth of an inch will produce ghosts which are seen in the second spectrum and are troublesome in the third. With very bright spectra these might even be seen in the first spectrum. Indeed an over exposed photographic plate would readily bring them out. When the error is very great, the primary line may be very faint or disappear altogether, the ghosts to the number of twenty or fifty or more being often more prominent than the original line. Thus, when bfia l = 2-405, 5-52, 8-65, etc. = 2*N -^ , the primary line disappears. When = 0, 3-83, 7-02, etc. = ZxN ^L , the ghosts of the first order will disappear. Indeed we can make any ghost disappear by the proper amount of error. Of course, in general r - 2 CM - 1) r j U n -- - t/ B _i /_> V Thus a table of ghosts can be formed readily and we may always tell when the calculation is complete by taking the sum of the light and finding unity. 540 HENRY A. ROWLAND 72 72 T2 TV 72 72 72 72 72 72 /2 72 72 72 72 t/0 "1 "2 "8 "4 "5 "6 "7 "8 "9 "10 "11 "12 "13 "U a i 1-000 2 980 010 4 038 6 832 089 002 8 716 136 005 1- 586 194 019 a 050 333 1 94 017 001 2 605 000 969 186 040 003 068 115 236 095 017 002 8 832 162 000 169 176 065 013 002 4 158 004 133 185 079 018 002 r , 031 107 009 133 153 068 017 -003 5 fi 520 000 022 116 077 etc. 059 013 128 131 061 -017 -003 7- 8 016 090 029 .000 055 090 013 etc. 085 Oil 035 114 -103 -050 -016 -003 -001 8' 10 654 000 060 075 002 etc. 065 003 048 055 002 -047 -101 -091 -051 -022 -Oil -009 -022 This table shows how the primary line weakens and the ghosts strengthen as the periodic error increases, becoming at 2nJV a 2-405. tt It then strengthens and weakens periodically, the greatest strength being transferred to one of the ghosts of higher and higher order as the error increases. Thus one may obtain an estimate of the error from the appearance of the ghost. Some of these wonderful effects with 20 to 50 ghosts stronger than the primary line I have actually observed in a grating ruled on one of my machines before the bearing end of the screw had been smoothed. The effect was very similar to these calculated results. DOUBLE PERIODIC ERROR Supposing as before that there is no overlapping of the lines, we have the following: Places. Intensities. [/ (ba^ ,/ (toirif } Primary line. = ,,. - [7i (ba^J ,7 (. Ghosts of 1st order. /> = fi ~ [J (ba^) /! (ba^J GRATINGS IN THEORY AND PRACTICE 541 Places. = /j. Intensities. g t ba a l4 = /JL ^L [J, (&z 1( J ^ (fo 2 ,O] 2 j- Ghosts of 2d order. , 5 = ft |* [ J 'fi /* ^t 7 I f Ghosts of 3d order. &* A* 9 = ,U T-^ 2 etc. etc. Each term in this table of ghosts simply expresses the fact that each periodic error produces the same ghosts in the same place as if it were the only error, while others are added which are the ghosts of ghosts. The intensities, however, are modified in the presence of these others. Writing ^ = ba lP . and c 2 = ba^. The total light, is 7 / + etc. which we can prove to be equal to 1. Hence the sum of all the light is still unity, a general proposition which applies to any number of errors. The positions of the lines when there is any number of periodic errors can always be found by calculating first the ghosts due to each error separately; then the ghosts due to these primary ghosts for it as if it were the primary line, and so on ad infinitum. In case the ghosts fall on top of each other the expression for the intensity fails. Thus when e 2 = 2e lt e 3 = 3e^ etc., the formula will need modification. The positions are in this case only those due to a single periodic error, but the intensities are very different. Places. Intensities. P = - ba a 542 HENRY A. ROWLAND Places. Intensities. AI _ fJL A. [/! (K,"i) /o (fas.i) J 3 (ba^J 7 2 (ba&J + etc.] 2 *" + [iAO /i (far,*0 + etc.] 8 , etc. etc. We have hitherto considered cases in which the error could not be corrected by any change of focus in the objective. It is to be noted, however, that for any given angle and focus, every error of ruling can be neutralized by a proper error of the surface, and that all the results we have hitherto obtained for errors of ruling can be produced by errors of surface, and many of them by errors in size of groove cut by the dia- mond. Thus ghosts are produced not only by periodic errors of ruling but by periodic waves in the surface, or even by a periodic variation in the depth of ruling. In general, however, a given solution will apply only to one angle and, consequently, the several results will not be identical; in some cases, however, they are perfectly so. Let us now take up some cases in which change of focus can occur. The term *r* in the original formula must now be retained. Let the lines of the grating be parallel to each other. We can then neglect the terms in z and can write r 2 = y 2 very nearly. Hence the general expression becomes where * depends on the focal length. This is supposed to be very large, and hence K is small. This integral can be divided into two parts, an integral over the groove and the intervening space, and a summation for all the grooves. The first integral will slightly vary with change in the distance of the grooves apart, but this effect is vanishingly small compared with the effect on the summation, and can thus be neglected. The displace- ment is thus proportional to K y*\ CASE I. LINES AT VARIABLE DISTANCES In this case we can write in general y = an + atf + a^n 3 + etc. As K, a u a 2 , etc., are small, we have for the displacement, neglecting the products of small quantities, (an + Oin a + a a n 8 + etc.) a 3 2] . GRATINGS IN THEORY AND PRACTICE 543 Hence the term a^n 2 can be neutralized by a change of forms ex- pressed by fjia 1 =K a 2 . Thus a grating having such an error will have a different focus according to the angle n, and the change will be -f- on one side and on the other. This error often appears in gratings and, in fact, few are without it. A similar error is produced by the plate being concave, but it can be distinguished from the above error by its having the focus at the same angle on the two sides the same instead of different. According to this error, a^n 2 , the spaces between the lines from one side to the other of the grating, increase uniformly in the same manner as the lines in the B group of the solar spectrum are distributed. For- tunately it is the easiest error to make in ruling, and produces the least damage. The expression to be summed can be put in the form ib (>! a 2 ) n 2 + ib/tatf + ib Oa 3 -f ib (/^ <*)'] n*+ etc.] The summation of the different terms can be obtained as shown below, but, in general, the best result is usually sought by changing the focus. This amounts to the same as varying K until //a x *a 2 = as before. For the summation we can obtain the following formula from the one already given. Thus Hence vn -\ e Zipn sm n P e ip (n - 1). sin p = e p( -i) m dp J I amp When n is very large, writing *^ = pn = n Nn -f q, we have dq Whence writing c = c' =. /JLCii, c" = b &a 3 + i c'" = etc., 544 the summation is HENRY A. ROWLAND ( + etc. sn dq rf* sin J 11 3 4823 " 5068 " 3612 3805 j, ft tt 4 4919 " 5133 " 3683 " 3875 j, * M 5 5050 'i 5288 " 3780 i 4005 k,l II 6 5097 " 5333 " 3821 " 4157 ft, I it 7 it 8 5242 1 1 5477 " 3937 " 4121 Z, m tt 9 5405 " 5662 'i 4073 " 4222 m, n, e ll 10 5582 'i 5816 4293 4376 n,f It 11 5782 5934 " 4343 " 4447 >f II 12 4157 " 4267 " 3129 " 3218 e II 13 4157 " 4325 " 3094 " 3246 e ll 14 3218 " 3318 ll 15 4391 i' 4643 'i 3292 " 3478 f,ff i 16 5788 5977 " 3864 " 3977 17 5788 5977 " 3864 " 3984 o ll 18 5715 " 5977 3875 " 3977 ll 19 20 5853 6569 3024 " 3267 Plates 7, 14 and 19 were imperfect, owing to clouds passing over the sun, although a part (3218 to 3318) of Plate 14 was used for interpola- tion, as observations were scanty in that region. It is seen that some of the plates have only one standard upon them. With a plane grating it would be impossible to work them up, but with the normal spectrum produced by the concave grating only one is necessary, as the multiplier to reduce readings to wave-lengths is nearly a constant. In working up a whole series of plates, there is no trouble in giving a proper value to the constant for any plate in the series which has only one standard. Plate 17 was measured twice by two dividing engines, and as it was a specially good plate, each measure was given a weight equal to one of the other plates. The principal error to be feared in these plates is a displacement of the instrument between the time of the exposure on the two spectra. This was guarded against by the method above de- scribed. In Plates 17 and 20 there was a portion of the plate on which both the spectra fell all the time, and thus gave a test of the displace- ment. This was found to be zero. The other plates overlap so much that there are generally two or more determinations of each line. A 36 562 HEXRY A. EOWLAXD comparison of these values shows little or no systematic variation in the different plates exceeding ^ division of Angstrom. Plates 16, 17, 18, and 5, 6, 8, all give the region 3900 as derived from 5200 and 5850, and