Full text of "The physical papers of Henry Augustus Rowland ... [microform]"

LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.
Gats

GENERAL

THE

PHYSICAL PAPERS

HENRY AUGUSTUS ROWLAND

THE

PHYSICAL PAPERS

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

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

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

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

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.

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,

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

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

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

"Burden
best" iron.

Welded and
turned.

Annealed.

17-63

148-61

0677

916

Normal.

II.

11 <{

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.

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.

HEXEY A. BOWLAND

STABLE i.

" BURDEN BEST" IRON, NORMAL.

T.
M?

C.T.G.

D.T.G.

B.C.

71.

D.F.

D.F.
2n. '

D.B.

Calcu-
lated.

A
^=S-

P.
M.'

3627-

4-5

1456

23-4

6-6

1083

1
08 715

4910

5845

390-7

528

187-

1284-

7080-

16-45

5501

54-6

910

6005

10920

10885

868-7

3894

2111-

3838-

7746-

20-2

6815

87-9

1-465

9667

14180

14074

1129

5280

4387-

6437-

8786-

28-6 ! 1-011

23-3

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

28-8

7-45

2-0

49590

30570

30740

2433 13310 36280-

22370-

94BO-

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-

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-

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-

175000

TABLE II.
"BURDEN BEST" IRON, MAGNETIC.

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-

143

1001

7039

560

1020

3.810

116900

30730

2446

.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-

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.

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-

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.

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

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.]

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

5) (H

'S "S

1=11

pa x- ^

Burnt.

Normal.
Magnetic.
Normal.

Burnt.

Burnt,

Magnetic.

o
3
*

"* "7?

O O

o o o o
1-1 T*< e*

g
to

O O
O O

C5 to <N

c o

-r

o
o

o eg

r-l X CO CO

cocS

t- t- 1- >

i- i> t-

I- t-

O C5

1 1

o o

. 00 35

o o

1C CO

O O O

O O
O O CO

o o

0^00 00

:i2

^ ^

- 1

5O 1- 1C 35

I-l

^H 1C 00

:r.
-f

Greatel
meabi

000
o o o

35 O i-( 35

CO -J ^-1 O

o o o

O O

to o

CO
OO
CO

O
1 1

|ll

. O 5 O5

iH t~ CO

cr.

etism.

o c _
So

' I- t-

rH r-l

OO
H

CO t- t-

iH i-l TH

Tension of
lines in kil.
per square
centim.

" i i i 1

r-l r-t r-l

S
"K

O O
O O

.00

i-H -H

I 177000

o o o

o
o
o

o
l-

1-H

Temper.

4J ^ ; 2

a
<

Carefully
annealed.

Natural.

: =

S a
o ^

** IT"

Quality of substanc

aj O ^

"~ '

-3 W
1

" O)

Nickel

d
^

I ^Q

if. . if i

2 S 2 .S

) SJD

III

PS pa

''2

52 HENRY A. EOWLAND

giving the tension of the lines of force per square centimetre and square
inch of section of the lines. These have been deduced from the formula

given by Maxwell ' 3 for the tension per square metre, which is 2C

absolute units of force.
This becomes

24655^00000 kil g rammes P er S( l uare centim > 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.

f 1. .

10.

2775

277

154700

I 2. .

196

250

147000

Mr. Joule. ^ *

0436

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

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

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

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.

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 = -

ic is Neumann's coefficient of induced magnetization = ^.

TABLE I.

CAST NICKEL, NOKMAL, AT 15 C.
Experiments made November 29, 1873.

Ob-
served.

Calcu-
lated.

Error.

Ob-
served.

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

1263

906

170-5

6-35

6-27

45 14

7451

165-1

166-8

1-7

2894

4557

589-3

13-06

13-08

56-12

11140

198-5

199-1

3788

7352

882-0

15-72

15-70

70-78

15410

217-8

217-5

-3

5018

10392

1221

17-25

17-21

77-52

17100

220-6

5454

11646

1355

17-47

90-76

20180

222-3

222-0

- -3

6483

13697

1599

17-61

17-60

115-4

25170

218-2

214-3

3-9

8313

16857

1994

17-28

16-98

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

195-3

34630

177-3

179-1

1-8

13320

21310

2740

14-03

14-12

229-5

37340

162-8

165-5

2-7

15720

21620

2953

12-87

13-02

275-9

40860

148-1

146-3

1-8

17960

22900

3230

11-71

11-46

415-2

46470

111-9

112-8

22560

23910

3665

8-82

8-77

727-0

52690

72-5

72-8

28020

24670

4135

5-69

5-64

1042

55680

53-4

52-8

-6

30680

25000

4344

4-17

63420

4940

ooo

= 222 sin

/"=

359

=17 6 sin

TABLE II.

CAST NICKEL, MAGNETIC, AT 12 C.
Experiments made December 6, 1873.

to.

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

TABLE III.

CAST NICKEL, MAGNETIC, AT 220 C.
Experiments made December 6, 1873.

as.

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

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

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.

140

3802

12.75

205

2833

18-75

455

2269

22-5

703

1835

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

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.

Ob-
served.

Calcu-
lated.

Error.

49-33

4303

87-24

3702

601

338-5

6-86

6-75

58-83

5608

95-32

4526

1082

441-6

7-51

7-44

76-47

8409

109-95

6175

2234

663-1

8-67

8-79

93-15

11623

124-8

7826

3797

917-5

9-85

9-81

113-0

14993

132-7

9805

5188

1193-1

10-48

10-44

129-3

17439

134-9

10580

6859

1387-8

10-66

10-72

159-4

22309

140-0

14090

8219

1775-3

11-06

11-00

189-0

26769

141-6

16260

10509

2130-3

11-19

10-97

219-6

30580

139-3

18200

12380

2433-5

11-01

10-83

264-7

35525

134-2

21120

14405

2827-0

10-60

10-50

351-1

43421

123-7

25670

17751

3455-0

9-76

9-73

400-0

46640

116-6

27830

18810

3711-5

9-20

9-34

552-1

55410

100-4

34090

21320

4409-0

7-91

8-16

732-1

63400

86-6

39850

23550

5045-0

6-81

6-93

999-8

71800

71-8

47310

24490

5714-0

5-63

5-55

1471

80770

54-9

55870

24900

6430-0

4-29

3-98

8160

c* +190* + 120

... -|i ain *y

TABLE V.

CAST COBALT, MAGNETIC, AT 5 C.
Experiments made November 28, 1873.

93.

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

HENRY A. ROWLAND

TABLE VI.

CAST COBALT, MAGNETIC, AT 230 C.
Experiments made February 3, 1874.

ft.

S3.

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

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 =

&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

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

will be very nearly proportional to the square of .

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 <d

a.
e

FIGURE 1.

The apparatus is represented in Fig. 1. To a straight bar of iron h,
7 in. long, in. thick, and f in. wide, are attached two pieces e e of
the same kind of iron by two set screws g g, which move in slots in the

76 HENRY A. EOWLAND

piece h. Into these pieces are screwed two tubes c made of iron and
having an internal diameter of about T 7 T in. and a thickness not to
exceed ^ in. Through these tubes the iron rods a I slide and are
held at any point by the screws d. One end b of this rod is rounded
off for diamagnetic experiments and the other enlarged and flattened
at the end for magnecrystallic experiments. On the tube c a helix of
N~o. 16 or No. 18 wire is wound so as to make up a thickness of -4 or -5
of an inch and having a length of 2 in. The object of the screws g is
principally to allow the rods a & to be reversed quickly and to adjust the
position of the helices. When the apparatus is to be used for only one
kind of work it can be much simplified by doing away with many of the
moving parts.

This instrument can be used either with the ordinary magic lantern,
or better, with one having, a vertical attachment. In the latter case
the plane of the instrument is horizontal and the substances are sus-
pended from a wire made quite small, so as not to cut off too much
light.

The suspending thread in the case of bismuth can be quite large
but for other bodies a single fibre of silk is best; these in the shape of
bars half an inch long can be each attached to a fibre having a little
wire hook at its upper end and hung in a cabinet until required.

The theory of feebly magnetic or diamagnetic bodies oscillating in
a magnetic field is very simple and yet the results are of the greatest
interest, especially the effect of the size of the apparatus, which is
here given for the first time.

2. THEORY

Let a very small particle of a body whose coefficient of magnetization
AC is very small, and either positive or negative, be placed in a magnetic
field of intensity R; it will then have an induced magnetic moment of
<vR, where v is the volume of the element. The force acting on this
particle to cause it to go in any given direction will be equal to the
product of the magnetic moment into the rate of variation of R in that

direction, 1 and hence is K vR ~r in the direction of x. The total force

acting on the body in the direction of x is therefore

1 Thomson, Reprint of Papers, art. 679, Prob. vii.

NEW DlAMAGNETIC ATTACHMENT TO THE LANTERN 77

and the other components of the force are

and

Let, now, the axis of z be vertical, the axis of x in the line of the
magnetic poles of the magnet, and y at right angles to both. Then
the moment of the forces acting on the body to turn it about the axis

of z is

where the integration extends throughout the volume of the body.

If the body is suspended so as to turn freely about the axis of z it
will vibrate about the position for which M is a minimum or else will
remain at rest at that point. The number of single oscillations made
when the angular elongation & is very small, is

1 / M

' T. V tfj'

in which M and $ must be measured simultaneously, and I is the
moment of inertia of the body.

I r r r

A/ I l/f
\ J J J

i Jw d(i^)\, ^ ^

y , 3 -, \dxdydz.
\ J dx dy j

Xow let us suppose that the whole apparatus changes size, the relation
between the parts remaining constant, so that the apparatus becomes
m times as great as before. Then x, y, dx, dy, and dz will increase ra

times and /, m 5 times. To determine the changes in ^ ^ and -X *

aye? ^y

we make use of the theorem of Sir Win. Thomson, that " similar bars
of different dimensions, similarly rolled, with lengths of wire propor-
tional to the squares of their linear dimensions, and carrying equal
currents, cause equal forces at points similarly situated with reference
to them." But as the above only applies to equal currents, I have
generalized it in the following: In any two magnetic systems whatever,
similar in all their parts and composed of any number of permanent or
electro-magnets, wires carrying currents, or bodies under magnetic induc-
tion, the magnetic force at similar points of each will be the same when the
following conditions are complied with: 1st, the magnetic materials at
similar prints in the two systems must be exactly the same in quality and

78 HENRY A. KOWLAND

temper; 2d, the permanent magnets must be magnetized to the same degree
at similar points of the systems; 3d, the coils of the electro-magnets and
other wires or bundles of wires carrying the current must have similar
external dimensions in the two systems and must have the product of the
current by the number of wires passing through similar sections of the two
systems proportional to the linear dimensions of the systems.

This will apply to the case we are considering when the product of
the current by the number of the turns of wire varies in direct propor-
tion to the size of the apparatus. Hence in this case \ and !-i f

dx ay

will vary inversely as m. Hence we see that n will be inversely pro-
portional to the size of the apparatus; and although we have only
proved this for the case when * is small, it is easy to see that it is
perfectly general. The advantage of small diamagnetic apparatus is
thus apparent, for the smaller we make it the more vibrations the bar
will make in a given time and the more promptly will the results be
shown.

It might be thought that by hanging a very small bar in the field oi'
a large magnet, we might obtain just as many vibrations as by the use
of a small apparatus; but this is not so, for Sir Wm. Thomson has
shown 2 that the number of oscillations of a feebly magnetic or diamag-
netic body of elongated form in a magnetic field is nearly independent
of the length when that is short. So that the only way of increasing
the number of vibrations is to decrease the size of the whole apparatus,
or to increase the power of the magnets; the latter has a limit and
hence we become dependent on the former.

The theory of the effect of the size of the body is very simple, and we
may proceed as follows. Let the body be in the form of a small bar
whose sectional area, a, is very small compared with its length, and let
f be the angle of the axis of the bar with the line joining the poles, and
r the radius vector from the origin. Developing R 2 as a function of
x and y by Taylor's theorem, and noting that as R is symmetrical with
reference to the planes XZ and YZ, only the even powers of x and y
can enter into the development, we have, calling R the value of R
at the origin,

2 \ dy? dy

r#(/2n

2.3.4V dtf dtfdf dy*

2 Reprint of Papers, art. 670. Remarques sur les oscillations d'aiguilles non crys-
tallisees.

NEW DlAMAGNETIC ATTACHMENT TO THE LANTERN 79

When the vibrating body is very small the first two terms will suffice:
hence we have

M= i a

in which I is the length of the bar. If d is the density of the body
(weight of a unit of volume), I = ^ and n becomes

in which, however, it is to be noted that ^ .7 is essentially negative

and so the sign of the term containing it will be positive in the actual
development.

This equation is independent of the dimensions of the body, and
hence we conclude that when the body is small and very long as com-
pared with its other dimensions, the number of vibrations which it will
make in a given field is dependent merely on its coefficient of magneti-
zation and on its density; a result first given by Sir Wm. Thomson, in
the paper referred to. I have given it once more and put it in its
present form merely to call attention to the facility with which can
be obtained from it when we have measured R in different parts of the
field by known methods. This could be done by means of a rotating
coil as used by Verdet, or by my magnetic proof plane which I will
soon describe, combined with my method of using the earth inductor.
This will give the best method that I know of for obtaining K for
diamagnetic or weak paramagnetic substances.

Troy, January 15, 1875.

8
NOTES ON MAGNETIC DISTKIBUTION

[Proceedings of the American Academy of Arts and Sciences, XI, 191, 19^, 187(i. Pre-
sented June 9, 1 875]

In two papers which have recently appeared on this subject, by Mr.
Sears (Amer. Jour, of Science, July, 1874), and Mr. Jacques (Proc.
Amer. Acad. of Sciences, 1875, p. 445), a method is used for determining
magnetic distribution, founded on induced currents, in which results
contrary to those published by M. Jamin have been found. It does not
seem to have been noticed that the method then used does not give
what we ordinarily mean by magnetic distribution. In mathematical
language, they have measured the surface integral of magnetic induc-
tion across the section of the bar instead of along a given length of its
surface. 1 M. Jamin's method gives a result depending on the so-called
surface density of the magnetism, which is nearly proportional to the
surface integral of the magnetic induction along a given length of the
bar. Hence the discrepancy between the different results. Had the
experiments of Mr. Sears and Mr. Jacques been made by sliding the
helix inch by inch along the bars, their results would have confirmed
those of M. Jamin. Four or five years ago, I made a large number of
experiments in this way, which I am now rewriting for publication, and
where the whole matter will be made clear. At present, I will give the
following method of converting one into the other. Let Q be the sur-
face integral of magnetic induction across the section of the rod, and

let Qe be that along one inch of the rod: then Qe <x ^.x beinar the

(IX

distance along the rod. Hence, M. Jamin's results depend on the rate
of variation of the magnetization of the rod, while those of Mr. Sears
and Mr. Jacques depend on the magnetization. In conclusion, let me
heartily agree with Mr. Jacques's remarks about M. Jamin's conclusions
from his experiments. Such experiments as those give no data what-
ever for a physical theory of magnetism, and can all be deduced from
the ordinary mathematical theory, which is independent of physical

1 Maxwell's Electricity and Magnetism, art. 402.

NOTES ON MAGNETIC DISTRIBUTION 81

hypothesis, combined with what is known with regard to the magnetiz-
ing function of iron. This will be shown in the paper I am rewriting.
It seems to me that M. Jamin's method is very defective; and I know
of no method of experimenting, which is theoretically without objection
except that of induced currents, and this I have used in all my experi-
ments on magnetic distribution for the last four or five years, and have
developed into a system capable of giving results in absolute measure.
Mr. Jacques is to be congratulated on pointing out these errors in
M. Jamin's conclusions.

Troy, June 7, 1875.

NOTE ON KOHLKAUSCJFS DETERMINATION OF THE ABSO-
LUTE VALUE OF THE SIEMENS MERCURY UNIT OF
ELECTRICAL RESISTANCE

[Philosophical Magazine [4], L, 161-163, 1875]

In looking over Kohlrausch's paper 1 upon the determination of a
resistance in absolute measure, with a view to undertaking something
of the kind myself, and also, if possible, to discover the reason of the
difference from the results of the Committee of the British Association,
I think I have come across an error of sufficient magnitude and in the
proper direction to account for the 2 per cent difference. Kohlrausch's
experiments were made with such great care and by so experienced a
person that it is only after due thought and careful consideration that
I take it upon me to offer a few critical remarks.

We observe, then, first of all, that the principal peculiarity of his
method consists in doing away with all measurements of the coils of
the galvanometer, and in its place making accurate determinations of
the logarithmic decrement both with the circuit closed and open, to-
gether with various absolute determinations rendered necessary by this
change. In this way the logarithmic decrement is raised from being a
small correction to a most important factor in the equation. Hence
it is that we should carefully scrutinize the theory and see whether it
be correct enough for this purpose ; for only an approximation is needed
for the first method.

The resistances to a bar magnet swinging within a coil may be divided
into two principal parts first, that due to the resistance of air and
viscosity of suspending fibre, and, second, that due to the induced cur-
rent in the coils. The first resistance is usually taken as proportional
to the velocity, and thus assumes the viscosity of the air to be the most
important element. This is proba,bly true in most cases where the
motion is slow. This factor is quite small compared with the second
when the magnet is large and heavy and the coils wound close to it, as

^oggendorff's Annalen, Erganzungsband vi, p. 1; translated in Phil. Mag., S. 4,
vol. xlvii, pp. 294, 342.

NOTE ox KOHLRAUSCH'S DETERMINATION 83

in Kohlrausch's instrument. Kohlrausch's principal error lies in the
omission of the coefficient of self-induction from his equations.

For the sake of clearness, and because the subject is quite often
misapprehended, I shall commence at the beginning and deduce nearly
all equations.

Let us proceed at first in the method of Helmholtz, using the nota-
tion of Maxwell's ' Electricity.'

Let a current of strength / be passing in a circuit whose resistance
is 7?, and coefficient of self-induction L. Also let a magnet be near the
circuit whose potential energy with respect to the circuit is IV. Let A
be the electromotive force of the battery in the circuit.

The work done by the battery in the time dt is equal to the sum of
the work done in heating the wire, in moving the magnet, and in
increasing the mutual potential of the circuit on itself. 2 Hence we have

AUt = PRdt + l~dt + -L j
dt 2

and if A is equal to zero, we find

/=_.7r + L*L\

If we apply this to the case of a magnet swinging within a coil the
angle of the magnet from a fixed position being x, we have since -j-

&3s

is the moment of the force acting on the magnet with unit current and
may be denoted by q,

dx , r

where my R is Kohlrausch's w.

This expression differs from that used by Kohlrausch in the addition
of the last term, which is the correction due to self-induction. The
last term vanishes whenever the magnet moves with such velocity as
to keep the induced current constant ; but in the swinging of a galvano-
meter-needle it has a value.

To form the equation of motion of the needle, we can proceed the
rest of the way as Maxwell has done (Electricity, art. 762). Assuming
that all frictional resistances to the needle are proportional to the
velocity of the needle, we have

B< S + c w + l)x = r ' ....... ^

where B, C, and D are constants.

2 See remarks in Maxwell's ' Electricity,' art. 544, near bottom of page.

84 HENRY A. ROWLAND

Eliminating / between this equation and (1), we find

At first sight this equation will appear to be the same as that of Max-
well; but on further examination we see that it is more general in the
value of q.

Equation (3) is the correct equation to use in this case, and reduces
to that of Kohlrausch when L = 0.

To see how this error will affect Kohlrausch's results, we must re-
member that he uses this equation to find the constant of his galvano-
meter, on which his whole experiment depends; and the error is so
interwoven with all his results .that an entire recomputation is neces-
sary, provided the data for calculating the coefficient of self-induction
of the galvanometer coils and earth inductor can be obtained.

The equation

t* tl

* 2 + / 2 - 2 + /S

does not hold when self-induction is considered ; and so his fundamental
equation (1) is not correct, containing a twofold error.

The linear differential equation (3) is easily solved; but as the results
are complicated, it is hardly worth while at present, until a recalcula-
tion can be made. I prefer to solve it on the supposition that L is
small, and thus merely obtain a correction to Kohlrausch's equation
connecting t and t , after which equation (15) or (17) (Maxwell's ' Elec-
tricity/ art. 762) can be used when made more general by substituting
q for Om.

As far as I have had time to go at present, the correction seems to
be in the direction of making Kohlrausch's determination more nearly
coincide with that of the Committee on Electrical Standards of the
British Association. Other engagements occupy my attention at pres-
ent ; but I hope to see these corrections made to an otherwise excellent
determination of this most important unit.

London, August 4, 1875.

PKELIMINAEY NOTE ON A MAGNETIC PEOOF PLANE

[American Journal of Science [3], X, 14-17, 1875]

About four years ago I made a large number of experiments on the
distribution of magnetism on iron and steel bars by means of a coil of
wire sliding along the bar; the induced current in the coil as measured
by a galvanometer was a measure of the number of lines of force cut by
the coil and can be found in absolute measure by my method of using
the earth inductor. These researches have never yet been published
owing to circumstances beyond my control, but are known to quite a
number of persons in this country, and will soon be published. The
method there used is the only correct one that I know of for experi-
menting on magnetic distribution, and my purpose in this note is to
extend it to bodies of all shapes, so that experiments on magnetic dis-
tribution may become as simple and easy to perform as those on elec-
trical distribution. And so well has my magnetic proof plane accom-
plished this that I can illustrate the subject to my classes with the
greatest ease.

The apparatus required is merely a small coil of wire i to ^ inch in
diameter, containing from 10 to 50 turns, and a Thomson galvanometer.
When we require to reduce to absolute measure, another coil about a
foot in diameter and containing 20 or 30 turns is required. Having
attached the small coil (or, as I call it, the magnetic proof plane) to
the galvanometer, we have merely to lay it on the required spot, and
when everything is ready, to pull it away suddenly and carry it to a
distance, and the momentary deflection of the galvanometer needle will
be proportional to that component of the lines of force at that point
which is perpendicular to the plane of the coil. And if we apply it to
the surface of a permanent magnet the so-called surface density of the
magnetism at that point will be nearly proportional to the deflection.
In the case of an electro-magnet the surface density will be nearly pro-
portional to the deflection minus the deflection which would be pro-
duced by the helix alone, though the last is generally small and may be
neglected. I use the words nearly proportional in the above statement
because thev are only exactly true in the cases where the lines of force

8G HENKY A. KOWLAND

proceed from the surface in a perpendicular direction; otherwise the
deflections must be multiplied by the secant of the angle made by the
lines of force with the surface of the magnet. In the case of an electro-
magnet made of very soft iron, theory shows that the lines pass out
nearly perpendicular to the surface and so no correction is needed.

We can also, by a coil of this kind, determine the intensity of the
magnetic field at any point and thus be able to make a complete map
of it. Having done this, we have all the data necessary to substitute
in the formula which I have given in this Journal, 1 and by a simple
experiment can thus determine the coefficient of magnetization of any
diamagnetic or weak paramagnetic body probably in a more accurate
manner than any Weber used. Only the largest-sized magnets could of
course be used for this purpose with any accuracy, and indeed they are
always to be preferred in obtaining the distribution by this method.

Having obtained the distribution for any given magnet, the distribu-
tion for any similar magnet of the same material but of different size
becomes known by a well-known law of Sir William Thomson.

As, in the present state of our knowledge, magnetic measurements
are of small value unless made on the absolute scale, we require to
reduce our results to this system. There are several methods of doing
this, but the simplest is that which I have used in my experiments on
magnetic permeability, and consists in including an earth inductor in
the circuit. A coil laid on a perfectly level surface is sufficient for
this : when this is turned over, the induced current will be equal to C =

%n ~VA

where n is the number of turns in the coil, A its mean area, V
-Ti-
the vertical component of the earth's magnetism, and R the resistance
of the circuit. When the small coil is pulled suddenly away the current

will be C" = *-&?, and so we have Q = 2V^, in which when a
li an 6

Thomson galvanometer is used C' and C can be replaced by the cor-
responding deflections: hence = 2V~-, in which a and n' are the

an D

area and number of turns in the small coil and Q is that component of
the magnetic field we are measuring in the direction of the axis of the
small coil.

As an illustration of this method I will give a few experiments made
with the magnets of a Euhmkorff diamagnetic apparatus, which was
altogether about 2 ft. long and had its magnets 2 in. in diameter, with

'On a new diamagnetic attachment to the lantern, &c., this Journal, May, 1875.

PRELIMINARY NOTE ON A MAGNETIC PROOF PLANE 8?

a hole in. in diameter through them for experiments on the rotation
of the plane of polarization of light, but which in these experiments
were closed by the solid poles which were screwed on. The first experi-
ments were with two discs of iron, 4*6 in. in diameter and If in. thick,
screwed on to the poles. In the first place the poles were turned away
from one another, the current being sent through only one magnet,
and the values of the magnetic field obtained at different points close to
the surface of the disc. These may be numbered as follows : No. 1, at
centre of face of disc; No. 2, on face of disc half an inch from the edge;
No. 3, on centre of edge of disc. The measures are on the metre, gram,
second system.

1st. Strength of current, 4-4 farads per second.

1. 2220. 2. 3550. 3. 4440.

2nd. Strength of current 8-3 farads per second.

1. 3600. 2. 5300. 3. 7500.

Next the poles were turned toward each other and the current sent
through both magnets, so as to make the poles of the same name.
Current 4 '6 farads per second.

1st. Distance of poles, 3 in.

1. 1300. 3. 3800.

2nd. Distance of poles, 1^ in.

1. 600. 3. 4000.

Here we see an approach to one of Faraday's places of no magnetic
action.

After this the current in one of the magnets was reversed so as to
make the poles opposite. Current the same.

1st. Distance of poles, 3 in.

1. 5800. 2. 8200. 3. 6700.

2nd. Distance of poles, 1 in.

1. 9800. 2. 7500. 3. 5800.

It is curious to note how the distribution changes with the distance of
the discs; thus, on one disc free from the other, the edge of the disc
has the greatest magnetic surface density, but when the two discs form
opposite poles and are 3 in. apart, position 2 gives the greatest effect,
while, when they are 1 in. apart, the field is greatest at the centre.
This entirely agrees with theory.

The conical poles for diamagnetic experiments were then screwed on.
These were portions of cones with an angle at vertex of about 60, with
the vertex considerably rounded off. They were one inch apart and
the poles were opposite. Current 4-4 farads per second.

88 HENRY A. KOWLAND

At centre of field between the poles 12500

On the axis near one pole 32100

On cone one inch from vertex 11000

On cylindrical portion of magnet 2f inches from the

vertex of the cone 5800

These poles were now replaced by frustums of cones with flat ends,
the original diameter of the iron, 2 inches, being reduced at the end to
If inches, and they were placed \ inch apart. The field in this case
between them was 61000, or nearly up to the maximum of magnetiza-
tion of nickel at common temperatures, and above that at high tem-
peratures.

Troy, April 1, 1875.

STUDIES ON MAGNETIC DISTK1BUTION

[Philosophical Magazine [4], L, 257-277, 348-367, 1875]
[American Journal of Science [3], X, 325-335, 451-459, 1875; XI, 17-29, 103-108, 1876]

PART I. LINEAR DISTRIBUTION

CONTENTS

I. Preliminary remarks.
II. Mathematical theory.

III. Experimental methods for measuring linear distribution.

IV. Iron rods magnetized by induction.

V. Straight electro-magnets and permanent steel magnets.
VI. Miscellaneous applications.

In a paper of mine published about two years ago, I alluded to some
investigations which I had made in 1870 and 1871 on the distribution
of magnetism. It is with diffidence that I approach this subject, being
aware of the great mathematical difficulties with which it is surrounded.
But as the facts are still in advance of what is known on the subject,
and as I see that other investigators * are following hard upon my foot-
steps, I thought it would be well to publish them, particularly as it is
no fault of mine that they did not appear some years ago. 2 The mathe-
matical theory which I give, although not particularly elegant, will at
least be found to present the matter in a new and more simple light,
and may be considered simply as a development of Faraday's idea of
the analogy between a magnet and a voltaic battery immersed in water.
I shall throughout speak of the conduction of, and resistance to, lines
of magnetic force, and shall otherwise treat them as similar to lines of
conducted electricity or heat, it now being well established from the
researches of Professor Maxwell and others that this method gives
exactly the same results as the other method of considering the action
to take place at a distance.

In arranging this paper I have thought best to give the theory of

1 Particularly M. Jamin.

2 All the experiments referred to in this paper were made in the winter of 1870-71.

90 HENRY A. BOWLAND

the distribution first, and then afterwards to see how the results agree
with experiment; in this way we can find out the defects of the theory,
and what changes should be made in it to adapt it to experiment.

At present I am acquainted with two formulae giving the distribu-
tion of magnetism on bar magnets: the first was given by Biot, in his
Traite de Physique Experimentale et Mathematique, vol. iii, p. 77, and
was obtained by him from the analogy of the magnet to a dry electric
pile, or to a crystal of tourmaline electrified by heat. He compared
his formula with Coulomb's observations, and showed it to represent
the distribution with considerable accuracy. Green, in his ' Essay/
has obtained a formula which gives the same distribution; but he ob-
tains it by a series of mathematical approximations whi^h it is almost
impossible to interpret physically. M. Jamin has recently used a
formula of the same form; but I have as yet been unable to find how
he obtained it. My own formulae are also quite similar to these, but
have the advantage of being obtained in a more simple manner than
Green's ; and, what is of more consequence, all the limitations are made
at once, after which the solution is exact; so that although they are
only approximate, yet we know just where they should differ from
experiment.

II.

If we take an iron bar and magnetize one end of it either by a magnet
or helix, we cause lines of magnetic induction s to enter that end of the
bar, and, after passing down it to a certain distance, to pass out into
the air and so round to the bar again to complete their circuit. At
every part of their circuit they encounter some resistance, and always
tend to pass in that direction where it is the least: throughout their
whole course they obey a law similar to Ohm's law; and the number
of lines passing in any direction between two points is equal to the
difference of magnetic potential of those points divided by the resist-
ance to the lines.

The complete solution of the problem before us being impossible, let
us limit it by two hypotheses. First, let us assume that the permea-
bility of the bar is a constant quantity; and secondly, that the resist-
ance to the lines of induction is composed of two parts, the first being
that of the bar, and the second that of escaping from the bar into the

3 For difference between lines of magnetic force and lines of magnetic induction
see Maxwell's 'Treatise on Electricity and Magnetism,' arts. 400, 592, and 604.

STUDIES ON MAGNETIC DISTRIBUTION 91

medium - and that the latter is the same at every part of the bar. The
first of these assumptions is the one usually made in the mathematical
theory of magnetic induction; but, as has been shown by the experi-
ments of Miiller, and more recently by those of Dr. Stoletow and my-
self, this is not true; and we shall see this when we come to compare
the formula with experiment. The second assumption is more exact
than the first for all portions of the bar except the ends.

Let us first take the case of a rod of iron with a short helix placed on
any portion of it, through which a current of electricity is sent. The
lines of magnetic induction stream down the bar on either side: at
every point of the bar two paths are open to them, either to pass further
down the rod, or to pass out into the air. We can then apply the
ordinary equations for a derived circuit in electricity to this case.
Let n be the magnetic permeability of the iron,

R be the resistance of unit of length of the rod,

R' be the resistance of medium along unit of length of rod,

/> 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>* =

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.

Q'.
Calcu-

Error of

Q'.
Calcu-

Error of

served.

lated.

Q,.

served.

lated.

....

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.

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<tfA_80-5.

quantity; but it has been shown by Dr. Stoletow and myself, independ-
ently of each other, that JJL increases as the magnetism of the bar in-
creases when the latter is not great. Hence between and 8 inches
the resistance of the bar, R, is greater than at succeeding points, and
hence a less number of lines of induction pass down the bar from 8
towards than would be given by the formula, which has been adapted
to the average value of E at from 9 to 14 inches. In Table II this
same fact shows itself towards the end of the Table, and would prob-
ably be more prominent had the Table been carried further. However,
in this Table all things have combined to satisfy the formula with great
accuracy.

In Table III we come across a fact of an entirely different nature
from the above. Fig. 2 is the plot of this Table, and gives the values
of Q' ( at different parts of the rod.

102

HENRY A. EOWLAND

TABLE III.
BAB -39 INCH DIAMETER. AT END OF BAR.

served.

Qe.

Calcu-
lated.

Error of

served.

Q'-
Calcu-
lated.

Error of
Q'-

1
2
3

19-7
16-3
16-0

15-2
15-3
15-5

4-5
1-0
-5

19-7
36-0
52-0

15-2
30-5
46-0

4-5
5-5
6-0

4
5
6

15-8
16-5
17-0

15-9
16-3
16-9

+ -1
-2
-1

67-8
84-3
101-3

61-8
78-1
95-0

6-0
6-2
6-3

7
8
9
10
11
12
13
14
15
16

17-6
18-4
19-2
20-3
21-8
22-8
84-8
26-8
28-8
31-8

17-6
18-4
19-4
20-5
21-7
23-1
24-7
26-5
28-4
30-5

+ -2
+ -2
-1
+ -3
-1
-3
-4
1-3

118-9
137-3
156.5
176-8
198-6
221-4
246-2
273-0
301-8
333-6

112-6
130-9
150-3
170-7
192-2
215-3
239-9
266-4
294-6
325-1

6-3
6-4
6-2
6-1
6-4
6-1
6-3
6-6
7-2
8-5

Q' t =7-6(10 os7t-)-io-'OS7L) ; Q'=89(10 37i 10- 37t ).

The horizontal line in the figure represents values of L, and the verti-
cal ordinates are values of Q' g . The full line gives the observed dis-
tribution, and the dotted line that according to the formula.

15 10 5 O

FIG. 2. Distribution at end of bar.

The formula gives the distribution very nearly for all points except
those near the end. The formula indicates that Q' f decreases contin-
ually toward the end; but by experiment we see that it increases near
this point. On first seeing this, I thought that it was due to some
residual magnetism in the bar; but after repeating the experiment
several times with proper care, I soon found that this was always the
case. I give the following explanation of it : In the f ormulse we have
assumed R', the resistance of the medium, to be a constant; now this
resistance includes that of the lines of force as they pass from the rod
through the medium and thus back to the other end of the rod ; and of

STUDIES ON MAGNETIC DISTRIBUTION 103

this whole quantity the part which affects the relative distribution at
any part of the rod most is that of the medium immediately surrounding
that part; and so the parts near the end have the advantage over those
further back, inasmuch as the lines can pass forward as well as outward
into the medium. The same thing takes place in the case of the dis-
tribution of electricity, where the "density" is inversely proportional
to the resistance which the lines of inductive force experience from
the medium; and here we find that the "density" is greatest on the
projections of the body, showing that the resistance to the lines of in-
duction is less in such situations, and by analogy showing that this
must also be the case for lines of magnetic force. But this effect is
not very great in cylinders until quite near the end; for Coulomb, in a
long electrified cylinder, has found the density at one diameter back
from the end only 1-25 times that at the centre; and so there is prob-
ably a long distance in the centre where the density is sensibly constant.
Hence we may suppose that our second hypothesis, that R' is a con-
stant, will be approximately correct for all parts of a bar except the
ends, though of course this will vary to some extent with the distribu-
tion of the lines in the medium; at least the change in E' will be
gradual except near the end, and so may be partially allowed for by
giving a mean value to r.

Hence we see that could the formula be so changed as to include
both the variation of R and of R', it would probably agree with the
three Tables given.

To study the effect of variation in the permeability more carefully,
we can proceed in another manner, and use the formulae only to get
the value of r at different parts of the rods.

No matter how r may vary, equations (2) and (3) will apply to a very
small distance Z along the rod; and as the orgin of coordinates may be
at any point on the rod, if Q r and Q' f are taken at one point and Q and
Q t at another point whose distance from the first is Z, we shall have the
four equations

Calling " =H and ? = G, we shall find, on eliminating C and A
and developing r ' and ?~ rt ,

104

HENRY A. EOWLAND

? m 1***-i),

f \ (jf + ti /

or, to a greater degree of approximation,

+ 1-6

(9ft)

Before applying these formulae to any series of observations, the
latter should be freed from most of the irregularities due to accidental
causes. For this purpose the following Tables have been plotted and a
regular curve drawn to represent as nearly as possible the observations;
in other cases a column of differences was formed and plotted. In
either case the ordinates of the curves were accepted as the true quan-
tities. But, for fear that some might accuse me of tampering with my
observations, I have in all cases added these as they were obtained.

TABLE IV.
BAR -19 INCH DIAMETER. AT CENTRE OF BAR.

Qe-

Observed.

Qi.

Corrected.

Q'.
Corrected.

r " IT

1 K'
r 2 ~ K

2
3
4
5

24-0
17-0
13-7
11. 6

10-2

24-0
17-0
13-7
11-65
10-15

151-7
127-7
110-7
97.0
85-4

041
0256
0192
0168

24.4
39-1
52-1
59-5

9-0

0150

66-7

7
8

8-0
7-1

8.0
7-15

66-2

58-2

0142
0150

70-4
66-7

9
10
11
12
13
14
15
28^

6-4
5-7
4-9
4-4
3-6
3-3
22-4

6-35
5-65
5-0
4-4
3.9
3-4
22-4

51-1
44-7
39-1
34-1
29-7
25-8
22-4

0159
0160
0167
0180
0184
0184

62-9
52-5
59-9
55-6
54-3
54-3

The correction is necessary, because small irregularities in the obser-
vations will produce immense changes in r 2 .

Table IV contains some of the best observations I have obtained.
It is from a bar 57 inches long with a helix 1| inch long in the centre
to magnetize it. Each quantity is the mean of six observations, these
being made on both ends of the bar and with the current in opposite
directions.

In this Table a source of error was guarded against which I have not

STUDIES ON MAGNETIC DISTRIBUTION 105

seen mentioned elsewhere. When a bar of iron is magnetized at any
part and the distribution over the rest quickly measured, on being then
allowed to stand some time and the distribution again taken, it will have
changed somewhat, the magnetism having, as it were, crept down the
bar further. Hence in this Table time was allowed for the bar to reach
its permanent state.

1 R r
On looking over column 6, which contains the values of -^ -^ = R'a/i

(equation 7), we observe that as Q' decreases, the value of R'ap. first
increases and then decreases. Now it is not probable that R' undergoes
any sudden change of this sort; and so it is probably due to change in
the permeability of the rod. Hence by this method we arrive at the
same results as by a more direct and exact method. 7 But by this means
we are able to prove in the most unequivocal manner that magnetic
permeability is a function of the magnetization of the iron and not of the
magnetizing force. Hence it is that I have preferred, in my papers on
Magnetic Permeability, to consider it in this way in the formulae and
also in the plots, while Dr. Stoletow (in his paper, Phil. Mag., January,
1873) plots the magnetizing-function as a function of the magnetizing
force.

When we plot the results in this Table with reference to Q' and R'a^,
the effect of the variation of R' is apparent; and we see, on comparing
the curve with those given in my paper above referred to, that R' in-
creases as L increases, at least between L = 2 and L = 8, which is as
we should suppose from the arrangement of the apparatus. For this
Table I happen to have data for determining Q in absolute measure;
and these show that the maximum value of n should be about where
the Table shows it to be.

This method of finding the variation of p is analogous to that of
finding conductivity for heat by raising the temperature of one end
of a bar and noting the distribution of heat over the bar; indeed the
curves of distribution are nearly the same in the two cases.

If it were thought worth while, it would be very easy to obtain a
curve of magnetic distribution for a rod and then enclose the whole
rod in a helix and determine its curve of permeability. This would
give data for determining R' in absolute measure at every point of the
rod.

To complete the argument that the variation of r z is in great measure
due to that of //, I have caused the magnetizing force on a bar to vary.

7 Phil. Mag., August, 1873.

106

HENRY A. EOWLAND

Tables V, VI, and VII are from a bar 9 feet long and -25 inch in
diameter. At the centre a single layer of fine wire was wound for a
distance of 1 foot; and the current for magnetizing the bar was sent
through this. The zero-point was at the centre of this helix and at the
centre of the bar; so that the observations on the first 6 inches include
the part of the bar covered by the helix.

The values of Q' f are the sum of four observations on each end of
the bar and with the current reversed. The three Tables are compar-
able with each other, the same arbitrary unit being used for all.

TABLE V.
MAGNETIZING CURRENT -176.

served.

Qe-

Cor-
rected.

1 R'

F' = R~-

Qe".

Calcu-
lated.

2-7

2-40

6-9

7-32

12-7

12-54

18-2

18-31

24-4

24-87

5
6
7
8
9
10
11
12
13
14
15 .
16
17 j.
18 '
End.

32-4
31-5
28-2
24-9
21-4
18-6
16-8
14 2
12-0

17-7

11-6
22-4

31-7
32-0
28-2
24-7
21-7
19-0
16-4
14-2
12-0
10-0
8-2
6-6
5-1
22-4

220-5
188-5
160-3
135-6
113-9
94-9
78-5
64-3
52-3
42-3
34-1
27-5
22-4

0190
0212
0218
0236
0252
0278
0311
0367
0404
0440
0445
0570

52-4

47-2
45-9
42-4
39-7
36-0
32-2
27-2
24-8
22-7
22-5
17-5

32-38

A ^

OS
00

t-L

Here we see an excellent confirmation of the results deduced from
Table IV. In Table V, where the magnetizing force is very small, and
where, consequently, no part of the iron has yet reached its minimum

1 R'
resistance, the value of t ~ ^ R'ap. decreases continually as the value

of Q' decreases, as it should do. In Table VI, with a higher magnetiz-
ing power, which was sufficient to bring a portion of the bar to about

the minimum resistance, we see that -5 remains nearly stationary for a

short distance from the helix and then decreases in value. In Table
VII, where the bar is highly magnetized and the portion near the zero-

STUDIES ON MAGNETIC DISTRIBUTION

107

TABLE VI.
MAGNETIZING CURRENT -31.

served.