thus give a test of the relative accuracy of these latter regions. It is seen that the two results of the region 3900 differ by about -015 division of Angstrom. Were the wave-lengths of the region 5170 to 5270 to be increased by -020 the discrepancy would cease. The amount of this quantity seems rather large to be accounted for by any displacement of the spectra on the plates, but still this may be the cause. Again, it is possible that different gratings may give this difference of wave-length from the cause I have mentioned above. This cause, as I have shown, exists in the same degree in plane gratings as in concave. I have not attempted to correct it in this case, but have simply taken the mean of the two values for the region 3900, and so distributed the error. This is the greatest discrepancy I have found in the results except in the extreme red. Thus the region 3100 to 3200, a portion for which Plate 20 is to be relied upon, gives the wave-length of the ultra violet -01 division of Angstrom higher from the region 4200 than from 6300. As the dis- crepancies in this region before the invention of the concave grating were often a whole division of Angstrom, I have regarded this result as satis- factory. Indeed, until we are able to make all sorts of corrections due to the change in the index of refraction of the air with the Barometer and thermometer, it seems to me useless to attempt further accuracy. With the advent of photographic plates into the table, especially the longer ones required for metallic spectra, it becomes necessary to cor- rect them for the departure from the normal spectrum due to the use of long plates. The plates in the box are bent to the arc of a circle of radius r. When afterwards straightened we measure the distance by a linear dividing engine. Hence, what we measure is the arc with radius r. Let and ft be the angles of incidence and diffraction from the grating. We have then to express ft in terms of d. Let X be the wave-length, and n and N the number of lines on the grating to 1 mm. and the order of the spectrum respectively. Then A = T7 (sin a + sin /? ) ; nN %r <5 / sin j3 = - Tr sin cos [r + p ~ H A \ In these formula? a is the angle to the centre of the photographic plate, and ft and d are also measured from the centre, f is the angle TABLE OF STANDARD WAVE-LENGTHS OF THE SPECTRAL LINES 563 between the radius from the centre of the photographic plate and the line drawn from that point to the centre of the grating. When prop- erly adjusted, f will be zero. Also, we make 2 r = R, to obtain perfect focus throughout. So that / = ^ (sin 4- sin -g-j . nN\ 2 / Calling ^ O the wave-length at the centre of the plate, we have ap- proximately * The first quantity, - , is the value of / ^ , assuming the spectrum to ^ ?l jLJ be normal. The last term is the required correction expressed in terms of the provisional wave-length. The correction in actual practice has been made from a plot of the correction on a large scale, and never amounted to more than a few hundredths of a division of Angstrom, even for the longest plate. In two or three plates the camera was displaced, so that 7- had a value. In such cases no attempt was made to measure f , but the plates were only used for local interpolation by drawing a curve through certain points used as substandards. These substandards Mere principally used for working up the last set of photographic plates containing the solar spectrum and the metal spectra of the same or higher orders, or both. Some of them contained three metallic spectra. Thus the region 3900 in the solar spectrum has been obtained from both wave-lengths 5200 and 5850. The mean of these gave values of the substandards for working up the plates taken at this point, and containing also metallic lines at 2700. Again, the boron lines 2496 and 2497 have been obtained from the regions 4800, 3200 and 3600. The mean values give substandards for working up the metallic spectra of that region. Also the near coinci- dence in the values of the wave-lengths of these lines indicate the rela- tive accuracy of the regions 2496, 3200, 3600, and 4800. The use of these substandards is as follows: The photographic plates, mostly 19 inches long, were measured mostly on a machine giving wave- lengths direct. The differences of the results from the substandards were then plotted on a paper having the curve of correction for length upon it in such a way that the final marks should theoretically be a straight line. This was actually the case in all but a few plates, in 564 HENKY A. ROWLAND which the camera was displaced. A straight line was then passed through all the marks as nearly as may be, and the correction taken off. This correction could thus be obtained to T^TF division of Angstrom, and amounted to only a few hundredths of a division at most. Possibly T 1 - division of Angstrom was the greatest correction required for length. In this way each plate represents the average of all the wave-length determinations throughout its extent, and will not admit of any correc- tion save a linear one, should such ever be required in working over the table again. In every plate having a solar and metallic spectrum upon it, there is often indeed always a slight displacement. This is due either to some slight displacement of the apparatus in changing from one spectrum to the other, or to the fact that the solar and the electric light pass through the slit and fall on the grating differently. In all cases an at- tempt was made to eliminate it by exposing on the solar spectrum, both before and after the axe, but there still remained a displacement of TTTF to yf-g- division of Angstrom, which was determined and corrected for by measuring the difference between the metallic and coinciding solar lines, selecting a great number of them, if possible. The changes from sun to arc light are much more extensive than from one order of solar spectrum to another. In two cases I have tested the latter and found no displacement, and have no fear that it exists in the others. In working up the plates, I have started at the plates whose centre is at wave-length 4600, and proceeded either way from that point. For this purpose I have used the plates originally obtained for metallic spectra, generally using the lines due to the impurities. The method, I believe, is obvious from the table. For a long region no substandard^ are necessary, but are used whenever they become so. [The tables are omitted.! 52 THE SEPAKATION OF THE EAEE EAETHS [Johns Hopkins University Circulars, No. 112, pp. 73, 74, 1894] In the course of several years' investigations of the so-called " rare earths," such as yttrium, erbium, holmium, cerium, etc., I have devised several methods for their separation. I wish to give an account of these now, and hope soon to be able to publish a complete description of my work and its results. It was evident very early in the work that cerium, lanthanium, praseo- dymium, neodymium and thorium differed from the yttrium group, and I have seen no reason to suppose that they can be divided any further. All of these "earths" appear, in varying proportions, in such minerals as gadolinite, samarskite, yttrialite, cerite, etc. Besides the elements of the cerium group here present there are at least seven other substances. For the present I shall speak of them as a, 6, i, d, h, n, c, fc. Their properties are as follows: PKOPEBTIES OF ELEMENTS Substance a This is the principal element of yttrium and may possibly be divided into two in the future, as I have observed a variation in the arc spec- trum on adding potash or soda. However, this is no more evidence than occurs in the case of iron or zirconium. I give a process below for pro- ducing this pure. Properties. No absorption bands. Oxalate and oxide pure white. It occurs in the sun. Its properties are those of yttrium as hitherto ob- tained, but I am the first to obtain it with any approach to purity. Mixture of I, i and d These seem to be the principal ingredients in so-called "erbium." Oxalate is red. Oxide is pure white. Absorption band is that of "erbium." It colors the electric arc green, and shows the "erbium" emission bands on heating white hot. The substance b is strong in gado- 566 HENRY A. EOWLAISTD Unite and weak in samarskite. The solution has the absorption bands of " erbium " and most of these seem to belong to & rather than i. How- ever, we can readily prove that the absorption bands of erbium belong to two substances, as we can produce a decided variation in it. I cannot reconcile this with my spectrum work without assuming a fourth ingredient in " erbium." Substance & is in the sun, but not i. With 6 and i the substance d always occurs. Substance d This is the principal impurity of a sample of yttrium, kindly furnished me by Dr. Kriiss, which my process of making yttrium separates out. It has not been obtained pure, but occurs strongly in the yellow part of the oxides. It is in the sun. By aid of ferrocyanide of potassium the substance a can be obtained pure from d. With this exception d occurs in all the preparations of the yttrium group and cannot be separated from &, i, c, n, h, or any of the other substances. Indeed, I have found it in some specimens of cerium and lanthanium, although in traces only. On account of the trouble caused by it and its universal presence, I propose the name demonium for it. Its principal spectrum line is at w. 1. 4000-6 nearly. Substance h This occurs mainly in samarskite. Hints toward its separation will be given below, but I have otherwise obtained none of its properties. Substances n, Ic and c These always occur with d and form a group intermediate between the yttrium and cerium groups. They can be separated from these by sul- phate of potassium or sodium by always taking in intermediate portions of the precipitate. They seem to have a weak absorption spectrum in the visible spectrum and strong in the ultra violet, especially If. Chemical Separation The first process that suggests itself is that by the sulphates of soda or potash. This is the usual method for separating the cerium from the yttrium groups. When the solution of earth and the sulphate solution are both hot and concentrated, everything except some scan- dium comes down. When done in the cold with weaker solutions, there is more or less complete separation of the cerium group. Let the mixed THE SEPARATION OF THE RARE EARTHS 567 earths be dissolved in a very slight excess of nitric acid and diluted some- what (possibly 1 k. to 2 or 3 litres). Place in a warm place, add lumps of sulphate of soda, and stir until no more will dissolve. Continue to add and stir for a day or two until the absorption lines of neodymium disappear from the solution. Filter off and call the solution No. 1. Add caustic potash to the precipitated sulphates and wash so as to leave the oxides once more. Dissolve in nitric acid and precipitate again with sulphate of soda, calling the nitrate No. 2. Proceed in this way pos- sibly 10 or more times. The nitrates contain less and less earths; and the precipitate is more and more the pure cerium group; but a dozen precipitations still leave some impurity. The portions 1, 2, 3, etc., show decreasing "erbium" absorption bands, and the spectrum shows that the substances a, 6, d, i are gradually sepa- rated out with parts 1, 2, etc., while the numerous fine lines belonging to d, n, c, etc., with the cerium group, fill the spectrum of the portions 8, 9, 10, etc. This intermediate group has only very weak absorption bands and evidently has three or four elements in it, as I have produced at least that number of variations in its spectrum. The group can be obtained fairly free from , 5, and i, but the substance d persists in all the filtrates and in the precipitated cerium group also. This interme- diate group d, n, etc., seems to be in greater proportion in samarskite than in gadolinite, and there seem to be more elements in samarskite than in gadolinite. One of these I have called li. The oxides, especially for samarskite, are very yellow and dark. Sulphate of potash has a decided action in separating a and i from 6, a and i coming down first. After two months, the solution gradually drying, the proportion of & to a in the filtrate increased many times. Sulphate of soda has an action of the same kind, but much weaker. After leaving two months over sulphate of potash and soda, the follow- ing was the result of analysis of the soluble part as compared with the original mixture: Sulphate of Potash. Sulphate of Soda. Ge., La., etc. o o a Weak Medium weak b Much stronger Stronger c oo d Unchanged Unchanged t Weaker Medium strong o Stronger Weaker The oxide of the members of this group which are only slightly pre- cipitated by the sulphates of soda and potash is pure snow-white, and hence those of & and i must be so. 568 HENRY A. KOWLAND The substance d comes down slightly sooner than a by sulphate of soda, but slightly slower by sulphate of potash. Hence, in purifying yttrium (substance a) for the last time from the ce. group, sulphate of potash will increase d in the filtrate and sulphate of soda will decrease it. Action of oxalic acid When the oxalates of the mixed earths, free from the ce. group, are boiled in water to which nitric acid is added, they are more or less dis- solved, leaving a coarse, heavy, red oxalate yielding a pale yellow oxide. The nitrate, set aside to cool, deposits more of the oxalates and leaves a filtrate which contains several of the unknown elements, as also what re- mains of the ce. group. On separating the ce. group the remainder is quite different from the heavy red oxalate, but there is far from complete separation. The analysis showed the following: a, &, c, d, li, i, n. I have not found the separation particularly useful, and it seems to be more apparent than real as tested by the spectroscope. Ferrocyanide of potassium This is the most useful process and easily separates the element a, pure and free from all others. To obtain pure a from the mineral gado- linite, Fergusonite or Samarskite: First obtain the crude mixed earths in the usual manner. Then sepa- rate the cerium group as usual until the absorption bands of neodymium no longer appear. For the complete separation without loss this must be done several times, as much of the yttrium group is carried down with the first precipitate, as we have before seen. The separation of the yttrium (a) from the other elements is effected by precipitating the latter from a weak acid solution by ferrocyanide of potassium. For this purpose the filtrate, after separating the cerium group, can be used at once by slightly acidulating with nitric acid, dilut- ing and adding a weak solution of ferrocyanide of potassium. No pre- cipitate should appear at once, but by standing for an hour or so some will come down. Add more ferrocyanide of potassium and repeat until the filtrate no longer shows the bands of so-called erbium. After this it is best to precipitate with oxalic acid or oxalate of potassium and ignite the precipitate so as to get the earth. Dissolve this in nitric acid and add only water enough to make a very concentrated syrupy solution. THE SEPARATION OF THE RARE EARTHS 569 Place in a beaker at least three inches in diameter and examine with a spectroscope of low power for absorption bands. Probably the bands of neodymium and " erbium " will appear. Separate the first by sulphate of sodium as usual, and the last by ferrocyanide of potassium from an acid solution as above. The filtrate will then contain the pure yttrium a, whose calcined oxalate will be pure white without trace of yellow. After separation of iron, calcium, and possibly manganese, the earth will be a pure element as far as I can tell spectroscopically. However, like Zr, Fe and many other substances, the addition of Na or K to the elec- tric arc while obtaining the spectrum will change the intensity of cer- tain lines of the spectrum, while others are unchanged. If this is con- sidered as evidence of the existence of two elements, then the same evi- dence will apply to Fe and Zr. The reason for believing that the sub- stance thus found is an element is based on the fact that its spectrum remains unaltered in all minerals and after all chemical operations that I have been able to devise. Furthermore, I believe that the new pro- cess is not only more easy than any other, but also that it has given a single element for the first time, as it eliminates the element d. The yield will of course depend on the amount of purity required. From the earths of gadolinite about one-tenth of quite pure yttrium (a) can be ob- tained and about one-twentieth of very pure. I have determined spectroscopically that when, by the above process, the absorption band of "erbium" at last disappears from 3 in. of strong solution, all the other elements have also disappeared. By taking the first precipitate several times by ferrocyanide of potas- sium from an acid solution, a mixture of many elements is obtained which contains much of that element to which the so-called "erbium" band is due. By dissolving a weighed quantity of this mixture in nitric acid and water and examining the band spectrum, I have determined the limit when the band can no longer be seen. Thus I have proved that when the band vanishes from 3 inches of concentrated syrupy solution of yttrium there cannot exist in it more than -| per cent of the mixed element as compared with the yttrium, and there is probably less. I have not found ferrocyanide of potassium useful in the further separation of the elements, but only in separating out a from the others. When the neodymium band has disappeared by use of sulphate of sodium, all the other elements of the cerium group have disappeared. The element thorium is sometimes present in the crude earths, but dis- appears after a while from the purified earths. The conditions for its disappearance I have not determined. 