CoV-
rected.

Cor-
rected.

t-2.

9''-
Calcu-
lated.

16-3

17-3

22-0

22-3

32-4

32-28

43-8

43-34

5
6

7
8
9 I

11 i

8
gj

16 (
17 f

1ft I

55-9
55-2
46-8

81-3
61-8
46-4
35-4
22-0

55-1
48-1
42-3
37-4
33
29-0
25-3
21-9
18-7
15-6
12-7
9-8

391-9
336-8
288-7
246-4
209
176-0
147-0
121-7
99-8
81-1
65-5
52-8

0204
0201
0202
0220
0243
0262
0300
0352
0405
0479

49-0
49-7
49-5
45-5
41-2
38-2
33-3
28-4
24-7
20-9

55-90

End.

43-0

TABLE VII.
MAGNETIZING CURRENT 1-12.

served.

Cor-
rected.

r 2 .

1
r*

Qi'.
Calcu-
lated.

762-4

3-5

758 9

....

2-58

9-4

....

749-5

....

8-29

15-4

734- 1

....

15-78

4
5

6
7
8
9
10
11
12
13
14
15
16
17
18 ^
19}
20 *

27-5
44-3
66-6
71-2
59-5
51-0
45-2
40-3
36-3
33-3
30-6
28-1
25-6
23-4
20-0

34-0

71-2
59-7
51-2
45-2
40-3
36-8
33-5
30-5
28-0
25-4
22-7
20-3
18-1
16-0

706-6
662-3
595-7
524-5
464'- 8
413-6
368-4
328-1
291-3
257-8
227-3
199-3
173-9
151-2
130-2
112-8
96-8

0239
0200
0162
0141
0120
0107
0110
0116
0118
0140
0147
0161
0180

41-8
50-0
61-7
70-9
83-3
93-5
90-9
86-2
84-7
71-4
68-0
62-1
55-6

26-70
43-36
69-37

it
I

End.

108 HENEY A. ROWLAND

points approaches the maximum of magnetization, a increases in value

as we pass down the bar; and having reached its maximum at L= 11
nearly, it decreases. These Tables, then, show in the most striking
manner the effect of the variation of the magnetic permeability of iron
upon the distribution of magnetism.

It is evident that these Tables also give the data for obtaining the
relative values of R' at different parts of the bar; but the results thus
obtained are conflicting, and will need further experiment to obtain
accurate results. Where such a small magnetizing force is used as in
Table V it is almost impossible to attain accuracy ; and allowance should
be made for this in deducing results from it. The greatest liability to
error is of course where the magnetization is small; for any small re-
sidual magnetism which the bar may contain will be more apparent
here although great care was taken to remove all residual magnetism
before use. Besides this there are many other disturbances from which
the higher magnetizing powers are free.

If we accept Green's formula as correct, these observations give us data
for determining the magnetizing-f unction of iron in a unique manner, for
nearly all other methods depend on absolute measurements of some
kind. Thus the least value of r z in Table IV for a rod -19 inch diam-
eter is -0142, which gives p= -01132, which in Green's formula (equa-
tion 8) gives //=3388 for the greatest permeability of this iron; and
this is as nearly right as we can judge for this kind of iron. It is to be
noted that Green's formula has been found for the portion of the bar
covered by the helix; but, as seen from my formulse, it will approxi-
mately apply to all portions, though it would be better to find a new
formula for each case.

We shall, toward the last, resume this subject again; and so will leave
it for the present.

The results which I have now given, and indeed all the results of this
paper, have been deduced not only from the observations which I pub-
lish, but from very many others; so that my Tables may be considered
to represent the average of a very extended series of researches, though
they are not really so.

Let us now consider the case of that portion of the bar which is
covered by the helix. First of all, when the helix is symmetrically
placed on the rod, equations (5) and (6) will apply. As Q" is the

STUDIES ox MAGNETIC DISTRIBUTION

109

quantity which is usually taken to represent the distribution of mag-
netism, being nearly proportional to the "surface-density" of mag-
netism, I shall principally discuss it.

In the first place, then, this equation (5) shows that the distribution
of magnetism in a very elongated electromagnet, and indeed in a steel
magnet, does not change when pieces of soft iron bars of the same
diameter as the magnet are placed against the poles, provided that equal
pieces are applied to both ends; otherwise there is a change. This result
would be modified by taking into account the variation of the permea-
bility, &c.

Let us first consider the case where the rod projects out of the end
of the helix, as in Tables V, VI, and VII. By giving proper values to
the constants, we obtain the results given in the last column of the

TABLE VIII.

Strength of magnetizing current.

108.

194.

378.

600.

!2-7
2-4

3-2

2-7

7
9
9

6
6

3-3

3-9

1-7

4-0

6-0

4-0

3-2

5-7

8-7

9-3

14-7

Tables. The agreement with observation is in most cases very perfect.
We also see the same variation of r that we before noticed in the rest of
the curves, and we see that it is in just the direction theory would
indicate from the change of p.

In these Tables we come to a very important subject, and one to
which I called attention some years back namely, the change in the
distribution when the magnetizing force varies, and which is due to change
of permeability. The following Tables and figures show this extremely
well, and are from very long rods with a helix a foot long at their
centre, as in the last three Tables. The bar in both these Tables was
19 inch in diameter and 5 feet long. The zero-point was at the centre
of the bar and of the helix. The Tables give values of Q' e for the
magnetizing forces which appear at the head of each column, and which
are the tangents of the angles of deflection of the needles of a tangent-
galvanometer. Table VIII only gives the part covered by the helix.
Both Tables are from the mean of both ends of the bar.

110

HENRY A. EOWLAND

These experiments show in the most positive manner the effect we
are considering; and we are impressed by them with the great compli-
cation introduced into magnetic distribution by the variable character
of magnetic permeability.

In Fig. 3 I have represented the distribution on half the bar, as given
in Table IX, the other half being of course similar. Here the greatest

TABLE IX.

257.

B.
363.

A.
1-303.

2-5

3-1

1-1
1-3

7-2

4-1
5-9

2-1
4-0

6-1

8-2

9-6

7-7

10-9

18-6

7-9

11-5

21-3

6-5

9-0

16-8

10
12
15
18
30

10-0
6-2
5-0
2-0
2-0

15-0
10-9
9-8
4-7
3-6

27-4
20-9
21-5
14-8
16-5

5 10 15 20

FIG. 3. Plot of Table IX, showing surface-density for different values of the

magnetizing force.

change is observed in the part covered by the helix, though there is
also a great change in the other part. These Tables show that, as
the magnetization of the bars increases, at least beyond a certain point,
the curves on the part covered by the helix increase in steepness; and
the figure even shows that near the middle of the helix an increase of
magnetizing force may cause the surface-density to decrease; and Table
VIII shows this even better. Should we calculate Q", however, we
should always find it to increase with the magnetizing force in all cases.
These effects can be shown also in the case where the bar does not

STUDIES ON MAGNETIC DISTRIBUTION

111

extend beyond the helix, but not nearly so well as in this case, seeing
that here Q" can obtain a greater value.

Assuming that /u is variable, the formula indicates the same change
that we observe; for as Q" increases from zero upwards, ft will first
increase and then decrease ; so that as we increase the magnetizing force
from zero upwards, the curve should first decrease in steepness and
then increase indefinitely in steepness. In these Tables the decrease
of steepness is not very apparent, because the magnetization is always
too great; and indeed on this account it is difficult to show it; but in
Tables V, VI, and VII this action is shown to some extent by the

TABLE x.

x and L.

A.
245.

B.
360.

600.

D.
1-09.

+ 17-6

+ 29-4

+ 52-0

+ 108-7

+ 9-6

+ 16-8

+ 31-5

+ 60-1

+ 7-4

+ 13-1

+ 24-3

+ 45-8

+ 5-4

+ 9-8

+ 19-1

+ 34-1

+ 3-4

+ 7-2

+ 14-7

+ 22-8

+ 2-0

+ 4-6

+ 9-9

+ 16-0

-f 0-6

+ 2-4

+ 5-4

+ 9-6

0-8

+ 0-3

+ 1-2

+ 0-6

1-8

1-6

2-1

0-3

9
1 f\

3-6

6-6

8-8

5-0

6-3

8-6

15-6

7-4

10-0

16-4

27-1

8-4

10-0

16-9

26-5

6-0

7-9

14-5

22-6

5-2

-7-0

12-5

21-0

~i a

5-3

11-9

19-0

9-4

19-1

31-2

5-3

15-2

6-5

19-3

Ort

5-6

6-0

_ 0-7

1-2

values of r in the formulae. The change of distribution with the helix
arranged in this way at the centre of the bar is greater than in almost
every other case, because the magnetism of the bar, Q", can change
greatly throughout the whole length of the helix, and thus the value
of r be changed, and so the distribution become different.

The next case of distribution which I shall consider is that of a very
long rod having a helix wound closely round it for some distance at
one end.

Table X is from a bar 9 feet long with a helix wound for one foot
along one end. The bar was -25 inch in diameter. All except the first

112

HENRY A. KOWLAND

column is the sum of two results with the current in^ opposite direc-
tions, and after letting the bar stand for some time, as indeed was done
in nearly every case. The first column contains twice the quantities
observed, so as to compare with the others. The zero-point was at the
end of the bar covered by the helix.

The value of Q"^ between and 1 includes the lines of force passing
out at the end of the bar, and is therefore too large.

In Fig. 4 we have a plot of the results found for this bar. The
curves are such as we should expect from our theory, except for the
variations introduced by the causes which we have hitherto considered.
Thus the sharp rise in the curve when near the end of the bar has
already been explained in connection with Table III. A small portion

FIG. 4. Plot of Table X.

of it, however, is due to those lines of induction which pass out through
the end section of the bar; and in future experiments these should be
estimated and allowed for.*

To estimate the shape of the curve theoretically in this case, let us
take equation (4) once more, and in it make s'=oo and s" = \/TZR',
which will make it apply to this case. We shall then have A' = 1,
and A" =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 :

05.

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.

Q- 4irA.

Observed. . Observed.

4irA.

Computed.

Error.

22-5 41-1

33-9

7-2

}

12-6 25-1

26-9

' +1-8

19-3 19-3

18-9

0-4

12-0 12-0

11-7

-3

6-6 6-6

7-1

+ -5

3-9 3-9

4-0

+ -1

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.

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.

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

8-2
6-1

16-4
12-2

5-9
4-3

11-8
8-6

I 8-2

8-2

4-0

7-3

7-4

5-5

5-3

2-9

4-8

8-6

3-6

2-7

2-5

3-0

1-6

2-9

4
6

1-7

1-0

2-2

1-1

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

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.

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.

Qe-

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.

Soft Steel, A.

Hard Steel, B.

4.A.

Qe-

47TA.

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 the Theory of the Normal Magnets,' Comptes Rendus, March 31, 1873;
translated in Phil. Mag., June, 1873.

STUDIES ON MAGNETIC DISTRIBUTION 123

lame et avec une quatrieme. Finalement les deux courbes se joignent
au milieu."

In applying the formula to this case of a compound magnet, we have
only to remark that when the bars lie closely together they are theoret-
ically the same as a solid magnet of the same section, but are practically
found to be stronger, because thin bars can be tempered more uniformly
hard than thick ones. The addition of the bars to each other is similar,
then, to an increase in the area of the rod, and should produce nearly
the same effect on a rod of rectangular section as the increase of

diameter in a rod of circular section. Now the quantity p = ~* is

nearly constant in these rods for the same quality of steel, whence r
decreases as d increases; and this in equation (17) shows that as the
diameter is increased, the length being constant, the curves become
less and less steep, until they finally become straight lines. This is
exactly the meaning of M. Jamin's remark.

Where the ratio of the diameter to the length is small, the curves of
distribution are apparently separated from each other and are given by
the equation

which is not dependent on the length of the rod This is exactly the
result found by Coulomb (Biot's Physique, vol. iii, pp. 74, 75). M.
Jamin has also remarked this. He states that as he increases the num-
ber of plates the curves approach each other and finally unite; this he
calls the " normal magnet ; " and he supposes it to be the magnet of
greatest power in proportion to its weight. "From this moment,"
says he, "the combination is at its maximum." The normal magnet,
as thus defined, is very indefinite, as M. Jamin himself admits.

By our equations we can find the condition for a maximum, and can
give the greatest values to the following, supposing the weight of the
bar to be a fixed quantity in the first three.

1st. The magnetic moment.

2nd. The attractive force at the end.

3rd. The total number of lines of magnetic force passing from the
bar.

4th. The magnetic moment, the length being constant and diameter
variable.

Either of these may be regarded as a measure of the power of the
bar, according to the view we take. The magnetic moment of a bar is
easily found to be

124 HENRY A. ROWLAND

M 4rr 2 fl' 1 2~rl4-c-rt h ( 19 )

and if ? is the weight of a unit of volume of the steel and W is the
weight of the magnet, we have finally

M- -*

This only attains a maximum when - oo , or the rod is infinitely

long compared with its diameter.

The second case is rather indefinite, seeing it will depend upon
whether the body attracted is large or small. When it is small, we
require to make the surface-density a maximum, the weight being con-
stant. We find

which attains a maximum as before when -, oo When the attracted

body is large, the attraction will depend more nearly upon the linear
density,

which is a maximum when - 7 - .

a p

For the third case we have the value of Q" at the centre of the bar
from equation (6),

The condition for a maximum gives in this case

5 _ 1-65
d~~ p

For the last case, in which the magnetic moment for a given length
is to be made a maximum, we find

b_-l
d~ p'

This last result is useful in preparing magnets for determining the

STUDIES ON MAGNETIC DISTRIBUTION 125

intensity of the earth's magnetism, and shows that the magnets should
be made short, thick, and hard for the best effect. 11

But for all ordinary purposes the results for the second and third
cases seem most important, and lead to nearly the same result; taking
the mean we find for the maximum magnet

fCtA\

(24)

We see from all our results that the ratio of the length of a magnet
to its diameter in all cases is inversely as the constant p. This con-
stant increases with the hardness of the steel; and hence the harder the
steel the shorter we can make our magnets. It would seem from this
that the temper of a steel magnet should not be drawn at all, but the
hardest steel used, or at least that in which p was greatest. The only
disadvantage in using very hard steel seems to be the difficulty in
imparting the magnetism at first; and this may have led to the practice
of drawing the temper; but now, when we have such powerful electro-
magnets, it seems as if magnets might be made shorter, thicker, and
harder than is the custom. With the relative dimensions of magnets
now used, however, hardening might be of little value.

We can also see from all these facts, that if we make a compound
magnet of hardened steel plates there will be an advantage in filing
more of them together, thus making a thicker magnet than when they
are softer. We also observe that as we pile them up the distribution
changes in just the way indicated by M. Jamin, the curve becoming
less and less steep.

Substituting in the formula the value of p which we have found for
Stub's steel not hardened, but still so hard as to rapidly dull a file, we
find the best ratio of length to diameter to be 33-8 and for the same
steel hardened, about 17, though this last is only a rough approxima-
tion. This gives what M. Jamin has called the normal magnet. The
ratio should be less for a U-magnet than for a straight one.

For all magnets of the same kind of steel in which the ratio of
length to diameter is constant the relative distribution is the same;
and this is not only true for our approximate formula, but would be
found so for the exact one.

Thus for the " normal magnet " the distribution becomes

11 Weber recommends square bars eight times as long as they are broad, and tem-
pered very hard. (Taylor's Scientific Memoirs, vol. ii, p. 86.)

126

HENEY A. ROWLAND

where C is a constant, and x is measured from the centre. The distri-
bution will then be as follows :

X _

609

1-27

2-05

3-02

4-26

This distribution is not the same as that given by M. Jamin; but as
his method is so defective, and his " normal magnet " so indefinite, the
agreement is sufficiently near.

The surface-density at any point of a magnet is

d =

(25)

which, for the same kind of steel, is dependent only on ? and -3-
Hence in two similar magnets the surface-density is the same at similar

.1 .2 .A .4 .5

FIG. 8. Distribution on "normal magnet."

points, the linear density is proportional to the linear dimensions, the
surface integral of magnetic induction over half the magnet or across
the section is proportional to the surface dimensions of the magnets,
and the magnetic moments to the volumes of the magnets. The forces
at similar points with regard to the two magnets will then be the same.
All these remarks apply to soft iron under induction, provided the
inducing force is the same and hence include Sir William Thomson's
well-known law with regard to similar electromagnets; and they are
accurately true notwithstanding the approximate nature of the formula
from which they have here been deduced.

Our theory gives us the means of determining what effect the boring
of a hole through the centre of a magnet would have. In this case R'

STUDIES ON MAGNETIC DISTRIBUTION 127

is not much affected, but R is increased. Where the magnet is used
merely to affect a compass-needle, we should then see that the hole
through the centre has little effect where the magnet is short and thick ;
but where it is long, the attraction on the compass-needle is much dimin-
ished. Where the magnet is of the U-form, and is to be used for
sustaining weights, the practice is detrimental, and the sustaining-power
is diminished in the same proportion as the sectional area of the magnet.
The only case that I know of where the hole through the centre is an
advantage, is that of the deflecting magnets for determining the inten-
sity of the earth's magnetism, which may be thus made lighter without
much diminishing their magnetic moment.

In conclusion, let me express my regret at the imperfection of the
theory given in this paper; for although the equations are more general
than any yet given, yet still they rest upon two quite incorrect hypoth-
eses; and so, although we have found these formula? of great use in
pursuing our studies on magnetic distribution, yet much remains to be
done. A nearer approximation to the true distribution could readily
be obtained; but the result would, without doubt, be very complicated,
and would not repay us for the trouble.

In this paper, as well as in all others which I have published on the
subject of magnetism, my object has not only been to bring forth new
'results, but also to illustrate Faraday's method of lines of magnetic
force, and to show how readily calculations can be made on this system.
For this reason many points have been developed at greater length than
would otherwise be desirable.

ON THE MAGNETIC EFFECT OF ELECTEIC CONVECTION *

[American Journal of Science 13], XV, 30-38, 1878]

The experiments described in this paper were made with a view of
determining whether or not an electrified body in motion produces
magnetic effects. There seems to be no theoretical ground upon which
we can settle the question, seeing that the magnetic action of a con-
ducted electric current may be ascribed to some mutual action between
the conductor and the current. Hence an experiment is of value. Pro-
fessor Maxwell, in his ' Treatise on Electricity/ Art. 770, has computed
the magnetic action of a moving electrified surface, but that the action
exists has not yet been proved experimentally or theoretically.

The apparatus employed consisted of a vulcanite disc 21-1 centi-
metres in diameter and -5 centimetre thick which could be made to
revolve around a vertical axis with a velocity of 61- turns per second.
On either side of the disc at a distance of -6 cm. were fixed glass plates
having a diameter of 38-9 cm. and a hole in the centre of 7-8 cm. The
vulcanite disc was gilded on both sides and the glass plates had an
annular ring of gilt on one side, the outside and inside diameters being
24-0 cm. and 8-9 cm. respectively. The gilt sides could be turned
toward or from the revolving disc but were usually turned toward it so
that the problem might be calculated more readily and there should
be no uncertainty as to the electrification. The outside plates were
usually connected with the earth; and the inside disc with an electric
battery, by means of a point which approached within one-third of a
millimetre of the edge and turned toward it. As the edge was broad,
the point would not discharge unless there was a difference of potential
between it and the edge. Between the electric battery and the disc,

1 The experiments described were made in the laboratory of the Berlin University
through the kindness of Professor Helmholtz, to whose advice they are greatly in-
debted for their completeness. The idea of the experiment first occurred to me in
1868 and was recorded in a note book of that date.

Ox THE MAGNETIC EFFECT OF ELECTRIC CONVECTION 129

a commutator was placed, so that the potential of the latter could be
made plus or minus at will. All parts of the apparatus were of non-
magnetic material.

Over the surface of the disc was suspended, from a bracket in the
wall, an extremely delicate astatic needle, protected from electric
action and currents of air by a brass tube. The two needles were 1-5
cm. long and their centres 17-98 cm. distant from each other. The
readings were by a telescope and scale. The opening in the tube for
observing the mirror was protected from electrical action by a metallic
cone, the mirror being at its vertex. So perfectly was this accom-
plished that no effect of electrical action was apparent either on charg-
ing the battery or reversing the electrification of the disc. The needles
were so far apart that any action of the disc would be many fold greater
on the lower needle than the upper. The direction of the needles was
that of the motion of the disc directly below them, that is, perpendicular
to the radius drawn from the axis to the needle. As the support of
the needle was the wall of the laboratory and the revolving disc was on a
table beneath it, the needle was reasonably free from vibration.

In the first experiments with this apparatus no effect was observed
other than a constant deflection which was reversed with the direction
of the motion. This was finally traced to the magnetism of rotation
of the axis and was afterward greatly reduced by turning down the
axis to -9 cm. diameter. On now rendering the needle more sensitive
and taking several other precautions a distinct effect was observed of
several millimetres on reversing the electrification and it was separated
from the effect of magnetism of rotation by keeping the motion con-
stant and reversing the electrification. As the effect of the magnetism
of rotation was several times that of the moving electricity, and the
needle was so extremely sensitive, numerical results were extremely
hard to be obtained, and it is only after weeks of trial that reasonably
accurate results have been obtained. But the qualitative effect, after
once being obtained, never failed. In hundreds of observations extend-
ing over many weeks, the needle always answered to a change of electri-
fication of the disc. Also on raising the potential above zero the action
was the reverse of that when it was lowered below. The swing of the
needle on reversing the electrification was about 10- or 15- millimetres
and therefore the point of equilibrium was altered 5 or 7| millimetres.
This quantity varied with the electrification, the velocity of motion,
the sensitiveness of the needle, etc.
9

130 HENRY A. EOWLAND

The direction of the action may be thus defined. Calling the motion
of the disc -\- when it moved like the hands of a watch laid on the
table with its face up, we have the following, the needles being over
one side of the disc with the north pole pointing in the direction of
positive motion. The motion being -f> 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

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-

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

68-5
76-5
68-0

8-25

290

97-
91-5
100-

7-00

282

59-
65-5
58-5

6-75

265

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

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),

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)

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.

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.

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

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

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.

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 <f _ GKw ]_

: *tan?>(l + /)/7~ $t "\nearly,

1 ;

sin

where we have substituted <p /3 for <p in Maxwell's equation in the
term involving t. In this equation <p is measured from the magnetic
meridian; but let us take (p as the angle from the point of equilibrium.
Then tp' = <p' + a and (p" = <p" , where <p' and (f ' are for negativa

rotation and (p" and <p" for positive rotation and = arc sin

Let

Then CR =

CR" =

tan 4'" (1 + '
R,= l(R' + R"}.

Where R' and R" are the apparent values of the resistance as calculated
from the negative and positive rotations, and R, is the mean of the

Reports on Electrical Standards,' p. 103.

150 HENRY A. KOWLAXD

two as taken from the table published by the British Association Com-
mittee. If R is the true resistance,

1 1

We shall then find approximately

n _ 1 + tan v' ; ' tan a _ I tan <l'" tan a

~ /., sin a V- tan a
-ft 1

tan f/ \ sin ^"/\ tan

When a is small compared with </'" or 0', and when these are also small,
we have

R = R, (1 + a 2 (a 2 - | 0) + &c.).

So that by taking the mean of positive and negative rotations, the
effect of torsion is almost entirely eliminated. Now a is the angle by
which the needle is deflected from the magnetic meridian by the torsion

1 / /?' \
and its value is ( 1 -^ ) nearly, when a is small, and this, in one

Kr \ ** I

or two of their experiments, exceeds unity or a exceeds 28. 6, which

is absurd. Taking even one of the ordinary cases where -> = 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,

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.

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

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

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

(1
O -2 _ 12^ A

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<t-ooe><MiT-io w

t-OOOOOOOOOCOO CO CO7O5OOOOOCOO5SNOO

COCOCO CO COCOCOCOCOCOCOCOCOCOCOCO

-^ (Mooascoioaot-co

Ti'COCO-^COCO^COCOCOCOWCOeOCOCOCOCO'l'COCOCOCOCO

l-t-ICOOO'*<?O5Ol'- l OaICOCO*-i

176 HENRY A. ROWLAND

e = + -00003 ,
/ = + '00003 ,
a + 'b + c + d + e +f= '00017.

For A and B, log "=11-4566587
For A and C, log "=11-2882590
For B and C, log " = 11-1917176

The distance of the mirror from the scale varied between 192-3 and
193-5 cm.

Should we reject the quantity 34-831 in the third experiment so as
to make the mean result of that experiment 34-744 instead of 34-773,
we should obtain as a mean result of the whole

34-7156 -0053,

which has a less probable error than when the above observation is re-
tained. The number of plus and minus errors are also more nearly
equal and the greatest difference from the mean 1 part in 1100.
However the two results do not differ more than 1 part in 10,000.
We shall take

R = 34-719 -007 earth - at 17' C .
second.

as the final result.

DISCUSSION

On glancing over the table we see that the number of negative errors
greatly exceed the number of positive, but, if we take only the four
errors which are greater than 1 part in 5,000, we shall find two of them
negative and two positive.

Combining the results with the different coils we have

A and B .................... 34-696 -005

A and C .................... 34-744 -Oil

B and C .................... 34-716 -007

Had we no other results to go by, we might suppose that the value of
M might not have been found as exactly for these coils as we have
supposed them to be. But if we include the preliminary results re-
jected on account of the imperfect circle used, we shall find
A and B .................... 34-704 -006

A and C .................... 34-718 -017

B and C .................... 34-758 -016

which has the greatest error in an entirely different place.

From the first series the probable error of each determination of M
is 1 in about 2,000. But as this includes the experimental errors which

177

are about equal to TfrW, the real probable error of M must be about
1 part in 2,500. The number of observations is however too small for
an exact estimate of the probable errors.

Taking the results with currents of different strengths, we find
For strongest current .................... 34-716

For medium current ...................... 34-715

For weakest current ...................... 34-727

which are almost perfectly accordant. Taking the results from the
method of recoil and the ordinary method, we find

For ordinary method .............. 34-726 -010

For method of recoil .............. 34-705 -006

If the probable error is subtracted from the first and added to the
second they will very nearly equal each other. Hence the difference is
probably accidental. Indeed, by the combination of the results it does
not seem possible to find any constant source of error, and therefore
the errors should be eliminated by the combination of the results.
In the final result

= 34-7192 -0070

the probable error, -0070, includes all errors except the ratio of G
to G". We may estimate the probable error of G at ^jVff and of G"

Hence the final probable error of R, including all variables, is
or -04 per cent,

or # = 34-7 19 '015.

The probable error of the British Association determination was -08
per cent, not including the probable error of the constants; and of Kohl-
rausch's determination db -33 per cent, including constant errors.

COMPARISON WITH THE OHM

The difficulty in obtaining proper standards for comparison has been
explained above and I shall have to wait until the arrival of the new
standard before making the exact comparison. At present I give the
following results, which seem to warrant the rejection of Messrs. Elliott
Bros'. 10-ohm standard and to make that of Messrs. Warden, Muirhead
and Clark correct. I shall designate the coils by the letter of the firm
and by the number of ohms. Experiment gave the following results:

W (10) = 1-00171 X E (10), experiment of June 8, 1877.

W (10) = 1-00166 X E (10), experiment of Feb. 23, 1878.

W (1,000): W (100):: W (10): -999876 E (I), experiment of Febru-
ary 23, 1878.
12

178 HENRY A. EOWLAND

Now the greatest source of error in making coils is in passing from
the unit to the higher numbers. As the reproduction of single units
is a very simple process the single ohm is without much doubt correct,
and as the above proportion is correct within one part in 8,000 of what
it should be, it seems to point to the great exactness of the standards
then used, seeing that the exactness of the proportion could hardly have
been accidental. It is also to be noted that Messrs. Warden, Muirhead
& Clark's 10-ohm standard agreed more exactly with a set of coils by
Messrs. Elliott Bros, than their own unit E (10).

The resistance of my coil as derived from the different standards is
as follows :

From Elliott Bros, resistance coils 34-979 ohms.

From Elliott Bros. 10-ohm standard 35-083 ohms.

From W., M. & C.'s 10-ohm standard 35-024 ohms.

From W., M. & C.'s 100-ohm standard 35-035 ohms.

These give for my determination the values of the ohm as follows :

From Elliott Bros, resistance coils . . .-99257 earth q ^*'

sec.

From Elliott Bros. 10-ohm standard -98963 "

From W., M. & C.'s 10-ohm standard -99129

From W., M. & C/s 100-ohm standard -99098

For the reasons given above I accept the mean of the last two results
as the value of the ohm.

To preserve my standard I have made two extra copies of it, the one
in German silver and the other in platinum silver alloy. The com-
parisons are given below. No. 1 is in German silver and the other in
platinum silver alloy. The temperature is 17- C.

No. 1 1-00034 June, 1877.

No. 1 1-00029 Feb., 1878.

No. II -99630 June, 1877.

No. II -99932 Feb., 1878.

These are the values of the copies in terms of the original standard

whose resistance is 34-719 earth quad \

sec.

From these results it would seem that the German silver of which
the standard and No. I were composed was perfectly constant in resist-
ance. The wire has been in my possession for several years and seems
to have reached its constant state.

The final result of the experiment is

1 ohm = -9911 earth

sec.

ON PEOFESSOES AYETON AND PEEEY'S NEW THEOEY OF
THE EAETH'S MAGNETISM, WITH A NOTE ON A NEW
THEOEY OF THE AUEOEA l

[Philosophical Magazine, [5], VIII, 102-106, 1879. Proceedings of the Physical Society,

III, 93-98, 1879]

Some years ago, while in Berlin, I proved by direct experiment that
electric convection produced magnetic action; and I then suggested to
Professor Helmholtz that a theory of the earth's magnetism might be
based upon the experiment. But upon calculating the potential of
the earth required to produce the effect, I found that it was entirely
too great to exist without producing violent perturbations in the planet-
ary movements, and other violent actions.

I have lately read Professors Ayrton and Perry's publication of the
same theory; and as they seem to have arrived at a result for the
potential much less than I did, I have thought it worth while to publish
my reasons for the rejection of the theory.

The first objection to the theory that struck me was, that not only
the relative motion but also the absolute motion through space of the
earth around the sun might also produce action. And to this end I
instituted an experiment as soon as I came home from Berlin.

I made a condenser of two parallel plates with a magnetic needle
enclosed in a minute metal box between them; for I reasoned that, when
the plates were charged and were moved forward by the motion of the
earth around the sun, they would then act in opposite directions on
the enclosed needle, and so cause a deflection when the electrification
of the condenser was reversed. On trying the experiment in the most
careful manner, there was not the slightest trace of action after all
sources of error had been eliminated.

But the experiment did not satisfy me, as I saw there was some
electricity on the metal case surrounding the needle. And so I attacked
the problem analytically, and arrived at the curious result that if an
electrified system moves forward without rotation through space, the

1 Read before the Physical Society, June 29th.

180 HENRY A. KOWLAND

magnetic force at any point is dependent on the electrical force at that
same point or, in other words, that all the equipotential surfaces have
the same magnetic action. Hence, when we shield a needle from elec-
trostatic action, we also shield it from magnetic action.

This theorem only applies to irrotational motion, and assumes that
the elementary law for the magnetic action of electric convection is the
same as the most simple elementary law for closed circuits. Hence we
see that, provided the earth were uniformly electrified on the exterior
of the atmosphere, there would be no magnetic action on the earth's
surface due to mere motion of translation through space.

In calculating the magnetic action due to the rotation, I have taken
the most favorable case, and so have assumed the earth to be a sphere
of magnetic material of great permeability, ft. It does not seem prob-
able that it would make much difference whether the inside sphere
rotated or was stationary; or at least the magnetic action would be
greatest in the latter case; and hence by considering it stationary we
should get the superior limit to the amount of magnetism.

Let a be the radius of the sphere moving with angular velocity w,
and let a be its surface-density in electrostatic measure, and n the ratio
of the electromagnetic to the electrostatic unit of electricity. Then the
current-function will be

<p we? I sin Odd = wa? cos .

n J n

Hence (Maxwell's ' Treatise/ 672) the magnetic potential inside the
sphere is

8:: ff
u =

and outside the sphere

= -TT - war cos ,
o n

^ n r 2

The magnetic force in the interior of the sphere is thus

F=i* wa.

or the field is uniform. If the electric potential of the sphere on the
electrostatic system is V, we may write

^T
which is independent of the dimensions of the sphere.

AYRTOX AND PEEEY'S THEOEY OF THE EAETH'S MAGNETISM 181

In this uniform field in the interior of the sphere, let a smaller
sphere of radius a! be situated; the potential of its induced magnetiza-
tion will he

^ 1 ./' C08<?

Hence the expression for the potential for the space between the two
spheres will be

and outside the electrified sphere it will be

i *ww r\ I Q

w \ fi + 2/ r 2

Let us now take the most favorable case for the production of mag-
netism that we can conceive, making a! = a and fj. = ; we then have

n r 2

which is the potential of an elementary magnet of magnetic moment

^Va\
n

But Gauss * has estimated the magnetic moment of the earth to be

3-3092a 3 .
on the millimetre rag. second system. Hence we have

V= 3-3092
w

for the potential in electrostatic units on the mm. mg. second system.
In electromagnetic units it is thus

V, = 3-3092 ;
w

and hence in volts it is this quantity divided by 10 11 .

As the earth makes one revolution in 23 56' 4", or in 86164 seconds,
we have

"86164'
and

n = 299,000,000,000 * millims. per second.

8 Taylor's Sclent. Mem., vol. ii, p. 225.

3 From a preliminary calculation of a new determination made with the greatest
care, and having a probable error of 1 in 1300.

182 HENRY A. KOWLAND

Hence the earth must be electrified to a potential of about

41 X 10 15 volts *

in order, under the most favorable circumstances, to account for the
earth's magnetism. This would be sufficient to produce a spark in
atmospheric air of ordinary density of about

6,000,000 miles!

Professors Ayrton and Perry have only found the potential 10 8 volts,
or 400,000,000 times less than I find it.

It was this large quantity which caused me to reject the theory; for
I saw what an immense effect it would have in planetary perturbations ;
and I even imagined to myself the atmosphere flying away, and the
lighter bodies on the earth carried away into space by the repulsion.
And, doubtless, had not Professors Ayrton and Perry made some mis-
take in their calculation by which the force was diminished 16 x 10 16
times, they would have feared like results.

For according to Thomson's formula, the force would be equal to a
pressure outwards of

r- V *
~ 8*a* '

which amounts to no less than

1,800,000 grms.

per square centimetre! or 10,000 kil. per square inch! Such an electro-
static force as this would undoubtedly tear the earth to pieces, and dis-
tribute its fragments to the uttermost parts of the universe. If the
moon were electrified to a like potential, the force of repulsion would
be greater than the gravitation attraction to the earth, and it would
fly off through space.

For these reasons I rejected the theory, and now believe that the
magnetism of the earth still remains, as before, one of the great mys-
teries of the universe, toward the solution of which we have not yet
made the most distant approach.

4 That this is not too great may be estimated from my Berlin experiment, where a
disk moving 5,000,000 times as fast as the earth with a potential of 10,000 volts,
produced a magnetic force of T] ^ ffTr of the earth's magnetism,

5,000,000 x 10,000 x 50,000=2,500,000,000,000,000,

which is of the same order of magnitude as the quantity calculated, namely 61 x
10 15 . It can be seen that this reasoning is correct, because the formulae show that
two spheres of unequal size, rotating with equal angular velocity and charged to the
same potential, produce the same magnetic force at similar points in the two systems.

AYRTOX AND PERRY'S THEORY OF THE EARTH'S MAGNETISM 183

In connection with the theory of the earth's magnetism, I had also
framed a theory of the Aurora which may still hold. It is that the
earth is electrified, and naturally that the electricity resides for the
most part on the exterior of the atmosphere and that the air-currents
thus carry the electricity toward the poles, where the air descending
leaves it and that the condensation so produced is finally relieved
by discharge.

The total effect would thus be to cause a difference of potential be-
tween the earth and the upper regions of the air both at the poles and
the equator. At the poles the discharge of the aurora takes place in
the dry atmosphere. At the equator the electrostatic attraction of the
earth for the upper atmospheric layers causes the atmosphere to be in
unstable equilibrium. At some spot of least resistance the upper atmos-
phere rushes toward the earth, moisture is condensed, and a conductor
thus formed on which electricity can collect; and so the whole forms a
conducting system by which the electric potential of the upper air and
the earth become more nearly equal. This is the phenomenon known
as the thunderstorm.

Hence, were the earth electrified, the electricity would be carried to
the higher latitudes by convection, would there discharge to the earth
as an aurora, and passing back to the equator would get to the upper
regions as a lightning discharge, once more to go on its unending cycle.
I leave the details of this theory to the future.

Baltimore, May 30, 1879.

Appendix. Since writing the above, Professors Ayrton and Perry's
paper has appeared in full ; and I am thus able to point out their error
more exactly. Their formula at the foot of page 40G is almost the
same as mine; but on page 407, in the fourth equation, the exponent of
n should be -f- instead of \, which increases their result by about
600,000,000, and makes it practically the same as my own.

Rotterdam, July 13.

ON THE DIAMAGNETIC CONSTANTS OF BISMUTH AND
CALC-SPAK IN ABSOLUTE MEASUKE

[American Journal of Science [3], XVIII, 360-371, 1879]

PART I. BY H. A. ROWLAND

Since my experiments on the magnetic constants of iron, nickel and
cobalt, I have sought the means of determining those of some diamag-
netic substances, and to that end have described a method in this
Journal for May, 1875 (vol. ix, page 357). As Mr. Jacques, Fellow of
the University, was willing to take up the experimental portion, I have
here worked up the subject more in detail and brought the formulae
into practical shape. No experiments have been made on this subject
so far, but some rough comparisons with iron have been made by
Becquerel, Plucker and Weber. But as iron varies so greatly, and as
the methods of experiment are inexact, we cannot be said to know
much about the subject. As, however, the relative results of these
experiments and those of Faraday can be accepted as reasonably exact
for diamagnetic substances and weak paramagnetic ones, it is only
necessary to make a determination of one substance such as bismuth,
and then the rest can be readily found. But as bismuth is very crys-
talline it is necessary to make our formulae general, unless we use bis-
muth in a powder, which would introduce error.

The general method of experiment has been indicated in the paper
before referred to, but I may here state that it consists in counting
the number of vibrations made by a bar hung in the usual manner
between the poles of an electromagnet. The distribution of the mag-
netic force in the field being known, we can then calculate the force
acting on the body, and the comparison of thi? with the time of vibra-
tion gives us the means of determining the constant sought. But I
will leave the more exact description to be given by Mr. Jacques in the
experimental part.

DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 185

EXPLORATION OF FIELD

The first operation to be performed is to find a formula to express
the force of the field at any point, and an experimental means of deter-
mining it in absolute measure. The magnet used was one on the
method of Euhmkorff, and hence the field was nearly symmetrical
around the axis of the two branches, and also with respect to a plane
perpendicular to the axis at a point midway between its poles. Should
any want of symmetry exist by accident, it will be nearly neutralized
in its effect on the final result, seeing that the diamagnetic bar hangs
symmetrically.

The proper expansion of the magnetic potential for this case is
therefore a series of zonal spherical harmonics, including only the un-
even powers. Hence, if V is the potential,

V=A l Q t r + A HI Q til i+A w QS + etc., . . . . (1)

where r is the distance from the centre of symmetry, Q t , Q tit , etc.,
are the spherical harmonics with respect to the angle between r and
the axis, and A t , A ltl , A v , etc., are constants to be found by experi-
ment. The only method known of measuring a strong magnetic field
with accuracy is by means of induced currents, and in this case I have
used a modification of the method of the proof plane as I have described
it in this Journal, III, vol. x, p. 14. In the method there described the
coil was to be drawn rapidly away from the given point: in the present
case the coil was moved along the axis, thus measuring the difference
of the field at several points; on then placing it at the centre and
drawing it away, the field was measured at that point. The field at
the other points "along this axis could then be found by adding the
measured difference to this quantity. This method is far more accu-
rate than the direct measurement at the different points.

When a wire is moved in a magnetic field the current induced in it
is equal to the change of its potential energy, supposing it to transmit
a unit current, divided by the resistance of the circuit. The potential
energy of a wire in a magnetic field is (Maxwell's Elec., Art. 410),

P=I(n- + m:V- + nV

J \ dx dy dz

which is simply the surface integral of V over any surface whose edge
is in the wire.

In the present case, take the axis of x in the direction of the axis of
the poles and the surface, S, parallel to the plane YZ, and let p be the

186 HENRY A. EOWLAND

distance in this plane from the centre of the coil we are calculating.
Then

dV ' , ( n
- 1

for a single circle.
From(l)

and /^a--l; r' = - ,

where // = cos (9 ,

p _

For a circle of rectangular section we must obtain the mean value of
this quantity throughout the section of the coil.

1 fxo + lr, /po+H

M=- r I I Pdxdp,

r lZ t/x lr, t/Po-H

where X Q and [) are the values of x and f> 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"

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 <p, where <p cos -1 , is

j pi

-.- = v X" 1 (k^Tc^ sin <p cos <p .

By observing the moment of the force which acts on a crystal placed
in a uniform magnetic field we can thus find the value of k i k 2 or
the difference of the magnetic constant along the axis and at right
angles to it. The differences of the constants can also be found in the
case of crystals with three axes by a similar process.

The next case which I shall consider is that of a bar hanging in a

DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 189

magnetic field. Let the field be symmetrical around an horizontal axis,
and also with reference to a plane perpendicular to that axis at the
centre. If the bar is very long with reference to its section and a
plane can be passed through it and the axis we must have Z = 0, and
the equation becomes

Let the axis of X coincide with the long axis of the bar, as this will
in the end lead to the most simple result, seeing that we have to inte-
grate along the length of the bar.