570 HENRY A. ROWLAND The elements which persist to the last by the ferrocyanide process are & and i, while by Kriiss' process the element d persists the longest. As & -J- i has an absorption spectrum and d probably not, the test of purity by absorption bands is very complete in the new process. Note. For help in this investigation my thanks are due to a large number of gen- tlemen. Professor Schapleigh has sent me a large collection of substances, Mr. Hidden, Professor Wolcott Gibbs, and Professor F. W. Clarke many minerals, Profes- sor Kriiss several specimens, and Professor Barker and others have helped me in many ways. 57 NOTES OF OBSERVATION ON THE RONTGEN RAYS BY HENRY A. ROWLAND, N. R. CARMICIIAEL, AND L. J. BRIGGS [American Journal of Science [4], /, 247, 248, 1896 ; Philosophical Magazine |5], XLI, 381, 382, 1896] The discovery of Hertz some years since that the cathode rays pene- trated some opaque bodies like aluminium, has opened up a wonderful field of research, which has now culminated in the discovery by Rontgen of still other rays having even more remarkable properties. We have confirmed, in many respects, the researches of the latter on these rays, and have, repeated his experiment in photographing through wood, aluminium, cardboard, hard rubber, and even the larger part of a milli- meter of sheet copper. Some of these photographs have been indistinct, indicating a source of these rays of considerable extent, while others have been so sharp and clear cut that the shadow of a coin at the distance of 2 cm. from the photographic plate has no penumbra whatever, but appears perfectly sharp even with a low power miscroscope. So far as yet observed the rays proceed in straight lines and all efforts to deflect them by a strong magnet either within or without the tube have failed. Likewise prisms of wood and vulcanite have no action whatever so far as seen, and, contrary to Rontgen, no trace of reflection from a steel mirror at a large angle of incidence could be observed. In this latter experiment the mirror was on the side of the photographic plate next to the source of the rays, and not behind it, as in Rontgen's method. We have, in the short time we have been at work, principally devoted ourselves to finding the source of the rays. For this purpose one of our tubes made for showing that electricity will not pass through a vacuum was found to give remarkable results. This tube had the aluminium poles within 1 mm. of each other and had such a perfect vacuum that sparks generally preferred 10 cm. in air to passage through the tube. By using potential enough, however, the discharge from an ordinary Ruhmkorff coil could be forced through. The resistance being 572 HENEY A. ROWLAND so high the discharge was not oscillatory as in ordinary tubes but only went in one direction. In this tube we demonstrated conclusively that the main source of the rays was a minute point on the anode nearest to the cathode. At times a minute point of light appeared at this point, but not always. Added to this source the whole of the anode gave out a few rays. From the cathode no rays whatever came, neither were there any from the glass of the tube where the cathode rays struck it as Rontgen thought. This tube as a source of rays far exceeded all our other collec- tion of Crookes' tubes and gave the plate a full exposure at 5 or 10 cm. in about 5 or 10 minutes with a slow-acting coil giving only about 4 sparks per second. The next most satisfactory tube had aluminium poles with ends about 3 cm. apart. It was not straight, but had three bulbs, the poles being in the end bulbs and the passage between them being rather wide. In this case the discharge was slightly oscillatory, but more electricity went one way than the other. Here the source of rays was two points in the tube, a little on the cathode side of the narrow parts. In the other tubes there seemed to be diffuse sources, probably due in part to the oscillatory discharge, but in no case did the cathode rays seem to have anything to do with the Rontgen rays. Judging from the first two most definite tubes the source of the rays seems to be more connected with the anode than the cathode, and in both of the tubes the rays came from where the discharge from the anode expanded itself to- ward the cathode, if we may roughly use such language. As to what these rays are it is too early to even guess. That they and the cathode rays are destined to give us a far deeper insight into nature nobody can doubt. Baltimore, Feb. 20, 1896. 58 NOTES ON RONTGEN KAYS BY H. A. ROWLAND, N. R. CARMICHAEL, AND L. J. BRIGGS [Electrical World, XXVII, 452, 1896] In the ' American Journal of Science ' for March we made a few notes of our researches on the Rb'ntgen rays, reaching the provisional con- clusion that the main source of the rays was at the anode, and that the cathode rays seemed to have nothing to do with the phenomena pre- sented. A further study of the source of the rays in many other tubes has led us to modify this conclusion somewhat, for, while we still think the anode or its equivalent is the main source of the rays, yet we now have evidence in some of the tubes that it is necessary for the cathode rays to fall on the anode in order that the Rontgen rays may be formed. In our tubes with a very high vacuum the other sources of rays are very faint indeed. We have never obtained any rays from the cathode except in one case, where undoubtedly there were electrical oscillations which made the cathode momentarily an anode. It can be readily proved that these oscillations always exist in the case of low resistance tubes, and these are probably the cause of many errors in estimating the source of the rays. In some cases we have found very faint sources of rays as Rontgen found them, where the cathode rays struck the glass, but not where they struck a piece of platinum kept at nearly zero potential. On the anode theory, this might be explained by the fact that the bombarding cathode rays, coming in periodical electrified showers, alternately raise and lower the potential of the glass, thus making it alternately an anode and cathode. In the case of the platinum, this could not occur to the same extent. That feeble Rontgen rays emanate from some bodies when bombarded by the cathode rays, we are willing to admit, and, in fact, had long ago come to that conclusion. But we do not agree with Prof. Elihu Thom- son's general conclusion that these rays are always given out from bom- barded surfaces, as we have a tube, with platinum in the focus of a con- cave electrode, which emits no rays whatever from the platinum, even 574 HENRY A. Rovv LAND when the platinum is red hot from the bombardment, the concave elec- trode being the cathode and a third wire the anode. The same tube, with the platinum made an anode and the concave electrode a cathode, produces a profuse radiation of Rontgen rays in all directions on the side of the platinum bombarded by the cathode rays, and none on the other side. In the first case we obtained no rays from the cathode, no rays from the bombarded surface, and only a very weak effect from the anode, indeed almost nothing. Hence the condition for the production of the rays seems to be neither the one or the other but a combination of the two, and we now believe as far as we can yet see that the necessary condition for their production is an anode bom- barded by the cathode discharge. The anode may be, however, an in- duced anode formed on the glass, and the cathode rays may vary a great deal and cease to present the usual appearance of cathode rays. Thus, in the best tube that we have, originally made for showing that electricity will not pass through a vacuum, the main source is a point on the end of the anode, where a little point of light appears. Sometimes, across the little interval of 1 mm. between the electrodes, a faint spark or arc crosses from one electrode to the other, and we think that the rays come out especially well under these conditions. Here the action of the bombarding cathode discharge is rather obscure. This little point of light also sometimes appears on the red hot platinum anode men- tioned above, and we have seen it in other tubes, always at the place where Rontgen rays are apparently found. Prof. Elihu Thomson has kindly sent us some sketches of tubes hav- ing the anode bombarded by the cathode, and we had previously de- signed some tubes of similar shape, but have not yet found anybody in this country capable of making a sufficiently good vacuum. In many of our best tubes the vacuum is so perfect as to cause a resistance equal to a five or six inch spark in the air. The better the vacuum the greater the number of rays sent out. However, for sharpness of detail, nothing equals the perfect vacuum tube, having its electrodes one mm. apart. Such a tube has been de- signed by one of us, but we have not been able to get the proper exhaustion. As to other sources of Rontgen rays, we have tried a torrent of elec- tric sparks in air, from a large battery, and have obtained none. Of course, coins laid on or near the plate under these circumstances, pro- duce impressions, but these are, of course, induction phenomena. As to sunlight, Tyndall, Abney, Graham