Let r be the length along the bar from the centre to any point, and
let 6 be the angle made by the bar with the axis of symmetry : then

1 dV

j>- 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 (<?#
= U S in0\ A] (QW sin 2 - Q? cos 0) + A] tl ($&' sin 2 9

- Q'L cos o) -jj- + ^ v (g; $;' sin 2 - c: cos o) .. + ^^

+ sn tf - ,,, cos ^ - + A,A, ((QW + Q'W sin' o

-2QW cos^) + A tll A,((Q' tll <?,' + Q'^Q'^ sitf o

C=+U\A* ((Qff + QV sin 2 e - Q& cos 9) + 3A' tl ((Q

'^ sin 2 e - Q HI Qf HI cos *)-.+ 5 J 2 ((^ v ^,' - #; 2 ) sin 2

- cos

cos

sn e - 5, V + t J cos o) -.
+ *Q'<& + 3 sin 2 -

Where

Q, =cos0,

Q M = J (5 cos 3 e 3 cos 0) ,

Q, = i (63 cos 5 70 cos 3 + 15 cos 0) ,

^; =Y (21 cos 4 0-14 cos 2 + 1),

<?'/ -o,

cos 3 7cos0),

fj. = COS 0.

DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 191

A = 1 sin 0\ ( A] + 1 1 A*,? + -LV/ A * 1 * ZA. A F + Y- AA #
- ^ 6 )/' + (-

= 4 sn - J -

- m* A ni AJ?) t jf + (if s AIJI _
+ -i |s. J /y ^j 6 ) // + (i-W- 5 - ^' ^ 8 - -
(7 = -^-

Or we can write

A = 41 sin { L>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

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

COS a sin a d a + I I Sin 2 a d a,

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

147

850

Small.

170 "

809

154 "

817

Fibre.

Large.

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 <u

~:i

Con

"3 53*0

- -

|:||^

CM I i

a
5

"a It?

S m 'S

S ^*^

Measured

P<w

3^-* i-i

3-2 oo -3
2 o o

3-2-0^.

Calori-
meter.

Photo-
meter.

perpen-
dicular to
paper, L.

Average,

03 c

CO 3, "

|
03

fl ^S

goo'S'S

gflj 5S ="

too ao

iaIS

be-a ft

201

580

580
201

17-5
13-5

13-1
10-1

2-57

2.82

l-75
l-62

3486
3540-

i 109-0

6-8

4-8

580
201

201
580

38-5
44-6

28-9
33-5

2.74
2 76

2 -44
2 -29

5181-

4898-

1 204 3

12-8

8-9

850
809

809
850

19-0
12-2

14-3
9-2

2.81
2.79

l-54

2483-
3330-

i 133-4

8-3

5-8

817

17-2

2.73

l-28

2708-

209-6

13-1

9-2

Ox THE EFFICIENCY OF EDISON'S ELECTRIC LIGHT 203

The increased efficiency, with rise of temperature, is clearly shown
by the table, and there is no reason, provided the carbons can be made
to stand, why the number of candles per horse power might not be
greatly increased, seeing that the amount which can be obtained from
the arc is from 1000 to 1500 candles per horse power. Provided the
lamp can be made either cheap enough or durable enough, there is no
reasonable doubt of the practical success of the light, but this point
will evidently require much further experiment before the light can be
pronounced practicable.

In conclusion, we must thank Mr. Edison for placing his entire
establishment at our disposal in order that we might form a just and
unbiased estimate of the economy of his light.

27
ELECTEIC ABSORPTION OF CRYSTALS

BY H. A. ROWLAND AND E. L. NICHOLS '

[Philosophical Magazine [5], XI, 414-419, 1881; Proceedings of the Physical Society, IV,

215-221, 1881]

The theory of electric absorption does not seem to have as yet
attracted the general attention which its importance demands; and
from the writings of many physicists we should gather the impression
that the subject is not thoroughly understood. Nevertheless the sub-
ject has been reduced to mathematics; and a more or less complete
theory of it has been in existence for many years. Clausius seems to
have been the first to give what is now considered the best theory.
His memoir, ' On the Mechanical Equivalent of an Electric Discharge/
&c., was read at the Berlin Academy in 1852. 2 In an addition to this
memoir in 1866 he shows that a dielectric medium having in. its mass
particles imperfectly conducting would have the property of electric
absorption. Maxwell, in his ' Electricity,' art. 325, gives this theory
in a somewhat different form, and shows that a body composed of layers
of different substances would possess the property in question. One
of us, in a note in the ' American Journal of Mathematics/ No. 1,
1878, put the matter in a somewhat different form, and investigated
the conditions for there being no electric absorption.

All these theories agree in showing that there should be no electric
absorption in a perfectly homogeneous medium. A mass of glass can
hardly be regarded as homogeneous, seeing that when we keep it
melted for a long time a portion separates out in crystals. Glass
can thus be roughly regarded as a mass of crystals with their axes in
different directions in a medium of a different nature. It should
thus have electric absorption. Among all solid bodies, we can select

1 Communicated by the Physical Society, having been read May 14th, 1881.

2 1 have obtained my knowledge of this memoir from the French translation, en-
titled Tkeorie Mecanique de la Chaleur, par R. Clausius, translated into French by F.
Folie: Paris, 1869. The 'Addition' does not appear in the memoir published in
Pogg. Ann., vol. Ixxxvi, p. 337, but was added in 1866 to the collection of memoirs.

ELECTRIC ABSORPTION OF CRYSTALS 205

none which we can regard as perfectly homogeneous along any given
line through them, except crystals. The theory would then indicate
that crystals should have no electric absorption; and it is the object of
this paper to test this point. The theory of both Clausius and Max-
well refers only to the case of a condenser made of two parallel planes.
In the ' Note ' referred to, one of us has shown that in other forms
of condenser there can be electric absorption even in the case of homo-
geneous bodies. Hence the problem was to test the electric absorp-
tion of a crystal, in the case of an infinite plate of crystal with parallel
sides. The considerations with regard to the infinite plate were
avoided by using the guard-ring principle of Thomson.

The crystals which could be obtained in large and perfect plates
were quartz and calcite. These were of a rather irregular form, about
35 millim. across and 3 millim. thick, and perfectly ground to plane
parallel faces. There were two quartz plates cut from the same crystal
perpendicular to the axis, and two cleavage-plates of Iceland spar.
There were also several specimens of glass ground to the same thickness ;
the plates were all perfectly transparent, with polished faces. Exam-
ined by polarized light, the quartz plates seemed perfectly homo-
geneous at all points except near the edge of one of them. This one
showed traces of amethystine structure at that point; and a portion
of one edge had a piece of quartz of opposite rotation set in; but the
portion which was used in the experiment was apparently perfectly
regular in structure. The fact that there are two species of quartz,
right- and left-handed, with only a slight change in their crystalline
structure, and that, as in amethyst, they often occur together, makes
it not improbable that most pieces of right-handed quartz contain
some molecules of left-handed quartz, and vice versa. In this case
quartz might possess the property of electric absorption to some
degree. But Iceland spar should evidently more nearly satisfy the
conditions. It is unfortunate that the two pieces of quartz were not
cut from different crystals.

This reasoning was confirmed by the experiments, which showed
that the quartz had about one-ninth the absorption of glass; but that
the Iceland spar had none whatever, and is thus the first solid so far
found having no electric absorption. Some crystals of mica, &c., were
tried; but calc spar is the only one which we can say, a priori, is per-

s [There is a gap in the printed article. On examination of the various plates if
the Physical Laboratory of the Johns Hopkins University, some have been found on
about 2 mm. thickness, which are probably those used in this research.]

206 HENKY A. EOWLAND

fectly homogeneous. Thus mica and selenite are so very lamellar in
their character, that few specimens ever appear in which the lamina
are not more or less separated from one another; and thus they should
have electric absorption.

In the ordinary method of experimenting with the various forms of
Leyden jar, there are, besides the residual discharge due to electric
absorption in the substance of the insulator, two other sources of a
return charge. The surface of the glass being more or less conduct-
ing, an electric charge creeps over the surface from the edges of the
tinfoil. In discharging the jar in the usual way by a connecting wire,
this surface remains charged, and the electricity is gradually con-
ducted back to the coatings, and thus recharges them. If, further-
more, the coatings be fastened to the glass with shellac or other cement,
the return charge may be partly due to it; for we have between the
coatings not merely glass, but layers of glass, cement, &c., which the
theory shows to give a residual discharge. Besides the coatings are
not planes; and hence, as one of us has shown, there may be a return
charge, even if the glass gave none between infinite planes. If the
plates were merely laid on the glass without cementing, the same
result would follow, since the insulator would then consist of air and
glass in layers.

In the present research these were sources of error to be avoided,
since the residual discharge due to the insulating plates themselves
were to be compared. The condenser-plates were copper disks. These
were amalgamated, so that there was a layer of mercury between them
and the dielectric, which excluded the air and conducted the electricity
directly to the surface of the dielectric : thus the condition of a single
substance between the plates was fulfilled. The errors due to the
creeping of the charge over the surface of the dielectric and that due
to the plates not being infinite were avoided, the first entirely and the
second partially, by the use of the guard-ring principle of Sir Win.
Thomson.

Plate IV represents this apparatus. The plate of crystal, c, was
placed between two amalgamated plates of copper, a and &, over the
upper one of which the guard-ring, d, was carefully fitted; this ring,
when down, served to charge and discharge the surface around the
plate, a; and so the errors above referred to from the creeping of the
charge along the plate, and from the plate not being infinite, were
avoided.

PLATE IV.

208 HENEY A. KOWLAND

The charging battery consisted of six large Leyden jars of nearly a
square foot of coated surface each, charged to a small potential.
Although accurate instruments were at hand for measuring the poten-
tial in absolute measure, it was considered sufficient to use a Harris
unit-jar for giving a definite charge; for very accurate measurements
were not desired, and the Harris unit-jar was entirely sufficient for the
purpose. The return charge was measured by a Thomson quadrant-
electrometer of the original well-known form.

The apparatus shown in Plate IV performs all the necessary opera-
tions by a half turn of the handle e. By two half turns of the handle,
one forward and the other back, the crystal condenser could be succes-
sively charged from the Leyden battery, discharged, the guard-ring
raised, the upper plate, a, again insulated, and the connection made
with the quadrant-electrometer.

The copper ring, d, was suspended by three silk threads from the
brass disk, /, which in turn could be raised and lowered by the crank, g.
A small wire connected the ring with the rod on which was the ball, h.
This rod was insulated by the glass tube i, and could revolve about an
axis at fc. By the up-and-down motion of the rod the ball came into
contact with the ball (Z) connected with the earth, or the ball (ra) con-
nected with the battery. When the cranks were in the position shown
in the figure, the heavy ball n caused the ball h to rise and press
against I; but when / descended, the piece o pressed on the rod and
caused h to fall on m.

Another rod, q, also more than balanced by a ball, r, was insulated by
a glass tube, s, and connected with the quadrant-electrometer by a
very fine wire. It could also turn around a pivot at t; so that when
the ring u rested upon it, it fell on the upper condenser-plate a, and
connected with the electrometer; when the weight u was raised by the
crank v, the rod rested against f, and so connected the electrometer to
the earth, to which the other quadrants were already connected.

At the beginning of an experiment, the insulating plate to be tested
having been placed between the condenser-plates a and &, the handle
was brought into such a position that the ring, d, rested on the plate
around a. The lengths of the threads between d and f were such that o
for this position of the handle did not touch w, and so li remained in
connection with the earth; and so d was also connected with the earth,
and thus also with &. On now turning the handle further, the ball li
descended to the ball m, and thus charged the condenser for any time
desired. On now reversing the motion, the following operations took
place :

ELECTRIC ABSORPTION OF CRYSTALS

209

First, the ball h rose and discharged the condenser.

Second, the guard-ring d ascended.

Third, the rod q, which had been previously in contact with p, thus
bringing the quadrant-electrometer to zero, now moved down and rested
on the upper condenser-plate a. Thus any return charge quickly showed
itself on the electrometer. The amount of deflection of the instru-
ment depends upon the character of the dielectric, its thickness, the
charge of the battery, the time of contact with the battery, and upon
the length of time of discharging.

Ill

In comparing the glass with the crystal plates, the electrometer was
rendered as little sensitive as the ordinary arrangement of the instru-
ment without the inductor-plate would allow. The electric absorption
of the glass plates for a charge in the battery of two or three sparks
from the Harris unit-jar then sufficed, after 20 or 30 seconds contact
with the battery and 5 seconds discharging time, to give a deflection of
about 200 scale-divisions, which were millimetres. The quartz and
calcite plates were then alternately substituted for the glass, the same
charge and the same intervals of contact being used, and the resulting
deflections noted two plates of each substance of the same thickness
being used.

The results of the measurements are given in the following Tables,
the effect of the glass being called 100.

TABLE I.

April 12, 1880.

Charge of battery, 2 sparks.

Contact, 30 seconds.

Glass (1st plate) 100-0

Quartz (1st plate) 17-1

" (2nd plate). 20-0

Calcite (1st plate) 0.0

" (2nd plate) 0-0

(b)

April 13, 1880.

Charge of battery, 3 sparks.

Contact, 20 seconds.

Glass (1st plate) 100-0

Quartz (1st plate) 19-3

Calcite (1st plate) 0-0

April 14, 1880.
Charge, 3 sparks.
Contact, 10 seconds.
Plates carefully dried by being in desic-
cator over night.

Glass (1st plate) 100-0

Quartz (1st plate) 10-7

Calcite (1st plate) 0-0

(d)

April 22, 1880.

Charge, 2 sparks.

Contact, 30 seconds.

Plate in desiccator since April 14.

Glass (2nd plate) 100-0

" (1st plate) 96-3

Quartz (1st plate) 13-4

" (2nd plate) 12-1

Calcite (1st plate) 0-0

" (2nd plate) 0-0

210

HENKY A. ROWLAND

TABLE II.

MAT 1. RELATIVE EFFECTS FOR DIFFERENT INTENSITIES OF CHARGE AND
TIME OF CONTACT

Charge of
Battery.

Material.

Deflections, in millimetres.

Contact,
5 seconds.

Contact,
10 seconds.

Contact,
30 seconds.

One spark. . . J

Glass (1st)
Quartz (1st)...
Calcite (1st)...

133-0
13-0
0-0

189-3
22-7
0-0

225-0
34-3
0-0

Two sparks. . J

Glass (1st)
Quartz (1st)...
Calcite (1st). . .

Off the scale
24-0
0-0

Off the scale
35-0
0-0

Off the scale
50-0
0-0

These Tables seem to prove beyond question that calcite in clear
crystal has no electric absorption. Quartz seems to have about ^ that of
glass; but we have remarked that quartz is not a good substance to test
the theory upon.

Some experiments were made with cleavage-plates of selenite, which
are always more or less imperfect, as the laminae are very apt to sepa-
rate. These gave, however, effects about -J or ^ those of glass.

In order to test still further the absence of electric absorption in
calcite, the electrometer was rendered very sensitive, and the calcite
plates were tested with gradually increasing charges, from that which
in glass gave 200 millim. after 1 second contact, up to the maximum
charge (ten sparks of the unit-jar) which the condensers were capable
of carrying. In these trials, the calcite still showed no effect, even
with 30 seconds contact. During these experiments glass was fre-
quently substituted for the calcite, to leave no question but that the
apparatus was in working order.

It is to be noted that the relative effects of the quartz and the glass
were different for dried plates and plates exposed to the atmosphere.
This was possibly due to the glass being a better insulator, and thus
retaining its charge better when dry than in its ordinary condition.

Thus we have found, for the first time, a solid which has no electric
absorption; and it is a body which, above all others, the theory of
Clausius and Maxwell would indicate. The small amount of the effect

ELECTRIC ABSORPTION OF CRYSTALS 211

in quartz and selenite also confirms the theory, provided that we can
show that in the given piece of quartz some molecules of right-handed
quartz were mixed with the left; for we know that the theoretical con-
ditions for the absence of electric absorption are rarely satisfied by
laminated substances like selenite or mica. If the theory is con-
firmed, the apparatus here described should give the only test we yet
have of the perfect homogeneity of insulating bodies; for any optical
test cannot penetrate, as this does, to the very structure of the
molecule.

[Presented to the Congress of Electricians, Paris, September 17, 1881, and here
translated from their Proceedings]

[Johns Hopkins University Circulars, No. 19, pp. 4, 5, 1882]

Among the subjects to be discussed by this Congress is that of atmos-
pheric electricity, and I should like, at this point, to urge the import-
ance of a series of general and accurate experiments performed simul-
taneously on a portion of the earth's surface as extended as possible.
Here and there on the globe, it is true, an observer has occasionally
performed a series of experiments, extending even over several years:
but the different observers have not worked in accordance with any pre-
concerted plan, it has not been possible to compare their instruments,
and even where absolute measurements have been obtained, the exact
meaning of the quantity measured has not been perceived. Let us
take, for instance, Sir William Thomson's water dropping apparatus,
which is used at the Kew Observatory. This apparatus is composed
of one tube rising a few feet above the building and of another tube
near the ground, so that it is in the angle made by the house and the
ground. This apparatus indicates a daily variation in the electricity
of the atmosphere, but the result is evidently influenced by the condi-
tions of the experiment. Another observer who should fit up an appar-
atus in another country might obtain entirely different conditions, so
that it would be impossible to compare the results. Hence the neces-
sity of having a system.

The principal aim of scientific investigation is to be able to under-
stand more completely the laws of nature, and we generally succeed in
doing this by bringing together observation and theory. In science
proper, observations and experiments are valuable only in so far as they
rest on a theory either in the present or in the 'future. We can as yet
present only a plausible theory of atmospheric electricity, but the real
way of arriving at the truth in this case is to let ourselves be guided in
our future experiments by those which have hitherto been made on
this subject.

ON ATMOSPHERIC ELECTEICITY 213

The principal facts which have been discovered can be stated in a few
words. In clear weather, the potential increases as we go higher, at
least for certain parts of Europe, and there is a diurnal and annual
variation of this quantity which the presence of fogs causes also to vary.
The first observers were inclined to attribute the electricity of the
atmosphere to the evaporation of water, and an old experiment which
consisted in dropping a ball of red-hot platinum into water placed on a
gold leaf electrometer, was supposed to confirm this view. Even re-
cently a distinguished physicist held this opinion in the case of electric
storms. Now when a ball of platinum is thus dropped into water, the
excessive commotion thus produced will certainly give rise to electricity;
but to assert that this electricity is due to evaporation may very well
be an error. It is true that occasionally a red-hot meteorite may fall
into the sea, reproducing thus the laboratory experiment; but most of
the water is evaporated quietly. Eecently one of my students used
under my direction a Thomson quadrant electrometer in order to inves-
tigate this question, and although he evaporated large quantities of
different liquids, he did not find any trace of electrization. I hope to
prove thus conclusively that the electricity of the atmosphere cannot
be the result of evaporation.

Sir William Thomson thinks that the experiments which have been
made hitherto indicate that the earth is charged negatively. This con-
clusion would certainly explain all the experiments hitherto performed
in Europe ; but the only method of reaching certainty on this point is to
execute a series of experiments on the whole surface of the globe, and
it is this method that I propose to-day. This series of experiments
would furnish data for determining not only the fact of terrestrial
magnetism, but also by the aid of Gauss's theorem the amount of the
charge on the solid portion of the earth; however, this amount cannot
be determined for the upper atmosphere. What we want to know is
the law according to which the electric potential varies as we ascend
on the whole surface of the globe and at the same instant of time, so
that it may be possible to obtain the surface integral of the rate of
variation of the potential over the whole globe. If the earth were ever
to receive an increase of charge coming either from the exterior or from
the upper atmosphere, this increase would be known. When, in the
London Physical Society, I criticized the theory of Profs. Ayrton and
Perry on terrestrial magnetism, I gave at the end of my paper a brief
outline of a recent theory on auroras and storms, which was built on
the hypothesis of the electrization of the earth. After mature reflec-

214 HENKY A. ROWLAND

tion I still wish to present to you this theory, which deserves to be
thought of in mapping out a system of international experiments on
atmospheric electricity.

Suppose Sir William Thomson's explanation is correct and that the
earth is charged with electricity, let us examine what would then
happen. If the earth were not exposed to disturbing causes, a portion
of the electricity of the globe would discharge itself into the atmosphere
and would distribute itself nearly as uniformly as the resistance of the
air would allow. The exterior atmosphere thus charged would set itself
in motion, and we should have winds produced by the electric repul-
sions, and this would last until the electricity had been distributed in a
uniform manner on the earth and in the exterior strata of the atmos-
phere ; when all would be still once more. An observer stationed on the
earth would have no idea of the charge of the exterior atmosphere; but
he would discover the charge of the earth by means of the ordinary
instruments used in experiments on the electricity of the atmosphere,
such as Becquerel's arrows and Thomson's water dropping apparatus.
There would be another result which however could not be measured by
observers situated on the earth, namely, the extension of the atmos-
phere beyond the limits determined by calculation. The rarefied air
being electrified would repel itself, and possibly there would be then in
the exterior atmosphere a region in which the pressure would vary s T ery
slightly for a great difference of elevation. We have learned from
auroras and meteors that the atmosphere extends to a much greater
distance than that indicated by Newton's logarithmic formula, but I
think that what I have said is the first rational explanation of this fact.

Observe now what would happen if the earth of which we speak were
subject to the disturbing causes which exist on our globe; the most
important of these disturbing factors are the winds and the general
atmospheric circulation. This circulation constantly carries the atmo-
sphere from the equator to the two poles, but with very little uni-
formity. However, near the poles there must be many points at which
the air comes down towards the earth and thus shapes its course towards
the equator. Now a body which is a bad conductor, like air, when it is
charged tends to carry its charge along with it wherever it goes, and
thus the air carries its charge until the moment when it descends
towards the earth; then it will leave it behind in the exterior atmo-
sphere, in accordance with the tendency of electricity to remain at the
surface of charged bodies. The charge will therefore accumulate in the
exterior atmosphere, until there is a great tension; the atmosphere

ON ATMOSPHERIC ELECTRICITY 215

will then discharge itself either towards the earth or through the rare-
fied air in the shape of an aurora. At these points the rarefied air
probably heaps itself up to a greater height than elsewhere, which
would explain the great height at which auroras are sometimes observed.

The equilibrium which existed previously at the equator would also
be destroyed by the absence, at this point, of the primitive charge in
the exterior atmosphere, and the earth would have a tendency to dis-
charge itself towards the exterior atmosphere. Owing to the difference
in the conditions at this point, this tendency will be apt to show itself
by the storms which arise oftenest in the equatorial region. Thus the
electricity of the earth would tend to circulate in the same way as the
air from the equator to the poles and conversely.

But I do not intend to insist upon this theory here; I wish simply
through it to bring out the importance of establishing on the whole
surface of the globe a system of general observations on atmospheric
electricity. Even if the theory is false, it is only by observation that
the truth can be attained. In my opinion, it is almost unworthy of the
advanced state of our sciences to-day, that it should be at present impos-
sible for us to indicate accurately the origin of the energy which mani-
fests itself in auroras and storms. For I have pointed out above that
it is necessary to give up explaining these phenomena by the hypothesis
of the production of electricity by evaporation.

I propose therefore that from this section of the Congress a com-
mittee be formed to examine what is to be done in order to establish
on the whole earth, and especially in the polar regions, a systematic
series of observations on atmospheric electricity.

EDITORIAL NOTE. International Commission of Electricians

[Professor Rowland sailed from New York, October 14, to attend an
international commission of electricians, then about to assemble in
Paris. Professor John Trowbridge of Cambridge sailed about the same
date. These two gentlemen were selected to represent the United
States government by the Department of State Congress having made
provision for the appointment of two civilian commissioners.

This official commission is the outgrowth of the congress of electri-
cians which was held a year ago in Paris. That body requested the
French government to invite other nations to unite in constituting
three international commissions for the study of certain specified
problems, namely:

I. A re-determination of the value of the ohm.

216 HENRY A. ROWLAND

II. (a) atmospheric electricity.

(&) protection against damage from telegraphic and telephonic
wires (pa ratonn erres) .

(d) the establishment of an international telemeteorographic

line.

III. Determination of a standard of light.

The study of atmospheric electricity was proposed to the congress by
Mr. Rowland. After hearing his paper on this subject, the section to
which he belonged adopted on his motion the following resolution which
was subsequently approved by the entire congress.

Resolved that an international commission be charged with determin-
ing the precise methods of observation for atmospheric electricity, in
order to generalize this study on the surface of the globe.

As Mr. Eowland did not retain his manuscript, the foregoing trans-
lation of the paper as it is printed in the Comptes Rendus of the con-
gress has been made b} r Mr. P. B. Marcou and is printed here with the
author's consent.]

34
THE DETEEMINATION OF THE OHM

EXTKAIT P'UNE LETTKE DE M. HENKY A. ROWLAND

[Conference Internationale pour la Determination des Unites Electriques. Proces-Ver-
baux, Deuxieme Session, p. 37, Paris, 1884]

Les experiences relatives a la determination de 1'ohm ont ete pre-
parees a Baltimore au moyen d'une partie du credit de 12,500 dollars
alloue dans ce but, 1'annee derniere, par le Congres des Etats-Unis.

Apres une etude preliminaire, les appareils destines a ces exper-
iences ont ete mis en construction en juin 1883. Les autorites de
1'Universite Johns Hopkins ont bien voulu mettre a ma disposition
une construction qui est situee en dehors de la ville, a 1'endroit appele
Clifton, et qui a ete transformed en laboratoire.

La source d'electricite qui servira aux experiences est une pile
secondaire du systeme Plante, chargee par une machine dynamo-elec-
trique actionnee par une machine a vapeur d'environ 5 chevaux de force.

Trois methodes au moins seront employees pour la determination
de 1'ohm. La premiere repose sur 1'induction mutuelle de deux circuits ;
j'ai deja fait usage de cette methode en 1878, mais dans les nouvelles
experiences les dimensions des appareils seront considerablement aug-
mentees; les bobines auront un metre de diametre.

La deuxieme methode est basee sur 1'echauffement d'un conducteur
par le courant electrique, le meme fil etant echauffe successivement par
le courant et par des moyens mecaniques. Les appareils employes
seront ceux qui m'ont servi, en 1879, pour determiner 1'equivalent
mecanique de la chaleur. Afin d'eviter les pertes, le calorimetre sera
rempli d'un liquide non conducteur au lieu d'eau. Pour mesurer
1'energie electrique, on a construit un electrodynamometre ayant des
bobines d'un metre de diametre.

La troisieme methode est celle de Lorenz. Pour determiner la
vitesse du disque, il sera f-ait usage d'un diapason mu par un mecanisme
d'horlogerie, construit par Kb'nig, de Paris.

La comparison de 1'unite de FAssociation Britannique avec 1'unite
mercurielle est pies d'etre terminee; en dehors de cela, aucun resultat

218 HENRY A. EOWLAND

n'a ete obtenu jusqu'a present, mais je crois pourvoir donner mes re-
sultats definitifs en novembre.

Comme ces experiences seront faites avec les precautions les plus
grandes et dans des conditions tres favorables, grace a la generosite du
Congres, il est a esperer qu'aucune decision concernant la valeur defi-
nitive de 1'ohm ne sera prise avant cette epoque; de cette maniere, les
Etats-Unis et d'autres pays pourront accepter 1'etalon arrete.

HENEY A. KOWLAND.

THE THEOKY OF THE DYNAMO

[Report of the Electrical Conference at Philadelphia in November, 1884, pp. 72-83, 90, 91,
104-107, Washington, 18S6 ; Electrical Review (N. Y.), November 1, 8, 15, 22, 1884]

I will now proceed with the discussion of ' The Theory of the
Dynamo-Electric Machine.' I only claim in the skeleton of the theory
which I have here prepared to give a few points which may be of inter-
est and possibly of value to those who are constructing these machines.

The principal losses of the machine I put down under the following
heads: (1) Mechanical friction; (2) Foucault currents in the armature;
(3) energy of the current used in sustaining the magnet; (4) self-induc-
tion of the coils; (o) heating of the armature.

Of course the efficiency of the machine would be equal to the whole
work of the machine minus the different losses divided by the work,
namely : ,

JJT w LL efc.

Thus, when the losses are known, the efficiency of the machine is
known.

The mechanical friction I shall not discuss.

With respect to Foucault currents in the armature, by dividing up
the armature in the proper way, we can get rid of most of these. It is
very often effected in the Siemens armature by dividing up the arma-
ture into discs.

I have purposely omitted the loss due to change of magnetism in the
armature as the armature revolves. 1 drew attention to this fact sev-
eral years ago. It has been recently experimented upon and found
that, although there is some heating effect, it is very small indeed.

With respect to the energy used in sustaining the magnet, if the
magnet were of steel there would, of course, be no loss. The only
reason for not using a steel magnet is that the field is comparatively
weak. The field of a steel magnet is, I suppose, less than one-third of
the field due to a good electro-magnet; the two could not be made
equal by any possible means. Therefore, in most dynamo machines,
the magnet is produced by the current.

220 HENRY A. KOWLAKD

It is a question what the form of the magnet and the position of
these coils should be in order to get the greatest field with the least
xpenditure of energy. I have one or two propositions to make on this
subject which I think are of some interest.

The first proposition I have to make is that a round magnet is better
than one of elongated cross-section. If the coils are long, and they
are usually long enough for the purpose, although the theory assumes
an infinite length, the magnetic force at any time acting on a round
iron core is exactly the same as on an elongated core. But the area
of a circular section is much greater than that of an elongated section
of the same circumference, and therefore the same amount of wire
which would be used to go around the elongated magnet, would, if
extended on a circular section of the same circumference, surround
much more iron.

The principal object of making an elongated magnet is that it may
include the whole length of the armature. Most makers who adopt
this form think it better to elongate the cross-section than to have a
long pole piece. But we have seen that the round form is more efficient
in general than the elongated form, and the only question is whether it
will be more efficient in this particular case. I shall proceed in this
theory upon the known fact that we can consider lines of force as if
they were conducted by the iron and the air outside. The conductivity
of the iron for the lines of force is very great, much greater than that
of air. I experimented on it many years ago, and my idea is that it
Varies (according to the degree of magnetization) from several hundred
up to 5,000 times that of air. The conductivity for iron is very great,
especially for wrought iron; for cast iron it is probably less. Therefore
the lines of force will be conducted down through the iron from any
point over a circular cross-section very nearly as easily as they are from
an elongated cross-section, and the saving in the wire will be con-
siderable.

I have another proposition to make with respect to the magnet, and
that is that one circuit of the lines of force is better than a number.
There is a loss from having a number of electro-magnets, even if they
are round. For this reason, that the same magnetic force is acting in
each of these coils provided there is the same number of wires per unit
of length; and the same wire will go more times around the same iron
concentrated in one magnet than when subdivided into several, and
will, therefore, act upon it with more magnetizing force.

That proposition not only applies to this form of magnet (Fig. 1),

THE THEORY OF THE DYNAMO

but it also applies to the form where we have the armature revolving
between two magnets like this (Fig. 2), because we can turn this lower
magnet over and bring the two together. The circuits of the lines of
force are around in this direction and in this (arrows, Fig. 2). So that
there are two circuits of the lines of force instead of one. The energy
expended for a given amount of work will be less with this form (Fig. 1)
than with this (Fig. 2). That is of very great value to makers of
machines.

The theorem applies to a number of those old machines where there

FIG. i.

Fio. 2.

was a very large number of little magnets revolving around other little
magnets. More work is used in sustaining the magnets in that form
of machine than in the more modern form where we have only a few
circuits.

I had a number of drawings made of magnets in the Electrical Exhi-
bition, and I find very great difference in this respect; more difference
where Siemens armatures are used than in any other kind. In dis-
cussing these drawings I do not give any names, nor say whether one
machine as a whole is better or worse than another.

First, I will discuss the general forms of the magnet, and then I wish
to say something in respect to the form of the pole pieces that inclose

222

HENRY A. KOWLAND

the armature. Of course this form belongs both to the Gramme ring
and the Siemens armature. Most modern machines are of this nature,
either Gramme or Siemens, and we may consider them both one if
we wish.

We will now proceed with respect to the field in this form of magnet
(Fig. 3). The lines of force proceed down the magnet, and are sup-
posed to go across here (a &), where wires wound around the revolving
armature cut them, and so produce a current. It is evident that any
lines which escape across this open space (arrows) are lost. If there

FIG. a.

FIG. 4.

was any leakage of the wire around the magnet, the current, instead of
going around the magnet, would go off somewhere else, and we should
consider the machine defective because there was a loss of the current.
Sq if any of these lines of force, instead of going directly across there
(a &), go across the open space (arrows), as they naturally would do, all
those lines of force are lost, and we would have to add so much more
current in order to make up for this outside loss. I have an illustra-
tion of such losses of lines of force from a drawing, which I will give
you (Fig. 4).

This machine has two magnets one above and one below. The lines

THE THEORY OF THE DYNAMO

223

of force pass up through here (abed) and then out and around through
here (e e), &c., to complete the circuit. As I saw the machine in the
exhibition these outside pieces (ee) were closer to the poles of the
magnets than I have drawn them. If they are put too near, some lines
of force, instead of passing across the field of force, where the wires
revolve, as they ought to do, pass off at these openings, the circuits
going around in this way (arrows f f). In this case there is a loss due
to leakage of the lines of force, and we shall therefore have to expend

FIG. 5.

FIG. 6.

more energy in keeping up the magnet. There is energy expended in
keeping up the field outside as well as in keeping up the field through
the armature. It is important that this point should be considered.
These questions, ' How many lines of force go across this opening and
are effective in producing the current, and how many escape off without
passing through the opening and are lost?' are just as important as
the question of the leakage of the current in the wire. There are
defects in many of these machines in that respect. In this form of
machine (Fig. 1), where there is a simple circuit, this magnet has to be

224: HENKY A. KOWLAND

attached somewhere. Very often the magnet is turned vertically, poles
downward, and attached to a cast-iron bench. I have no doubt that
some lines of force are lost (not much perhaps) in passing across from
the magnet to this iron bench. The makers of the machine, I suppose,
considered this to some extent, but what is needed is measurement on
that point.

Here is another form of magnet (Fig. 5). That machine would be
defective. It has two magnets and two magnetic circuits in the place
of one, and many of the lines of force probably make little private cir-
cuits of their own around in that way (arrows). Those lines of force
are of course lost, and it is more or less defective in that respect. It
would be better to diminish the number of magnetic circuits to one.

(I am only giving a general idea of the principle of these machines,
and I do not refer to any in particular.)

It is also important that these lines of magnetic induction shall find
easy passage around in order to produce the most intense field. Thus
the opening between the armature and pole pieces must be made as
small as possible, in order that the lines of force may find easy passage
across it. Everybody recognizes that. Suppose we had a machine made
in the following manner (Fig. 6), in which there is a magnet with
a Gramme ring here (a), and pole piece here (&), a ring here (c), and
pole piece here (d), but no pole pieces opposite these. How are the
lines of force to pass around ? I do not know that it would be easy to
see how. They evidently go around here (arrows) and get to the other
side the best way they can. There is no easy passage around for the
lines of force in this case.

A MEMBER. May they not to some extent follow the shaft ?

Professor EOWLAND. It is evident that if the shaft is made large
enough some go along the shaft in that way (arrows), but there is no
easy way for them to get around.

I have here a formula for the amount of work which one has to
expend upon a magnet in order to produce a certain effect. I will take
the case which I have considered most efficient, where there is one
magnetic circuit. It is an original idea of Faraday that these lines of
force are conducted. We suppose the lines of force to pass through
the iron and across the opening in this way (arrows, Fig. 1), and they
are caused to do that by what may be called the magneto-motive force
of the helix.

I will just obtain an expression for the number of lines of force B.
This is not the quantity which Maxwell considers, but it includes the

THE THEORY OF THE DYNAMO 225

whole number of lines of force which pass through the magnet. We
may write B, proportional to N, the number of turns of the wire around
the magnet, and C, the current; and inversely proportional to the re-
sistance to these lines of force in going around the circuit. The resist-
ance to the lines of force is proportional to L, the length of the iron of
the system, divided by S, the cross-section of the magnet, supposing it
to be uniform, into //, the magnetic permeability of the iron (or the
conductivity of the iron for the lines of force). This quantity ft varies
with the current, and can readily be obtained. Some years ago I gave
a formula for it. It can be expressed simply as dependent upon the
magnetization of the iron and a constant depending upon the iron
alone. We have something more to add:

Let I be twice the width of the opening between armature and pole
piece, and A the area across which the lines of force flow; then we

have to add -i and another quantity, which we can call p, which depends

upon the resistance of these lines of force which escape in all direc-
tions and represents the loss due to that escapement. Thus we have
the final value for the number of lines of force (or rather induction)
in the magnet

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.

[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

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.

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 <?m. in length, protected by a glass tube. The needle-

25-1 HENEY A. EOWLAND

system is made by fitting two small square blocks of wood on an alumi-
nium wire; on two sides of each of the wooden blocks are cemented
small scraps of highly magnetized watch-spring. The needle thus made
is about 1 X 1 X 10 mm.

The mirror is fixed just below the upper needle, and is read by a
telescope 200 cm. distant. The plane of the mirror is at an angle
of 45 with the plane of the disks for convenience. The whole is sup-
ported by the board 00 attached to a wall -bracket.

Two controlling magnets (W W) with their poles turned in opposite
directions are used. By means of the up and down motion of either
magnet, any change in the sensitiveness can be attained; and by the
motion in azimuth, the zero point is controlled. The advantage of its
use lies in the extremely delicate means it affords of changing the
sensitiveness, much more delicate than with a single magnet.

The bed-plate B is screwed to one end of a table, at the other end of
which a countershaft is placed (Fig. 2). This is run by an electric
motor in the next room, the belt running through the open doorway.
The motor is 14 metres from the needle.

Although the disks and countershaft were carefully balanced when
first set up, and the table braced and weighted by a heavy stone slab,
yet at the speed used, 125 per second, the shaking of the entire appar-
atus was considerable; the needle was so unsteady that it could not be
read. This was seen to be due to vibrations of the telescope itself and
not to the needle. To prevent it, each leg of the table on which the
telescope rested was set in a box about 30 cm. deep filled with saw-
dust, and a heavy stone slab was placed on top of this table. This
entirely did away with the trouble; the swing of the needle was as
regular when the apparatus was revolving as when it was at rest.

The two hard rubber rings (RR) mentioned above have grooves cut
in their peripheries ; in these grooves wires are wound. These serve as
a galvanometer for determining the needle-constant. When not in use
they are held in the position shown in the figure, but when it is desired
to determine the needle-constant they are slipped on the shoulders
(AAAA) and pushed up in contact with the back of the disks. Each
has two turns: this arrangement will be referred to as the disk-
galvanometer.

If a known current is sent through the disk-galvanometer, and the
geometrical constant be known, the part of the constant depending on
the field and needle is determined.

The current is measured by a sine-galvanometer, placed in another

ELECTRON AGXETIC EFFECT OF COXYECTIOX-CURREXTS .*'>">

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
<riiard-ring have a diameter of 35 cm., and the movable disk a diameter
of 10 cm.

The routine of the observations was as follows: A determination
of H and the needle-constant (/?) was first made. The electrostatic
gauge was then set at a certain point, and readings of difference of
potential were taken. The disks were now started, electrified, and a
series of three elongations of the needle taken; the electrification re-
versed and three more elongations taken, &c.

About every five minutes speed-readings had to be noted, and at each
reversal it was necessary to replenish the charge in order to keep the
gauge-arm just at the mark. In this way a ' series ' of readings con-
sisting of about 25 reversals was made. After the series, electrometer
readings were again taken; the conditions were then changed in some
way. and another series begun.

The circumstances to be changed are : distance of disks from needle ;
distance of glass plates from needle; electrification; and direction of
rotation.

The calculation of the deflexion is based on the assumption that the
magnetic effect of a rotating charge is proportional to the quantity of
electricity passing any point per second, just as with a conduction-
current. Below are the formulae used.

256 HEXEY A. ROWLAND

In the equations the letters have the following meanings. All quan-
tities are given in terms of C. G. S. units.

X= Distance from centre of disk to lower needle.
r = Distance from centre of disk to upper needle.
c = Radius of disk.
I = Distance between needles.
a = Radius of windings of disk-galvanometer.
i = Distance, centre of disk-galvanometer to lower needle.
p = Distance, centre of disk-galvanometer to upper needle.
N = Number of revolutions per second.

a = Surface-density of electrification in electrostatic measure.
V= Ratio of the units.

a = Angle of torsion of the electro-dynamometer.
<f> = 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

.'. 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. ^.

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

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:

I = sin <p.

/. 7=10-* 5-46 ZTsin f,
and

/5 = 10-*. 5-46

tan P

For measurement of H :
Electrodynamometer,

ls =0- z jr V sin a.

^ = constant of windings = 10~ 3 . 6'454.
K- moment of inertia = 10 2 . 8-266.
T= time of one swing =2-441.
.-. i = 10~ 2 . 7-59 Vsin .

Tangent galvanometer:

i = |C tan d = ^ tan 8 .
2-w

n = no. turns = 10.
b = radius turns = 49-98.
.-. t = 0-795 JJ tan d,

and, substituting the value of t,

JI=10-'. 9-55 ***.
tan d

260 HENRY A. KOWLAND

Surface density (a):

a is obtained from electrometer-readings.