Bell and others, have NOTES ox KONTGEN KAYS 575 shown that some of the rays penetrate vulcanite and other opaque bodies, and we have only to look at an unpainted door, on the other side of which the sun is shining, to convince ourselves that sunlight penetrates wood to a considerable depth. As to the theory of the Eontgen rays we know little. If the rays are vibrations we can readily determine a rough limit to their length, from the sharpness of the shadows. Thus our photographs have such sharpness that the complete waves cannot be more than -0005 cm. long, but are probably much shorter. This is independent of whether the waves are longitudinal like sound or transverse like light, and of course only applies to that portion of them which affects the photographic plate. There may be others of larger size that do not affect the plate. All efforts to bend the rays from their course, either within or with- out the tube, by means of a strong magnetic field, have failed, both in our hands and in those of others, and thus, if the rays are radiant parti- cles of matter, they cannot be highly charged particles like the cathode rays. The rays are not refracted by any solid bodies so far tried, and this seems to be against their being waves either in air or ether. They pass through solid bodies, and thus their wave-lengths cannot be very small. We have before seen that it cannot be very great. They cannot be sound waves as they proceed for some distance through a very perfect vacuum. Altogether we are at a loss for a theory. If we have not yet got a satisfactory theory of light after more than a hundred years of labor, how can we hope to have a theory of the Kontgen rays after knowing of them for only a few months? Let us suspend our judgment for a while, and let us, above all things, be willing to alter our opinions at any moment when fresh light appears. 59 THE RONTGEN RAY, AND ITS RELATION TO PHYSICS (A TOPICAL DISCUSSION) [Transactions of the American Institute of Electrical Engineers, XIII, 403-410, 430, 431, 1896] OPENING REMABKS BY PROF. HENRY A. ROWLAND MR. PRESIDENT AND GENTLEMEN: A gentleman asked me a few mo- ments ago if I knew anything about the X-ray. I told him no; that what I was going to tell to-night was what I did not know about the X-ray. I do not suppose anybody can do any more than that, because all of us know very little about it. We were very much surprised, something like a year ago, by this very great discovery. But I cannot say that we know very much more about it now than we did then. The whole world seems to have been working on it for all this time without having discovered very much more with respect to it. Now, I suppose it is not necessary for me to go into the history of the thing. We all know it; how Lenard first, probably, discovered these rays, or discovered something very similar to them; how Rontgen after- wards found their particular use, their penetrating power, and so on, although Lenard had found something similar to that before. It is thus not necessary for me to go into the history of the matter, but simply to go over, to some extent, what we know with regard to these rays at the present time. First, there was some discussion, some time ago, as to the source of these rays. Rontgen found that their source was any point that, the cathode rays struck upon; and you will remember that when we first knew about these rays they were often called cathode rays. Many persons thought that the cathode rays came through the glass, and Lenard first thought that they did come through his little window, and it is probable that they do at the present time. But the kind of rays that we are considering are very different from the cathode rays. Six months ago there was quite a discussion in regard to the source, and I believe it was finally determined that they came from points where the cathode rays strike. At the same time I was rather opposed to that. In one of my tubes I found that the rays came from THE RONTGEN RAY AND ITS RELATION TO PHYSICS 577 the anode. I had only the ordinary assortment of Crookes' tubes, and one of the tubes had aluminum wires which were a millimeter apart. In one of these the source of the rays was a point upon the anode not upon the cathode at all. It was a very small point. The photo- graphs which I obtained by that tube were sharper than any I had seen before. They are so very sharp that in estimating the shadow of an object I determined that the point could not have been a thousandth of an inch in diameter. Therefore the source in this case was a very minute point upon the anode, and that point was nearer the cathode, and I suppose some of the cathode rays might have struck upon it, and it might have obeyed the law that the point where these X-rays are formed is the point on the anode where the cathode rays strike. I had another very interesting tube, and I was going to bring some of the photographs here to-night; but I thought they were so small that it would be almost impossible to see them. I tried the three cases in this tube: First, the case where the cathode rays strike upon the anode. In that case I got very many Rontgen rays. Then I tried the case where the cathode rays strike upon an object a piece of platinum. I did not get any rays whatever then. Now, some people say that they come from the point where the cathode ray strikes. I did not get any whatever in that case. In this case the cathode ray struck upon a piece of platinum in the centre of a bulb, and no rays were given out by the anode either. Therefore I seemed to have a crucial experiment in each; I seemed to have the case where the cathode ray strikes upon the anode, and I got lots of rays. Then I had the case where the cathode rays strike on a piece of platinum, and I did not get anything at all. Then where the anode itself was free and no cathode rays struck it, I did not get anything from it. It seemed to me as if the source was most abun- dant when the cathode ray struck upon the anode; and that is the theory, we know, upon which nearly all tubes are formed at the present time. You have the focus tubes in which you focus the cathode rays upon the anode, and in that case you have a very abundant source of rays; but I do not believe you ever could get as small a source of rays as I got with that first tube, where I had a source of a thousandth of an inch diameter. Having such a small source of rays, it gave me a limit to the wave-length, if there were waves at all; it would give me a limit to the wave-length of which I will speak in a moment. As to whether there are any rays where the cathode rays strike on any other objects, we know that there are very feeble ones. It seems to be almost neces- sary in order to get an abundant source that you should have cathode 37 578 HENRY A. EOWLAND rays strike on the anode. However, that is a point of discussion. Now, as to the source of electricity, we have generally the Euhmkorff coil. There is one source of which I saw a little note in ( Nature,' where a man had used a large Holtz machine with very good effects. Now it is very much easier for many persons to use a Holtz machine than to use a Euhmkorff coil. There are many cases where one cannot have a large battery; and this man said that with the Holtz machine he got as great an effect as with the Euhmkorff coil. Then we have the Tesla coil, etc. By the way, speaking of the Tesla coil, I am not sure but that you might look back and find that it is very similar to the Henry coil. Henry originally experimented on the induction of electricity, transmit- ting a spark of electricity from one coil and getting a spark from an- other, and the Tesla coil is something like that, except that it is made so as to produce a much more voluminous spark. We all know the properties of the Eontgen rays they go in a straight line. Every effort to deviate them from a straight line, by any means whatever, has failed, except that when they strike upon an object they are reflected. Now, it is a question for discussion as to whether there is any regular reflection. They strike upon an object, and you get some- thing from that object which will affect a photographic plate. Are those rays which you get from the object Eontgen rays still, or do the Eontgen rays strike upon this object and generate in it some sort of rays which come out, different from the Eontgen rays, and affect the plate? We do not know that. Neither are we quite positive whether there is any reflection of the rays. We know there is turbid reflection you may call it rays strike on the object, and the object becomes a source of rays of some kind. Nobody has ever found out what sort of rays come from the object. Something comes from it, and we generally imagine, and indeed we often state, that they are Eontgen rays that come off the object. But we have good reason to suppose that they may be something else; and they may or may not be regular reflections; some persons say they are and some that they are not. I have seen some photographs made in this city which indicated regular