V *-f i/

A = corrected area of movable plate
f=*r{5im

.: V = 10 X 1'756 D iJ~uT,

and ff = 1-397 - VaT.

e '

As soon as the attempt was made to electrify the apparatus, diffi-
culties of insulation were met with. The charged system was quite
extensive, and the opportunity for leakage was abundant; in addition,
the winter here has been very damp. Most of the trouble of this kind
has been due to the glass in the apparatus; in no case where glass was
used as an insulator has it proved satisfactory, not even when the air
was dry. First, the stand with glass legs, on which the Ley den- jar
battery was placed, was found to furnish an excellent earth-connection.

Paraffin blocks interposed stopped this. The reversing-key had
three glass rods in it, all of which were found to leak ; six different spec-
imens of glass, some bought particularly for this as insulating glass,
were all found to allow great leakage. Shellacing had no effect. Hard
rubber was finally substituted for glass ; and after that the key insulated
very well, even in damp weather.

On charging the glass plates, the disks being earthed, it seemed
almost as if there was a direct earth-connection, so rapid was the fall of
the charge. This was not regarded at the time, as the plates were
always kept earthed ; but later, when it became necessary to charge the
plates, the insulation had to be made good.

Investigation showed that this was caused by leakage directly through
the substance of the glass to the brass back-pieces (H H). Hard rubber
pieces were substituted, and the trouble was entirely removed.

There was at first a deflexion in reversing the electrification while
the disks were at rest. This was of course due to direct electrostatic
effect; but it was not for some time clear where the point of weakness
in the electrostatic screen lay. It was found to be the faulty contact
between the tinfoil covering of the glass tube and the brass collar; the
brass had been lacquered. After this was corrected there was never

ELECTROMAGNETIC EFFECT OF COXVECTION-CUKRENTS 261

again any deflexion on reversing the charge, although the precaution
was taken of testing it every day or so.

The currents induced in the axle by the rotation caused no incon-
venience; if the disks are rotated in the same direction their effect is
added, while the effect of the axles is in opposite directions. Even
when the disks were rotated oppositely, the deflexion due to the axles
was only 3 or 4 cm., and remained perfectly constant.

On running the disks, unelectrified, without the glass plates between
them and the needle, a deflexion of 4 or 5 cm. was noticed. This was
perfectly steady deflexion, and could easily be shown to be due to the
presence of the plate, as it ceased when the plates were replaced.

This was very troublesome for a time, especially as the presence of a
brass plate in place of the glass was found to diminish the deflexion,
but did not bring the needle back to zero as the glasses did. On look-
ing at the figure (Plate Y, Fig. 1) it will be seen that there is a brass
plug (/) closing the bottom of the tube in which the needle is placed.
The rapid rotation of the disks caused a very appreciable exhaustion
at the centre, and consequently a steady stream of air was sucked down
the tube through the open mouthpiece, and out through the imperfect
connection of the plug. Air-currents were not at first suspected, as the
deflexion was so very steady. The brass plate used was smaller than
the glass, and hence did not completely shield the tube.

After the brass back-pieces (H H) had been taken out, and a hard
rubber substituted, it was found that with one direction of rotation the
needle was extremely unsteady; it would run up the scale for several
centimetres, stop suddenly, &c. evidently a forced vibration. This
was traced to air-currents also. Now, the air blew into the open mouth
of the cone. The apparatus had been run for some months with this
open, and not the slightest irregularity had been seen. But the hard
rubber pieces were very much larger than the brass ones which were
removed ; they filled up the lower space to a greater extent, and deflected
the air upwards more than before, causing the unsteadiness. With the
opposite rotation the air was thrown down instead of up, and conse-
quently did not affect the needle.

The first systematic observations were made in January, 1889, with
the disks charged and plates earthed. The deflexion on reversing was
got without difficulty, and it was in the direction to be expected; that
is, with positive electrification, the effect was equivalent to a current in
the direction of motion of the disk. A number of series were taken in
the next two months; they agreed among themselves well enough, but

262 HENEY A. EOWLAND

did not follow the law assumed. The deviation can best be explained
in this way: The equations above show that for a fixed position of

N~ D N

the disks J oc a-, a-x. If then, N and /9 being constant, the con-
p e p

denser plates are moved up to the disk, step by step, thus varying e,
and D be changed at the same time so as to keep D/e <xa, a constant,
the deflexions should be constant.

Such was not found to be the case; the deflexions were directly
proportioned to e instead of being constant : that is, with greater differ-
ence of potential, the deflexions were greater, although the surface
density remained constant. Finally this was found to be due to a
charge on the back surface of the gold coating. The end of the axle
comes nearly up to the surface of the disk and taken with all the brass
work must form a condenser of a certain capacity with the inner face
of the gold foil.

This made a change necessary in the method of working; the disks
had to be earthed and the glasses charged. This was done; but now
the deflexions were found always to be greater with positive rotation
(Zenith, North, Nadir, South) then with negative.

It was considered possible that the brushes might have something
to do with this, so they were taken off. Earth connection with the disk
was made by drilling through to the surface of the disk in the line of
the axle and setting in a screw, which came flush with the surface and
also made contact with the axle; this, however, made no difference, the
deflexions for negative rotation were always smaller.

Table I gives the results of a number of observations. All were
taken with the plates charged and the disks earthed by means of the
axle.

The meaning of the letters has been given; l//9is directly propor-
tional to the needle sensitiveness.

The sudden variations in the values of 1//9 are due to changes pur-
posely made in the needle.

The last column gives the values of V. This work is not intended
as a determination of V, but the calculation is made merely to show to
what degree of approximation the effect follows the assumed law.

The deflexions are about the same as those obtained in the Berlin
experiments 5 to 8 mm. on reversing. The force measured then
was 1/50000 H; now it is 1/125000 H. The sensitiveness of the needle
in the two cases was almost the same. In the former experiment a
force of 3 X 10~ 7 deflected the needle 1' of arc; the corresponding num-

ELECTROMAGNETIC EFFECT OF CONVECTION-CURRENTS

263

ber now is 2-7 X 10~ 7 r slightly more sensitive. The scale distances
were 110 and 200 cm. respectively. So this experiment gives about

TABLE I.

No.

Rotation.

<r.

1//3.

2A.

mm.

2-54

1-24

122

1-16

1-50. 10 5

5-3

2-42.101

2-57

125

1-30

3-11

9-0

3-38

129

1-23

2-15

6-94

3-00

129

1-23

5-58

3-68

1-21

127

1-21

2-25

5-6

3-74

133

1-21

5-7

3-74

130

1-47

8-4

3-10

133

1-47

7-3

3-64

1-24

121

1-32

2-22

9-4

2-26

130

1-32

7-2

3-16

125

1-26

2-17

7-6

2-70

126

1-26

5-7

3-64

2-85

1-50

125

1-19

2-23

6-5

2-82

129

1-19

5-0

3-78

125

1-11

2-19

5-85

2-82

1-43

127

1-08

2-35

7-3

2-46

128

1-08

5-4

3-32

129

1-08

5-3

3-42

3-22

1-80

123

1-13

2-44

5-1

3-30

124

1-13

4-9

3-48

3- 19 x ]0i

TABLE II.

#13.

#14-

mm.

6-7

5-1

4-9

6-6

3-9

7-6

5-3

8-0

5-0

5-8

5-2

6-3

4-9

8-0

5-0

4-3

4-4

5-9

6-6

6-0

5-0

6-5

5-0

the same scale-deflexion at twice the distance with a force ^ as great.
The agreement between the two is seen to be quite good.

The observations, except Nos. 1, 2, 15, and 18 given above, were taken

264 HENRY A. EOWLAND

in pairs first one direction of rotation and the other immediately after-
wards, everything except the rotation being kept constant.

The table shows that, in every case except one, the deflexion for
negative rotation is appreciably smaller than the corresponding positive.

The difference is too great to be due to accidental errors in the read-
ings, as the following table, giving the successive deflexions in the case
of #13 and #14 will show.

There is but one deflexion in #13 as small as the mean of #14, and
but one in #14 as large as the mean of #13.

This is a fair example of the way the deflexions run. As a further
illustration of this take#17 and#18; these two are identical in arrange-
ment, but the direction of rotation is in one case got by crossing the
belts from the countershaft to the disks and leaving the main bolt
straight; in the other the main belt is crossed while the auxiliary belts
are straight. The deflexions are the same. This, too, shows that the
difference cannot be due to any effect of the countershaft. The cause
of this has not yet been explained. The work is to be continued with
this and also with new apparatus, made like the Berlin apparatus, but
with the disk much larger, 30 cm. in diameter; at least double the
speed then obtained will be used. This ought to give deflexions on
reversal of 1-5 to 1-7 cm.

The values of V do not agree so well as might be looked for; but.
when, in addition to the numerous difficulties already mentioned, the
smallness of the deflexion is considered, and the possibility of the needle
being affected by currents or magnets in other portions of the labora-
tory, so far away as not to be guarded against, and which might well be
changed between the time of taking the observation and the determin-
ation of the needle-constant, and, finally, that a distubing cause of some
kind is still undoubtedly present, the agreement is seen to be as good
as could justly be expected.

Physical Laboratory, Johns Hopkins University,
April 22, 1889.

NOTE, added April 29

There seems to be a misunderstanding in certain quarters as to the
nature of the deflexion obtained in Prof. Eowland's first experiment.
The paper reads : " The swing of the needle on reversing the electri-
fication was about 10 to 15 mm., and therefore the point of equilibrium
was altered 5 to 7-5 mm/' This has been construed to mean that the

ELECTROMAGNETIC EFFECT OF CONVECTION-CURRENTS 265

deflexion was merely a throw, and that no continuous deflexion was
obtained. This is entirely erroneous; there was always a continuous
deflexion. The throw was read merely because the needle was always
more or less unsteady, and better results could be got by seizing a
favorable moment when the needle was quiet and reading the throw,
than by attempting to take the successive elongations, or waiting for
the needle to come to rest. In the experiment described above the
needle was very steady and no such trouble was experienced. On elec-
trifying, the needle would take up a certain position and would remain
there as long as the charge was kept up ; on reversal, it would move off
to a new and perfectly definite position about 6 to 7 mm. away, and
remain there, &c. H. A. E.

C. T. H.

ON THE RATIO OF THE ELECTROMAGNETIC TO THE
ELECTROSTATIC UNIT OF ELECTRICITY

Br flcxKr A. ROWLAXD, with the *UUnc<r of E. H. BALL mud L. B. FLETCMEK

(PkitMipktrml MmpuiHe [5J, XXVIII. 304-315, 1889; 4wrfe SOWTM/ / &* [S],

JTJTJT K///, 299-998, IMf]

The determination described below was made in the laboratory of
the Johns Hopkins University about ten years ago, and was laid aside
for further experiment before publication. The time never arrived to
complete it, and I now seize the opportunity of the publication of a
determination of the ratio by Mr. ROM in which the same standard
condenser was used, to publish it. Mr. Rosa has used the method of
getting the ratio in terms of a resistance. Ten years ago the absolute
resistance of a wire was a very uncertain quantity and, therefore, I
adopted the method of measuring a quantity of electricity electro-
statically and then, by passing it through a galvanometer, measuring it
electromagnet ically.

The method consisted, then, in charging a standard condenser, whose
geometrical form was accurately known, to a given potential as meas-
ured by a very accurate absolute electrometer, and then passing it
through a galvanometer whose constant was accurately known, and
measuring the swing of the needle.

DESCBIPTIOX OF IXSTBCTCEXTS

Ekctrt/rnetT. This was a very fine instrument made partly according
to my design by Edelmann, of Munich, As first made, it had many
faults which were, however, corrected here. It is on Thomson's guard
ring principle with the movable plate attached to the arm of a balance
and capable of accurate adjustment. The disc is 10-18 cm. diameter
in an opening of 10-38 cm. and the guard plates about 33-0 cm. diam-
eter. All the surfaces are nickel plated and ground and polished to
optical surfaces and capable of accurate adjustment so that the dis-
tance between the plates can be very accurately determined. The
balance is sensitive to a mg. or less and the exact position of the beam

RATIO Of ffx-JUxmrntaftLomtem^f. 10 TEr.m !'<iHi!if '^TH* TTSTHT Bfl

:- :\ : I'.-':.:: .::._- ' - : : ' - :-.r in i ' -.-: -: " -, . --- :;; -/.: -

^ :. iesiedi throttgh-

ovt iis attire nnge bjr Tailing; the detracts and weights to give the

constant puifnlial of a standard gaiage r and fband to give relative icad-

:r_- ' "::;: 1 in ^ - '.^i.-:. I' - :---;-: --: ->.: :-;^- : :. ;-;- ;- ->.-:

..._. ,' 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 <nard rin<r could be made to almost

IT JT ^ Ij

i.~ -7'r7. "- ~~ potential "i khe ~~~.

where 4 is the drnfanrr of the plates, w the absolute force on the

_. . -;-_: -\i-.-_ j.- i J_ -; . :^ -.;-.-; -. - \ According " iTaiw ?I1

where ^ aia^ ^ are the iradn. of the disc anxi the openrng^ foe it
= Rl // _-.. .':.-. \i.i- :orred Ha^ Aaal 1
nenee we kave^ finaEhr r

Stmmioni canaVvwr. This Terr aenate instrument was made from

irsj-- '-- )[? ".---,- -'- . r -, y..~ 5Tork, L~ : :onsisted ' J >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:

300-59
300-17
296-72
297-84
298-90
298-57
299-05
300-80
296-56

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

to O . _

^ O rH x2

CO to rH 1C t- "- 1 T*<

to CO O5 t- CO T* . * <M
O 1ft CO T* t- rH T*( O 00 r-l O

OS IM CO . ' CD ;2 00 35
CO rH IM

O 00 xo
to eo I-H * oo x

toCOOSO COGO 7J
COlCrH-*CO CO -<t<Ol> ^" to <M
rH ... . .
Oi (M I CO 0-* OS 10
* CO 1 35

*" *> X^

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?

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

D CO CO O CO 00 ^O> O
00 O CO T*< 1ft CO i lot- to O
r-t ... . . . 35
O OJ * CO 2 -* OS
1C CO ___ffl

* 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
<M CO rH 35

CO CO O OS CO OS .CO CO
00 O CO -<f CO .H IN O t- ' t-

1-1 o <M 4< ' eo o": t^ *

to co r__s

CD
rH

to rH XO

co to t- co o x
to sowos coos co

OOlCrH-*t- CO COOOO ^^ (M CO

2 *8

os t- o 10 co ra t-

CO CO O OO CO 00 ^to to

rH ... . . . .

O5 CM 5? CC OT* CO 00
53 CO rH 35
IM

00 O IN * CO -* rH O t- t-
rH ... . . . oo

SIN CO CO 2 CO 05
CO " O*

CO * xo

CO CO W to * ^rH

to eo c ? co to 3s

^ 00 ^/ .

o t- xS
a> t- os o <?* OT o

CO CO O 1O CO OS ^1C Tj<
OOOW-<*<CO i-( COOt- <M 00

OOtoO*-^-* Tt< (MOOO < **^ CO rH

OS IM IM CO OTt< * O
(M CO ^H O

Q IN CO CO 5] O O5
ffl CO " rH N

CO T XO

eo eo i> 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

lO CO """' r-l

TjH CO t- XIC

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

CD CO I- to 1C ^rH

to cotoco coic i-_ t-
coto<M-*l- I-H toooo ** co x

rH . ... . . . .

OS (M IM CO OTJI OS CO
CQ CO rH OS

1C CO ___S

OS CO O *< <-> -*
O CO OS 35 CO CO . -<fi 00
COO(N-*O5 * T-IOCO ^ I-

O CQ CQ CO |5 CO 05

to co ^_l_fi

1C CO * x,c

co co t- to co N co

1C COOSrH COt- 00
OOtolM^OO * CXJOOO ^2 CO t-
-H . . . . . . '~ l . .

OS (M (M CO 0-* ->< t-
!M CO rH (35
IM

* X-JO

^ (M X.2

OS CO 00 * i-H O

to co os os co co ^-<* ic
OO<M-*OS o to o o - 1 eo

i 1 -. CO

SIN 50 *2 05
CO ^ r-l d

t-^

CO S xS

eo eo os ic oo ^' to

to CO * 35 CO O ^O t-
O5to-*rt<T>l rH COOOO IM t-
rH ... . . . 00
OS N 55 CD 31 * OS
<M CO "^ 7

-5

* ^ o

os co <M ^so N to co

CO CO O CO CO CO .30 >
OOW-fr-i i-H COOCO rH to

1-1 o w co co |2 ^ os
to co r ^ i i yt

S <M x

eo eo os to 05 N oo
to co t- rH co o ^i co

OSlC-*-*?} ,-H toOOO rH CO

' ... . . . t-

OS (M eo 2 *> OS

co Hl___S

TK ^^

OS CO 00 -* CO Xu/5 (M
CO CO O 00 CO CO X 00 t>
OO5rt<rH * rHO5 -H CO
r^ * '"/-k^* CO
O ~ CO CO J * OS
to CO OJ

CO O ^-s
N O x2

eo eo oo to GO CD

to CO OO 00 CO W X CO to
OClC^^rH 1C i-HOGO Tj( 00
r-( . . . ^ . CO
OS (M CO CO 2 "- 1 05
<J* CO (M

GO t- xto
OS CO to 1C CO !>

CO CO IM OO CO * ^CO -H

ooo^Ttioo * rHot> to w .

rH -^ , o

O IM CO CO 2 *

to co TO

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

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 <M 0* CO 3 W

iM yi "co

OS Sto ^
O5 CO CO 1C O " 35
CO CO CO 00 CO to .CO 1C
OOCM-*O * rH t- to <?
rH __n . O
!M * CO .3 *

to co " co

CO CO * ?? ^
to CO t- CO IM x t^ 30
OtoCO^O rH -*OOO rj<lft-

<M n_u rH

OS (M CO CD 2I t- O
M CO "CO

O S ~ CX-e |t5 5ZJ ^ H ^ rH

C-. O

O 8 ~ QfX'S re *K << fH e -; rH

EATIO OF ELECTROMAGNETIC TO ELECTROSTATIC UNIT 275

In taking the mean, I have ignored the difference in the weights due
to the number of observations, as other errors are so much greater than
those due to estimating the swing of the needle incorrectly.

It will be seen that the series with one discharge is somewhat greater
than with a larger number. This may arise from the uncertainty of
the correction for the greater number of discharges, and I think it is
best to weight them inversely as this number. As the first series has,
also, nearly twice the number of any other, I have weighted them as
follows :

Wt. vxlO- 8

8 298-80

4 298-48

3 297-26

2 297-15

1 296-69

Mean 298-15

Or v = 29815000000 cm. per second.

It is impossible to estimate the weight of this determination. It is
slightly smaller than the velocity of light, but still so near to it that
the difference may well be due to errors of experiment. Indeed the
difference amounts to a little more than half of one per cent. It is seen
that there is a systematic falling off in the value of the ratio. This is
the reason of my delaying the publication for ten years.

Had the correction, A, for the number of discharges been omitted,
this difference would have vanished; but the correction seems perfectly
certain, and I see no cause for omitting it. Indeed I have failed to find
any sufficient cause for this peculiarity which may, after all, be acci-
dental.

As one of the most accurate determinations by the direct method and
made with very elaborate apparatus, I think, however, it may possess
some interest for the scientific world.

47
NOTES ON THE THEORY OF THE TRANSFORMER

[Johns Hopkins University Circulars, No. 99, pp. 104, 105, 1892; Philosophical
Magazine |51, XXXIV, 54-57, 1892 ; Electrical World, XX, 20, 1892]

As ordinarily treated the coefficient of self and mutual induction of
transformers is assumed to be a constant and many false conclusions
are thus drawn from it.

I propose to treat the theory in general, taking account of the hyster-
esis as well as the variation in the magnetic permeability of the iron. 1

The quantity p as used by Maxwell is the number of lines of magnetic
induction enclosed by the given conductor. This will be equal to the
number of turns of the wire into the electric current multiplied by the
magnetic permeability and a constant. But the magnetic permeability
is not a constant but a function of the magnetizing force, and hence we
must write

p Bny + C(nyY + D(ny} b + etc.

Where B, C, etc., are constants, n is the number of turns and y the
strength of current.

In this series only the odd powers of y can enter in order to express
the fact that reversal of the current produces a negative magnetization
equal in amount to the direct magnetization produced by a direct cur-
rent. This is only approximately true, however, and we shall presently
correct it by the introduction of hysteresis. It is, however, very nearly
true for a succession of electric waves.

To introduce hysteresis, first suppose the current to be alternating so
that y = c sin (bt -f- e) where t is the time and e the phase. The intro-
duction of a term A cos (U -\- e) into the value of the number of lines
of induction will then represent the effect very well. But the current
is not in general a simple sine curve and so we must write

y = a x sin (bt + e^ + a 2 sin (2bt + e 2 ) + a s sin (3bt + e 3 ) + .

1 The problem is treated by the method of magnetic circuit first applied by me to
iron bars in my paper on 'Magnetic Distribution' (Pliil. Mag., 1875), and afterwards
to the magnetic circuit of dynamos at the Electrical Conference at Philadelphia in
1884. I also used the same method in my paper on magnetic permeability in 1873.

NOTES ON THE THEORY OF THE TRANSFORMER 277

In this case it is much more difficult to express the hysteresis empir-
ically. In most cases the first term in the value of y is the largest. A
term of the same nature as before will, in this case, suffice to express
the hysteresis approximated. We can then write for the total flux of
magnetic induction

p = A cos (U + ei) + Buy + Cn 3 y* + Dtfy 5 + etc.

Problem 1. To find the electromotive force necessary to make the
electric current a sine curve in a transformer without secondary. Let
the resistance be E, and make y = c sin (bt). Then Maxwell's equation
becomes

Substituting the value of y we have

E= (RcAbn} sin (bt} + Bncb cos (bt} + 3 Cn 3 sin 2 (bt) cos bt + etc.
But

Sin *bt cos bt = \ (cos bt cos 3 U}
Sin *bt cos U = jig. (cos 5 bt 3 cos 3 U + 2 cos bt)
Si n 6 ^ cos bt = etc.

Hence the electromotive force that must be given to the circuit must
contain not only the given frequency of the current but also frequencies
of 3, 5, 7, etc., times as many. In other words, the odd harmonics.

Problem 2. Transformer without secondary, the electromotive force
being a sine curve.

E sin U = Ry + n .
ct t

First it is to be noted that when we place in this equation the general
value of y and make the coefficients of like functions of bt zero, all the
even harmonics will strike out.

Hence the value of the electric current will be

y = a 1 sin(W + i) + 3 sin (3 bt + e 3 )+a 6 sin (5bt + e t )+.
Substituting this value in the value for p, the equation is theoretically
sufficient to determine a v a z , etc., and e lf e 3) etc. The equations are
cubic or of higher order and the solution can only be approximate and I
have not thought it worth while to go further with the calculation.
However, it is easy to draw the following conclusion:

1. A simple harmonic current through an iron transformer will pro-
duce a secondary electromotive force and current, or both, which con-
tain not only the fundamental period but the higher odd harmonics.

278 HENRY A. HOWL AND

2. This effect is not due to hysteresis but to the variation in the mag-
netic permeability.

3. The harmonics increase with the increase in magnetization of the
iron and nearly vanish as the magnetization decreases, although it is
doubtful if they ever quite vanish. Hence, an increase of resistance
will decrease the harmonics.

4. In the method of introducing the hysteresis into the equations, it
enters as an addition to the resistance in the term Ra { -f- Anb, where
R is the resistance, a^ the maximum current, A the coefficient of hyster-
esis, which is dependent upon the amount of magnetization of the iron,

n the number of turns of wire, and b= is 2- divided by the time of

a complete period.

The introduction of the hysteresis into the ordinary equations, there-
fore, presents little or no difficulty.

Many observers have noted that the current curve in a transformer
was not a sine curve and Prof. Ayrton has shown the presence of the
odd harmonics but gives no explanation. Mr. Fleming has attributed
them to hysteresis, but I believe the present paper gives the first true
explanation.

Problem 3. To find the work of hysteresis. Let the .resistance, R,
be zero. The work done will then be the integral of the current times
the electromotive force, or

(1 P fit
dt a

the integral to be taken for one period of the current.

27T

f*** I d*u dii 1

w= I- bA sin (bt + e,} y + Bny / + (7n s 3 y 2 - 7 f- + \dt

I II \ ' if a J fjf -J fit

/ V |_ Ui J

w = A ~a\.
o

All the other terms are zero.

In a unit of time the energy absorbed is

Steinmetz has found by experiment that this varies as the 1-6 power
of the magnetic induction. Of course the present theory gives nothing
of this but only suggests a way of introducing the hysteresis into cal-
culations of this nature. For this purpose replace A by A 1 ^- 6 and the

NOTES ON THE THEOBY OF THE TRANSFORMER 279

work of hysteresis becomes -=- a which is thus the formula of Stein-

metz.

In the case where a secondary exists the number of turns of wire
being n 1 and the current y 1 , we have simply to replace ny in the above
formula by ny -}- n^y 1 and change the phase of the hysteresis term so
as to be 90 from the combined magnetizing force, ny -f- n^y 1 . The
equations of the currents will then be, by Maxwell's formula,

E=Ry + n

which suffice to determine both y and y 1 . The result is too complicated
to be attractive. The equations show, however, that the odd harmonics
must appear in either the electromotive forces or the primary or second-
ary currents, if not in all of them at once. The exact distribution is
only a case of complicated calculation.

It is to be specially noted that all formulae by which self induction is
balanced by a condenser will not be correct when applied to an iron
transformer but only to an air transformer. They will, however, apply
approximately to iron transformers in which the magnetization is small
and thus probably will apply better to transformers with an open
magnetic circuit than with a closed one.

Also an iron transformer should not be compared with an air trans-
former or two iron transformers with different magnetizations with
each other.

In conclusion I may add that the mathematical difficulties might be
overcome by another mode of attack but other work draws me in
another direction and I leave the matter to be worked up further by
others.

NOTES ON THE EFFECT OF HARMONICS ON THE TRANS-
MISSION OF POWER BY ALTERNATING CURRENTS

[Electrical World, XX, 368, 1892; La Lumiere Electrique, XL VII, 42-44, 1893]

In a recent number of The Johns Hopkins University Circular and
the Phil. Mag. for July, 1892, x I have shown that an iron transformer
introduces harmonics of the periods 3, 5, 7, etc./ times the fundamental
period into the currents and electromotive forces both primary and
secondary of a transformer and that these increased in value as the
iron was more and more magnetized.

It is my present object to call attention to the effect of these har-
monics on the transmission of power and its measurement. For light-
ing purposes they are evidently of very little significance, as currents
of all periods are equally efficient in producing heat. There is a loss,
however, in the fact that they cause more loss of heat in the wires and
the iron of the transformers. But for the transmission of power the
case is very different. Here the motors are designed to run at speeds
dependent on the period; if there is more than one period the adjust-
ment fails, and there is a loss. The harmonics are thus useless in the
transmission of power by synchronous motors, and are of very little use
in motors with revolving fields. In these cases the harmonics travel
around the circuits, heating the wires and the iron without producing
valuable work. They then represent an almost complete loss in the
transmission of power, and as they may contain 10, 20 or even 30 or 40
per cent of the current, according to the magnetization of the trans-
former, they are probably responsible for some loss of efficiency in many
cases, as will be shown further on.

Indeed, I believe they are the explanation of many seeming mysteries
in the working of alternating current motors.

Special arrangements of condensers and coils can be made to pick
out these harmonics so that they become more important than the

1 See also the Electrical World of July 9, 1892.

2 The periods 2, 4, 6, etc., can evidently be introduced by magnetizing the iron of
the transformer in one direction by a constant current, or having it originally with
an asymmetrical magnetic set.

EFFECT OF HARMONICS ON THE TRANSMISSION OF POWER 281

original period. This may occur accidentally and cause many curious
results in the working of motors.

It is, then, of the first importance in the transmission of power that
the curves shall be pure sine curves, and dynamos, 3 transformers and
motors must be designed in the future with reference to this point.
It would seem, also, that most calculations on the efficiency of power
transmission by alternating currents must be at fault unless they
include the action of the harmonics.

As to the amount of loss from this cause it is difficult to decide in
general. With synchronous motors the harmonics simply flow around
the wires without producing useful current of any kind. But this may
not cause great loss if the resistance is small. Indeed, considerable
distortion may represent small loss of power in certain cases and great
loss in others, according to the difference of phase of the current and
electromotive force in the harmonics.

In the case of motors with rotary fields the harmonics produce fields
revolving with velocities 3, 5, 7, etc., times the primary field. Now it
is essential for the efficiency of these motors that the armature shall
revolve nearly as fast as the field, and hence the efficiency for the
harmonics must be very small indeed, and this must decrease the effi-
ciency of the apparatus as a whole.

As to the heating of the wires by the harmonics, it is easy to see that
the total heating due to all the currents of different periods will simply
be the sum of the heatings due to each of the currents separately.

The effect of harmonics on the hysteresis is much more complicated
and can hardly be calculated without further experiment. However,
the following hypotheses may give some idea of the action. Let the
primary electromotive force be considered unity, and let a 3 , a 5 , etc., be
the electromotive forces of the harmonics. If these acted separately
on the hysteresis the total would be :

Again, if they all combined so that the maximum electromotive force
is equal to the sum of them all, the hysteresis will be nearly:

3 Dynamos and motors introduce the odd harmonics on account of the variations
of the self-induction of the machine, which becomes very apparent when a strong
current is flowing. The armature reactions may also introduce the harmonics.

282 HENRY A. EOWLAND

However, it is hardly probable that this last condition would be often
satisfied, in which case this formula would give too great a value.
When the harmonics are small this last formula can be written nearly

As an example, suppose a 3 =-3 and a 5 -2 and a 7 = 1, these two
formula give an increase of 10 and 24 per cent in the loss due to
hysteresis.

The current heating is only

l + a\ + a\ + etc. 4
Or, in the example,

1 + -09 + -04 + -01 == 1-14.

It would seem, then, that the losses due to hysteresis and current
heating may be much increased by the harmonics.

I believe the statement has been made that the form of the curve
does not influence the hysteresis. This is evidently incorrect, unless
we take the top of the curve to reckon from, in which case the statement
agrees with the second hypothesis given above if the harmonics are of
the proper phase.

To estimate the influence on the efficiency of a plant, assume the
efficiency of the dynamo and synchronous motor with primary currents
as each equal to 90 per cent, and of the two transformers equal to 93
per cent, and assume that all the currents have the same harmonics as
given above. The total efficiency will be 70 per cent. If the harmonics
are now added, the 30 per cent loss will become about 35 per cent, the
efficiency will be decreased to 65 per cent nearly, a loss of 5 per cent.
There is too much assumption about this calculation to warrant full
belief, and the figures are given more as a challenge to further investi-
gation than as facts. That there is a decrease of efficiency is certain,
but the amount must be determined by further experiment and mathe-
matical investigation. But, however small the loss, provided it occurs
in the transformers or the dynamos and motors, it may be of great
consequence on account of its heating effect, because the output of
these is limited by the amount of the heat generated.

The practical conclusion seems to be that transformers and the arma-
tures of dynamos to be used in the transmission of power must be
designed for low magnetizations. By experiment with transformers,

4 This formula assumes that the resistance is the same for the harmonics, whereas
it is greater on account of the ' skin ' effect.

EFFECT OF HARMONICS ox THE TRANSMISSION OF POWER 283

made by Dr. Duncan in this laboratory, immense distortion of the
curves has been found when the induction exceeds 12,000 lines per
square centimetre, while the curves are comparatively smooth with only
5000; hence I scarcely think it advisable to use more than 5000 for
transformers, even though low frequency were used. As to dynamos
and motors the limit will depend on the variety of machine used and
will not influence the better class very much.

The fixing of the limit of magnetization of transformers at 5000
causes the output with given current to vary inversely as the frequency.
As the hysteresis with slow frequency will be less, we may increase the
current somewhat to make up for it. As to the exact law, it depends
on the relative dimensions of wire and iron. Practically we might
estimate for an ordinary transformer that the output varied inversely
as the eight-tenth power of the frequency.

The law that the output varies inversely as the four-tenth power of
the frequency assumes that the magnetization increases with decrease
of frequency and thus distorts the curves as shown above.

The immense increase of the size and cost of transformers when dis-
tortion of the curve is avoided precludes the use of very low frequencies
even were it otherwise desirable.

It is to be noted that the action of the iron in producing harmonics
is directly on the electromotive force, and the amount of current flow-
ing will depend on the resistance and the self-induction of the circuit.
The resistance, owing to so-called ' skin ' effect, will be greater for the
harmonics than for the fundamental period. Self-induction depending
on the air will always diminish the harmonics, while if it is due to iron
it may either increase or decrease them according to their phase.

The measurement of the energy supplied by an alternating current is
also much complicated by the presence of harmonics.

Let the current be

C = A^ sin (bt + <i) + A s sin (3 U -f ?> 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 <p + A 3 B, cos O 3 - 8 ) + A, B, cos (cr 5 - <?' 5 ) + etc.]

284 HENRY A. EOWLAND

An ordinary wattmeter in the form of an electrodynamometer with
non-inductive coils would give the correct value of this quantity, but
any attempt to multiply the mean electromotive force by the current
and the cosine of the phase would lead to an incorrect result unless this
was done for each harmonic separately.

It is to be noted that the introduction of condensers to balance self-
induction will only work for one period at a time.

Indeed very many of the results hitherto obtained by observers and
theorists will require modification in the presence of these harmonics.

It would seem from the above that the transmission of a current for
electric lighting is quite a different thing from the transmission of a
suitable current for motors. It will be remembered that the transmis-
sion in the Frankfort-Lauffen experiment was one of a lighting current
alone and that some mystery seems to hang over the motor tests. Can
the presence of these harmonics have anything to do with this ?

[The Engineering Magazine, VIII, 589-596, January, 1895]

It is not uncommon for electricians to be asked whether modern
science has yet determined the nature of electricity, and we often find
difficulty in answering the question. When the latter comes from a
person of small knowledge which we know to be of a vague and general
nature, we naturally answer it in an equally vague and general manner;
but when it comes from a student of science anxious and able to bear
the truth, we can now answer with certainty that electricity no longer
exists. Electrical phenomena, electrostatic actions, electromagnetic
action, electrical waves, these still exist and require explanation; but
electricity, which, according to the old theory, is a viscous fluid throw-
ing out little amoeba-like arms that stick to neighboring light sub-
stances and, contracting, draw them to the electrified body, electricity
as a self-repellent fluid or as two kinds of fluid, positive and negative,
attracting each other and repelling themselves, this electricity no
longer exists. For the name electricity, as used up to the present time,
signifies at once that a substance is meant, and there is nothing more
certain to-day than that electricity is not a fluid.

This makes the task of one who attempts to explain modern elec-
trical theory a very difficult one, for the idea of electricity as a fluid
pervades the whole language of electrical science, and even the defini-
tions of electrical units as adopted by all scientists suggest a fluid theory.
No wonder, then, that some practical men have given up in despair
and finally concluded that the easiest way to understand a telegraph
line is to consider that the earth is a vast reservoir of electrical fluid,
which is pumped up to the line wire by the battery and finally descends
to its proper level at the distant end. Is not this the proper conclusion
to draw from that unfortunate term ' electric current ' ? Kemember-
ing this fact, that we cannot yet free ourselves from these old theories,
and exactly suit our words to our meaning, we shall now try to under-
stand the modern progress in electrical theory.

This whole progress is based upon something in the human mind
which warns us against the possibility of attraction at a distance

286 HENRY A. ROWLAND

through vacant space: Newton felt this impossibility in the case of
gravitation, but it is to Faraday that we must look principally for the
idea that electrical and magnetic actions must be carried on by means
of a medium filling all space and usually called the ether. The develop-
ment of this idea leads to the modern theory of electrical phenomena.

Take an ordinary steel magnet and, like Faraday, cover it with a
sheet of paper, and upon this sprinkle iron filings. Mapped before us
we see Faraday's lines of magnetic force extending from pole to pole.
We can calculate the form of these lines on the supposition that a
magnetic fluid is either distributed over the poles of the magnet or
on its molecules, assuming that attraction takes place through space
without an intervening medium. But at this idea the mind of Faraday
revolted, and he conceived that these lines, drawn for us by the iron
filings, actually exist in the ether surrounding the magnet; he even
conceived of them as having a tension along their length and a repul-
sion for one another perpendicular to their length.

Two magnets, then, near each other, become connected by these lines,
which, like little elastic bands always pulling along their length, strive
to bring the magnets together. These so-called lines of force (now
called tubes of force) were, by his theory, conducted better by iron and
worse by bismuth than by the ether of space, and so gave the explana-
tion of magnetic attraction and diamagnetic repulsion.

The same theory of lines of force was also applied by Faraday to
electrified bodies, and thus all electrostatic attractions were explained.
By this idea of lines of force it will be seen that Faraday did away
with all action at a distance and with all magnetic and electrical fluids,
and substituted, instead, a system in which the ether surrounding the
magnet or the electrified body became the all-important factor and the
magnet or electrified body became simply the place where the lines of
force ended: where a line of magnetic force ended, there was a portion
of imaginary magnetic fluid: where a line of electric force ended, there
was a portion of imaginary electric fluid. As the quantities of so-
called plus and minus electricity in any system are equal, we can
thus imagine every charged electrical system to be composed of a
group of tubes of electrical force (more strictly electric induction)
which unite the plus and minus electrified bodies, each unit tube having
one unit of plus electricity on one end and one unit of minus electricity
on the other. The tension along the tube explains the reason why
such an arrangement acts as if there were real plus and minus elec-
trical fluids on the ends of the tube, attracting one another at a dis-

MODERN THEORIES AS TO ELECTRICITY 287

tance. Consider a plus electrified sphere far away from other bodies.
The lines of force radiate from it in all directions, and, heing symmetri-
cal around the sphere, they pull it equally in all directions. Now
bring near it a minus electrified body, and the lines of force turn toward
it and become concentrated on the side of the sphere toward such a
body. Hence the lines pull more strongly in the direction of the
negative body, and the sphere tends to approach it.

In the case of a conducting body the lines of force always pass out-
wards perpendicularly to the surface, and hence, if we know the distri-
bution of the lines over the surface, or the so-called surface density of
the electricity, we can always tell in which direction the body tends to
move. It is not necessary to know whether there are any attracting
bodies near the conductor, but only the distribution of the lines. These
lines then do away with all necessity for considering action at a dis-
tance, for we only have to imagine a kind of ether in which lines of
force with given properties can exist, and we have the explanation of
electric attraction.

But the question now arises as to how the lines of electric force can
be produced in the ether, or, in other words, how bodies can be charged.

In the first place we know that equal quantities of plus and minus
electricity are always produced. As an illustration, suppose it is re-
quired to charge two balls with electricity. Pass a conducting wire
between them with a galvanic battery in its circuit. The galvanic
battery generates the lines of force ; these crowd together around it and
push each other sideways until their ends are pushed down the wire
and many of them are pushed out upon the balls.

When the tension backwards along the lines of force just balances
the forward push of the electromotive force of the battery, equilibrium
is established. If the wire is a good conductor, there may be electrical
oscillations before the lines come to rest in a given position, and this I
shall consider below.

The motion of the ends of the lines of force over and in the wire
constitutes what is called an electric current in the wire which is
accompanied by magnetic action around it and also by waves of electro-
magnetic disturbance which pass outward into space.

If, after equilibrium is established, we remove the wire, we have
simply two charged spheres connected by lines of electrostatic force
and thereby attracted to each other. If we replace the battery by a
dynamo or by an electric machine the effect is the same.

But there is another way by which bodies are often charged and

288 HENEY A. EOWLAND

that is by friction. In this case we can suppose the glass to take hold
of one end of the lines of force and the rubber the other end and it is
then only necessary to pull the bodies asunder to fill the space with
lines. The friction is merely needed to bring the two bodies into inti-
mate contact and remove them gently from each other.

The following considerations may guide us in understanding the
details of the process. It is well known from Faraday's researches
that a given quantity of electricity has a fixed relation to the chemical
equivalents of substances. Thus it requires 10,000 absolute electro-
magnetic units of electricity to deposit 114 grams of silver, 68 grams of
copper, 34 grams of zinc, etc.

Hence we can consider, for instance, in chloride of silver that the
atoms of silver are joined to the atoms of chlorine by lines of electro-
static force which hold them to each other. If, by rubbing the chloride
of silver, we could remove the chlorine on the rubber while leaving
the silver, we could stretch them asunder and so fill space with the lines
of electrostatic force. According to this theory, then, each atom has
a number of lines of force attached to it, and it is only by stretching
the atoms apart that we can fill an appreciable space with them and so
cause electrostatic action at a distance.

We come to the conclusion, then, that all electrification is originally
produced by separating the atoms of bodies from one another, which
can be done by breaking contact, by friction, or by direct chemical
action of one substance on another, or in some other manner not so
common. The lines of electrostatic force in a case of electricity at
rest must always begin and end on matter, and they can never have
their ends in space free from matter. The ends can be carried along
with the matter, constituting electric convection, or they can slide
through a metallic conductor or an electrolyte or rarefied gas, making
what we call an electric current; but, as they cannot end in a vacuum,
they cannot pass through it. Thus we conclude that a vacuum is a
perfect non-conductor of electricity.

The exact process by which the ends of the lines of force pass
through and along a conductor can at present be only dimly imagined,
and no existing theory can be considered as entirely satisfactory. In
the case of an electrolyte, however, we can form a fairly perfect picture
of what takes place as the decomposition goes on. Thus, in the case of
zinc and copper in hydrochloric acid, we can imagine the zinc plate
attracting the chlorine of the acid, thus stretching out the natural line
of electric force connecting the chlorine atom and the first hydrogen

MODERN THEORIES AS TO ELECTRICITY 289

atom; we can imagine the atoms of chlorine and hydrogen in the body
of the liquid recombining with each other and their lines of force unit-
ing until they form a complete line long enough to stretch from the
zinc to the copper plate; and all without once making a line of force
without its end upon matter. We can further imagine the ends of this
line sliding along the copper and zinc plates to the conducting wires
and down their length, thus making an electric current and carrying
the energy of chemical action to a great distance.