reflections. At the same time I would not be positive as to whether there was any regular reflection. It is rather doubtful. It is a point to be determined. Then the fluorescence that is the way Eontgen originally found the ray. You know the way they produce fluorescence the photographic effect you all know that. You all know that the magnet does not affect them does not turn these rays from a straight line. The polarization of the rays: We have no evidence whatever as to THE RONTGEN KAY AND ITS RELATION TO PHYSICS 579 the polarization. If they were very small waves, transverse waves, like light, we ought to be able to polarize them. Becquerel, by exposing certain phosphorescent substances to the sun, obtained from them cer- tain rays which penetrated objects like aluminium,. etc. But these rays were evidently small rays of light, because he could polarize them, and he could refract them, and they were probably very short waves of ultra violet light. But we never have been able to discover that there was any such effect in a Rontgen ray. Some persons have claimed that they got polarization; but if there ever was any polarization, it is very small, indeed. One of the principal advances in respect to these rays is that made by J. J. Thomson, in considering the electric discharge of bodies. He has published most valuable results with regard to the effect of these rays upon gases. When the rays fall upon a gas, they affect the gas in some way so that it becomes a conductor. Now, you can subject the gas to these rays and allow the gas to go through a tube off into another vessel, so that it will discharge an electrified body in that vessel. But he has found the most interesting result that it will not continue long to affect these bodies. After one has allowed a certain amount of electricity to pass through it, it then becomes an insulator again. It only allows a certain amount of electricity to go through it. That is easily explained or you can explain it by the Rontgen rays liberating the ions, and only a certain amount of them. Just as soon as these are used up in the conduction of the gas, then it ceases to conduct. So that a certain amount of gas will conduct a certain amount of electricity, and then it stops conducting. That is a most interesting result. It is one of the great advances we have made since Rontgen's discovery. Rontgen knew nearly all we know now about these rays. We have discovered very little indeed; but that point I think we have at least discovered. Then it is said that these rays affect a selenite cell in the same way that light affects it it changes the resistance of the selenite cell. Of course, we are only considering the theory to-night; at least I am, and we do not have to consider the bones, and so on. I have had some students at work in my laboratory, and it was with the utmost difficulty that I kept them from photographing bones. Bones seemed to be the principal object to be photographed by the Rontgen rays when they were first discovered, and I suppose it is the same now. Most people connect Rontgen rays with bones; but I do not intend to say very much about them. Now, one important point with respect to these rays is as to whether 580 HENRY A. ROWLAND they are homogeneous. Are they like light which can he divided up into a large number of different wave-lengths, or are they homogeneous? There seems to be a great deal of evidence that they are not all the same; that one ought to get a spectrum of them in some way. We can filter them a little bit through objects. After they are filtered through an object, they are probably a little different from what they were before, and some objects probably let through different rays from others. In ' Nature ' Mr. Porter, I believe, has shown experiments upon that. He divides rays into three kinds. At least he finds that under certain circumstances the rays will penetrate bones better than in other cases bones or any other object they have more penetrating power, and they go through many of those objects that ordinarily stop them. By heat- ing up the tube, and by various arrangements of his spark-gaps, etc,, and putting little wires around his tubes, and so on, he can cause them to generate different kinds of rays. That is a very important point, if it is substantiated, and there seems to be little reason to doubt that a number of rays really do exist; that whatever they are that come from the object, they are not all the same; some of them penetrate bodies better than others, and very likely some one will get up some sort of filter that will filter them out, and allow us to use them and to find if they have different properties. At the present we are rather in the dark with regard to this point. Now I come to the theory of these rays. What is the cause of all these phenomena? There was a time when we were rather self- satisfied, I" think, with regard to theories of light. We thought that Fresnel and others had discovered what light was some sort of vibra- tion in the ether; we called it ether; if it had these, waves going through it, then it would produce light, and we were pretty well convinced that the waves were transverse, because we would polarize them; so that we began to be satisfied that we knew something about light. Then Max- well was born, and he proved that these rays were electromagnetic very nearly proved it. Then Hertz came along and actually showed us how to experiment with these Maxwell waves, most of which were longer than those of light. At the same time they were of the same nature. Well, we got a rather complicated sort of ether by that time. The ether had to do lots of things. One must put upon the ether all the communication between bodies. For instance, what communication is there between this earth and the sun? Why, you have light coming from it and heat. Radiation you might call it all. We have radiation. Then some people thought they discovered electromagnetic disturbance THE RONTGEN RAY AND ITS RELATION TO PHYSICS 581 from the sun. Sometimes they have seen a sun spot and noted a deflec- tion of the magnetic needle on the earth. Very likely that is true. I don't know that they have discovered any electrostatic effect. But we know that electrostatic effects will be carried on through as perfect a vacuum as you can get. Then we have gravitation action too. Now, you have got all those things electromagnetic action, light which would be an electromagnetic phenomenon, and then we have gravitation, and we have got to load the ether with all those things. Then we have got to put matter in the ether and have got to get some connection between the matter and the ether. By that time one's mind is in a whirl, and we give it up. Now we have got something worse yet we have got Rontgen rays on top of all that. Here is something that goes through the ether, and it not only goes through the ether but shoots in a straight line right through a body. Now, what sort of earthly thing can that be? A body will stop light or do something to it as it goes through; but what on earth can it be that goes through matter in a straight line? Why, our imagination doesn't give us any chance to do anything with that pro- blem. It is a most wonderful phenomenon. Now, we can suppose that they are ultra violet light. Indeed, we can get a limit to the wave- length to some extent. Nobody, however, has ever proved that the Ront- gen rays are waves. But we can get a limit of the wave-length if they are waves, because when I have a tube that gives me a shadow which is only a thousandth of an inch broad, or rather from the greatest intensity out to clear glass a thousandth of an inch broad, I can calculate the wave-length of the thing that would produce such a shadow. It has got to be very small indeed; one knows that right away, because any ordinary light would make a few waves at the edge of the shadow, and by measuring those waves you could get the wave-lengths of the light. But there was no appearance whatever on any of my photographs of any such phenomenon as that. I did not have any of these waves at the edge of the shadow whatever. It went directly from blackness to light. But putting it under the microscope and measuring from almost imag- inary points, from lightness to darkness, I could get a limit to the wave- length. Now, as to that limit, I published it in one of the journals six months ago, or more, and it came at about one-seventh, I think, that of yellow light. Others have determined the wave-length and got even below one-seventh that of yellow light. Some have got one- thirtieth that of yellow light, and so on. Some of them I am rather doubtful about, because they say they have bands. If they have bands 582 HENRY A. ROWLAND and diffraction bands, that would prove instantly that the Rontgen rays are waves. But I have never seen the slightest phenomenon of that sort. It is very doubtful that it exists, and those persons who have had it will have to show their photographs very clearly to make us believe it. And therefore we have no evidence whatever that the rays are waves. At the same time we have no evidence that they are not waves. They might be very short waves infinitely short waves. Let us see what would happen if they were infinitely short waves. They might be so very short as to be too fine-grained for any of our methods of polarization or reflection. Waves are reflected from a solid body regularly reflected, because they interfere after they come from the body. You can get the direction the angle of incidence equals the angle of reflection; you can get that by means of considering them as waves and as interfering after they come from the object. Well, if the object, however, is a very rough sort of thing compared with the wave- length, you will not get a regular reflection. That is what might hap- pen in the case of Rontgen rays. And then again, with regard to refraction of the light, the theory of refraction which comes from con- sidering molecules imbedded in the ether will give you some limit. When we go beyond that limit, we get no refraction. The bending of the violet rays increases up to a certain point and then goes back. We have a case of anomalous refraction very often in some substances like fuchsine, aniline dyes, and so on. Therefore the action of refraction can be accounted for by having very short waves. But when we treat of the theory of the case we have the little molecules of a gas knocking against each other, and they can only go a little distance. We call that the free path of the gas a very small distance in the ordinary air. Those molecules cannot go more than this very small distance before they stop. Well, now, why should little, short waves of light pass through the gas and not be stopped too? When the waves are very short indeed, it seems to me that the object would be entirely opaque to them, because they would strike upon those molecules, unless they could pass directly through the molecules. You would therefore neces- sarily have these little short waves going directly through the mole- cules, which we generally think is almost impossible in case of light. And that is one very great objection that I have to that theory. Then we have another theory that these are not transverse waves at all; that they are waves like sound, and very short indeed. Well, what would happen then? If they are very short indeed, you have the same objection: They would all strike against the molecules, and they THE ROXTGEN RAY AND ITS RELATION TO PHYSICS 583 would be dispersed very quickly. The shorter the wave-lengths, the more they are dispersed. Take, for instance, short waves that bob against a boat and are reflected back. Thus, if you have a big, long ocean wave, it sweeps around a boat and goes on without being troubled by the boat at all. The shorter the waves, the more they are bothered by the boat, and so it is with respect to other waves the short waves would probably be stopped by the molecules. So I do not see what we can do with regard to it in that respect. According to Maxwell's law, waves like sound do not exist in the kind of ether that he suggested. But that is all based upon a certain theory that the lines of force were always closed. He introduced into his equation an expression which indicated that every line of force was a closed path coming back upon itself or ending in electricity, one or the other. Now, if we throw out that, then we can get this kind of compressional waves in the ether. Now, it is not at all impossible that they exist, and as to whether they would go through molecules any better than light waves do, nobody can tell; but it is possible that they might. But if there are waves at all, they must be very short waves. You cannot get over that fact if they are waves at all, they must be short. Then, of course, you have the other theory of little particles of matter flying out from the body, passing through the glass and all other bodies, until they reach a photographic plate or any other place where we are notified of their presence, and these little particles make their way through the air or any other substance. Now, why should not the little particles be stopped very quickly by bodies as well as if the rays were waves? You see we are in trouble here too. Why are not the waves stopped? Why are not the little particles stopped? Stokes has given some sort of a theory with regard to this that, instead of having a wave motion in the ether, the rays are impulses a sudden impulse one wave, for instance not a series of waves at all, but one impulse coming out from the tube. I think if he had seen any very sharp shadows obtained from the Rontgen rays he would not have given that theory. He probably has seen only those very hazy outlines that very many persons take for Rontgen photographs. But if he had seen any very defined ones very sharp ones he probably would not have given that theory, because if the Rontgen rays are waves at all, they must be short, and there must be a long series of them to make sharp shadows. This is why Newton gave up the wave theory of light. You remember he gave up this theory because he found that light went straight past an object instead of curving around into the shadow as much as sound 584 HENRY A. ROWLAND does. But he was not quite up to his usual pitch when he made that statement, because if he had thought a moment he would have seen that very short waves will go more nearly in a straight line than long ones. But any single impulse, such as Stokes suggests, would go into the shadow. The only wave motion that would go in a straight line is a series of waves, one after another. Therefore, these rays cannot he single impulses coming irregularly. Prof. Michelson has suggested a theory of rays based on something like vortex rings in the ether. Now, if we have an ether that can carry on light waves and electromagnetic waves, it cannot be a perfect fluid; it has got to be something else. You cannot very well imagine vortex rings in such an ether. So that we are met at every point by some objection. We have been studying light for hundreds of years; we are not anywhere near satisfied with the theory yet, and we cannot very well be expected to be satisfied with the theory of Rontgen rays in one year. Well, I think that is all I can say with regard to the subject, and I hope the other gentlemen who are to carry on the discussion will satisfy you on all these points that I have brought up and left unanswered. [There followed a discussion by Professor Elihu Thomson, Professor M. I. Pupin, and others.] PROF. ROWLAND: I made a few notes with regard to what has been said, but they are made in such a way that I do not believe that I can interpret them myself, especially as the hour seems to be getting rather late. One or two remarks, however, I would like to make. When Prof. Thomson said that he got such a large amount of rays from an insulated piece of platinum by letting the cathode rays fall upon it, he made a sketch. With the exception of this end, which was flat, that is the kind of thing that I used. Now, there was absolutely no effect when this was made an anode and this a cathode, so that all the cathode rays were striking on the platinum. I have the photo- graph; I got no effect whatever. Now, if Prof. Thomson got an effect in this case and I did not get an effect in that case, I have got a case, at least, where none of these rays were produced by the falling of the cathode rays upon the object. It doesn't make any difference how many other persons have something in which they do get an effect. If I did not get an affect, that is one case, understand. That is the case where the cathode ray fell on an object and I got no Rontgen ray. THE RONTGEN RAY AND ITS RELATION TO PHYSICS 585 If other people got them in other ways, why, there is something else coming in. I don't know what it is. PROF. THOMSON: I should like to say just there, Professor, if you would allow me, that I used exactly that arrangement first, and got rays with the concave cathode. The anode at this end and the inter- posed plate of platinum between, with that wire extending outward, is the standard form of Crookes' tube the first tube, in fact, that I used. I got not only sharp effects but rays. THE CHAIRMAN: Was the platinum red? PROF. THOMSON: The platinum was red yes, of course, and it was a vigorous source of rays. I got rays with the same tube that Professor Rowland does not get them. PROF. ROWLAND: Well, that has nothing to do with the point. The point that I raise is this, that there was certainly no doubt that I did not get any, and the cathode rays were falling from the object. That is the thing. Now, one thing that I wish to remark is that most people draw a tube like that. They don't say where the wires go. Mine generally went out, so that they were very far away from this object. By curving wires around in different ways I can get an inductive action. I don't doubt that I could fix up a tube so that I could get lots of rays out of any part. However, the time is passing, and I will just say one word with regard to the point Prof. Thomson raised with regard