If the ends of the lines should slide along the wire without any
resistance, the wire would be a perfect conductor: but all substances
present some resistance, and in this case heat is generated. This we
always find where an electric current passes along a wire: as to the
exact nature of this resistance or the nature of metallic conduction in
general we know little, but I believe we are approaching the time when
we can at least imagine what happens in this most interesting case.

Besides the heating due to the electric current, steadily flowing, we
must now account for the magnetic lines of force surrounding the cur-
rent and the magnetic induction of one current on the other.

If the current is produced by the ends of the tubes of electrostatic
force moving along the wire, then we may imagine that the movement
of the lines of electrostatic force in space produces the lines of mag-
netic force in a direction at right angles to the motion and to the
direction of the lines of electrostatic force. At the same time we must
be careful not to assume too readily that one is the cause and the other
the effect : for we well know that a moving line of magnetic force (more
properly induction) produces, as Faraday and Maxwell have shown, an
electric force perpendicular to the magnetic line and to the direction of
motion. Neither line can move without being accompanied by the
other, and we can, for the moment, imagine either one as the cause of
the other. However, for steady currents, it is simpler to take the mov-
ing lines of electrostatic force as the cause and the magnetic lines as
the effect.

We have now to consider what happens when we have to deal with
variable currents rather than steady ones.

In this case we know from the calculations of the great Maxwell
and the demonstrations of Hertz that waves of electromagnetic disturb-
ance are given out. To produce these waves, however, very violent
disturbances are necessary. A fan waved gently in the air scarcely
produces the mildest sort of waves, while a bee, with comparatively
small wings moved quickly and vigorously, emits a loud sound.
19

290 HENKY A. KOWLAND

So, with electricity, we must have a very violent electrical vibration
before waves carrying much energy are given out.

Such a vibration we find when a spark passes from one conductor
to another. The electrical system may be small in size, but the im-
mensely rapid vibrations of millions of times per second, like the quick
vibration of a bee's wing, sends out a volume of waves that a slowly
moving current is not capable of producing. The velocity of these
waves is now known to be very nearly 300,000 kilometers per second.
This is exactly the velocity of waves of light, or other radiation in
general, and there is no doubt at present in the minds of physicists
that these waves of radiation are electromagnetic waves.

By this great discovery, which almost equals in importance that of
gravitation, Maxwell has connected the theories of electricity and of
light, and no theory of one can be complete without the other. Indeed
they must both rest upon the properties of the same medium which
fills all space the ether.

Not only must this ether account for all ordinary electrical and mag-
netic actions, and for light and other radiation, but it must also account
for the earth's magnetism and for gravitation.

To account for the earth's magnetism, we must suppose the ether
to have such properties that the rotation of ordinary matter in it pro-
duces magnetism. To account for gravitation it must have such prop-
erties that two masses of matter in it tend to move toward each other
with the known law of force, and without any loss of time in the action
of the force. We know that moving electrical or magnetic bodies re-
quire a time represented by the velocity of light before they can attract
each other in the line joining them. But, for gravitation, no time is
allowable for the propagation of the attraction.

But the problem is not so hopeless as it at fiist appears. Have we
not in two hundred and fifty years ascended from the idea of a viscous
fluid surrounding the electrified body and protruding arms outward to
draw in the light surrounding bodies to the grand idea of a universal
medium which shall account for electricity, magnetism, light, and
gravitation ?

The theory of electricity and magnetism reduces itself, then, to the
theory of the ether and its connection with ordinary matter, which we
imagine to be always immersed in it. The ether is the medium by
which alone one portion of matter can act upon another portion at a
distance through apparently vacant space.

Let us then attempt to see in greater detail what the ether must
exDlain in order that we may, if possible, imagine its nature.

MODERN THEORIES AS TO ELECTRICITY 291

1st. It must be able to explain electrostatic attraction. These
electrostatic forces are mostly rather feeble as we ordinarily see them.
Air breaks down and a spark passes when the tension on the ether
amounts to about j^-g- pound to the square inch. It is the air, how-
ever, that causes the break-down. Take the air entirely away, and we
then know no limit to this force. In a suitable liquid it may amount
to 500 times that in air or 5 pounds to 1 square inch, and become a
very strong force indeed. In* a perfect vacuum the limit is unknown,
but it cannot be less than in a liquid, and may thus possibly amount
to hundreds, if not thousands, of pounds to the square inch.

2d. It must explain magnetic action. These actions are apparently
stronger than electrostatic actions, but in reality they are not neces-
sarily so. A tension on the ether of only a few hundred pounds on
the square inch will account for all magnetic attraction that we know of,
although we are able to fix no limit to the force the ether will sustain.
No signs have ever been discovered of the ether breaking down.

Again, we must be able to account for the magnetic rotation of
polarized light as it passes through the magnetic field; and it can only
be accounted for by assuming a rotation around the lines of mag-
netic force. This action, however, takes place only while the lines
of magnetic force pass through matter, and it has never been observed
in the ether itself. The velocity of rotation, however, is immense, the
plane of polarization rotating in some cases 300,000,000 times per
second.

The ether must also account for the earth's magnetism. If we
assume that magnetic lines of force are simply vortex filaments in the
ether, we have only to suppose that the ether is carried around by the
rotation of the earth, and we have the explanation needed. The mag-
netism of the earth would then be simply a whirlpool in the ether.

3d. The ether must be able to transmit to a distance an immense
amount of energy either by means of electromagnetic waves as in light
or by the similar action which takes place in the ether surrounding a
wire carrying an electric current.

The amount of energy which can be transmitted by the ether in
this manner is enormous, far exceeding that which can be carried by
anything composed of ordinary matter. Thus take the case of sun-
light: on the earth's surface illuminated by strong sunlight a horse-
power of energy falls on every 7 square feet. At the surface of the
sun the etherial waves carry energy outward at the rate of nearly 8000
horse-power per square foot!

292 HENRY A. EOWLAND

Again, an electric wire as large as a knitting needle, surrounded
with a tube half an inch in diameter in which a perfect vacuum has
been made to prevent the escape of electricity, may convey to a dis-
tance a thousand horse-power, indeed even ten thousand or more horse-
power, there being apparently no limit to the amount the ether can
carry.

Compare this with the steam-engine, where only a few hundred
horse-power require an enormous and clumsy steam pipe. Or, again,
the amount carried by a steel shaft, which, at ordinary rate of speed,
would require to be about a foot in diameter to transmit 10,000 horse-
power.

When we compare the energy transmitted through a square foot of
ether in waves, as in the case of the sun, with the amount that can be
conveyed by means of sound waves in air or even sound waves in steel,
the comparison becomes simply ridiculous, the ether being so im-
mensely superior. As quick as light, the ether sends its wave energy
to the distance of a million miles while the sluggard air carries it one.
Thus, with equal strain on each, the ether carries away a million times
the energy that the air could do.

4th. The ether must account for gravitation. For this purpose we
are allowed no time whatever to transmit the attraction. As soon as
the position of two bodies is altered, just so soon must the line of action
from one to the other be in the straight line between them.

If this were not so, the motion of the planets around the sun would
be greatly altered. Toward the invention of such an ether, capable
of carrying on all these actions at once, the minds of many scientific
men are bent. Now and then we are able to give the ether such proper-
ties as to explain one or two of the phenomena, but we always come
into conflict with other phenomena that equally demand explanation.

There is one trouble about the ether which is rather difficult to
explain, and that is the fact that it does not seem to concentrate itself
about the heavenly bodies. As far as we are able to test the point,
light passes in a straight line through space even when near one of
the larger planets, unless the latter possesses an atmosphere. This
could hardly happen unless the ether was entirely incompressible or
else possessed no weight.

If the ether is the cause of gravitation, however, it is placed out-
side the category of ordinary matter, and it may thus have no weight
although still having inertia, a thing impossible for ordinary matter
where the weight is always exactly proportional to inertia.

MODEEN THEOKIES AS TO ELECTBICITY 293

Ether, then, is not matter, but something on which many of the
properties of matter depend.

It is curious to note that Newton conceived of a theory of gravita-
tion based on the ether, which he supposed to be more rare around
ordinary matter than in free space. But the above considerations
would cause the rejection of such a theory. We have absolutely no
adequate theory of gravitation as produced by ether.

To explain magnetism, physicists usually look to some rotation in
the ether. The magnetic rotation of the plane of polarization of light
together with the fact of the mere rotation of ordinary matter, as
exemplified by the earth's magnetism, both point to rotation in the
ether as the cause of magnetism. A smoke ring gives, to some extent,
the modern idea of a magnetic line of force. It is a vortex filament
in the ether.

Electrostatic action is more difficult to explain, and we have hardly
got further than the vague idea that it is due to some sort of elastic
yielding in the ether.

Light and radiation in general are explained when we understand
clearly magnetic and electrostatic actions as the two are linked together
with certainty by MaxwelFs theory.

Where is the genius who will give us an ether that will reconcile
all these phenomena with one another and show that they all come
from the properties of one simple fluid filling all space, the life-blood
of the universe the ether?

[American Journal of Science [4], IV, 429-448, 1897 ; Philosophical Magazine [5], XL V,

66-85, 1898]

The electrical quantities pertaining to an electric current which it
is usually necessary to measure, outside of current, electromotive force,
watts, etc., are resistances, self and mutual inductances and capacities.
I propose to treat of the measurement of alternating currents, electro-
motive force and watts in a separate paper. Eesistances are ordinarily
best dealt with by continuous currents, except liquid resistances. I
propose to treat in this paper, however, mainly of inductances, self and
mutual, and of capacities together with their ratios and values in abso-
lute measure as obtained by alternating currents. I also give a few
methods of resistance measurement more accurate than usually given
by means of telephones or electrodynamometers as usually used and
specially suitable for resistances of electrolytic liquids.

I have introduced many new and some old methods, depending upon
making the whole current through a given branch circuit equal to zero.
These always require two adjustments and they must often be made
simultaneously. However, some of them admit of the adjustments
being made independently of each other, and these, of course, are the
most convenient. But all these zero methods do not admit of any
great accuracy unless very heavy currents are passed through the
resistances. The reason of this is that an electrodynamometer cannot
be made nearly as sensitive for small currents as a magnetic galvano-
meter. The deflection of an electrodynamometer is as the square of
the current. To make it doubly sensitive requires double the number
of turns in both the coils. Hence we quickly reach a limit of sensitive-
ness. It is easy to measure an alternating current of -0001 ampere and
difficult for -00001 ampere. A telephone is more sensitive and an
instrument made by suspending a piece of soft iron at an angle of 45,
as invented by Lord Eayleigh, is also probably more sensitive.

For this reason I have introduced here many new methods, depend-
ing upon adjusting two currents to a phase-difference of 90 which I
believe to be a new principle. This I do by passing one current through

ELECTEICAL MEASUREMENT BY ALTERNATING CURRENTS 295

the fixed and the other through the suspended coil of an electrodynamo-
meter. By this means a heavy current can be passed through the fixed
coils and a minute current through the movable coil, thus multiplying
the sensitiveness possibly 1000 times over the zero current method.

I have also found that many of the methods become very simple if
we use mutual inductances made of wires twisted together and wound
into coils. In this way the self inductances of the coils are all practi-
cally equal and the mutual inductances of pairs of coils also equal.
Hence we have only to measure the minute difference of these two to
reduce the constants of the coil to one constant, and yet by proper
connections we can vary the inductances in many ratios. Three wires
is a good number to use. However, the electrostatic induction between
the wires must be carefully allowed for or corrected if much greater
accuracy than y^ is desired.

By these various methods the measurement of capacities and induc-
tances has been made as easy as the measurement of resistances, while
the accuracy has been vastly improved and many sources of error
suggested.

Relative results are more accurate than absolute as the period of an
alternating current is difficult to determine, and its wave form may
depart from a true sine curve.

Let self inductances, mutual inductances, capacities and resistances
be designated by L or I, M or ra, C or c, E or r with the same suffixes
when they apply to the same circuit, the mutual inductance having two
suffixes. Let & be 2 TT times the number of complete periods per second,

or & = 2-n. The quantities &L, bM or ^ are of the dimensions of

resistance and thus -^., &*LC or b*MC have no dimensions. I'LM, -^

or -fy have dimensions of the square of resistances.

Where we have a mutual inductance M 12 , we have also the two self
inductances of the coils L t and L 2 . When these coils are joined in the
two possible manners, the self inductance of the whole is

L, + Z 2 + ZM U or L! + L, - 2M n .

In case of a twisted wire coil the last is very small. Likewise
L 1 L 2 3/ 2 12 will be very small for a twisted wire coil, as is found by
multiplying the first two equations together.

If there are more coils we can write similar equations. For three
coils we have

296 HENRY A. KOWLAND

12 + 2M 1

2.
3.

Connecting them in pairs, we have the self inductances

L 1 + L 2 2M 12 L 1 + L 3 2M 13

There are many advantages in twisting the wires of the standard
inductance together, but it certainly increases the electrostatic action
between the coils. This latter source of error must be constantly in
mind, however, and, for great accuracy, calculated and corrected for.
But by proper choice of method we may sometimes eliminate it.

For the most accurate standards, I do not recommend the use of
twisted wire coils, at least without great caution. But for many pur-
poses it certainly is a great convenience, especially where only an
accuracy of one per cent is desired. In some calculations I have made,
I have obtained corrections of from one to one-tenth per cent from
this cause.

For twisted wires the above results reduce to 3L -f- 61f, 3L 2M .
Similar equations can be obtained for a larger number of wires. For
twisted wire coils, n wires joined abreast, the self induction is

-=1 , which is practically equal to L or M. The resistance

is E/n.

When we have n = p -\- m wires twisted and wound in a coil and we
connect them p direct and m reverse, the resistance and self induction
will be

nR*+FR[AC+CnAB] , If [n (A + B) 0~\ + VABC
(nR)*+(bC? 2

where R is the resistance of one coil and

A = L + (n
B=L - M

This gives self inductances and resistances equal or less than L and R.
The correction for electrostatic induction remains to be put in. For
the general case, the equation is very complicated for coils abreast,
with mutual inductances.

The number of mutual inductances to be obtained is M for two
wires, 0, M, 2M for three wires, 0, M, 2M, 3M for four wires, etc. From

297

these results we see that we are always able to reduce mutual to self
inductance. Measuring the self inductance of a coil connected in
different ways, we can always determine the mutual inductances in
terms of the self inductances.

Thus we need not search for methods of directly comparing mutual
inductances with each other, although I have given two of these, but
we can content ourselves with measuring self inductances and capaci-
ties. Fortunately most of the methods are specially adapted to the
latter, the ratio of self inductance to capacity being capable of great
exactness by many methods.

In the use of condensers I have met with great difficulty from the
presence of electric absorption. I have found that this can be repre-
sented by a resistance placed in the circuit of the condenser, which
resistance is a function of current period.

I have developed MaxwelPs theory of electric absorption in this
manner. Correcting his equations for a small error, I have developed
the resistance and capacity of a condenser as follows:

Let a condenser be made of strata of thicknesses a x a 2 , etc., and
specific induction capacities fc x Jc 2) etc., and resistances p^ p 2 , etc. Then
we have

where

etc.

Mr. Penniman has experimented in the Johns Hopkins University
laboratory with condensers by method 25 and found some interesting
results. With a mica standard condenser of microfarad he was not

298 HENEY A. KOWLAND

able to detect any electric absorption, although I have no doubt one
of the more accurate methods will show it.

With a condenser, probably of waxed paper, he found

Number of complete Capacity in Apparent resistance

periods per second. microfarads. in ohms.

14-0 4-64 139-6

32-0 4-96 34-1

53-3 4-96 20-5

131-1 4-94 5-2

The first value of the capacity seems to be in error, possibly one of
calculation. However, the result seems to show a nearly constant
capacity but a resistance increasing rapidly with decrease of period, as
Maxwell's formula show. The constant value of the capacity remains
to be explained.

Mr. Penniman will continue the investigation with other condensers,
liquid and solid, as well as plates in electrolytic liquids.

The results in the other measurements have been fairly satisfactory,
but many of the better methods have only been recently discovered and
are thus untried. But we must acknowledge at once that work of the
nature here described is most liable to error. Every alternating cur-
rent has, not only its fundamental period, but also its harmonics, so
that very accurate absolute values are almost impossible to be obtained
without great care. To eliminate them, I propose to use an arrange-
ment of two parallel circuits, one containing a condenser and the other
a self-inductance, each with very little resistance. The long period
waves will pass through the second side and the short ones through the
condenser side. By shunting off some of the current from the second
side, it will be more free from harmonics than the first one.

However, in a multipolar dynamo, especially one containing iron,
there is danger of long period waves also, which this method might
intensify. A second arrangement, using the condenser side, might
eliminate them. However, many dynamos without iron and without
too many poles and properly wound produce a very good curve without
harmonics, especially if the resistance in the circuit is replaced by a
self inductance having no iron. These remarks apply only to absolute
determinations. Eatios of inductance, self and mutual, and capacity
are independent of the period, and thus it can always be eliminated.
Measurements of resistances also are independent.

But there are other errors which one who has worked with continuous

ELECTRICAL MEASUREMENT BY ALTERNATING CURRENTS 299

currents may fall into. Nearly all alternating currents generate elec-
tromagnetic waves which are so strong that currents exist in every
closed circuit with any opening between conductors in the vicinity.

We eliminate this source of error by twisting wires together and other
expedients. But in avoiding one error, we plunge into another. For,
by twisting wires we introduce electrostatic capacity between them,
which may vitiate our results. Thus, in methods 23 or 24 for com-
paring mutual inductances, if there is electrostatic capacity between
the wires, a current will flow through the electrodynamometer in the
testing circuit and destroy the balance.

Various expedients suggest themselves to eliminate this trouble, as,
for instance, the variation of the resistance A in the above, but I shall
reserve them for a future paper. I may say, however, that it is some-
times possible, as in method 12 for instance, to choose a method in
which the error does not exist.

However, with the best of methods, much rests with the experimenter,
as errors from electromagnetic and electrostatic induction are added
to errors from defective insulation when we use alternating currents.

These errors are generally less than one per cent, however, and intel-
ligent and careful work reduces them to less than this.

The following methods generally refer by number to the plate on
which the resistances, etc., are generally marked. One large circle
with a small one inside represent an electrodynamometer. Of course
the circuit of the small coil can be interchanged with the large one.
Generally we make the smaller current go through the hanging coil.

By the methods 1 to 14, we adjust the electrodynamometer to zero
by making the phase difference in the two coils 90. For greatest
sensitiveness, the currents through the two coils must be the greatest
possible, heating being the limit. This current should be first calcu-
lated from the impedance of the circuit, as there is danger of making
it too great.

In the second series of methods, 15-26, the branch circuit in which
the current is to be is indicated by 0.

Resistances in the separate circuits are represented by R, R', R t , etc.,
and r, r', r t , etc. Corresponding self inductances and capacities in the
same circuits are L, L', L t , etc., and I, I', I,, etc., or C, C', C ',, etc., and
c, c', c t , etc. b = 27tn where n is the number of complete current waves
per second.

The currents must be as heavy as possible, ^ ampere or more, and it
is well to make those that require a current of more than j-^ ampere of

300 HENKY A. EOWLANB

larger wire freely suspended in oil. A larger current can, however, be
passed through an ordinary resistance box for a second or two without
danger. A few fixed coarse resistances of large wire in air or oil with
ordinary resistance boxes for fine adjustment, are generally all that
are required. Special boxes avoiding electrostatic induction are, how-
ever, the best, but are not now generally obtainable.

In some methods, such as 8, 9, 10, etc., we can eliminate undesirable
terms containing the current period by using a key which suddenly
changes the connections before the period has time to change much.

In using twisted wire mutual inductances, methods 7 and 12 are
about or entirely free from error due to electrostatic action between
the wires. In all the methods this error is less when the resistance of
the coils is least and in 23 and 24 when A is least. In method 8 the
error is very small when the coil resistances and R are small and r great.
In this method with 1 henry and 1 microfarad the error need not
exceed 1 in 1000. Probably the same remarks apply to 9, 10, 11, also.
By suitable adjustment of resistances in the other method, the error
may be reduced to a minimum. It can, of course, be calculated and
corrected for.

An electrodynamometer can be made to detect -OOC1 ampere without
making the self inductance of the suspended coil more than -0007
henrys or that of the stationary coils more than -0006 henrys, the
latter coil readily sustaining a current of -^ amperes without much
heating.

An error may creep in by methods 1-14 if the current through the
suspension is too great, thus heating it and possibly twisting it. This
should be tested by short circuiting the suspended coil or varying the
current. For the zero method it is eliminated by always adjusting
until there is no motion on reversing the current through one coil.

Inductances containing iron introduce harmonics and vary with cur-
rent strength. Thus they have no fixed value.

Closed circuits or masses of metal near a self inductance, dimmish
it, and increase the apparent resistance which effects vary with the
period. Short circuits in coils are thus detected.

Electrolytic cells act as capacities which, as well as the apparent
resistance, vary with the current period. They also introduce har-
monics. The same may be said of an electric arc.

An incandescent lamp or hot wire introduces harmonics into the
circuit.

Hysteresis in an iron inductance acts as an apparent resistance in

ELECTKICAL MEASUREMENT BY ALTERNATING CURRENTS 301

the wire almost independent of the current period, and does not, of
itself, introduce harmonics. The harmonics are due to the variation
of the magnetic permeability with the amount of magnetization.

Electric absorption in a condenser acts as a resistance varying with
the square of the period, the capacity also varying, as I have shown
above.

In general any circuit containing resistances, inductances and capaci-
ties combined acts as a resistance and inductance or capacity, both of
which vary with the current period, the square of the current period
alone entering. For symmetry the square of the current period can
alone enter in all these cases and those above.

Hence only inductances containing no iron or not near any closed
metallic circuits have a fixed value. The same may be said of con-
densers, as they must be free from electric absorption or electrolytic
action to have constants independent of the period. There is no ap-
parent hysteresis in condensers and the constants do not apparently
vary with the electrostatic force.

The following numbers indicate both the number of the method and
the figures in the plate, p. 302.

Method 1.

L' _ [r (R. + R'
~c

Method 2.

-R.R"} \_R, (r+R"} + R u (r + fl,)]

Method 3.
In (1) make R' = R" = R, t = Q or in (2) make R" = R t = 0, R,, = <x> ,

^ = rR

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}

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

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 '-"

+ 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

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

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

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,

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

method if it is sensitive enough, as the value of -jj, should be accurately

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

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

R"R-R'R

R (R"

_
r(R' + R"}

FIG. 3.

R, \
R' b / n

,_ Kn a

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 <f> = 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 -

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 y/ r R'

Resis. of
R' circuit
in ohms.

Resistance
due to
absorption.

422-

6 488-6 5457-3 347

39-29

5-30

1488-

6 488-2

123

40-50

6-73

984-

40-72

6-91

2671-

41-116

7-30

423-

357

41-237

7-42

5474-

464

41-42

7-61

6734-

374

41-67

7-86

1 ohm in R"=f

scale divisi

7486-

638

41-64

7-83

9466-

41-85

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.

R//

348-5

488-6

396-3

11020-7

55-61

7488-

849-2

55-41

844-1

4026-

55-07

3485-

396-1

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 C<f iu etc. be the currents, A' and A" reversing commutators,
R", R and r the resistance of the different circuits, L" and L the self-
inductances, If the mutual inductance of the coils B\ and B 2 by which
it is placed. When a periodic electromotive force a m is applied to
A, B the quantity to be found is C^ C 8 cos ($ 3 0J where <p, fa
is the difference of phase.

326 HENRY A. KOWLAND

The current in the R" circuit is then

C ci (bt + < J^/
^ r - T>H

+ 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

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

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

. 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

2-5983

310

2311

1158

1159-0

1-3099

1161

103

1659

1661-2

1-8727

109

1664

1800

1802-6

2-0288

1806

887-15 149

4776

4786-5

5-3956

196

4818

Current increased about 2 times.

A + C 901

902

141

4787

4781

5-3898

184

4807

887

05 211

5936

5958

6-7170

264

5982

6575

6602

7-4430

104

6631

887

45 158

4778

4795

5-4036

192

4813

183

1146

1-9922

186

1148

643

642

7242

643

502

5658

503

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.

f-62 499-69

638-85

4750-48

1150-94

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

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.

Correc.

Queen.

R+r.

rec. age.

A'.

Ratio.

902-

-14-55 887-

90 + s

503

-62 502

5664

u u

90+s

503

133

u it

88 + s

522

it u

88 + 8

502

501

5653

P Q

902 55

888

17 + s

644

u u

18 + s

644

" 643

7251

133

11 u

17+s

643

u 11

17 + s

643

" 642

7234

902-4

" 887-

28 + s

1159

it ti

28 + s

1159

1158-

1-3050

133

it u

24 + 8

1157

it it

26 + s

1158

" 1157

1-3034

C + PI

902-

' 887

105 + s

1658

I 11

110 + s

1664

1660

1-8713

133

1 If

101+8

1656

t II

106 + s

1660

" 1657

1 8683

C + P a

902-5

' 887-

10 + 8

1803

u u

12+8

1805

" 1803

2-0261

133

ti i<

8+8

1800

It 11

8 + 8

1800

" 1799

2-0221

PI + PS

902-4

" 887-

60 + s

2306

2307

2-5995

+ c

u u

2310

133

11 11

56 + s

2304

2-5951

tt u

57 + s

2305

902-43

" 887-

85 + s

4703

II 11

106 + s

4724

" 4712

5-3080

133

902-4

" 887-

82 + 8

4704

11 It

85 + s

4707

ii 4704

5-2991

A + C

902-35

887-

1146+s

9149

u u

1227 + 8

9233

" 9190

10-3515

133

902-4

887-

1170 + s

9171

u u

1194 + s

9191

9181

10-3395

A + C

902 35

" 887-

111+s

2550

+ 2M

it it

146 + 8

2556

2553

2-8716

133

u u

38+s

2548

u it

38 + s

2548

" 2548

2-8701

A + C

902 6

888-05

123

5852

ii if

169

5898

" 5880

6-6225

133

u u

134

5863

u u

140

5869

" 5865

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+<M . The resistance by R", /, R and r. The capacity by C.
The self -inductance by L. A' and A" are reversing commutators and
F the terminals of the fixed coils and H the terminals of the hanging
coil of the electrodynamometer.

334

HENEY A. EOWLAND

If now a periodic electromotive force is applied to the terminals A
and B the equations connecting the different currents are as below,
from which equations the quantity C^C Z cos (fa < 3 ) is to be found,
which is proportional to the deflection. From the figure

"+ -i-V
ibc /

FIG. 8.

In the same way it is found that
0* = i

FIG. 9.

Therefore the real part is

& cos (t, - 0.) = 01

ibc

/ rr'

ELECTRICAL MEASUREMENTS

335

where D is the deflection. When D is equal to zero

\-r'} A = o

In the experiments by this method the microfarad Elliott condenser
was used, and it was compared with the different coils P 1} P z , A, and C.
The connections were made with open leads and open resistances were
used as far as possible, but it was necessary to use resistance boxes for
the last adjustments. The connections having been made as in figure,
the process of experimenting was to keep r and / constant and to
adjust R" and R until there was no deflection of the hanging coil. The
resistance of the circuits R" -\- r' and R -\- r were then measured on a
Wheatstone bridge. The commutator A' was reversed and the process
was repeated. The condenser had absorption (see p. 323) which caused
the resistance R" -f- r' to be increased by 7-11 ohms. When the capac-
ity is calculated, taking into account the absorption, it is called the
corrected capacity, as in the other tables of the paper.

COLLECTED RESULTS.

n=133.

Results found by taking sum

and diff . of separate

measurements.

5648 (C + Y l )C=P l

5730 (C + PI + P a ) (C + P a )=P,

7187 (C + P a ) C=P 2

7269 (C + P. + P,) (C + P,) = P,

3029 (C + P,) P, = C

2990 (C + P S ) P 4 =C

3065 (C + P, + P a ) P, P 2 =C

3022 (A + C) C=A

2917 (C + P, + P 2 ) C=P, + P a

2888 P, + P a

8677 C + P,

8718 (C + Pj + P.,) P a =C + P 1

0298 (C + P, + P a ) P,=C + P a

5920 P! + P a + C

6025 A + C=A + C

In method 12 corrections due to the hanging coil and fixed coils were
calculated so that the ratio of the resistances would give the ratio of the
self-inductances direct. In this method (6) since the capacity was in
circuit with the hanging coil, the self-inductance was so small that it
was neglected. The self-inductance of the coils P, etc., which were
joined in circuit with the fixed coils, were increased by the self-induc-
tance of the fixed coils, that is by -0164 henry.

Coils.

n=40.
Results found
by direct
measurement,

Results found Results found
by taking by direct
sum diff., etc., meas. of coils
of separate and combination
meas. of coils.

5664

5663
5734

5653

P 2

7251

7211

7282

7233

9 1

1-3050

1-3049

1-3034

1-3010

1-3070

5-3080

5-3175

5-2991

5-:

P +P

1-2945

1-2915

C + P,
ii

1-8713

1-8714
1-8744

1-8683

1-
1-

C + P a

+ PI + PJ

2-0261
2-5995

2-0331
2-5965

2-0221
2-5951

2-
2-

A + C

6-6225

6-6130

6-6054

336

HENEY A. ROWLAND

The table below gives the various results.

N. Coil.

Queen in Position
current with of
R"+r. H"+r. R+r. Product. A'. L.

40 P

(1 U

2008-
2005-

205-
200-

1095-7 2198522- 1

7251
0164

3373

7415

33 "

<i U

2024-5
2025-5

221-
222-

" 2218792- 1
" 2

7223
0164

3330

Cor.
C.

3323

40 A 12741-5

133

12720-
" 12716-

3430-8
3425-8

3448-8
3447-0

1578-5
1578-4

30-
30-

236-
220-

98-
93-

1241-85 15922394-

15775610-

1140-8

106 + s 1140-8
105 + s

57 +s 1088-9

58 + s '<

3911004-

3933354-

1718719-7

7397

5-3080
0164

5-3244

5-2991
0164

5-3155

1 3050
0164

1-3214

1-3034
0164

1-3198

5653
0164

5817

3344

3368

3379

3355

3384

3363

3346

This method can be used with great accuracy for the comparison of
the capacity of a condenser with a standard condenser. In the com-
parison, first one condenser and then the other would be placed in the
R -f- r circuit. If the two condensers are of nearly the same capacity,
the degree of accuracy of the comparison depends upon the accuracy
with which R" -f- r' can be set. The degree of accuracy of setting
R" -f- r' varies with the value of the self -inductance with which the
condensers are compared. In the experiments just given, using the
different coils, the degree of accuracy with which two ^ microfarad con-
densers could have been compared would vary from 1 part in 2000 to
one part in 14000. The two condensers are supposed to be without
absorption, as its presence would cause trouble unless the absorption
resistances were known.

ELECTFJCAL MEASUREMENTS 337

Resume. Summing up the results deduced in this paper, it is seen
that the methods for the absolute determination of self-inductance
and capacity do not give as concordant results as could be wished. The
irregularity of results was caused, in the most part, both in the deter-
mination of self -inductance and capacity by the variation of the periods
of the currents used in the experiments. As the period enters directly
into the determination of self-inductance and capacity, all variations
of the period will appear in the results. The determination of capacity
is complicated by the presence of electric absorption (p. 323 et seq.).
The effect of electric absorption is shown to be that of an added resist-
ance in series with the condenser, called absorption resistance. A
direct method is given by which absorption resistance can be measured
(p. 319), and experiments are given which show that when condensers
possessing absorption are in series or in parallel, their absorption re-
sistances act under these conditions as ohmic resistances in series with
the separate condensers (p. 323). Absorption resistance is also found
to be extremely sensitive to temperature.

The methods for the comparison of two self-inductances or a self-
inductance and a capacity are independent of the period, and when the
self-inductances are of different magnitudes the comparison can be
made with an accuracy of 1 part in 10000. These methods, therefore,
give a means of comparison of a self-inductance with a standard self-
inductance, or a capacity with a standard capacity to an accuracy of 1
part in 10000, or they allow the establishment of standards.

EESISTANCB TO ETHEEEAL MOTION

Br H. A. ROWLAND, N. E. GILBERT AND P. C. MCJUNCKIN
[Johns Hopkins University Circiilars, No. 146, p. 60, 1900]

An attempt has been made to determine within what limits it is
possible to say that there is no frictional or viscous resistance in the
ether of space. Modern theories of magnetism are based on some kind
of rotary or vortical motion in the ether and if a piece of iron is mag-
netized we imagine that the molecules, or something about them, rotate
also. The existence of permanent magnets shows that any retardation
due to any kind of resistance must be very slight.

In the case of an electro-magnet, any energy used in overcoming such
resistance, if it exists, must be derived from the exciting current and
the disappearance of such energy will produce an apparent resistance
added to that of the wire. An attempt was therefore made to deter-
mine whether a wire carrying a current had the same electrical resist-
ance when producing a magnetic field that it had when not producing it.

The experiment consisted in winding two coils of wire together on
an iron core and determining whether the resistance was the same in
two cases :

(1). When the current was so passed through the coils that both
produced a field in the same direction.

(2). When the current was so passed that the fields produced counter-
balanced each other.

The great difficulty in the experiment lay in the necessity of measur-
ing the resistance of a coil in which a comparatively large current was
flowing. In order to overcome the effect of changes in resistance due
to changes in temperature, two coils were wound, as nearly as possible
identical, and these double coils were used for the four arms of a
Wheatstone's bridge so that the temperature would rise in all four arms
equally. Each coil consisted of about 2500 turns of doubled No. 30
copper wire, the whole enclosed in an iron case, boiled in wax for five
hours and cooled in a vacuum. The insulation resistance was then
about eleven megohms. Iron cores were used and it was found that
the cases effectually protected the coils against sudden changes in tern-

339

perature due to air currents as well as serving for yokes to the magnets.
A current of one-tenth ampere was used which insured a high state
of magnetization in the iron when two coils were in series, giving 5000
turns.

The coils were connected in the bridge in such a way that the two
coils in one case formed the opposite arms of the bridge. By means
of a reversing switch the current in one of these coils could be reversed.
This changed the field which might affect two opposite arms of the
bridge and thus doubled the deflection. Another switch might have
been inserted in the other pair of arms and thus doubled the deflection
again but errors due to the switches would also have been doubled and
no advantage gained. The switch was carefully constructed with large
copper rods dipping into copper mercury cups but, at best, the inac-
curacies of the switch limited the accuracy of the experiment.

The fine adjustments were made by resistance boxes shunted round
one of the coils. About 15,000 ohms in this shunt balanced the bridge.
A change of one ohm in the shunt gave a deflection of two millimeters
and indicated a change in the resistance of the arm of yinnnnr ohm. The
whole resistance being over 100 ohms this would give a determination
of one part in 2,000,000 or, since the deflection is doubled, one part in
4,000,000 for each arm. The result of 30 readings each way was that
the shunt resistance was about 3-4 ohms less with magnetic field than
without. The shunt was so placed that this gives a less resistance by
one part in 1,200,000 when producing a magnetic field.

The above result is in the wrong direction. The difficulty may lie in
the fact that the galvanometer, though used at night, was unsteady at
best, or it may be due to leakage. The resistance of the coils was 100
ohms while the insulation resistance was 11,000,000 ohms. If the leak-
age is symmetrical along the doubled wire it will not affect the galvano-
meter upon reversing the current in one coil. This assumption may
not be justified.

PART III

HEAT

ON THE MECHANICAL EQUIVALENT OF HEAT, WITH SUB-
SIDIAEY RESEAKCHES ON THE VARIATION OF THE
MERCURIAL FROM THE AIR THERMOMETER, AND ON
THE VARIATION OF THE SPECIFIC HEAT OF WATER l

[Proceedings of the American Academy of Arts and Sciences, XV, 75-200, 1880]

INVESTIGATIONS ON LIGHT AND HEAT, made and published wholly or in part with
appropriation from the RUMFOBD FUND

Presented June llth, 1879

CONTENTS

I. Introductory remarks .... 343

II. Thermometry 345

(a.) General view of Thermom-
etry 345

(&.) The Mercurial Thermometer 346
(c.) Relation of the Mercurial

and Air Thermometers 352

1. General and Historical

Remarks .... 352

2. Description of Appa-

ratus 358

3. Results of Comparison 366
(d.) Reduction to the Absolute

Scale 381

Appendix to Thermometry . 384

III. Calorimetry 387

(a.) Specific Heat of Water . 387
(6.) Heat Capacity of the Calo-
rimeter 399

IV. Determination of Equivalent . 404

(a.) Historical Remarks . . . 404

1. General Review of

Methods 405

2. Results of Best Deter-

minations .... 409
(&.) Description of Apparatus 422

1. Preliminary Remarks . 422

2. General Description . 424

3. Details 426

1. Estimation of Work

Done 430

2. Radiation 435

3. Corrections to Ther-

mometers, etc. . . 439
(d.) Results 441

1. Constant Data . . . 441

2. Experimental Data and

Tables of Results . 441
Concluding Remarks and Criti-
cism of Results and Methods 465

I. INTRODUCTOKY REMARKS

Among the more important constants of nature, the ratio of the
heat unit to the unit of mechanical work stands forth prominent, and

1 This research was originally to have been performed in connection with Professor
Pickering, but the plan was frustrated by the great distance between our residences.
An appropriation for this experiment was made by the American Academy of Arts
and Sciences at Boston, from the fund which was instituted by Count Rumford, and
liberal aid was also given by the Trustees of the Johns Hopkins University, who are
desirous, as far as they can, to promote original scientific investigations.

344 HENEY A. KOWLAND

is used almost daily by the physicist. Yet, when we come to consider
the history of the subject carefully, we find that the only experimenter
who has made the determination with anything like the accuracy
demanded by modern science, and by a method capable of giving good
results, is Joule, whose determination of thirty years ago, confirmed
by some recent results, to-day stands almost, if not quite, alone among
accurate results on the subject.

But Joule experimented on water of one temperature only, and did
not reduce his results to the air thermometer; so that we are still left
in doubt, even to the extent of one per cent, as to the value of the
equivalent on the air thermometer.

The reduction of the mercurial to the air thermometer, and thence
to the absolute scale, has generally been neglected between and 100
by most physicists, though it is known that they differ several tenths
of a degree at the 45 point. In calorimetric researches this may pro-
duce an error of over one, and even approaching two per cent, especially
when a Geissler thermometer is used, which is the worst in this respect
of any that I have experimented on; and small intervals on the mer-
curial thermometers differ among themselves more than one per cent
from the difference of the glass used in them.

Again, as water is necessarily the liquid used in calorimeters, its
variation of specific heat with the temperature is a very important
factor in the determination of the equivalent. Strange as it may
appear, we may be said to know almost nothing about the variation
of the specific heat of water with the temperature between and
100 C.

Regnault experimented only above 100 C. The experiments of
Hirn, and of Jamin and Amaury, are absurd, from the amount of varia-
tion which they give. Pfaundler and Platter confined themselves to
points between and 13. Miinchausen seems to have made the best
experiments, but they must be rejected because he did not reduce to
the air thermometer.

In the present series of researches, I have sought, first, a method
of measuring temperatures on the perfect gas thermometer with an
accuracy scarcely hitherto attempted, and to this end have made an
extended study of the deviation of ordinary thermometers from the
air thermometer; and, secondly, I have sought a method of determin-
ing the mechanical equivalent of heat so accurate, and of so extended
a range, that the variation of the specific heat of water should follow
from the experiments alone.

ON THE MECHANICAL EQUIVALENT OF HEAT 345

As to whether or not these have been accomplished, the following
pages will show. The curious result that the specific heat of water
on the air thermometer decreases from to about 30 or 35, after
which it increases, seems to be an entirely unique fact in nature, seeing
that there is apparently no other substance hitherto experimented upon
whose specific heat decreases on rise of temperature without change of
state. From a thermodynamic point of view, however, it is of the
same nature as the decrease of specific heat which takes place after
the vaporization of a liquid.

The close agreement of my result at 15 -7 C. with the old result of
Joule, after approximately reducing his to the air thermometer and
latitude of Baltimore, and correcting the specific heat of copper, is
very satisfactory to us both, as the difference is not greater than 1 in
400, and is probably less.

I hope at some future time to make a comparison with Joule's ther-
mometers, when the difference can be accurately stated.

II. THERMOMETKY
(a.) General View

The science of thermometry, as ordinarily studied, is based upon
the changes produced in bodies by heat. Among these we may mention
change in volume, pressure, state of aggregation, dissociation, amount
and color of light reflected, transmitted, or emitted, hardness, pyro-elec-
tric and thermo-electric properties, electric conductivity or specific in-
duction capacity, magnetic properties, thermo-dynamic properties, &c.;
and on each of these may be based a system of thermometry, each one
of which is perfect in itself, but which differs from all the others widely.
Indeed, each method may be applied to nearly all the bodies in nature,
and hundreds or thousands of thermometric scales may be produced,
which may be made to agree at two fixed points, such as the freezing
and boiling points of water, but which will in general differ at nearly,
if not all, other points.

But from the way in which the science has advanced, it has come
to pass that all methods of thermometry in general use to the present
time have been reduced to two or three, based respectively on the
apparent expansion of mercury in glass and on the absolute expansion of
some gas, and more lately on the second law of thermodynamics.