to the fluorescence over the surface of the glass. He thought something was stopped by the glass. I must say that Lenard, when he first experi- mented upon this subject and I regard his experiments as quite as valuable as Rontgen's, probably , he got several kinds of rays coming out through an aluminium window. He got rays which were deflected by the magnet, as well as others. He had not separated them, how- ever. When the Lenard paper came to the laboratory I remarked to my students: " That is the best discovery that has been made in many a day." I immediately set somebody to work experimenting. He tried to get some results and would probably have discovered the Rontgen rays at that time if it had not been that the University of Chicago called him off, and Johns Hopkins University was very poor and could not call him back, and he had to stop in the midst of his work. They always say in Baltimore that no man in that city should die without leaving something to Johns Hopkins. Now, Dr. Pupin mentioned a means of showing whether the rays were reflected a little reflector in which he had them brought to a focus, as I recollect it. I have read an account in which an experimenter did find the rays were brought to a 586 HENRY A. EOWLAND focus, showing, provisionally at least, that there was some regular reflec- tion. But these experiments should all be repeated many times before one actually believes them. We don't always believe what we read. Now, as to Helmholtz's theory of the motion of ether and so on well, as I said before, what is the motion of the ether? What is motion of the whole ether? You cannot move the ether in the whole universe all at once, and if you do not move the ether in the whole universe all at once but only move a part, then it is a wave, so it amounts to the theory that I gave an impulse, such as Stokes had. Now, an impulse such as Stokes had does not go in a straight line it goes around cor- ners and it does not go in. a straight line unless there are lots of waves coming out. We can readily prove that an ordinary molecule, vibrating to ordinary light, must give out a hundred thousand waves without much diminution of amplitude, or else you cannot have the sharp lines in the spectrum that we do. The molecule must vibrate a long time longer than any bell that we can make. We cannot find a bell that will give out a hundred thousand vibrations without much diminution. For ethereal waves something must vibrate to produce them. What it is I don't know that there is any necessity for discuss- ing, because you can discuss it forever and never get any nearer to it. Something vibrates. Now, the thing that vibrates we don't know. We don't know whether it is electricity or whether it is mechanical motion. We know nothing about it. I have often said to my students, when I showed them the spectrum of some substance like uranium, in which we were taking photographs which would be perhaps ten feet long so fine in grain that you could not put the point of a pencil on it without finding a line. There were thousands of lines. I said to them: " A molecule of matter is more complicated a great deal than a piano. Counting the overtones and everything, you would not probably get up anywhere near the number of tones you get out of a single molecule of uranium. Therefore it rather looks as if the uranium molecule was very complicated." Of course, all those spectrum lines do not indicate fundamental tones many are harmonics. Still it is rather a compli- cated thing to get a spectrum in which there are many thousands of lines. So when I come to think what a molecule is and try to get up some theory of it, I quite agree with Dr. Pupin that we don't know any- thing about it. 64 DIFFRACTION GRATINGS [Encyclopcenia Brltannica, New Volumes, III, 458, 459, 1902] The grating is an optical instrument for the production of the spec- trum ; it now generally replaces the prism in a spectroscope where large dispersion is needed, or when the ultra-violet portion of the spectrum is to be examined, or when the spectrum is to be photographed. The transparent grating consists of a plate of glass covered with lampblack, gold leaf, opaque collodion or gelatine, the coating being scratched through in parallel lines ruled as nearly equidistant as possible. When the lines are to be ruled very close together, a diamond ruling directly on glass is used. Other transparent materials, such as fluor spar, are sometimes substituted for glass. For certain researches on long waves the grating is made by winding a very fine wire, l-1000th inch in diam- eter, in the threads of two fine screws placed parallel to each other, soldering the wire to the screws and then cutting it away on one side of the screws. As the value of a grating is dependent upon the number of lines ruled, it is very desirable to have their number great. Glass is so hard that the diamond employed for the ruling wears away rapidly; and hence the modern grating is generally a reflecting grating, which is made by ruling on a speculum metal surface finely ground and pol- ished. On such a surface it is possible to rule 100,000 lines without damaging the diamond, although its point even then often wears away or breaks down. The lines are generally so close together as 15,000 or 20,000 to the inch, although it is feasible to rule them even closer say 40,000 to 50,000 to the inch. There is little advantage, however, in the higher number and many disadvantages. The grating produces a variety of spectra from a single source of light, and these are designated as spectra of the first, second, etc., order, the numbering commencing from the central or reflected image and proceeding in either direction from it. The dispersion depends upon the number of lines ruled in a unit of length^upon the order of the spectrum, and upon the angle at which the grating is held to the source of light. The defining power depends upon its width and the angles 588 HENKY A. EOWLAND made by the incident and diffracted rays, and is independent of the number of lines per unit of length ruled on the grating. If this num- ber is too small, however, the different order of the spectra will be too much mixed up with each other for easy vision. A convenient number is 15,000 to 20,000 lines to the inch, or from 6000 to 8000 to the centimetre. The defining power is defined as the ratio of the wave- length to the distance apart of the two spectral lines which can be just seen separate in the instrument. Thus the sodium or D lines have wave-lengths which differ from each other by -597 ftp, and their aver- age wave-length is 589-3 pp. A spectroscope to divide them would thus require a defining power of 988. The most powerful gratings have defining powers from 100,000 to 200,000. Lord Eayleigh's formula for the defining power is D = Nn. When D is the defining power, N is the order of the spectrum, and n is the total number of lines ruled on the grating. As the defining power increases with N, and since we can observe in a higher order as the number of lines ruled in a unit of length decreases, it is best to express the defining power in terms of the width of the grating, w. In this case we have for the maximum defining power D' = 20,000 w for small gratings, or D' = 15,000 w for extra fine large gratings, w being the width of the gratings in centimetres. It is seldom that very large gratings are perfect enough to have a defining power of more than 10,000 w, owing to imperfection of surface or ruling. The relative brightness of the different orders of spectra depend upon the shape of the groove as ruled by the diamond. No two gratings are ever alike in this respect, but exhibit an infinite variety of distributions of bright- ness. Copies of glass gratings can be made by photography, contact prints being taken on collodiochloride of silver or other dry plates. Eeflecting gratings can be copied by pouring collodion or gelatine over the grating and stripping off the films thus formed. The latter warps, however, and destroys the definition to a great extent. The grating always produces a brighter spectrum in the violet than a prism. In the green the reflecting speculum metal grating may be brighter than a prism spectroscope of five prisms, and for higher dispersion surpasses the prism spectroscope both in definition and brightness in all portions of the spectrum. To produce the pure spectrum from flat gratings, two telescopes are generally used, as in Fig. 1. DIFFRACTION GRATINGS 589 The telescopes are fixed, and the grating is turned on its axis to pass to different portions of the spectrum. As the glass of the telescopes absorbs the ultra-violet light, this portion of the spectrum is cut off FIG. 1. Method of using Flat Grating. A, source of light; , slit; C,<7, two tel- escopes, movable or fixed; Z>, grating, movable about its centre; E, eye-piece. entirely, unless quartz lenses are used. The concave grating avoids this trouble, and produces a spectrum without the aid of lenses, the lines being ruled on a concave surface instead of on a flat one. Such a 5