Each of these systems is perfectly correct in itself, and we have no
right to designate either of them as incorrect. We must decide a priori

346 HEJOIY A. EOWLAND

on some system, and then express all our results in that system: the
accuracy of science demands that there should be no ambiguity on that
subject. In deciding among the three systems, we should be guided
by the following rules :

1st. The system should be perfectly definite, so that the same tem-
perature should be indicated, whatever the thermometer.

2d. The system should lead to the most simple laws in nature.

Sir William Thomson's absolute system of thermometry, coinciding
with that based on the expansion of a perfect gas, satisfies these most
nearly. The mercurial thermometer is not definite unless the kind of
glass is given, and even then it may vary according to the way the bulb
is blown. The gas thermometer, unless the kind of gas is given, is not
definite. And, further, if the temperature as given by either of these
thermometers was introduced into the equations of thermo-dynamics,
the simplest of them would immediately become complicated.

Throughout a small range of temperature, these systems agree more
or less completely, and it is the habit even with many eminent physi-
cists to regard them as coincident between the freezing and boiling
points of water. We shall see, however, that the difference between
them is of the highest importance in thermometry, especially where
differences of temperature are to be used.

For these reasons I have reduced all my measures to the absolute
system.

The relation between the absolute system and the system based on
the expansion of gases has been determined by Joule and Thomson
in their experiments on the flow of gases through porous plugs (Philo-
sophical Transactions for 1862, p. 579). Air was one of the most
important substances they experimented upon.

To measure temperature on the absolute scale, we have thus only to
determine the temperature on the air thermometer, and then reduce
to the absolute scale. But as the air thermometer is very inconvenient
to use, it is generally more convenient to use a mercurial thermometer
which has been compared with the air thermometer. Also, for small
changes of temperature the air thermometer is not sufficiently sensi-
tive, and a mercurial thermometer is necessary for interpolation. I shall
occupy myself first with a careful study of the mercurial thermometer.

(6.) The Mercurial Thermometer

Of the two kinds of mercurial thermometers, the weight thermometer
is of little importance to our subject. I shall therefore confine myself

ON THE MECHANICAL EQUIVALENT OF HEAT 347

principally to that form having a graduated stem. For convenience
in use and in calibration, the principal bulb should be elongated, and
another small bulb should be blown at the top. This latter is also of
the utmost importance to the accuracy of the instrument, and is placed
there by nearly all makers of standards. 2 It is used to place some of
the mercury in while calibrating, as well as when a high temperature
is to be measured; also, the mercury in the larger bulb can be made
free from air-bubbles by its means.

Most standard thermometers are graduated to degrees; but Regnault
preferred to have his thermometers graduated to parts of equal capacity
whose value was arbitrary, and others have used a single millimeter
division. As thermometers change with age, the last two methods are
the best; and of the two I prefer the latter where the highest accuracy
is desired, seeing that it leaves less to the maker and more to the
scientist. The cross-section of the tube changes continuously from
point to point, and therefore the distribution of marks on the tube
should be continuous, which would involve a change of the dividing
engine for each division. But as the maker divides his tube, he only
changes the length of his divisions every now and then, so as to average
his errors. This gives a sufficiently exact graduation for large ranges
of temperature; but for small, great errors may be introduced. Where
there is an arbitrary scale of millimeters, I believe it is possible to
calibrate the tube so that the errors shall be less than can be seen with
the naked eye, and that the table found shall represent very exactly
the gradual variation of the tube.

In the calibration of my thermometers with the millimetric scale, I
have used several methods, all of which are based upon some graphical
method. The first, which gives all the irregularities of the tube with
great exactness, is as follows:

A portion of the mercury having been put in the upper bulb, so as
to leave the tube free, a column about 15 mm. long is separated off.
This is moved from point to point of the tube, and its length carefully
measured on the dividing engine. It is not generally necessary to
move the column its own length every time, but it may be moved
20 mm. or 25 mm., a record of the position of its centre being kept.
To eliminate any errors of division or of the dividing engine, readings
were then taken on the scale, and the lengths reduced to their value
in scale divisions. The area of the tube at every point is inversely as

*Geissler and Casella omit it, which should condemn their thermometers.

348 HENEY A. EOWLAND

the length of the column. We shall thus have a series of figures nearly
equal to each other, if the tube is good. By subtracting the smallest
from each of the others, and plotting the results as ordinates, with the
thermometer scale as abscissas, and drawing a curve through the points
so found, we have means of finding the area at any point. The curve
should not be drawn exactly through the points, but rather around
them, seeing they are the average areas for some distance each side of
the point. With good judgment, the curve can be drawn with great
accuracy. I then draw ordinates every 10 mm., and estimate the aver-
age area of the tube for that distance, which I set down in a table.
As the lengths are uniform, the volume of the tube to any point is
found by adding up the areas to that point.

But it would be unwise to trust such a method for very long tubes,
seeing the mercury column is so short, and the columns are not end to
end. Hence I use it only as supplementary to one where the column
is about 50 mm. long, and is always moved its own length. This estab-
lishes the volumes to a series of points about 50 mm. apart, and the
other table is only used to interpolate in this one. There seems to be
no practical object in using columns longer than this.

Having finally constructed the arbitrary table of volumes, I then
test it by reading with the eye the length of a long mercury column.
No certain error was thus found at any point of any of the thermom-
eters which I have used in these experiments.

While measuring the column, great care must be taken to preserve
all parts of the tube at a uniform temperature, and only the extreme
ends must be touched with the hands', which should be covered with
cloth.

If V is the volume on this arbitrary scale, the temperature on the
mercurial thermometer is found from the formula T = C V t , where
C and t are constants to be determined. If the thermometer contains
the and 100 points, we have simply

r _ 100
T~^T" *

'100 '0

Otherwise C is found by comparison with some other thermometer,
which must be of the same kind of glass.

It is to be carefully noted that the temperature on the mercurial
thermometer, as I have defined it, is proportional to the apparent ex-
pansion of mercury as measured on the stem. By defining it as pro-
portional to the true volume of mercury in the stem, we have to intro-
duce a correction to ordinary thermometers, as Poggendorff has shown.

Ox THE MECHANICAL EQUIVALENT OF HEAT 349

As I only use the mercurial thermometer to compare with the air
thermometer, and as either definition is equally correct, I will not
further discuss the matter, but will use the first definition, as being
the simplest.

In the above formula I have implicitly assumed that the apparent
expansion is only a function of the temperature; but in solid bodies
like glass there seems to be a progressive change in the volume as time
advances, and especially after it has been heated. And hence in mer-
curial and alcohol thermometers, and probably in general in all ther-
mometers which depend more or less on the expansion of solid bodies,
we find that the reading of the thermometer depends, not only on its
present temperature, but also on that to which it has been subjected
within a short time; so that, on heating a thermometer up to a certain
temperature, it does not stand at the same point as if it had been cooled
from a higher temperature to the given temperature. As these effects
are without doubt due to the glass envelope, we might greatly diminish
them by using thermometers filled with liquids which expand more
than mercury : there are many of these which expand six or eight times
as much, and so the irregularity might be diminished in this ratio. But
in this case we should find that the correction for that part of the
stem which was outside the vessel whose temperature we were deter-
mining would be increased in the same proportion; and besides, as all
the liquids are quite volatile, or at least wet the glass, there would be
an irregularity introduced on that account. A thermometer with liquid
in the bulb and mercury in the stem would obviate these inconven-
iences ; but even in this case the stem would have to be calibrated before
the thermometer was made. By a comparison with the air-thermom-
eter, a proper formula could be obtained for finding the temperature.

But I hardly believe that any thermometer superior to the mercurial
can at present be made, that is, any thermometer within the same
compass as a mercurial thermometer, and I think that the best result
for small ranges of temperature can be obtained with it by studying
and avoiding all its sources of error.

To judge somewhat of the laws of the change of zero within the
limits of temperature which I wished to use, I took thermometer No.
6163, which had lain in its case during four months at an average
temperature of about 20 or 25 C., and observed the zero point, after
heating to various temperatures, with the following result. The time
of heating was only a few minutes, and the zero point was taken imme-

350

HENRY A. KOWLAKD

diately after; some fifteen minutes, however, being necessary for the
thermometer to entirely cool.

TABLE I. SHOWING CHANGE OF ZERO POINT. -

Temperature
of Bulb
before finding
the Point.

Change of
Point.

Temperature
of Bulb
before finding
the Point.

Change of
Point.

22- 5

70-0

115

30-0

016

81-0

170

40-5

033

90-0

231

51-0

039

100-0

313

60-0

105

100-0

347

The second 100 reading was taken after boiling for some time.

It is seen that the zero point is always lower after heating, and that
in the limits of the table the lowering of the zero is about proportional
to the square of the increase of temperature above 25 C. This law
is not true much above 100, and above a certain temperature the
phenomenon is reversed, and the zero point is higher after heating;
but for the given range it seems quite exact.

It is not my purpose to make a complete study of this phenomenon
with a view to correcting the thermometer, although this has been
undertaken by others. But we see from the table that the error can-
not exceed certain limits. The range of temperature which I have
used in each experiment is from 20 to 30 C., and the temperature
rarely rose above 40 C. The change of zero in this range only amounts
to 0-03C.

The exact distribution of the error from this cause throughout the
scale has never been determined, and it affects my results so little that
I have not considered it worth investigating. It seems probable, how-
ever, that the error is distributed throughout the scale. If it were
uniformly distributed, the value of each division would be less than
before by the ratio of the lowering at zero to the temperature to which
the thermometer was heated.

The maximum errors produced in my thermometers by this cause
would thus amount to 1 in 1300 nearly for the 40 thermometer, and
to about 1 in 2000 for the others. Eather than allow for this, it is
better to allow time for the thermometer to resume its original state.

Only a few observations were made upon the rapidity with which
the zero returned to its original position. After heating to 81, the

Ox THE MECHANICAL EQUIVALENT OF HEAT 351

zero returned from 0-170 to 0-148 in two hours and a half.
After heating to 100, the zero returned from 0-347 to 0-110
in nine days, and to 0-022 in one month. Eeasoning from this, I
should say that in one week thermometers which had not been heated
ahove 40 should be ready for use again, the error being then supposed
to be less than 1 in 4000, and this would be partially eliminated by
comparing with the air thermometer at the same intervals as the ther-
mometer is used, or at least heating to 40 one week before comparing
with the air thermometer.

As stated before, when a thermometer is heated to a very high
point, its zero point is raised instead of lowered, and it seems probable
that at some higher point the direction of change is reversed again;
for, after the instrument comes from the maker, the zero point con-
stantly rises until it may be 0-6 above the mark on the tube. This
gradual change is of no importance in my experiments, as I only use
differences of temperature, and also as it was almost inappreciable in
my thermometers.

Another source of error in thermometers is that due to the pressure
on the bulb. In determining the freezing point, large errors may be
made, amounting to several hundredths of a degree, by the pressure of
pieces of ice. In my experiments, the zero point was determined in
ice, and then the thermometer was immersed in the water of the com-
parator at a depth of about 60 cm. The pressure of this water affected
the thermometer to the extent of about 0-01, and a correction was
accordingly made. As differences of temperature were only needed,
no correction was made for variation in pressure of the air.

It does not seem to me well to use thermometers with too small a
stem, as I have no doubt that they are subject to much greater irregu-
larities than those with a coarse bore. For the capillary action always
exerts a pressure on the bulb. Hence, when the mercury rises, the
pressure is due to a rising meniscus which causes greater pressure than
the falling meniscus. Hence, an apparent friction of the mercurial
column. Also, the capillary constant of mercury seems to depend on
the electric potential of its surface, which may not be constant, and
would thus cause an irregularity.

My own thermometers did not show any apparent action of this kind,
but Pfaimdler and Platter mention such an action, though they give
another reason for it.

352 HENRY A. EOWLAND

t *
(c.) Relation of the Mercurial and Air Thermometers ,J*

' ' &
1. GENERAL AND HISTORICAL REMARKS

* .-*
Since the time of Dulong and Petit, many experiments Have been

made on the difference between the mercurial and the air thermometer,
but unfortunately most of them have been at high temperatures. As
weight thermometers have been used by some of the best experimenters,
I shall commence by proving that the weight thermometer and stem
thermometer give the same temperature; at the same time, however,
obtaining a convenient formula for the comparison of the air ther-
mometer with the mercurial.

For the expansion of mercury and of glass the following formulae
must hold :

For mercury, V V (I + at +~W + &c.} ;
" glass. V = V\ (1 + at + /3f + tic.} ;

In both the weight and stem thermometers we must have V = V.

'0 "i ! 7 ! /vTo ! ~p ' V -^ L*~V I X> ~P O6, ).

1 + at + pt + <XC.

where V and V are the volumes of the glass and of the mercury
reduced to zero, and t is the temperature on the air thermometer.
The temperature by the weight thermometer is

P -1

where P , P , &c., are the weights of mercury in the bulb at C.,
t C., &c.

Now these weights are directly as the volumes of the mercury at 0.

/. -p = 1 + At + Bt* + &c.,
seeing that V is constant.

... 7'=100 ra ^ +B/ ' + * <; -

+ &c.'

In the stem thermometers we have V , the volume of mercury at 0,
constant, and the volume of the glass that the mercury fills, reduced
to 0, variable. As the volume of the glass T' is the volume reduced
to 0, it will be proportional to the volume of bulb plus the volume of
the tube as read off on the scale which should be on the tube.

ON THE MECHANICAL EQUIVALENT OF HEAT 353

T = 100 -Af, ;t _ (V',) = 10 ( F
^ + 5f + &c.

7*= 100

100 ^4 + (100)' B + &c.
which is the same as for the weight thermometer.
If the fixed points are and t' instead of and 100, we can write

&C '

At' + Et" + Ct' s + &c.

T-f

T= t 1 + (t - t)

As T and are nearly equal, and as we shall determine the constants
experimentally, we may write

t = T - at (f - t) (b - t} + &c.,

where t is the temperature on the air thermometer, and T that on the
mercurial thermometer, and a and & are constants to be determined for
each thermometer.

The formula might be expanded still further, but I think there are
few cases which it will not represent as it is. Considering & as equal
to 0, a formula is obtained which has been used by others, and from
which some very wrong conclusions have been drawn. In some kinds
of glass there are three points which coincide with the air thermometer,
and it requires at least an equation of the third degree to represent
this.

The three points in which the two thermometers coincide are given
by the roots of the equation

t(t'
and are, therefore,

In the following discussion of the historical results, I shall take
and 100 as the fixed points. Hence, i' = 100. To obtain a and &,
two observations are needed at some points at a distance from and
100. That we may get some idea of the values of the constants in
the formula for different kinds of glass, I will discuss some of the
experimental results of Eegnault and others with this in view.
23

354

HENRY A. ROWLAND

Regnault's results are embodied, for the most part, in tables given on
p. 239 of the first volume of his Relation des Experiences. The figures
given there are obtained from curves drawn to represent the mean of
his experiments, and do not contain any theoretical results. The direct
application of my formula to his experiments could hardly be made with-
out immense labor in finding the most probable value of the constants.

But the following seem to satisfy the experiments quite well:

Cristal de Choisy-le-Roi b = 0,

Verre Ordinaire b = 245,

Verre Vert b = 270,

Verre de Suede b = +10

a = .000 000 32.
\ = .000 000 34.
a = .000 000 095
a .000 000 14.

From these values I have calculated the following:

TABLE II. REGNAULT'S RESULTS COMPARED WITH THE FORMULA.

Choisy-le-Roi.

Verre Ordinaire.

Verre Vert.

Verre de Suede.

-2

a
o

2
o

fi
5

s
i

p
I

100

120120-12

120-09

+ 03

119-95119-90

+ 05

120-07

120-09

120-04120-04

140140-29

140-25

+ -04

139-85'139-80

+ 05

140-21140-22

140-11140-10

+ 01

160160-52

160 49 + 03! 159 74 159 72

+ 02

160-40160-39

+ 01

160-20160-21

180180-80

180-83 03

179-63179-68

180-60180-62

180-33180-34

200201-25201-28

199-70199-69

+ 01

200-80,200-89

200-50200-53

220221-82221-86

219-80219-78

+ 02

221-20221-23

320-75220-78

240242-55 ! 242-56

239-90239-96

241-60

241-63

241-16241-08

+ 08

260263-44263-46

260-20260-21

262-15262-09

+ -07

280284-48284-52

3280-58280-00

-02

282-85

282 63

+ -22

300305-72305-76

301-08301-12

320 S97 95 327 20

321-80321 -80

340

349 30

348-88

+ 42

434-00

342-64

+ 36

The formula, as we see from the table, represents all Eegnault's
curves with great accuracy, and if we turn to his experimental results
we shall find that the deviation is far within the limits of the experi-
mental errors. The greatest deviation happens at 340, and may be
accounted for by an error in drawing the curve, as there are few experi-
mental results so high as this, and the formula seems to agree with
them almost as well as Regnault's own curve.

3 Corrected from 280-52 in Regnault's table.

ON THE MECHANICAL EQUIVALENT OF HEAT

355

The object of comparing the formula with Regnault's results at
temperatures so much higher than I need, is simply to test the formula
through as great a range of temperatures, and for as many kinds of
glass, as possible. If it agrees reasonably well throughout a great
range, it will probably be very accurate for a small range, provided
we obtain the constants to represent that small range the best.

Having obtained a formula to represent any series of experiments,
we can hardly expect it to hold for points outside our series, or even
for interpolating between experiments too far apart, as, very often, a
small change in one of the constants may affect the part we have not
experimented on in a very marked manner. Thus in applying the
formula to points between and 100 the value of & will affect the
result very much. In the case of the glass Choisy-le-Eoi many values
of 6 will satisfy the observations besides 6 = 0. For the ordinary
glass, however, & is well determined, and the formula is of more value
between and 100.

The following table gives the results of the calculation.

TABLE III. REGNAULT'S RESULTS COMPARED WITH THE FORMULA.

Air
Thermom-

Calculated
a = -000 000 32
b = 0.

Calculated
o = -000 000 34
b = 245.

Observed.

Calculated
a = -000 000 44

Choisy-le-Koi.

Verre
Ordinaire.

10-00

10-07

10-10

19-99

20-12

20-17

29-98

30-15

30-12

+ 03

30-21

+ 09

39-97

40-17

40-23

49-96

50-17

50-23

59 95

60-15

60-24

60-21

69-95

70-12

70-22

70-18

80
90

79-96
89-97

80-09
90-05

80-10

80-11
90-07

+ 01

100

Kegnault does not seem to have published any experiments on Choisy-
le-Roi glass between and 100, but in the table between pp. 226, 227,
there are some results for ordinary glass. The separate observations
do not seem to have been very good, but by combining the total number
of observations I have found the results given above. The numbers in
the fourth column are found by taking the mean of Eegnault's results
for points as near the given temperature as possible. The agreement

356 HENRY A. EOWLAJSTD

is only fair, but we must remember that the same specimens of glass
were not used in this experiment as in the others, and that for these
specimens the agreement is also poor above 100. The values a =
.000,000,44 and & = 260 are much better for these specimens, and
the seventh column contains the values calculated from these values.
These values also satisfy the observations above 100 for the given
specimens.

The table seems to show that between and 100 a thermometer of
Choisy-le-Eoi almost exactly agrees with the air thermometer. But
this is not at all conclusive. Regnault, however, remarks, 4 that be-
tween and 100 thermometers of this glass agree more nearly with
the air thermometer than those of ordinary glass, though he states
the difference to amount to -1 to -2 of a degree, the mercurial ther-
mometer standing below the air thermometer. With the exception of
this remark of Eegnault's, no experiments have ever been published
in which the direction of the deviation was similar to this. All ex-
periments have found the mercurial thermometer to stand above the
air thermometer between and 100, and my own experiments agree
with this. However, no general rule for all kinds of glass can be
laid down.

Boscha has given an excellent study of Eegnault's results on this
subject, though I cannot agree with all his conclusions on this subject.
In discussing the difference between and 100 he uses a formula of
the form

T 1= t(lOQ t),
ct

and deduces from it the erroneous conclusion that the difference is
greatest at 50 C., instead of between 40 and 50. His results for
T t at 50 are

Choisy-le-Eoi .22

Verre Ordinaire +.25

Verre Vert +.14

Yerre de- Suede +.56

and these are probably somewhat nearly correct, except the negative
value for Choisy-le-Eoi.

With the exception of Eegnault, very few observers have taken up
this subject. Among these, however, we may mention Eecknagel, who

4 Comptes Rendus, Ixix.

Osr THE MECHANICAL EQUIVALENT or HEAT

357

has made the determination for common glass between and 100.
I have found approximately the constants for my formula in this case,
and have calculated the values in the fourth column of the following
table.

TABLE IV. RECKNAGEL'S RESULTS COMPARED WITH THE FORMULA.

Mercurial Thermometer.

Air
Thermometer.

Difference.

Observed.

Calculated.

10-08

20-14

30-18

40-20

50-20

60-18

70-14

70-15

+ 01

80-10

80-11

+ 01

90-05

90-06

+ 01

100

100-00

J=290, a = .000 000 33,

It will be seen that the values of the constants are not very different
from those which satisfy Eegnault's experiments.

There seems to be no doubt, from all the experiments we have now
discussed, that the point of maximum difference is not at 50, but at
some less temperature, as 40 to 45, and this agrees with my own
experiments, and a recent statement by Ellis in the Philosophical
Magazine. And I think the discussion has proved beyond doubt that
the formula is sufficiently accurate to express the difference of the
mercurial and air thermometers throughout at least a range of 200,
and hence is probably very accurate for the range of only 100 between
and 100.

Hence it is only necessary to find the constants for my thermometers.
But before doing this it will be well to see how exact the comparison
must be. As the thermometers are to be used in a calorimetric research
in which differences of temperature enter, the error of the mercurial
compared with the air thermometer will be

= a \U' 2 (J +

358 HENRY A. ROWLAND

which for the constants used in Eecknagel's table becomes

Error = d -- I = .000 000 33 1 29000 780^ + 3f \.
clt

This amounts to nearly one per cent at 0, and thence decreases to
45, after which it increases again. As only 0-2 at the 40 point
produces this large error at 0, it follows that an error of only 0-02
at 40 will produce an error of y^nro at 0. At other points the errors
will be less.

Hence extreme care must be taken in the comparison and the most
accurate apparatus must be constructed for the purpose.

2. DESCRIPTION OF APPARATUS
The Air Thermometer

In designing the apparatus, I have had in view the production of
a uniform temperature combined with ease of reading the thermom-
eters, which must be totally immersed in the water. The uniformity,
however, needed only to apply to the air thermometer and to the bulbs
of the mercurial thermometer, as a slight variation in the temperature
of the stems is of no consequence. A uniform temperature for the air
thermometer is important, because it must take time for a mass of air
to heat up to a given temperature within 0-01 or less.

Fig. 1 gives a section of the apparatus. This consists of a large
copper vessel, nickel-plated on the outside, with double walls an inch
apart, and made in two parts, so that it could be put together water-
tight along the line a &. As seen from the dimensions, it required
about 28 kilogrammes of water to fill it. Inside of this was the vessel
mdefghkln, which could be separated along the line d Ic. In the
upper part of this vessel, a piston, q, worked, and could draw the water
from the vessel. The top was closed by a loose piece of metal, o p,
which fell down and acted as a valve. The bottom of this inner
vessel had a false bottom, c I, above which was a row of large holes ;
above these was a perforated diaphragm, s. The bulb of the air ther-
mometer was at /, with the bulbs of the mercurial thermometers almost
touching it. The air thermometer bulb was very much elongated, being
about 18 cm. long and 3 to 5 cm. in diameter. Although the bulbs of
the thermometers were in the inner vessel, the stems were in the
outer one, and the reading was accomplished through the thick glass
window u v.

ON THE MECHANICAL EQUIVALENT OF HEAT

359

The change of the temperature was effected by means of a Bunsen
burner under the vessel w.

The working of the apparatus was as follows: The temperature
having been raised to the required point, the piston q was worked to
stir up the water; this it did by drawing the water through the holes

"31

FIG. 1.

FIG. 2.

at c I and the perforated diaphragm s, and thence up through the
apparatus to return on the outside. When the whole of the water is
at a nearly uniform temperature the stirring is stopped, the valve op
falls into place, and the connection of the water in the outer and inner
vessels is practically closed as far as currents are concerned, and be-
fore the water inside can cool a little the outer water must have cooled
considerably.

360 HENKY A. EOWLAND

So effective was this arrangement that, although some of the ther-
mometers read to 0-007 C., yet they would remain perfectly stationary
for several minutes, even when at 40 C. At very high temperatures,
such as 80 or 90 C., the burner was kept under the vessel w all the
time, and supplied the loss of the outer vessel by radiation. The inner
vessel would under these circumstances remain at a very constant tem-
perature. The water in the outer vessel never differed by more than
a small fraction of a degree from that in the inner one.

To get the and 100 points the upper parts of the vessel above
the line a & were removed, and ice placed around the bulb of the air
thermometer, and left for several hours, until no further lowering took
place. For the 100 point the copper vessel shown in Fig. 3 was used.
The portion y of this vessel fitted directly over the bulb of the air
thermometer. On boiling water in x, the steam passed through the
tube to the air thermometer. It is with considerable difficulty that
the 100 point is accurately reached, and, unless care be taken, the
bulb will be at a slightly lower temperature. Not only must the bulb be
in the steam, but the walls of the cavity must also be at 100. To
accomplish this in this case, a large mass of cloth was heaped over the
instrument, and then the water in x vigorously boiled for an hour or so.
After fifteen minutes there was generally no perceptible increase of
temperature, though an hour was allowed so as to make certain.

The external appearance of the apparatus is seen in Fig. 2. The
method of measuring the pressure was in some respects similar to that
used in the air thermometer of Jolly, except that the reading was taken
by a cathetometer rather than by a scale on a mirror. The capillary
stem of the air thermometer leaves the water vessel at a, and passes
to the tube &, which is joined to the three-way cock c. The lower part
of the cock is joined by a rubber tube to another glass tube at d, which
can be raised and lowered to any extent, and has also a fine adjustment.
These tubes were about 1-5 cm. diameter on the inside, so that there
should be little or no error from capillarity. Both tubes were exactly
of the same size, and for a similar reason.

The three-way cock is used to fill the apparatus with dry air, and
also to determine the capacity of the tube above a given mark. In
filling the bulb, the air was pumped out about twenty times, and
allowed to enter through tubes containing chloride of calcium, sulphuric
acid, and caustic soda, so as to absorb the water and the carbonic acid.

ON THE MECHANICAL EQUIVALENT OF HEAT

361

The Cathetometer

The cathetometer was one made by Meyerstein, and was selected
because of the form of slide used. The support was round, and the
telescope was attached to a sleeve which exactly fitted the support.
The greatest error of cathetometers arises from the upright support
not being exactly true, so that the telescope will not remain in level
at all heights. It is true that the level should be constantly adjusted,
but it is also true that an instrument can be made where such an ad-
justment is not necessary. And where time is an element in the
accuracy, such an instrument should be used. In the present case it
was absolutely necessary to read as quickly as possible, so as not to

FIG. 3.

leave time for the column to change. In the first place the round
column, when made, was turned in a lathe to nearly its final dimen-
sions. The line joining the centres of the sections must then have
been. very accurately straight. In the subsequent fitting some slight
irregularities must have been introduced, but they could not have been
great with good workmanship. 5 The upright column was fixed, and
the telescope moved around it by a sleeve on the other sleeve. Where
the objects to be measured are not situated at a very wide angle from
each other, this is a good arrangement, and has the advantage that any
side of the column can be turned toward the object, and so, even if it

4 The change of level along the portion generally used did not amount to more
than -1 of a division, or about -Olmm. at the mercury column, as this is about the
smallest quantity which could be observed on the level.

362 HENRY A. ROWLAND

were crooked, we could yet turn it into such a position as to nearly
eliminate error.

It was used at a distance of about 110 cm. from the object, and no
difficulty was found after practice in setting it on the column to j\ mm.
at least. The cross hairs made an angle of 45 with the horizontal, as
this was found to be the most sensitive arrangement.

The scale was carefully calibrated, and the relative errors c for the
portion used were determined for every centimeter, the portion of the
scale between the and 100 points of the air thermometer being
assumed correct. There is no object in determining the absolute value
of the scale, but it should agree reasonably well with that on the
barometer; for let H , H t , and H 1QO be the readings of the barometer,
and Ti , h t , and /t 100 the readings of the cathetometer at the temperatures
denoted by the subscript. Then approximately

(.#100 + /? 100 ) (fft> + ^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

t^,

>.-^

^ 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

"3 3
J

o ^

"** O>
d CO
S fl

03 pC]

'So h

CO ^

>-5 03

ffl

.rH

" v '

r~-

" v '

^r~

1 ^s 1

a g

^A-a.

s a

03
o

o]
8

2 , =

o
: <H

5 |^

3 CO

. t ~ i

03
*

'i o

CO
rH

^ a

> .2 "

r r

w S

1 ^ n

} CJ "

( n

-*"V**

i O

d ^

1 S

4 ^

*^ ^

ci?

TJ -*

W **

'S
O

a 1

filo

bffto

a *-

Oi CO

C35 O5

>-H

r*< DO
*

. M 5 ^H

CO CO

4i -*

* W

H) 0.0

** 2

*~
fc

_.-.^-.

^
"3

o "S

*~^

pL|

O ?

t oi

d d

a = 3

: w

rH .t

* -

S d

T-*

o' o*

> <u

ja *"

t^>

*> M

r-**~-*-~-

8*5

H O

000

O O

o o

O O CO

H CO

O O

^ o

a} ^

o ^*

o * co

CO O

O O

r- 1

t -u

ai "2

^i ^>

_l_ ^

^ s

> CQ

i "i

o o

Q EC

o o

1
1
o

* *

M 1-1

O CO CO

75 rH

rH O

gj ^

1 1

, ' <~

^ *

~ **

1^ CD

~*~

jf-o"

; S

!fl"i

-4-3

"o &

P-f d
2MB
03

woo

tO tn in

O CO
JO CO

00 CO

O O

rH rH

CO CO

*i
V

[O tj;

*- J3

o ^.2

n a -a

S U

> '

a _g

PH ff

t- co in

D CO CD

g I

co co

CO t-

iO
CO

CO
!>

CO -*
rH CO

i^.

a a

S"S a

os a

CO CO co

1-1 te

D ^

CO CO

JO CO

^ P< 03

'?^

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).

Kew.

3200

38-71

38-72 +-01

38-70

45-04

45-03

49-96

55-34

55-37

+ 03

55-34

60-07

60-05

60-06

65-39

65-41

+ 02

65-36

69-93

69-95

+ 02

69-93

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

95-40

+ 14

101-77

101-94

+ 15

109-16

109-15 -01

109-25

+ 08

212-00

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

- 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_

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

bioo

bioo-b

f/ioo or h.

Jhnn i . OinnrO _ 4 , A

bioo

a sani.

Absolute

value,

llmm.

27 mm.

005

00074

00087

0047

00087

Relative

value,

0-9

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.

Correction.

Calculated
Temperature.

Corrected
Temperature.

9-9971

0029

19-9946

0054

29-9924

0076

39-9907

0093

49-9894

0106

59-9865

0135

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

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.

6167.

Temperature
by 6167.

115-33

21-25

6-147

17 -1425

422-84

255-80

15-685

17-661

236

23 -793

534-71

341 05

19-157

24 -089

296

30 -582

653-49

431-71

22-833

30 896

314

38 -569

793 1 8

47-175

3 8 -93 5

366

51 -040

33-864

51 -320

280

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

t- CO

CD 71

CD
OS

OS CO
I- OS

CO rH
1C *3*

CO
CO

fij

o
l>

O O

00 rH

O O
CO -rfl
t- 00

o
>*

OS
OS

OS
OO

1C
OS
CO

OS 1C
oo os

CO 71

rH CO

00 05

OS
CO

O CO
CD t-

1C *

CO
00

S :

6 -3
E

o
t-

CO
rH

o
I-

OO rH

00 rH
Tf< 1C

CO T><

I- 00

OS
OS

1C r-i

00
t-

rH CO
O 1C

CO
71

rH I-

O rH

rH CO

O TjH

CO CO
77 OS

O OO

OS rH

CM *

OS CM

T* 1C

CO "*1<
t- 00

OO 7*
7* OO
rH SM

CO
00
OS

-J} ~

71 CO

OS
1C

CO 30
^H O
1C 71

o t-

CO CO
00 t-

rH OO
71 CM

71 *

CO CO

1C rH
<fl 1C

rH
1C

8 2

rH CO

0* 77

CO
77
7?

O
-f

* 3D

1C *

-H 7>

-,r -r

-f

CO
CM

OS o

X
CO

Tt< CO
rH

CD l>

O ^JH
* CO

CO O

Tjl O

CO -

o
CM

o o

00 rH

o o

OO rH

* 1C

o o
CO ^
l> 00

OS
OS

OS O H

OS O -

00
CO

OS t~

CO OS

rH <M

rH 1C

t- OS

iC
OS

rH
CO

o <*

CO t-

1C 1C

CO CD

CO CO

^ : ii

1C
CO

o ^*

CO 1C

CO
1C

30 O

CO t-

3D 77

OS rH

* *

CO
00

OS t-

t- t-

71 CO

O CO

CO OS

OS
OS

CO
CO

CO
rH

71 CD
t-

t- iC
77 CO

CO
rH

CO 77
OS 77
rH 77

CO
77

CO
CO

CO *

OS
CO

OS CO
CO O

rH
CO

rH O
CO CO

CD
CO

CO
00

CO
CO

OS
00

71 CO
71 iC

00 30

1C
1C
00

CO 1C
t- 00

00 00

rH
OS

CO 77

*f t*

OS OS

-H

III

00 -*
77 CO

1C t-

71 rH

00 00
O l-

OO
CO

t- CM

ID fl

OS
1C

iff

j> co

7 i

o *

1C 00

CO
00

O rn
rH rH

rfi

rH rH

t- O

rH . 71

O
77

1 i

|i?

o
o

77 SM

^ 1C
CO 77

CO
OS

CO 71

t- I

life

I-

?i ^

- 1

5 B-J5

77 CO

71 rH

77 77

CO CO

372

HENKY A. EOWLAND

s CD

HJa

O 0>

BcB

CO
-

-* t-

CO CO

I 1

i 1

rWjB

O OS

cxt

OS OS

c\->

;

00 CO

CO
CO

IO CO

O rH

*fl(

, .

fl CD

^ IO

J-^

IO~

rH 00

o
t-

CXI

IO IO

o
00

o
CO
CM

o
00
CO

1 ?*

OS 1-H

CXI

-4

rQ 1 CS

rH CXI

i-s

IO IO

i H ?

* +

OS O

00
rH

CO ->TI

TtH

I-H

rH T

OS OS

OS rH

ext

i-5

pa
<

O CO

rH
OS

CD
CO

-H

O CXt

rfl

Ttl

CO CO

t- t-

a> g-*^

OS CO

S!D

Tt<

S o

J^.

CXI O

-t!

|3f

rH
1

1 1

*H O
II

OJTJ

CO
rH

OS CO

o o

OS
CO

O5
00

CO
00

a 9

CO CO

CO CD

_> jg

5 '3

ON THE MECHANICAL EQUIVALENT OF HEAT

373

1 ,

; ;

CNJ

a SB o

o
IO

OS
04

00
CO

OS
OS

: ;

iH
CO

TH
TH

IO
CO

+
O

OS
CO

Os
OS

a
o

O CO
CO t-

00
CO

1 1

3*
i

fc-1

CO TH

to 04

I- CO

TH -H

-#
to

t^5 *

tO TH

CO 50
I- IO

OS
04

iH
00
CO

CO ^

CO ^
TH rH

CO
O4

o
to

04 CO
I- OS

Os
O4

00 Frt

"a 1

^ TH

g o*

t- iH

10
CO

00
TH

s ^
a

"*" ?

in" oo

4i Q>

OS IO
00 0*

* oo

04
IO

o
to

o oo

00 O

ft .

M >?

qj 03

- ^

^ E^ fl n
H W

*H g O

3fl

CO CO

CO
CO

OS O

OS |

y> <x>

*5 a

o3 si

T1 "

to 04

IO tO

TH TH

OS
CO
04

o
to

CO
CO

I-

OS
d

o5 5

hi -

IO IO

o o

<H
33 TJ
> <O

K " t~

33 .(- o

OS 04

CO T*

CO
CO

OS
CO

00
CO

OS
TH

t- t-

Os O
CO O

H 3

~ **

05 ^2

t> o

^ *

TX ^

to -4*

o 2

oj oj

t- 00

^1 CO

o
l-

00
CO

to OS
OS 04

t- o

a to

* s

1 co
1

o to

o
o

1 T

6 S

IO ;O
CO H/l
O OS

Os
CO

00
iO
CO

CO
CO

SS 5

CO CO

II II

^. Q

^ to

to to

IO IO

t- t-

to
to
t-

oo
to

10 to
o t-

a
m

III 6

TH O
TH

to to

to
to

CO
10

co
to

00
00

04
10
00

00 CO

t- t-

t"
o
a
H

5 *

TH
TH

CO
IO

00 00

8 1

<u ^ o

loL "

*& to

HjH CO

IO
O4

CO
OS

to o

C4 tO
CO CO

si g

10 iO

t- t-

IO
IO

I-

IO
IO

IO
10

IO
IO

IO IO
IO IO

t- z>

'S.SP M

S en
II

CO 04

IO CO

374

HENRY A. ROWLAND

a" 1

1C
CO

1 : :+ + + + + + + + :

fe"

;

Ifsjs

tf.

I-

o
I-

I-

o
t-

OS
CO

O5
1C

iffP

to
-f

o
o

o
to

1-H
CO

35
1C

<*> .
to t.

1C
CM

c-.

35
1C

"ill

1-H

00
1C

to
o

CO
CO
CO

l|s

CO
CM

Oi
O

05
00

1-H

CO
1C

1-H

00
1C

to
to

i-H

OS
CO
1C

to
o
o

CO
OS

GO
CO

(H *H
^

oo
o

1-H

o
I-

o
M

35
CO

c
1-

rO Q

1 1
GO
CM

CO
CO

oo
l-

t -

CO
Oi

GO
GO
O5

00
OS

CM
CM

1 1

to
o*

1-H

GO
00

I-

1-H

r-
t-

Oi
CO

I-

1C
1C
00

rH
OS

||||o

O5
00

I-

1-H

I-

i i 3
SS-o .

2 So

05
00

o
t-

1C
t-

GO
t-

L-

I-

t-
t-

to
I-

~i i A h .

1-H

Ox THE MECHANICAL EQUIVALENT OF HEAT

375

J-

fjg

O
+

(JJ

<d
M

-f.

O
O

4. ,

A *
B * i b

*i*s a

Iff

O
CO

00
O

CC
OS

1ft

E- 2 *^

H5|S

0.0

O
I-(

CO
CO

t-
n

O
O

l>
I-

O
00

Iff

O
O

l-
t-

,-H

-<tl

Iff

1ft

1ft
*

1ft
Iff
Iff

OS
00

CO
30

k g

O5
*
07

(?}

CO
CO

s"^

1
t-

00
CO

CO
OS

1ft
O

1ft

*
l>

00
00

*-H

Iff

CO
CO

1 1
CO

CO
CO
1 1

^-1
O

*
l-

i-H

I 1

O
CO

00
O

OS
0*

1-H
O

<M
C4

Iff

OS
OS

A|Q

CO
b-

*
t>
t-

Iff

CO
00
OS

Iff

1 1
<M

i-H

Iff

1ft

CO
O

CO
CO

1ft
so

-I

3i
CO
5N

*#
*

1ft
I-

OS
OS

O
O

OS
CXJ

1ft
01
<f

1
ta

O
OS

I 1
CO

t-
so
t-

*
*<

CO
-

OS
OS

i-H

to
cf

OS
O
CXJ

OS
CJ

1ft

00
OJ
9J

1-H
CO

1ft

CO
O*

JO
CO

as
*
i>

iff

c
Iff

CO
CO
00

t-
t-

op
Iff

00
rH

T-H

CO
(M
OS

OS
CO

1ft

Tfl

>**a'S

Is III

sggl-

CO
O

CO
OS-

o
*

t-
ot

<**

Ift

1 1

so
*
*

*<
Tjt

i-H

so
<?

T-H

00
CO
CM

<b,3

S *--a

ss
5 2 5

rH
rji

so
*

O
O

I-

I 1

OS
OS

Tfl
OS

*
t-

1ft
CO

Ift
t-

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:

000239
000166
000226
000155
000071
.000115

Date.

Weight.

C'.

Nov. 14

056920

Nov. 20

056985

Jan. 25

056986

Feb. 11

056997

June 8

056961

June 22

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

000236

Nov. 20

000218

Jan. 25

000217

Feb. 11

000197

June 8

000215

June 22

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.

or Correction to Air
Thermometer.

9-9972

0028

19-9952

0048

29-9939

0061

39-9933

0067

49-9932

0068

59-9937

0063

69-9946

0054

79-9956

0044

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.

923

- 917

_911

-911

240

20-557

20-409

20-350

20345

58-1

250

21-670

21.515

21-457

21-452

+ -217

+ -215

+ -214

+ 214

260

22-776

22-616

22 559 22 554

1-356

1-336

1-328

1 328

270

23-884

23-713

23-657

23.652

2-494

2-475

2-461

2-460

280

24-989

24-810

24-755

24-750

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 <Q CO O ">
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.

464

460

o o
.457 -457

230

17-198

17-067

17-009

17-005

240

18-056

17-920

17-861

17-8.57

+ 463

+ -460

+ 457 +-457

250

18-917

18-773

18-714

18-709

1-387

1-376

1-368 1-368

260

19-771

19-621 j 19-562

19-557

2-307

2-290

2-276 2-275

270

20-621

20-465 ! 20-406

20-401

3-216 3-192

3-174 3-173

280

21-469

21-306 1 21-247

21-242

4-122 4-092

4-069 4-068

290

22-308

22-139 22-081

22-076

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.

in iT 1 ?

-6

m i

--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>

036

034

230

16-478

16-356

16-298

16-294

+ 770

+ 764

+ 759

240

17-259

17-132

17-074

17-070

1-574

1-562

1-553

250

18-042

17-908

17-849

17-845

2 368

2-350

2-336

2-335

260

18-825

18-686

18-627

18-622

3-156

3-133

3-115

3-114

270

19-609

19-464

19-405

19-400

3-941

3-911

3 889

3-888

280

20-392

20-241

20-182

20-177

4-726

4-691

4-665

4-664

290

21-176

21-019

20-960

20-955

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.

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.

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

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

52
6-08
12-65
20-49
24-54
29 52
39-47
39-20

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

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

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

3-61
11-56
20-70
32-17
39-36

3-64
11-60
20-75
32-24
39-43
50-75
60-10
73-84
86-48
86-45
100-00

3-64
11-62
20-80
32-28
39-48
50-80
60-21
73-93
86-56
85-45
100-00

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.

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

39-337

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,

C(t- Q = _ T C(0 T a } dt nearly,

~ a /

0" 0'
t = c tf , _ T nearly,

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 = -

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

/:
S

a
a

;-'
ft

n
b

or
c

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

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 "

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

"3 Q." ''"'S

nr>

^ o + S

8*6=1

ii-OflJS

;

rH
t-

-** 0*^

rH
CO

^ M ^ O A

-*S Q

scaSri

O o ts-S~"

3
S

CO
35

CO
CO
CO

35
M
M

53
CO

CO
CO

CO
CO
CO

H -

o
"3 t

<H
CM

35
CO

K r^

l-H

i-l

I-

to + 38

fa
o

IA
O

O
00

o
CM

Iss

*.%>

France

Dussel

-3
a
i i

3
s

1 1

France

Austri

Hollan

OQ
o

France

00
CO

-i

""I

H
M

o
so

M
M
hi

J3
2

fl?

"P,

09
|

a
o
G

a
o

i i

-^ -

-1*

O
rH

- 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 <i u u u xxvi. . " "

v u u u u u xxvii. " "

i u u u X xxi. " "

vii Hirn, Theorie Mec. de la Chaleur, ser. 1, 3 me ed.
Tiii Edlund, Pogg. Ann., cxiv. I, 1865.

ix Favre, Comptes Rend., Feb. 15, 1858; also Phil. Mag., xv. 406.
x Violle, Ann. de Chim., ser. 4, xxii. 64.
xi Quintus Icilius, Pogg. Ann., ci. 69.
xli Boscha, Pogg. Ann., cviii. 162.
xiii Joule, Report of the Committee on Electrical Standards of the B. A., London,

1873, p. 175.

xiv H. F. Weber, Phil. Mag., ser. 5, v. 30.
xv Favre, Comptes Rend., xlvii. 599.
XTi Regnault, Rel. des Experiences, torn. ii.
xvil E. Wiedemann, Pogg. Ann., clvii. 1.

xvl11 Clement et Desormes, Journal de Physique, Ixxxix. 333, 1819.
xlx Laplace, Mec. Celeste, v. 125.

xx Masson, Ann. de Chim. et de Phys., ser. 3, torn. liii.
xxi Weisbach, Der Civilingenieur, Neue Folge, Bd. v., 1859.
xxii Hirn, Theorie Mec. de la Chaleur, i, 111.
xxiii Favre et Silbermann, Ann. de Chim., ser. 3, xxxvii. 1851.
xxiv Cazin, Ann. de Chim., ser. 3, torn. Ixvi.
xxv Dupr6, Ann. de Chim., 3 me ser., Ixvii. 359, 1863.
xxvi Kohlrausch, Pogg. Ann., cxxxvi. 618.
xsvii Rontgen, Pogg. Ann., cxlviii. 603.
xxvlil Jamin et Richard, Comptes Rend., Ixxi. 336.
xxix Tresca et Laboulaye, Comptes Rend., Iviii. 358. Ann. du Conserv. des Arts

et Metiers, vi. 365.

xxx Amagat, Comptes Rend., Ixxvii. 1325.
xxxi Mem. de 1'Acad. des Sci., 1738, p. 128.
xxxii Benzenberg, Gilbert's Annalen, xlii. 1.
xxxm Goldingham, Phil. Trans., 1823, p. 96.

xxxiv Ann. de Chim., 1822, xx. 210 also, (Euvres de Arago, Mem. Sci., ii. 1.
xxxv Stampfer und Von Myrbach, Pogg. Ann., v. 496.
xxxvi Moll and Van Beek, Phil. Trans., 1824, p. 424. See also Shroder van der Kolk,

Phil. Mag., 1865.
xxxvii p arr y an( j Foster, Journal of the Third Voyage, 1824-5, Appendix, p. 86. Phil.

Trans., 1828, p. 97.

xxxviii Savart, Ann. de Chim.; ser. 2, Ixxi. 20. Recalculated.
XMIX Bravais et Martins, Ann. de Chim., ser. 3, xiii. 5.
11 Regnault, Rel. des Exp., iii. 533.

xli Delaroche et Berard, Ann. de Chim., Ixxxv. 72 and 113.
xl " Puluj, Pogg. Ann., clvii. 656.

ON THE MECHANICAL EQUIVALENT OF HEAT 413

Estimating the weight rather arbitrarily, I have combined them as
follows :

No.

1
2
3

4
5
6
7
8
9
10

Velocity at 0- C.
Dry Air.

Estimated Weight
of Observation.

332-6

332-7

330-9

330-8

332-5

332-8

.332-0

331-8

332-4

330-7

Mean 331-75

Or, corrected for the normal carbonic acid in the atmosphere, it be-
comes 331-78 metres per second in dry pure air at C.

From Eegnault's experiments on the velocity in pipes I find by
graphical means 331-4 m. in free air, which is very similar to the above.

Calculation from Properties of Gases

K= specific heat of gas at constant pressure.
lc = specific heat of gas at constant volume.
p = pressure in absolute units of a unit of mass.
v = volume in absolute units of a unit of mass.
H = absolute temperature.
J= Joule's equivalent in absolute measure.
= K

General formula for all bodies:

_ 1

~~ l _j^_(dp_\ (dv_\ '

V 1 I dv \

r = -7-i-r-i

T _ /* ( dp \ / dv \ f
*' 7? \7fc).\dJ ) F^T'

414 HENEY A. ROWLAND

Also,

J= ~ ~^(!*L\ ~^L'
\ dp ),,, V

Application to gases; Rankine's formula is,

(4L) SB A/1 + *,*L *.},

\ d/j. h ii \ ;j. v J

dp- 1 - -, - . 1 +

If a.v is the coefficient of expansion between and 100, then

AI, = (1 + -00635m),
whence

where a' p and a, are the true coefficients of expansion at the given
temperature;

+ 5m *.*.

According to Thomson and Joule's experiments m = 0-33 C. for air
and about 2-0 for C0 2 . Hence //= 272 -99.

The equations should be applied to the observations directly at the
given temperature, but it will generally be sufficient to use them after
reduction to C. Using K = -2375 according to Regnault for air, we
have for the latitude of Baltimore,

From Rontgen's value r = 1-4053 = 430-3. 33

" Amagat's " 1-397 = 436-6.

" velocity of sound 331-78m. per sec. = 429'6.

33 R6ntgen gives the value 428-1 for the latitude of Paris as calculated by a formula
of Shroder v. d. Kolk, and 427-3 from the formula for a perfect gas, and these both
agree more nearly with my result than that calculated from my own formula.

ON THE MECHANICAL EQUIVALENT OF HEAT 415

Using Wiedemann's value for K, -2389, these become

= 427-8 ; -^ = 434-0 ; = 427-1 .
999

As Wiedemann, however, used the mercurial thermometer, and as
the reduction to the air thermometer would increase these figures from
2 to -8 per cent, it is evident that Eegnault's value for K is the more
nearly correct. I take the weights rather arbitrarily as follows :

Weight. J.

Eontgen 3 430-3

Amagat 1 436-6

Velocity of sound 4 429-6

Mean 430-7

And this is of course the value referred to water at 14 C. and in the
latitude of Baltimore. My value at this point is 427-7.

This determination of the mechanical equivalent from the properties
of air is at most very imperfect, as a very slight change in either f or
the velocity of sound will produce a great change in the mechanical
equivalent.

From Theory of Vapors

Another important method of calculating the mechanical equivalent
of heat is from the equation for a body at its change of state, as for
instance in vaporization. Let v be the volume of the vapor, and v' the
volume of the liquid, H the heat required to vaporize a unit of mass of
the water; also let p be the pressure in absolute units, and // the absolute
temperature. Then

The quantity H and the relation of p to // have been determined with
considerable accuracy by Regnault. To determine J it is only required
to measure the volume of saturated steam from a given weight of water;
and the principal difficulty of the process lies in this determination,
though the other quantities are also difficult of determination.

This volume can be calculated from the density of the vapor, but this
is generally taken in the superheated state.

416 HENRY A. KOWLAND

The experiments of Fairbairn and Tate 34 are probably the best direct
experiments on the density of saturated vapor, but even those do not
pretend to a greater accuracy than about 1 in 100. With Eegnault's
values of the other quantities, they give about Joule's value for the
equivalent, namely 425. Him, Herwig, and others have also made the
determination, but the results do not agree very well. Herwig even
used a Geissler standard thermometer, which I have shown to depart
very much from the air thermometer.

Indeed, the experiments on this subject are so uncertain, that physi-
cists have about concluded to use this method rather for the deter-
mination of the volume of saturated vapors than for the mechanical
equivalent of heat.

From the Steam-Engine and Expansion of Metals

The experiments of Hirn on the steam-engine and of Edlund on the
expansion and contraction of metals, are very excellent as illustrating
the theory of the subject, but cannot have any weight as accurate deter-
minations of the equivalent.

From Friction Experiments

Experiments of this nature, that is, irreversible processes for con-
verting mechanical energy into heat, give by far the best methods for
the determination of the equivalent.

Rumford's experiment of 1798 is only valuable from an historical
point of view. Joule's results since 1843 undoubtedly give the best
data we yet have for the determination of the equivalent. The mean of
all his friction experiments of 1847 and 1850 which are given in the
table is 425-8, though he prefers the smallest number, 423-9, of 1850.
This last number is at present accepted throughout the civilized world,
though there is at present a tendency to consider the number too small.
But this value and his recent result of 1878 have undoubtedly as much
weight as all other results put together.

As sources of error in these determinations I would suggest, first,
the use of the mercurial instead of the air thermometer. Joule com-
pared his thermometers with one made by Fastre. In the Appendix
to Thermometry I give the comparison of two thermometers made by
Fastre in 1850, with the air thermometer, as well as of a large number
of others. From this it seems that all thermometers as far as measured

3* Phil. Mag., ser. 4, xxi, 230.

ON THE MECHANICAL EQUIVALENT OF HEAT 417

stand above the air thermometer between and 100, and that the
average for the Fastre at 40 is about 0-1 C. Using the formula given
in Thermometry this would produce an error of about 3 parts in 1000
at 15 C., the temperature Joule used.

The specific heat of copper which Joule uses, namely, -09515, is
undoubtedly too large. Using the value deduced from more recent
experiments in calculating the capacity of my calorimeter, -0922,
Joule's number would again be increased 13 parts in 10,000, so that
we have,

Joule's value 423-9, water at 15-7 C.

Eeduction to air thermometer -|-1'3

Correction for specific heat of copper. . -f- -5
Correction to latitude of Baltimore. . . -f- -5

426-2

It does not seem improbable that this should be still further in-
creased, seeing that the reduction to the air thermometer is the smallest
admissible, as most other thermometers which I have measured give
greater correction, and some even more than three times as great as
the one here used, and would thus bring the value even as high as 429.

One very serious defect in Joule's experiments is the small range
of temperature used, this being only about half a degree Fahrenheit,
or about six divisions on his thermometer. It would seem almost im-
possible to calibrate a thermometer so accurately that six divisions
should be accurate to one per cent, and it would certainly need a very
skillful observer to read to that degree of accuracy. Further, the same
thermometer " A " was used throughout the whole experiment with
water, and so the error of calibration was hardly eliminated, the tem-
perature of the water being nearly the same. In the experiment on
quicksilver another thermometer was used, and he then finds a higher
result, 424-7, which, reduced as above, gives 427-0 at Baltimore.

The experiments on the friction of iron should be probably rejected
on account of the large and uncertain correction for the energy given
out in sound.

The recent experiments of 1878 give a value of 772-55, which re-
duced gives at Baltimore 426-2, the same as the other experiment.

The agreement of these reduced values with my value at the same
temperature, namely 427-3, is certainly very 'remarkable, and shows
what an accurate experimenter Joule must be to get with his simple
27

418 HENRY A. EOWLAND

apparatus results so near those from my elaborate apparatus, which
almost grinds out accurate results without labor except in reduction.
Indeed, the quantity is the same as I find at about 20 C.

The experiments of Him of 1860-61 seem to point to a value of the
equivalent higher than that found by Joule, but the details of the
experiment do not seem to have been published, and they certainly
were not reduced to the air thermometer.

The method used by Violle in 1870 does not seem capable of accur-
acy, seeing that the heat lost by a disc in rapid rotation, and while
carried to the calorimeter, must have been uncertain.

The experiments of Him are of much interest from the methods
used, but can hardly have weight as accurate determinations. Some
of the methods will be again lef erred to when I come to the description
of apparatus.

Method by Heat Generated by Electric Cwrent

The old experiments of Quintus Icilius or Lenz do not have any
except historical value, seeing that Weber's measure of absolute resist-
ance was certainly incorrect and we now have no means of finding its
error.

The theory of the process is as follows. The energy of electricity
being the product of the potential by the quantity, the energy ex-
pended by forcing the quantity of electricity, Q, along a wire of re-
sistance, R, in a second of time, must be Q Z R, and as this must equal
the mechanical equivalent of the heat generated, we must have JH
Q z Rt, where H is the heat generated and t is the time the current Q
flows.

The principal difficulty about the determination by this method
seems to be that of finding R in absolute measure. A table of the
values of the ohm as obtained by different observers, was published by
me in my paper on the 'Absolute Unit of Electrical Besistance/ in
the American Journal of Science, Vol. XV, and I give it here with
some changes.

The ratio of the Siemens unit to the ohm is now generally taken at
9536, though previous to 1864 there seems to have been some doubt
as to the value of the Siemens unit.

Since 1863-4, when units of resistance first began to be made with
great accuracy, two determinations of the heat generated have been
made. The first by Joule with the ohm, and the second by H. F.
Weber, of Zurich, with the Siemens unit.

Ox THE MECHANICAL EQUIVALENT OF HEAT

419

Each determination of resistance with each of these experiments
gives one value of the mechanical equivalent. As Lorenz's result was
only in illustration of a method, I have not included it among the exact
determinations.

TABLE XXXI.

Date.

Observer.

Value of Ohm.

Remarks.

1849

Kirchhoff

88 to -90

Approximately.

1851

Weber

95 to -97

Approximately.

1862

Weber

j 1-088
j 1-075

From Thomson's unit.
From Weber's value of Siemens unit.

1863-4

B. A. Committee

j 1-0000
} -993

Mean of all results.
Corrected by Rowland to zero vel-

ocity of coil.

1870

Kohlrausch

1-0193

1873

Lorenz

975

Approximately.

1876

Rowland

99113s

From a preliminary comparison with

the B. A. unit.

1878

H. F. Weber

1-0014

Using ratio of Siemens unit to ohm,

9536.

The result found by Joule was J= 25187 in absolute measure using
feet and degrees F., which becomes 429-9 in degrees C. on a mercurial
thermometer and in the latitude of Baltimore, compared with water
at 18-6C.

TABLE XXXII. EXPERIMENTS OF JOULE.

Observer.

Value of
B. A. Unit.

Mechanical equivalent
from Joule's Exp.

Mechanical equivalent
reduced to Air Ther-
mometer and cor-
rected for 8p. Ht. of
Copper.

B. A. Committee

1-0000

429-9

431-4

Ditto corrected by Rowland
Kohlrausch

993
1-0193

426-9
438-2

428-4
439-7

Rowland

9911

426-1

427-6

H. F. Weber

1-0014

430-5

432-0

The experiments of H. F. Weber 36 gave 428-15 in the latitude of
Zurich and for 1 C. on the air thermometer and at a temperature of
18 C. This reduced to the latitude of Baltimore gives 428-45.

My own value at this temperature is 426-8, which agrees almost
exactly with the fourth value from my own determination of the abso~
lute unit. 37

K Given -9912 by mistake in the other tables.
3Phil. Mag., 1878, 5th ser., v. 135.

37 The value of the ohm found by reversing the calculation would be -992, almost
exactly my value.

420

HENEY A. ROWLAND

There can be no doubt that Joule's result is most exact, and hence
I have given his results twice the weight of Weber's. Weber used a
wire of about 14 ohms' resistance, and a small calorimeter holding only
250 grammes of water. This wire was apparently placed in the water
without any insulating coating, and yet current enough was sent
through it to heat the water 15 during the experiment. No precau-
tion seems to have been taken as to the current passing into the water,
which Joule accurately investigated. Again, the water does not seem
to have been continuously stirred, which Joule found necessary. And
further, Newton's law of cooling does not apply to so great a range
as 15, though the error from this source was probably small. Further-

TABLE XXXIII.

EXPERIMENTS OF H. F. WEBER.

Mean of Joule and
Weber, giving Joule
twice the Weight of
Weber.

Observer.

Value of
B. A. Unit.

Mechanical equivalent
of Heat from Weber's
Experiments.

Mean equivalent re-
duced to Air Ther-
mometer in the Lati-
tude of Baltimore.

B. A. Committee

1-000
993
1-0193
9911
1-0014

427-9
424-9
436-2
424-1

428-5

430-2
427-2
439-1
426-4
431-4

Ditto corrected by Rowland
Kohlrausch

H. F. Weber

more, I know of no platinum which has an increase of coefficient of
001054 for 1 C., but it is usually given at about -003.

There can be no doubt that experiments depending on tKe heating
of a wire give too small a value of the equivalent, seeing that the
temperature of the wire during the heating must always be higher
than that of the water surrounding it, and hence more heat will be
generated than there should be. Hence the numbers should be slightly
increased. Joule used wire of platinum-silver alloy, and Weber plati-
num wire, which may account for Weber's finding a smaller value than
Joule, and Weber's value would be more in error than Joule's. Undoubt-
edly this is a serious source of error, and I am about to repeat an
experiment of this kind in which it is entirely avoided. Considering
this source of error, these experiments confirm both my value of the
ohm and of the mechanical equivalent, and unquestionably show a large
error in Kohlrausch's absolute value of the Siemens unit or ohm.

Ox THE MECHANICAL EQUIVALENT OF HEAT 421

The experiments of Joule and Favre, where the heat generated by
a current, both when it does mechanical work and when it does not,
are very interesting, but can hardly have any weight in an estimation
of the true value of the equivalent.

The method of calculating the equivalent from the chemical action
in a battery, or the electro-motive force required to decompose any
substance, such as water, is as follows:

Let E be such electro-motive force and c be the quantity of chemical
substance formed in battery or decomposed in voltameter per second.
Then total energy of current of energy per second is EQ, where Q is
the current, or cQHJ, where H is the heat generated by unit of c, or
required to decompose unit of c. Hence, if the process is entirely
reversible, we must have in either case

CHJ = E.

But the process is not always reversible, seeing that it requires more
electro-motive force to decompose water than is given by a gas battery.
This is probably due to the formation at first of some unstable com-
pound like ozone. The process with a battery seems to be best, and we
can thus apply it to the Daniell cell. The following quantities are
mostly taken from Kohlrausch.

The quantity c has been found by various observers, and Kohlrausch M
gives the mean value as -009421 for water according to his units (mg.,
mm., second system). Therefore for hydrogen it is -001047.

The quantity H can be observed directly by short-circuiting the
battery, or can be found from experiments like those of Favre and
Silbermann.

The electro-motive force E can be made to depend either upon the
absolute measure of resistance, or can be determined, as Thomson has
done, in electro-static units. In electro-magnetic units it is

Absolute Measure

Siemens. Ohms. according to my

Determination.

After Waltenhof en 11-43 10-90 10-80 XlO 10

" Kohlrausch 39 11-71 H'17 11-07X10 10

After Favre, 1 equivalent of zinc developes in the Daniell cell 23993
heat units;

. / E

38 Fogg. Ann., cxlix, 179.

39 Given by Kohlrausch, Pogg. Ann., cxlix, 182.

422 HEXRY A. ROWLAND

On the rag., mm., second system, we have -# = 10-935 X 10 10 , c =
001047, H = 23993, g = 9800-5 at Baltimore.

/. = 444160 mm. = 444-2 metres.
9

Using Kohlrausch's value for absolute resistance, he finds 456-5,
which is much more in error than that from my determination. I do
not give the calculation from the Grove battery, because the Grove
battery is not reversible, and action takes place in it even when no
current flows.

Thomson finds the difference of potential between the poles of a
Daniell cell in electro-static measure to be -00374 on the cm., grm.,
second system. 40 Using the ratio 29,900,000,000 cm. per second, as I
have recently found, but not yet published, we have 111,800,000 on
the electro-magnetic system or 11-18 X 10 10 on the mm., mg., second
system. This gives

= 474.3 metres.

General Criticism

All the results so far obtained, except those of Joule, seem to be of
the crudest description; and even when care was apparently taken in
the experiment, the method seems to be defective, or the determination
is made to rest upon the determination of some other constant whose
value is not accurately known. Again, only one or two observers have
compared their thermometers with the air thermometer, although I
have shown in ' Thermometry ' that an error of more than one per
cent may be made by this method. The range of temperature is also
small as a general rule and the specific heat of water is assumed con-
stant.

Hence a new determination, avoiding these sources of erfor, seems
to be imperatively demanded.

(6.) Description of Apparatus
1. PRELIMINARY EEMARKS

As we have seen in the historical portion, the only experiments of a
high degree of accuracy to the present time are those of Joule. Looked
at from a general point of view, the principal defects of his method
were the use of the mercurial instead of the air thermometer, and the
small rate at which the temperature of his calorimeter rose.

40 Thomson, Papers on Electrostatics and Magnetism, p. 246.

ON THE MECHANICAL EQUIVALEXT OF HEAT 423

In devising a new method a great rise of temperature in a short time
was considered to be the great point, combined, of course, with an accu-
rate measurement of the work done. For a great rise of temperature
great work must be done, which necessitates the use of a steam-engine
or other motive power. For the measurement of the work done, there
is only one principle in use at present, which is, that the work trans-
mitted by any shaft in a given time is equal to 2/r times the product of
the moment of the force by the number of revolutions of the shaft in
that time.

In mechanics it is common to measure the amount of the force
twisting the shaft by breaking it at the given point, and attaching the
two ends together by some arrangement of springs whose stretching
gives the moment. Morin's dynamometer is an example. Him 41 gives
a method which he seems to consider new, but which is immediately
recognized as Huyghens's arrangement for winding clocks without stop-
ping them. As cords and pulleys are used which may slip on each other,
it cannot possess much accuracy. I have devised a method by cog-
wheels which is more accurate, but which is better adapted for use in
the machine-shop than for scientific experimentation.

But the most accurate method known to engineers for measuring the
work of an engine is that of White's friction brake, and on this I have
based my apparatus. Him was the first to use this principle in deter-
mining the mechanical equivalent of heat. In his experiment a hori-
zontal axis was turned by a steam-engine. On the axis was a pulley
with a flat surface, on which rested a piece of bronze which was to be
heated by the friction. The moment of the force with which the fric-
tion tended to turn the piece of bronze was measured, together with
the velocity of revolution. This experiment, which Him calls a balance
de frottement, was first constructed by him to test the quality of oils used
in the industrial arts. He experimented by passing a current of water
through the apparatus and observing the temperature of the water be-
fore and after passing through. He thus obtained a rough approxima-
tion to Joule's equivalent.

He afterward constructed an apparatus consisting of two cylinders
about 30 cm. in diameter and 100 cm. long, turning one within the
other, the annular space between which could be filled with water, or
through which a stream of water could be made to flow whose tempera-
ture could be measured before and after. The work was measured by
the same method as before.

41 Exposition de la Theorie Mecanique de la Chaleur, 3 m 6d., p. 18.

424 HENRY A. BOWLAND

But in neither of these methods does Him seem to have recognized
the principle of the work transmitted by a shaft being equal to the
moment of the force multiplied by the angle of rotation of the shaft.
In designing his apparatus, he evidently had in view the reproduction
in circular motion of the case of friction between two planes in linear
motion.

Since I designed my apparatus, Puluj 42 has designed an instrument
to be worked by hand, and based on the principle used by Him. He
places the revolving axis vertical, and the friction part consists of two
cones rubbing together. But no new principle is involved in his appa-
ratus further than in that used by Him.

In my apparatus one of the new features has been the introduction
of the Joule calorimeter in the place of the friction cylinders of Him
or the cones of Puluj. At first sight the currents and whirlpools in
such a calorimeter might be supposed to have some effect; but when
the motion is steady, it is readily seen that the torsion of the calorimeter
is equal to that of the shaft, and hence the principle must apply.

This change, together with the other new features in the experi-
ments and apparatus, has at once made the method one of extreme
accuracy, surpassing all others very many fold.

2. GENEBAL DESCRIPTION

The apparatus was situated in a small building, entirely separate
from the other University buildings, and where it was free from dis-
turbances.

Fig. 6 gives a general view of the apparatus. To a movable axis, ab,
a calorimeter similar to Joule's is attached, and the whole is suspended
by a torsion wire, c. The shaft of the calorimeter comes out from the
bottom, and is attached to a shaft, ef, which receives a uniform motion
from the engine by mean's of the bevel wheels g and Ji. To the axis,
ab, an accurate turned wheel, M, was attached, and the moment of
the force tending to turn the calorimeter was measured by the weights
o and p, attached to silk tapes passing around the circumference of the
wheel in combination with the torsion of the suspending wire. To this
axis was also attached a long arm, having two sliding weights, q and r,
by which the moment of inertia could be varied or determined.

42 Pogg. Ann., clvii, 437.

"Joule's latest results were published after this was written, and I was not aware
that he, had made this improvement until lately. The result of his experiment, how-
ever, reached me soon after, and I have referred to it in the paper, but I did not see
the complete paper until much later.

ON THE MECHANICAL EQUIVALENT OF HEAT 425

FIG. 6.

426 HENRY A. EOWLAND

The number of revolutions was determined by a chronograph, which
received motion by a screw on the shaft ef, and which made one revo-
lution for 102 of the shaft. On this chronograph was recorded the
transit of the mercury over the divisions of the thermometer.

Around the calorimeter a water jacket, tu, made in halves, was
placed, so that the radiation could be estimated. A wooden box sur-
rounded the whole, to shield the observer from the calorimeter.

The action of the apparatus is in general as follows: As the inner
paddles revolve, the water strikes against the outer paddles, and so
tends to turn the calorimeter. When this force is balanced by the
weights op, the whole will be in equilibrium, which is rendered stable
by the torsion of the wire cd. Should any slight change take place in
the velocity, the calorimeter will revolve in one direction or the other
until the torsion brings it into equilibrium again. The amount of tor-
sion read off on a scale on the edge of Tel gives the correction to be
added to or subtracted from the weights op.

One observer constantly reads the circle Tel, and the other constantly
records the transits of the mercury over the divisions of the ther-
mometer.

A series extending over from one half to a whole hour, and record-
ing a rise of 15 C. to perhaps 25 C., and in which a record was made
for perhaps each tenth of a degree, would thus contain several hundred
observations, from any two of which the equivalent of heat could be
determined, though they would not all be independent. Such a series
would evidently have immense weight; and, in fact, I estimate that,
neglecting constant errors, a single series has more weight than all of
Joule's experiments of 1849, on water, put together. 44

The correction for radiation is inversely proportional to the ratio of
the rate of work generated to the rate at which the heat is lost;
and this for equal ranges of temperature is only 7 V as great in my
measures as in Joule's; for Joule's rate of increase was about 0-62 C.
per hour, while mine is about 35 C. in the same time, and can be in-
creased to over 45 C. per hour.

3. DETAILS
The Calorimeter

Joule's calorimeter was made in a very simple manner, with few
paddles, and without reference to the production of currents to mix

44 Forty experiments, with an average rise of temperature of 0-56 F., equal to
0-31 C., gives a total rise of 12 -4 C., which is only about two-thirds the average of
one of my experiments. As my work is measured with equal accuracy, and my
radiation with greater, the statement seems to be correct.

N THE MECHANICAL EQUIVALENT OF HEAT

427

up the water. Hence the paddles were made without solder, and were
screwed together. Indeed, there was no solder about the apparatus.

But, for my purpose, the number of paddles must be multiplied, so
that there shall be no jerk in the motion, and that the resistance may
be great; they must be stronger, to resist the force from the engine,
and they must be light, so as not to add an uncertain quantity to the
calorific capacity. Besides this, the shape must be such as to cause
the whole of the water to run in a constant stream past the thermom-
eter, and to cause constant exchange between the water at the top and
at the bottom.

FIG. 7.

FIG. 8.

Fig. 7 shows a section of the calorimeter, and Fig. 8 a perspective
view of the revolving paddles removed from the apparatus, and with the
exterior paddles removed from around it; which could not, however, be
accomplished physically without destroying them.

To the axis cb, Fig. 7, which was of steel, and 6 mm. in diameter, a
copper cylinder, ad, was attached, by means of four stout wires at e,
and four more at f. To this cylinder four rings, g, Ji, i, j, were attached,
which supported the paddles. Each one had eight paddles, but each
ring was displaced through a small angle with reference to the one
below it, so that no one paildle came over another. This was to make
the resistance continuous, and not periodical. The lower row of pad-
dles were turned backwards, so that they had a tendency to throw the
water outwards and make the circulation, as I shall show afterwards.

428 HENRY A. ROWLAND

Around these movable paddles were the stationary paddles, consist-
ing of five rows of ten each. These were attached to the movable
paddles by bearings,, at the points c and Jc, of the shaft, and were re-
moved with the latter when this was taken from the calorimeter.
When the whole was placed in the calorimeter, these outer paddles were
attached to it by means of four screws, I and m, so as to be immovable.

The cover of the calorimeter was attached to a brass ring, which
was nicely ground to another brass ring on the calorimeter, and which
could be made perfectly tight by means of a little white-lead paini
The shaft passed through a stuffing-box at the bottom, which was
entirely within the outer surface of the calorimeter, so that the heat
generated should all go to the water. The upper end of the shaft
rested in a bearing in a piece of brass attached to the cover. In the
cover there were two openings, one for the thermometer, and the
other for filling the calorimeter with water.

From the opening for the thermometer, a tube of copper, perforated
with large holes, descended nearly to the centre of the calorimeter.
The thermometer was in this sieve-like tube at only a short distance
from the centre of the calorimeter, with the revolving paddles outside
of it, and in the stream of water, which circulated as shown by the
arrows.

This circulation of water took place as follows. The lower paddles
threw the water violently outwards, while the upper paddles were pre-
vented from doing so by a cylinder surrounding the fixed paddles.
The consequence was, that the water flowed up in the space between
the outer shell and the fixed paddles, and down through the central
tube of the revolving paddles. As there was always a little air at the
top to allow for expansion, it would also aid in the same direction.
These currents, which were very violent, could be observed through
the opening's.

The calorimeter was attached to a wheel, fixed to the shaft db, by

Ox THE MECHANICAL EQUIVALENT OF HEAT 429

the method shown in Fig. 9. At the edge of the wheel, which was of
the exact diameter of the calorimeter, two screws were attached, from
which wires descended to a single screw in the edge of the calorimeter.
Through the wheel, a screw armed with a vulcanite point pressed upon
the calorimeter, and held it firmly. Three of these arrangements, at
distances of 120, were used. To centre the calorimeter, a piece of
vulcanite at the centre was used. By this method of suspension very
little heat could escape, and the amount could he allowed for hy the
radiation experiments.

The Torsion System

The torsion wire was of such strength that one millimeter on the
scale at the edge of the wheel signified 11-8 grammes, or ahout y^ of
the weights op generally used. There were stops on the wheel, so
that it could not move through more than a small angle. The weights
were suspended by very flexible silk tapes, 6 mm. or 8 mm. broad and
0-3 mm. thick. They varied from 4-5 k. to 8-5 k. taken together. The
shaft, ab, was of uniform size throughout, so that the wire c suspended
the whole system, and no weight rested on the bearings.

The pulleys, m, n, Fig. 6, were very exactly turned and balanced, and
the whole suspended system was so free as to vibrate for a considerable
time. However, as will be shown hereafter, its freedom is of little
consequence.

The Water Jacket

Around the calorimeter, a water jacket, t u, was placed, so that the
radiation should be perfectly definite. During the preliminary experi-
ments a simple tin jacket was used, whose temperature was determined
by two thermometers, one above and the other below, inserted in tubes
attached to the jacket.

The Driving Gear

The cog-wheels, g, h, were made by Messrs. Brown and Sharpe, of
Providence, and were so well cut that the motion transmitted to the
calorimeter must have been very uniform.

The Chronograph

The cylinder of the chronograph was turned by a screw on the shaft
ef, and received one revolution for 102 of the paddles; 155 revolutions
of the cylinder, or 15,810 of the paddles, could be recorded, though,

430 HENRY A. EOWLAND

when necessary, the paper could be changed without stopping, and the
experiment thus continued without interruption.

The Frame and Foundation

The frame was very massive and strong, so as to prevent oscillation;
and the whole instrument weighed about 500 pounds as nearly as could
be estimated. It was placed on a solid brick pier, with a firm founda-
tion in the ground. The trembling was barely perceptible to the hand
when running the fastest.

The Engine

The driving power was a petroleum engine, which was very efficient
in driving the apparatus with uniformity.

The Balance

For weighing the calorimeter, a balance capable of showing the
presence of less than T \ gramme with 15,000 grammes was used. The
weights, however, by Schickert, of Dresden, were accurate among them-
selves to at least 5 mg. for the larger weights, and in proportion for
the smaller. A more accurate balance would have been useless, as will
be seen further on.

Adjustments

There are few adjustments, and they were principally made in the
construction.

In the first place, the shafts ab and ef must be in line. Secondly,
the wheels rrm must be so adjusted that their planes are vertical, and
that the tapes shall pass over them symmetrically, and that their edges
shall be in the plane of the wheel Id.

Deviation from these adjustments only produced small error.

(c.) Theory of the Experiment
1. ESTIMATION OF WORK DONE

The calorimeter is constantly receiving heat from the friction, and
is giving out heat by radiation and conduction. Now, at any given
instant of time, the temperature of the whole of the calorimeter is not
the same. Owing to the violent stirring, the water is undoubtedly at
a very uniform temperature throughout. But the solid parts of the
calorimeter cannot be so. The greatest difference of temperature is
evidently soon after the commencement of the operation. But after

Ox THE MECHANICAL EQUIVALENT OF HEAT 431

some time the apparatus reaches a stationary state, in which, but for
the radiation, the rise of temperature at all points would be the same.
This steady state will be theoretically reached only after an infinite
time; but as most of the metal is copper, and quite thin, and as the
whole capacity of the metal work is only about four per cent of the
total capacity, I have thought that one or two minutes was enough to
allow, though, if others do not think this time sufficient, they can
readily reject the first few observations of each series. When there
is radiation, the stationary state will never be reached theoretically,
though practically there is little difference from the case where there is
no radiation.

The measurement of the work done can be computed as follows.
Let M be the moment of the force tending to turn the calorimeter, and
dd the angle moved by the shaft. The work done in the time t will
be fMdft. If the moment of the force is constant, the integral is
simply Mti; but it is impossible to obtain an engine which runs with
perfect steadiness, and although we may be able to calculate the inte-
gral, as far as long periods are concerned, by observation of the torsion
circle, yet we are not thus able to allow for the irregularity during one
revolution of the engine. Hence I have devised the following theory.
I have found, by experiments with the instrument, that the moment of
the force is very nearly, for high velocities at least, proportional to the
square of the velocity. For rapid changes of the velocity, this is not
exactly true, but as the paddles are very numerous in the calorimeter,
it is probably very nearly true. We have then

where C is a constant. Hence the work done becomes

n r (dov, a n r/dff\',.

W= C I -jj- \dO = C I ( rr \flt-

J \dt ) J \tltj

As we allow for irregularities of long period by readings of the tor-
sion circle, we can assume in this investigation that the mean velocity
is constant, and equal to t? . The form of the variation of the velocity
must be assumed, and I shall put, without further discussion,

We then find, on integrating from a to 0,

432 HENEY A. KOWLAND

which is the work on the calorimeter during one revolution of the
engine.

The equation of the motion of the calorimeter, supposing it to be
nearly stationary, and neglecting the change of torsion of the suspend-
ing wire, is

m dV WD , nt f- 2* A 2 A

+ Cvl (1 + c cos - - = 0,

TIT ^

g dt* 2 \ a

where m is the moment of inertia of the calorimeter and its attach-
ments, <p is the angular position of the calorimeter, W is the sum of
the torsion weights, and D is the diameter of the torsion wheel. Hence,

= L j J/ \_Cvl (I +

til (_

When WD = 2Cv Q z (I -\- -|c 2 ), the calorimeter will merely oscillate
around a given position, and will reach its maximum at the times t = 0,
a, a, &c.

The total amplitude of each oscillation will be very nearly

,,,_,,/ _ Cfrfra'c = WDga'c
v*m 2x*m '

If x is the amplitude of each oscillation, as measured in millimetres,
on the edge of the wheel of "diameter D, we have <p <p' =. -?.

Hence . c = ^,

where n is the number of revolutions of the engine per second.
Having found c in this way, the work will be, during any time,

w = TT WDN(l + c 2 ) ,
where N is the total number of revolutions of the paddles.

A variation of the velocity of ten per cent from the mean, or twenty
per cent total, would thus only cause an error of one per cent in the
equivalent.

Hence, although the engine was only single acting, yet it ran easily,
had great excess of power, and was very constant as far as long periods
were concerned. The engine ran very fast, making from 200 to 250
revolutions per minute. The fly-wheel weighed about 220 pounds, and
had a radius of 1 feet. At four turns per second, this gives an energy
of about 3400 foot-pounds stored in the wheel. The calorimeter re-
quired about one-half horse-power to drive it; and, assuming the same

ON THE MECHANICAL EQUIVALENT OF HEAT 433

for the engine friction, we have about 140 foot-pounds of work re-
quired per revolution. Taking the most unfavorable case, where all
the power is given to the engine at one point, the velocity changes
during the revolution about four per cent, or c would nearly equal .02,
causing an error of 1 part in 2500 nearly. By means of the shaking
of the calorimeter, I have estimated c as follows, the value of m being
changed by changing the weight on the inertia bar, or taking it off
altogether. The estimate of the shaking was made by two persons
independently.

m. x observed. c calculated.

2,200,000 grms. cm. a -6 mm. '016

3,100,000 " -36 " -013

11,800,000 " -13 " -017

Mean, c = '015

causing a correction of 1 part in 5000.

Another method of estimating the irregularity of running is to put
on or take off weights until the calorimeter rests so firmly against the
stops that the vibration ceases. Estimated in this way, I have found
a little larger value of c, namely, about -017.

But as one cannot be too careful about such sources of error, I
have experimented on the equivalent with different velocities and with
very different ways of running the engine, by which c was greatly
changed, and so have satisfied myself that the correction from this
source is inappreciable in the present state of the science of heat.

Hence I shall simply put for the work

w = xNWD,

in gravitation measure at Baltimore. To reduce to absolute measure,
we must multiply by the force of gravity given by the formula
g = 9-78009 + -0508 sm s ? ,

which gives 9-8005 metres per second at Baltimore. If the calorimeter
moved without friction, no work would be required to cause it to
vibrate back and forth, as I have described; but when it moves with
friction, some work is required. When I designed the apparatus, I thus
had an idea that it would be best to make it as immovable as possible
by adding to its moment of inertia by means of the inertia bar and
weights. But on considering the subject further, I see that only the
excess of energy represented by c 2 xNWD can be used in this way. For,
when the calorimeter is rendered nearly immovable by its great moment
28

^aas^=5r^=rR^cs=^^^j^s^xs^-Jua^

434 HENRY A. EOWLAXD

of inertia, the work done on it is, as we have seen, TtNWD (1 -f- c 2 );
but if it had no inertia, it is evident that the work would be only
TiNWD. If, therefore, the calorimeter is made partially stationary,
either by its moment of inertia or by friction, the work will be some-
where between these two, and the work spent in friction will be only
so much taken from the error. Hence in the latter experiments the
inertia bar was taken off, and then the calorimeter constantly vibrated
through about half a millimeter on the torsion scale.

Besides this quick vibration, the calorimeter is constantly moving to
the extent of a few millimetres back and forth, according to the vary-
ing velocity of the engine. As frequent readings were taken, these
changes were eliminated. In very rare cases the weights had to be
changed during the experiment; but this was very seldom.

The vibration and irregular motion of the calorimeter back and forth
served a very useful purpose, inasmuch as it caused the friction of the
torsion apparatus to act first in one direction and then in the other, so
that it was finally eliminated. The torsion apparatus moved very
freely when the calorimeter was not in position, and would keep
vibrating for some minutes by itself, but with the calorimeter there
was necessarily some binding. But the vibration made it so free that
it would return quickly to its exact position of equilibrium when drawn
aside, and would also quickly show any small addition to the weights.
This was tried in each experiment.

To measure the heat generated, we require to know the calorific
capacity of the whole calorimeter, and the rise of temperature which
would have taken place provided no heat had been lost by radiation.
The capacity of the calorimeter alone I have discussed elsewhere, find-
ing the total amount equal to -347 k. of water at ordinary tempera-
tures. The total capacity of the calorimeter is then A -f- -347, where
A is the weight of water. Hence Joule's equivalent in absolute meas-
ure is

T _

~ (

where n is the number of revolutions of the chronograph, it making
one revolution to 102 of the paddles.

The corrections needed are as follows :

1st. Correction for weighing in air. This must be made to W, the
cast-iron weights, and to A -f- -347, the water and copper of the calori-
meter. If / is the density of the air under the given conditions, the
correction is -835 A.

ON THE MECHANICAL EQUIVALENT OF HEAT 435

2d. For the weight of the tape by which the weights are hung.

rm,- "0006
This i

3d. For the expansion of torsion wheel, D' being the diameter at
20 C. This is -000018 (t" 20). Hence,

' "

where t i' is the rise of the temperature corrected for radiation.

2. RADIATION

The correction for radiation varies, of course, with the difference of
temperature between the calorimeter and jacket; but, owing to the
rapid generation of heat, the correction is generally small in proportion.
The temperature generated was generally about 0-6 per minute. The
loss of temperature per minute by radiation was approximately -00140
per minute, where is the difference of the temperature. This is one
per cent for 10 -7, and four per cent for 14 -2. Generally, the calori-
meter was cooler than the jacket to start with, and so a rise of about
20 could be accomplished without a rate of correction at any point
of more than four per cent, and an average correction of less than two
per cent. An error of ten per cent is thus required in the estimation
of the radiation to produce an average error of 1 in 500, or 1 in 250
at a single point. The coefficients never differ from the mean more
than about two per cent. The observations on the equivalent, being
at a great variety of temperatures, check each other as to any error in
the radiation.

The losses of heat which I place under the head of radiation include
conduction and convection as well. I divide the losses of heat into the
following parts: 1st. Conduction down the shaft; 2d. Conduction by
means of the suspending wires or vulcanite points to the wheel above;
3d. True radiation; 4th. Convection by the air. To get some idea of
the relative amounts lost in this way, we can calculate the loss by
conduction from the known coefficients of conduction, and we can get
some idea of the relative loss from a polished surface from the experi-
ments of Mr. Nichol. In this way I suppose the total coefficient of
radiation to be made up approximately as follows:

Conduction along shaft ............ -00011

Conduction along suspending wires. . . . -00006

True radiation .................... -00017

Convection ........................ -00106

Total . -00140

436 HENEY A. EOWLAND

The conduction through the vulcanite only amounts to -0000002.

From this it would seem that three-fourths of the loss is due to
radiation and convection combined.

The last two losses depend upon the difference of temperature be-
tween the calorimeter and the jacket, but the first two upon the differ-
ence between the calorimeter and frame of the machine and the wheel
respectively. The frame was always of very nearly the same tempera-
ture as the water jacket, but the wheel was usually slightly above it.
At first its temperature was noted by a thermometer, and the loss to
it computed separately; but it was found to be unnecessary, and finally
the whole was assumed to be a function of the temperature of the
calorimeter and of the jacket only.

At first sight it might seem that there was a source of error in
having a journal so near the bottom of the calorimeter, and joined to
it by a shaft. But if we consider it a moment, we shall see that the
error is inappreciable; for even if there was friction enough in the
journal to heat it as fast as the calorimeter, it would decrease the
radiation only seven per cent, or make an average error in the experi-
ment of only 1 in 700. But, in fact, the journal was very perfectly
made, and there was no strain on it to produce friction; besides which,
it was connected to a large mass of cast-iron which was attached to
the base. Hence, as a matter of fact, the journal was not appreciably
warmer after running than before, although tested by a thermometer.
The difference could not have been more than a degree or so at most.

The warming of the wheel by conduction and of the journal by fric-
tion would tend to neutralize each other, as the wheel would be warmer
and the journal cooler during the radiation experiment than the fric-
tion experiment.

The usual method of obtaining the coefficient of radiation would be
to stop the engine while the calorimeter was hot, and observe the
cooling, stirring the water occasionally when the temperature was read.
This method I used at first, reading the temperature at intervals of
about a half to a whole hour. But on thinking the matter over, it
became apparent that the coefficient found in this way would be too
small, especially at small differences of temperature; for the layer
next to the outside would be cooled lower than the mean temperature,
and the heat could only get to the outside by conduction through the
water or by convection currents.

Hence I arranged the engine so as to run the paddles very slowly,
so as to stir the water constantly, taking account of the number of

ON THE MECHANICAL EQUIVALENT OF HEAT

437

the revolutions and the torsion, so as to compute the work. As I had
foreseen, the results in this case were higher than by the other method.
At low temperatures the error of the first method was fifteen per cent;
but at high, it did not amount to more than about three to five per
cent, and probably at very high temperatures it would almost vanish.

I do not consider it necessary to give all the details of the radiation
experiments, but will merely remark that, as the calorimeter was nickel-
plated, and as seventy-five per cent of the so-called radiation is due
to convection by the air, the coefficients of radiation were found to be
very constant under similar conditions, even after long intervals of
time.

The experiments were divided into two groups; one when the tem-
perature of the jacket was about 5 C., and the other when it averaged
about 20 C.

The results were then plotted, and the mean curve drawn through
them, from which the following coefficients were obtained. These
coefficients are the loss of temperature per minute, and per degree
difference of temperature.

TABLE XXXV.* COEFFICIENTS OF RADIATION.

Difference be-
tween Jacket and
Calorimeter.

Jacket 5.

Jacket 20.

00138

00134

00135

00130

+ 5

00137

00132

00142

00138

00148

00144

00154

00150

00158

.00154

As the quantity of water in the calorimeter sometimes varied slightly,
the numbers should be modified to suit, they being true when the total
capacity of the calorimeter was 8-75 kil. The total surface of the
calorimeter was about 2350 sq. cm., and the unit of time one minute.
To compare my results with those of McFarlane and of Nichol given
in the Proc. K. S. and Proc. R. S. E., I will reduce my results so that
they can be compared with the tables given by Professor Everett in his
' Illustrations of the Ccntimeter-Gramme-Second System of Units/
pp. 50, 51.

* [There is no table numbered XXXIV.]

438

HENRY A. ROWLAND

The reducing factor is -0621, and hence the last results for the jacket
at 20 C. become:

TABLE XXXVI.

Difference of
Temperature.

Coefficient of Radia-
tion on the C. G. S.

System.

McFarlane's
Value.

Ratio.

000081

000168

2-07

000082

000178

2-17

000086

000186

2-16

000089

000193

2-17

000093

000201

2-16

000096

000207

2.15

The variation which I find is almost exactly that given by McFar-
lane, as is shown by the constancy of the column of ratios. But my
coefficients are less than half those of McFarlane. This may possibly
be due to the fact that the walls of McFarlane's enclosure were black-
ened, and to his surface being of polished copper and mine of polished
nickel: his surface may also have been better adapted by its form to
the loss of heat by convection. The results of Nichol are also much
lower than those of McFarlane.

The fact that the coefficients of radiation are less with increased
temperature of jacket is just contrary to what Dulong and Petit found
for radiation. But as I have shown that convection is the principal
factor, I am at a loss to check my result with any other observer.
Dulong and Petit make the loss from convection dependent only upon
the difference of temperature, and approximately upon the square root
of the pressure of the gas. Theoretically it would seem that the loss
should be less as the mean temperature rises, seeing that the air be-
comes less dense and its viscosity increases. Should we substitute
density for pressure in Dulong's law, we should have the loss by con-
vection inversely as the square root of the mean absolute temperature,
or approximately the absolute temperature of the jacket. This would
give a decrease of one per cent in the radiation for about 6, which is
not far from what I have found.

To estimate the accuracy with which the radiation has been obtained
is a very difficult matter, for the circumstances in the experiment are
not the same as when the radiation was obtained. In the first place,
although the water is stirred during the radiation, yet it is not stirred
so violently as during the experiment. Further, the wheel above the
calorimeter is warmer during radiation than during the experiment.

ON THE MECHANICAL EQUIVALENT OF HEAT 439

Both these sources of error tend to give too small coefficients of radia-
tion, and this is confirmed by looking over the final tables. But I have
not felt at liberty to make any corrections based on the final results, as
that would destroy the independence of the observations. But we are
able thus to get the limits of the error produced.

During the preliminary experiments a water jacket was not used,
but only a tin case, whose temperature was noted by a thermometer
above and below. The radiation under these circumstances was larger,
as the case was not entirely closed at the bottom, and so permitted more
circulation of air.

3. CORRECTIONS TO THERMOMETERS, ETC.

Among the other corrections to the temperature as read off from
the thermometers, the correction for the stem at the temperature of
the air is the greatest. The ordinary formula for the correction is
000156n( t"). But, in applying this correction, it is difficult to
estimate n, the number of degrees of thermometer outside the calo-
rimeter and at the temperature of the air, seeing that part of the stem
is heated by conduction. The uncertainty vanishes as the thermometer
becomes longer and longer, or rather as it is more and more sensitive.
But even then some of the uncertainty remains. I have sought to
avoid this uncertainty by placing a short tube filled with water about
the lower part of the thermometer as it comes out of the calorimeter.
The temperature of this was indicated by a thermometer, by aid of
which also the heat lost to the water by conduction through the ther-
mometer stem could be computed; this, however, was very minute com-
pared with the whole heat generated, say 1 in 10,000.

The water being very nearly at the temperature of the air, the stem
above it could be assumed to be at the temperature of the air indicated
by a thermometer hung within an inch or two of it. The correction for
stem would thus have to be divided into two parts, and calculated
separately. Calculated in this way, I suppose the correction is perfectly
certain to much less than one hundredth of a degree : the total amount
was seldom over one-tenth of a degree.

Among the uncertain errors to which the measurement of tempera-
ture is subjected, I may mention the following:

1. Pressure on bulb. A pressure of 60 cm. of water produced a
change of about 0-01 in the thermometers. When the calorimeter
was entirely closed there was soon some pressure generated. Hence
the introduction of the safety-tube, a tube of thin glass about 10 cm.

440 HENRY A. EOWLAXD

long, extending through a cork in the top of the calorimeter. The top
of the safety-tube was nearly closed by a cork to prevent evaporation.
Had the tube been shorter, water would have been forced out, as well
as air.

2. Conduction along stem from outside to thermometer bulb. To
avoid this, not only was the bulb immersed, but also quite a length of
stem. As this portion of the stem, as also the bulb, was surrounded
by water in violent motion, there could have been no large error from
this source. The immersed stem to the top of the bulb was generally
about 5 cm. or more, and the stem only about -8 cm. in diameter.

3. The thermometer is never at the temperature of the water, be-
cause the latter is constantly rising; but we do not assume that it is
so in the experiment. We only assume that it lags behind the water
to the same amount at all parts of the experiment, and this is doubt-
less true.

To see if the amount was appreciable, I suddenly threw the apparatus
out of gear, thus stopping it. The temperature was observed to con-
tinue rising about 0-02 C. Allowing 0-01 for the rise due to motion
after the word "Stop" was given, we have about 0-01C. as the
amount the thermometer lagged behind the water.

4. Evaporation. A possible source of error exists in the cooling of
the calorimeter by evaporation of water leaking out from it.

The water was always weighed before and after the experiment in
a balance giving -i. gramme with accuracy. The normal amount of
loss from removal of thermometer, wet corks, &c., was about 1 gramme.
The calorimeter was perfectly tight, and had no leakage at any point
in its normal state. Once or twice the screws of the stuffing-box
worked loose, but these experiments were rejected.

The evaporation of 1 gramme of water requires about 600 heat units,
which is sufficient to depress the temperature of the calorimeter about
0-07 C. As the only point at which evaporation could take place was
through a hole less than 1 mm. diameter in the safety-tube, I think it
is reasonable to assume that the error from this source is inappreciable.
But to be doubly certain, I observed the time which drops of water of
known weight and area, placed on the warm calorimeter, took to dry.
From these experiments it was evident that it would require a consid-
erable area of wet surface to produce an appreciable effect. This wet
surface never existed unless the calorimeter was wet by dew deposited
on the cool surface. To guard against this error, the calorimeter was
never cooled so low that dew formed; it was carefully rubbed with a

ON THE MECHANICAL EQUIVALENT OF HEAT 441

towel, and placed in the apparatus half an hour to an hour before the
experiment, exposed freely to the air. The surface being polished, the
slightest deposit of dew was readily visible. The greatest care was
taken to guard against this source of error, and I think the experiment
is free from it.

(d.) Results
1. CONSTANT DATA

Joule's equivalent in gravitation measure is of the dimensions of
length only, being the height which water would have to fall to be
heated one degree. Or let water flow downward with uniform velocity
through a capillary tube impervious to heat; assuming the viscosity
constant, the rate of variation of height with temperature will be
Joule's equivalent.

Hence, besides the force of gravity the only thing required in abso-
lute measure is some length. The length that enters the equation
is the diameter of the torsion wheel. This was determined under a
microscope comparator by comparison with a standard metre belong-
ing to Professor Eogers of Harvard Observatory, which had been
compared at Washington with the Coast Survey standards, as well as
by comparison with one of our own metre scales which had also been
so compared. The result was -26908 metre at 20 C.

To this must be added the thickness of the silk tape suspending the
weights. This thickness was carefully determined by a micrometer
screw while the tape was stretched, the screw having a flat end. The
result was -00031 m.

So that, finally, D' ~ -26939 metre at 20 C. Separating the con-
stant from the variable parts, the formula now becomes

JL = j*6-324^ ^ + .ooooiS 0" - 20) + *

g = 9-8005 at Baltimore.

It is unnecessary to have the weights exact to standard, provided they
are relatively correct, or to make double weighings, provided the same
scale of the balance is always used. For both numerator and denomi-
nator of the fraction contain a weight.

2. EXPEBIMENTAL DATA AND TABLES OF RESULTS

In exhibiting the results of the experiments, it is much more satisfac-
tory to compute at once from the observations the work necessary to
raise 1 kil. of the water from the first temperature observed to each sue-

442 HENRY A. EOWLAND

ceeding temperature. By interpolation in such a table we can then
reduce to even degrees. To compare the different results I have then
added to each table such a quantity as to bring the result at 20 about
equal to 10,000 kilogramme-metres.

The process for each experiment may be described as follows. The
calorimeter was first filled with distilled water a little cooler than the
atmosphere, but not so cool as to cause a deposit of dew. It was then
placed in the machine and adjusted to its position, though the outer half
of the jacket was left off for some time, so that the calorimeter should
become perfectly dry; to aid which the calorimeter was polished with a
cloth. The thermometer and safety-tube were also inserted at this
time.

After half an hour or so, the chronograph was adjusted, the outer half
of the jacket put in place, the wooden screen fixed in position, and all
was ready to start. The engine, which had been running quietly for
some time, was now attached, and the experiment commenced. First the
weights had to be adjusted so as to produce equilibrium as nearly as
possible.

The observers then took their positions. One observer constantly
recorded the transit of the mercury over the divisions of thermometer,
making other suitable marks, so that the divisions could be afterwards
recognized. He also read the thermometers giving the temperatures
of the air, the bottom of the calorimeter thermometer, and of the wheel
just above the calorimeter; and sometimes another, giving that of the
cast-iron frame of the instrument.

The other observer read the torsion wheel once every revolution of
the chronograph cylinder, recording the time by his watch. He also
recorded on the chronograph every five minutes by his watch, and like-
wise stirred the water in the jacket at intervals, and read its temper-
ature.

The recording of the time was for the purpose of giving the connect-
ing link between the readings of the torsion circle and of the ther-
mometer. This, however, as the readings were quite constant, had
only to be done roughly, say to half a minute of time, though the rec-
ords of time on the chronograph were true to about a second.

The thermometers to read the temperature of the water in the jacket
were graduated to 0-2 C., but were generally read to 0-1 C., and had
been compared with the standards. There was no object in using more
delicate thermometers.

After the experiment had continued long enough, the engine was

Ox THE MECHANICAL EQUIVALENT OF HEAT 443

stopped and a radiation experiment begun. The last operation was to
weigh the calorimeter again, after removing the thermometer and safety
tube, and also the weights which had been used.

The chronograph sheet, having then been removed from the cylin-
der, had the time records identified and marked, as well as the ther-
mometer records. Each line of the chronograph record was then num-
bered arbitrarily, and a table made indicating the stand of the ther-
mometer and the number of the revolutions and fractions of a revolu-
tion as recorded on the chronograph sheet. The times at which these
temperatures were reached was also found by interpolation, and re-
corded in another column.

From the column of times the readings of the torsion circle could be
identified, and so all the necessary data would be at hand for calculating
the work required to raise the temperature of one kilogramme of the
water from the first recorded temperature to any succeeding tempera-
ture.

As these temperatures usually contained fractions, the amount of
work necessary to raise one kilogramme of the water to the even degrees
could then be found from this table by interpolation. Joule's equiva-
lent at any point would then be merely the difference of any two suc-
ceeding numbers; or, better, one tenth the difference of two numbers
situated 10 apart, or, in general, the difference of the numbers divided
by the difference of the temperatures.

It would be a perfectly simple matter to make the record of the tor-
sion circle entirely automatic, and I think I shall modify the apparatus
in that manner in the future.

It would take too much space to give the details of each experiment;
but, to show the process of calculation, I will give the experiment of
Dec. 17, 1878, as a specimen. The chronograph sheet, of course, I
cannot give. The computation is at first in gravitation measure, but
afterwards reduced to absolute measure.

The calorimeter before the experiment weighed 12-2733 kil.
The calorimeter after the experiment weighed 12-2716 kil.

Mean 12-2720 kil.
Weight of calorimeter alone 3-8721 kil.

. . Water alone weighed 8-3999 kil.

3470 kil.

Total capacity 8-7469 kil.

444 HENRY A. ROWLAND

The correction for weighing in air was -835 / -00106.
The total term containing the correction is therefore -99878.

log 86-324 =1-9361316

log -99878 = 1-9994698

1-9356014

log 8-7469 = -9418542

log const, factor = -9937472 = log 9-85706.

Hence the work per kilogramme is 9-85706 S~Wn in gravitation
measure, the term 2'Wn being used to denote the sum of products
similar to Wn as obtained by simultaneous readings of torsion circle
and records on chronograph sheet.

Zero of torsion wheel, 79-3 mm.

Value of 1 mm. on torsion wheel -0118 kil.

The following were the records of time on the chronograph sheet :

Time observed. Revolutions of Chronograph. Time calculated.

15 8-74 15-2

20 25-32 20-1

25 42-10 25-0

30 59-05 30-0

35 76-00 35-0

40 93-03 40-0

45 109-97 45-0

50 126-92 50-0

55 144.14 55-0

The times were calculated by the formula

Time = -294 X Revolutions + 12-66,

which assumes that the engine moves with uniform velocity. As the
principal error in using an incorrect interpolation formula comes from
the calculation of the radiation, and as this formula is correct within
a few seconds for all the higher temperatures, we can use it in the cal-
culation of the times.

The records of the transits of the mercury over the divisions of the
thermometer were nearly always made for each division, but it is use-
less to calculate for each. I usually select the even centimeters, and
take the mean of the records for several divisions on each side.

While the mercury was rising 1 cm. on No. 6163, there would be

ON THE MECHANICAL EQUIVALENT OF HEAT 445

about seven revolutions of the chronograph, and consequently seven
readings of the torsion circle, each one of which was the average for a
little time as estimated by the eye.

I have obtained more than thirty series of results, but have thus far
reduced only fourteen, five of which are preliminary, or were made with
the simple jacket instead of the water jacket, the radiation to which
was much greater, as there was a hole at the bottom which allowed more
circulation of the air. The mean of the preliminary results agrees so
closely with the mean of the final results, that I have in the end given
them equal weight.

On March 24th, the same thermometer was used for a second experi-
ment directly after the first, seeing that the chronograph failed to work
in the first experiment until 8 was reached. The error from this cause
was small, as the first experiment only reached to 26 C., and hence
there could have been no change of zero, as this is very nearly the tem-
perature at which the thermometer was generally kept.

Having thus calculated the work in conjunction with the tempera-
ture, I have next interpolated so as to obtain the work at the even de-
grees. The tables so formed I have combined in two ways : first, I have
added to the column of work in each table an arbitrary number, such as
to make the work at 20 about 10,000, and have then combined them as
seen in Table LI, and, secondly, I have subtracted each number from
the one 10 farther down the table, and divided the numbers so found
by 10, thus obtaining the mechanical equivalent of heat.

In these tables four thermometers have been used, and yet they were
so accurate that little difference can be observed in the experiments
which can be traced to an error of the thermometer, although the Kew
standard has some local irregularities. The greatest difference between
any column of Table LI and the general mean is only 10 kilogramme-
metres, or 0-023 degree, and this includes all errors of calibration of
thermometers, radiation, &c. This seems to me to be a very remarkable
result, and demonstrates the surpassing accuracy of the method. In-
deed, the limit of accuracy in thermometry is the only limit which we
can at present give to this method of experiment. Hence the large
proportional time spent on that subject.

The accuracy of the radiation is demonstrated, to some extent, by
the agreement of the results obtained even with different temperatures
of the jacket. But on close observation it seems apparent that the
coefficients of radiation should be further increased as there is a ten-
dency of the end figures in each series to become too high. This is

446 HENEY A. ROWLAND

exactly what we should suppo&e, as we have seen that nearly all sources
of error tend in the direction of making the radiation too small. For
instance, an error came from not stirring the water during the radiation,
and there must be a small residual error from not stirring so fast
during radiation as during the experiment. Besides this, some parts
around the calorimeter were warm during the radiation which were cool
during the experiment. And both of these make the correction for
radiation too small. However, the error from this source is small, and
cannot possibly affect the general conclusions. In each column of
Tables LI and LII a dash is placed at the temperature of the jacket,
and for fifteen degrees below this point the error in the radiation must
produce only an inappreciable error in the equivalent: taking the ob-
servations within this limit as the standards, and rejecting the others,
we should still arrive at very nearly the same conclusions as if we ac-
cepted the whole.

Most of the experiments are made with a weight of about 7-3 kil., as
everything seemed to work best with this weight But for the sake
of a test I have run the weight up to 8-6 and down to 4-4 kil., by which
the rate of generation of the heat was changed nearly three times.
By this the correction for the radiation and the error due to the irregu-
larity of the engine are changed, and yet scarcely an appreciable differ-
ence in the results can be observed.

The tables explain themselves very well, but some remarks may be
in order. Tables XXXVII to L inclusive are the results of fourteen
experiments selected from the total of about thirty, the others not hav-
ing been worked up yet, though I propose to do so at nry leisure.

Table LI gives the collected results. At the top of each column the
date of the experiment and number of the thermometer are given, to-
gether with the approximate torsion weight and the rate of rise of tem-
perature per hour. The dash in each column gives approximately the
temperature of the jacket, and hence of the air. There are four col-
umns of mean values, but the last, produced from the combination of
the table by parts, is the best.

Table LII gives the mechanical equivalent of heat as deduced from
intervals of 10 on Table LI. The selection of intervals of 10 tends
to screen the variation of the specific heat of water from view, but a
smaller interval gives too many local irregularities. In taking the
mean I have given all the observations equal weight, but as the Kew
standard was only graduated to -J F. it was impossible to calibrate it
so accurately as to avoid irregularities of 0-02C. which would affect

Ox THE MECHANICAL EQUIVALENT OF HEAT

447

the quantities 1 in 500. Hence, in drawing a curve through the results,
as given in the last column, I have almost neglected the Kew, and have
otherwise sought to draw a regular curve without points of inflection.
The figures in the last column I consider the best.

Table LIII takes the mean values as found in Tables LI and LII,
and exhibits them with respect to the temperatures on the different
thermometers, to the different parts of the earth, and also gives the
reduction to the absolute scale. I am inclined to favor the absolute
scale, using ra= -00015, as given in the Appendix to Thermometry,
rather than -00018, as used throughout the paper.

Table LIV gives what T consider the final result of the experiment.
It is based on the result ra= -00015 for the thermometers, and is cor-
rected for the irregularity of the engine by adding 1 in 4000.

The minor irregularities are also corrected so that the results signify
a smooth curve, without irregularity or points of contrary flexure.
But the curve for the work does not differ more than three kilogramme-
metres from the actual experiment at any point, and generally coincides
with it to about one kilogramme-metre. These differences signify
0-007 C. and 0-002 C., respectively. The mechanical equivalent is
for single degrees rather than for ten degrees, as in the other tables.

TABLE XXXVII. FIRST SERIES. Preliminary.
January 16, 1878. Jacket and Air about 14 C.

Correction.

~ =
IS

5 8 s
3 C

||1

S
P

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

2484

7864

289

80-0

+ 045

+ 161

25-943

101-214

7156

2912

8292

3340

8720

3767

9147

4193

9573

4619

9999

5048

10428

5472

10852

5899

11279

6326

11706

6753

12133

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.

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

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

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.

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

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.

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.

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

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.

Correction.

Corrected
Temperature.

Revolutions of
Chronograph
In.

Mean Weight
W.

o.e

ft|o

LJ 03 T 1

* tHCO
SH >s^

.2 &
*|M

Temperature.

Work per
Kilogramme.

Work per
Kilogramme
+ 4903.

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

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.

Correction.

Corrected
Temperature.

Revolutions of
Chronograph
2n.

Mean Weight
W.

Work per
Kilogramme
= 29-8816 Wn.

Temperature.

Work per
Kilogramme.

Work per
Kilogramme
+ 2250.

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

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

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.

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

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.

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.

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.

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.

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.

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

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.

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

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.

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

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

^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

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.

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

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->

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

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;<Mioaoocoa

jcad 3{JO^ i _j_ i-ii-is<(Moijcoco'* < '*icirtioo>i>t-oooooooioio

1 '- |

90iS8'6S

90iS8'6

eoo-*ooCMOcO'-it-O5inift<?>coo t- wo

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

-N

'8919 jo
mooq
58 aqnx

00 O!

m in

to
*t *<

'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

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

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

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.

Corrections.

Corrected Tem-
perature Abso-
lute Scale.

Revolution of
Chronograph
2n.

Mean Weight
W.

k e

11^
Sfi

Temperature.

Work per
Kilogramme.

Work per
Kilogramme
+ 2210.

Reduction
to Absolute
Scale.

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

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

, 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<t-OCOCDC35CMJO
CMt-rHjOO^OOCM?^rH

I CO CO ^ CM
GO O CO CO OS
lO O * GO CM
CD t- !> 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

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<D '8919 *i2^BM

jnoq J9d O g8
'? '9919 '8Z toN

S -jnoq J9d 98

'9919 '91 ^K

T-i O rH l> 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

Hill

lillllilllliil

OS O O O

COOOtOt-ICOO*OS'*r-lt-OtOCMt-

3 1 s S 1

ililsiiliillii

t- co os m o

s s 2 s a

**<

c
B

00 O CO CO
O) t- rH lO

f
-r

c
c

r.
o*
"*

1.-

rH O t-
(M l> -l

1-1

(TJ t> ^H

;

<M t- ^H W OS

^'OO'MCC'-HloOSCOOOWCOOiOOS

-t

o w o to o

00 O CO 10 00

s s a 2 2

i> cc Oi oo o

iOCO-HCOSMO-<*-i**OCOTjit-

-r

GO O CO 10 00

O O W5 ^ O
d t*- ^H iO C&

Oi ^ Oi rf< O

rH T-H O^ d d

8 9 9 z * * J

-.c

00 "*& C5 3O

S t^

- 1

3 s a a a

^_r^_^

L "

OS * O O O

iOOSCOO5gjJ<iHOSCO

2 5 S

coeo^*SIS*Sco^ : : : :

g 2 :

r-t

CO -* it) CO t-
UJ CS CJ (M

oosso' etteo^ocot-KSsoT-!

SJSJCOCOCOCOCOCOWCOCOWTjf'*

460

HENRY A. ROWLAND

t-^OS.^Ot-WM^C

-nlea^w^

:iSNS

EH
4

rHOOOOOOJl-0^^

P
O

lSI{)

OSOOOOOOCOt-t-t-t-l-t-

* ***

Nt-^OOOrHCROOOt-OJ

'08 -09Q

os.oooooot-oot-oot-t-t-

-*'*'*-*Ttl-*rtlTj<-*'*rt<

WrHOOOtOiHOSl-COOO

'61 '09Q

O5OiOOOOCOOOl-t-t-l-l>

**** * ThTj<'*'*

. owoi-rH>t-^weo

'il -09Q

: : :SSwS

*-*"*Ttl-<J<'<i<'*-'**'<J<-*

EH p.

w *

- ?

S w

H H

"i3 ABPI

S ,,
g g

<i
S d

1 '

J O

es^w

:..:::!.

01 oo so o

H R

O* <N O* (M

^ M

O5 ^ W Oi

w ^

h
o

*^^ A*BP^

t- > t- to

O* <M ** O*

. . fc. t- . < e ^

H
J

^. ueg png

: I :"NNWN

-J
p,

"*"*"* _________i______^L___

M
P

J9S W

: !

"31 ^OJBpf

'L ^OJBJ^[

i !
i i

i-H tQ O

-n

-dragx

O^OOt-OOOJO^NW^WOl-

ON THE MECHANICAL EQUIVALENT OF HEAT

461

^ d rH os oo t** co in *n

^rj<^^^inin

cococoininmin*nm

winminminifto
dddddddd

t-^rHocoincoin-*

in^-<jtincoincoin

eosococoininminin
d d d d d d d d d

inmininmininin
dddddddd

t- i>

* *

:::/::;::

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

'.'.'.'.'.'.'.'.

ooooomrHrHcoin

dddddddd

dCOt-t-COdCOOOO

00
CO

comininincocooin
o os t- in

::::::::

00
CO

00 *

t- in co in TH d o

coM<osOcoddCQia

t- O5 O d

cosoioeoinmininin
d d d d d d d d d

OS 30

o m co co
d d d d

OrHdCO**<inCOt-CO

ddddddddd

OSOrHdCO-^ineO

dsocoeoeocococo

462

HEXEY A. EOWLAND

Mechanical Equivalent of Heat. 10 Series on the

Mercurial Thermometric
Scale, the Glass similar
to the

1*|

i>iccoi-Haoz>iCTt<i-ioct-5O

: : :SS^^^S^^S

uipnBjj

.(M^-lOOOlCTt<CO-HOCOOt>

' ' : 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-<<MM<tOOOO<M'*
O'*COCS}t-r-llCOSCOOOCN}OO'*O5COl-
OO'IMCOCO'<tl'*Tj(lCicO5Ol~t-D-aOOO

Per Kilogr. of Water.

. lllOO'I .

oscjiCJOt-i-*t-ocoicooi-i:oocS'-i

CXJl~'-llCOTjHCCCOl-THlCOTtHOO<Mt-
<MeMCOCOM<^Tt<iC 1 C5O5Ct~t-t-003O

>B89?,9 W - n Son 3

.98000'T s ^ B
3

*CiC5OT^ i ^COCN('--tOSlCCOOt^- 1 ^THOS
OSCMlCOO-HTt<l>OCSJ)CCOTHCO!OO5r-l

Rc>-ino4ieoAci-iioOTfiaO'Mb<

<N<MCOCO"*<Tj<TtliClC5O5Ol-t-l OOOO

-9uiniBi!8ofi5i

CBSSOCSCSOOCOt-iCWOl-iCUJOCO
CO-HlCt-OcOSOOSIJiCOOOCOCOOS-H
< MI>T-ilCO'tlOO<Mt>i-liCO-*iCOCJt-

Temperature.

Approximate, Mercurial Thermom.

T^ i ( O5 C^l CO CO CO ^ ^ ^ iC iC *C 1C 5O 5O

oooooooooooooooo

C^CO^lC5O?>OOC35Ot lO5CO^iC5Ot-

f PL JO

<MiyicO'<*'icictot-t-ooooosoooi i

OOOOOOOoOOOO'-l'-'i-ii-l

(MCO^iCCOt^COOJO TJCO^iCcot-

.p PW e a

Hi iTHCSllMWCViCJCOCOCO^f^T^Tt*^

oooooooooooooooo

weo^wcot-coosorHWco^jcjoh-

VSSS8

?S-^lCt-OSOr-iSXJCO^lCtOOOCOC^H

MI9 a 1P a

co-*iC5Ocoo5Oi-iffjeo-*icot>aso

(MCO-*COt-OOOSOT-liNCO-*iCI>

Absolute Scalel

QIOOO- = i

OOOOOOOOOOOOOOr-lrH
OO OOOOOOOOOOOOOOO

WCO^io?ct-OOOSO'H(jjcO'*COl>

'81000' = Smsn

0<MC0^1CCOI-OOOSO^<MCO^>C501-

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<T)5

OJO1O1O1O1O1O1O1O1O1O1O1O1O1OJO1O1O1O1

WOOSt-COlC'^'COOI-Ht-lrHrHrHi-lOIOIeOCO

0*OO5t-COM<COOl*-lOeJSCSOSOSOOOO
Q000>*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 <-HOioioicocoTj<Tj(iciciCcocor-.i-oooo

COOSSOOt-Oll-OSt-W^OCOi-IOO^ttr-ICOOl
.r-.f->COCOOOOO11COOOCOlCOOOCOOOrH

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

eoeo-}<icciccocoi-t-coaooooioso5csoso

O1O1O1O1O1O1O*WO1O1O1O1O1O1O1O1CO1O1O1CO

oooso'i-Hoieo-HJiccdi-odosOrHoieo-^iceo't-odoso
rHr-ioioioioioioioioioioicococoeoeocococoroco'*

OOOSOr-lOICO^lCCOI^OOOSOrHOleO^lCCOl OOOSOO
1-HrHOIOIOIOIOIOlOlOlOIOICOCOCOCOCOCOCO

00 OS O rH

CO'

CO l-

eo t-

464

HENEY A. KOWLAND

TABLE LIV. FINAL MOST PROBABLE RESULTS.

Work.

Mechanical
Equivalent.

Work.

Mechanical
Equivalent.

O o *

-P

,io$

(BOOO

i .

,io5

<!~ .

S"5

2-2

lug

^G3 '

. S

-u"S

S OD 9

;3 t>

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

SS g

ttf)'* J 4^*

o p ~~ (

|o6

l"|l

|||"

2 K

S m

ID
g

2 =

5 w

00000.

0000.

00000.

0000.

2289

2443

10852

10835

426.1

4176

2720

2865

11278

11253

426.0

4175

3150

3286

11704

11670

425.9

4174

3580

3708

429.8

4212

12130

12088

425.8

4173

4009

4129

429.5

4209

12556

12505

425.7

4172

4439

4550

429.3

4207

12982

12922

425.6

4171

4868

4970

429.0

4204

13407

13339

425.6

4171

5297

5390

428.8

4202

13833

13756

425.5

4170

5726

5811

428.5

4200

14258

14173

425.6

4171

6154

6230

428.3

4198

14684

14950

425.6

4171

6582

6650

428.1

4196

15110

15008

425.6

4171

7010

7070

427.9

4194

15535

15425

425.7

4172

7438

7489

427.7

4192

15961

15842

425.7

4172

7865

7908

427.4

4189

16387

16259

425.8

4173

8293

8327

427.2

4187

16812

16676

425.8

4173

8720

8745

427.0

4185

17238

17094

9147

9164

426.8

4183

17664

17511

9574

9582

426.6

4181

18091

17930

10000

426.4

4179

18517

18347

10426

10418

426.2

4177

18943

18765

TABLE LV. QUANTITY TO ADD TO THE EQUIVALENT AT BALTIMORE TO
REDUCE TO ANT LATITUDE.

Latitude.

Addition in
Kilogramme-Metres.

+ 0.89

+ 0.82

+ 0.63

+ 0.34

+ 0.08

0.41

0.77

-1.06

1.26

-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.

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

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.

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

.0066

2.8

5.1

.0054

2.3

4.2

.0042

1.8

3.2

.0031

1.8

2.4

.0021

1.6

.0011

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

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

1-000

93229-7 ^

Copper

25541-

2430-2

092

2349-8 *

Brass

18901-

1800-0

091

1720-0

Brass stopper

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

767-0 774-0

3-3 2-8

2 -2

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-

o .

No.

Date.

Method.

Tern,
of

Joule's
Value.

mometer and Lati-
tude of Baltimore.

J.-R.

to ^

English

Metric

measure.

system.

1847

Friction of water

781.5

787.0

442.8

427.4

+ 15.4

1850

water

772.7

778.0

426.8

427.7

mercury

9 772.8

779.2

427.5

428.8

1.3

mercury

9 ! 775.4

781.4

428.7

428.8

iron

776.0

782.2

429.1

428.8

+ .3

iron

773.9

780.2

428.0

428.8

- .8

1867

Elec ric heating

18.6

428.0

426.7

+ 1.3

1878

Friction of water

14.7

772.7

776.1

425.8

427.6

- 1.8

12.7

774.6

778.5

427.1

428 .

15.5

773.1

776.4

426.0

427.3

- 1.3

14.5

767.0

770.5

422.7

427.5

- 4.8

17.3

774.0

777.0

426.3

426.9

In combining these so as to get at the true difference of Joule's and
my result, we must give these different determinations weights accord-
ing to their respective accuracy, especially as some of the results, as
No. 11, have very little weight. Joule rejected quite a number of his
results, but I have thought it best to include them, giving them small
weights, however. In this way we obtain a value for Joule's experiment

476 HENEY A. ROWLAND

of 426-75 at 14 -6, my value at this point being 427-52. The difference
amounts to 1 in 550 only. Giving the observations equal weight, this
would have been 1 in 430 nearly. The quantity 426-75 is what I find
at 18 C. So that my result at this particular temperature differs from
that of Joule only the amount that water changes in specific heat in
3-4C.

Joule's value is less than my value to the amount given, but the value
from the properties of air, 430-7 at 14 C. is greater, although the
method can have little weight.

It might be well to diminish my values by 1 part in 1000 so as to make
them represent the mean of Joule's and my own experiments. It is
seen that the experiment by the method of electric heating agrees very
exactly with the other experiments, because I have reduced it to my value
of the ohm. Hence I regard it as a very excellent confirmation of my
value of that unit.
Baltimore, February 16, 1880.

PHYSICAL LABORATOKY: COMPARISONS OF STANDARDS

[Johns Hopkins University Circulars, N~o. 3, p. 31, 1880]

In order to secure uniformity throughout the country in certain
physical standards, and to facilitate the use of the absolute system of
heat measurement, it has been thought advisable to organize in the
physical department of this University a sub-department, where com-
parisons of standards can be made.

Comparison of Thermometers. At present we are only able to make
comparisons of thermometers, and so to reduce their degrees to the abso-
lute scale of the perfect gas thermometer.

As the work is very laborious, it is proposed to make this sub-depart-
ment self-supporting, by a system of fees sufficient to cover the bare cost
of the labor, so that all may avail themselves of the facilities here
offered.

In a recent study of standard thermometers by Geissler, Baudin,
Fastre, Casella and from Kew, and the comparison of the same with
the air thermometer, the differences due to the variety of the glass
amounted to 0-2 or 0-3 C., and the differences from the air thermom-
eter were as high sometimes as 0-3 C. at the 40 point.

The error from using uncompared mercurial thermometers in calori-
metric investigations may amount to one or two per cent. For this
reason the air thermometer has been taken as the standard, and all com-
parisons will be reduced to the final absolute standard of the perfect
gas thermometer.

Very complete studies of thermometers have been made between
and 40 C., and a less complete study between and 100, and be-
tween 100 and 250. Up to 100 our thermometers have not only been
compared with the air thermometer, but also with standards by Fastre,
Geissler, Casella, Baudin and from Kew.

The study from to 40 has been published by the American Acad-
emy of Sciences, at Boston, in a memoir on the Mechanical Equivalent
of Heat. One of our thermometers is also now in the hands of Dr.
Joule, who has compared it with the original thermometers used by him
in the determination of the Mechanical Equivalent of Heat.

478 HENKY A. EOWLAND

The apparatus for the comparison up to 100 C. is described in the
paper above referred to. The thermometers are totally immersed in
the water with their stems very near the bulbs of the air thermometers.
From 100 up to 250 an oil bath is used, the bulbs only being in the
oil, but the stems are heated to the same degree by being in contact with
a heavy copper bar, whose temperature is noted by separate thermome-
ters.

The ordinary comparison is made with the stems of the thermometers
in a vertical position. Where they are used in a horizontal position a
correction will have to be made, and this correction will be determined
when it is so desired. When the comparison is made only to 40, we
can compare them in a horizontal position, but we cannot then insure
the same accuracy as when they are vertical, and it is never advisable to
use them in that position.

Where desired, a study will be made of the changes of the zero point
as a function of the temperature to which it has been heated, and of the
time, but this study is not advised, as it does not lead to very valuable
results.

Thermometers with metal, wooden or paper scales are generally too
poor to be worth comparison, and would often be spoiled by the immer-
sion in the water. Thermometers with metal caps of Geissler's form
are often injured, especially when heated to 250 C. Therefore, com-
parisons of thermometers of these classes will not be undertaken, ex-
cept in the case of standards long used for some particular purpose, or
in that of fine G-eissler thermometers.

Three intervals for the comparison have been selected.

A. Between and 40 for thermometers used for meteorological
observations, determination of the temperature of standards of length,
calorimetric determinations, and all purposes where extreme accuracy is
desired within that limit. To obtain the full value of such a compari-
son, thermometers should be graduated at least as fine as 0-1 C. or
0-2F.

B. Between and 100 C. It is advised that the thermometers gent
be graduated at least as fine as 0-2 C. or 0-5 F.

C. Between 100 and 250 for thermometers used by chemists in the
determination of melting or boiling points. Thermometers should be
graduated to 1 C. or 1 F.

Three kinds of comparison will be made for each of the intervals
to 40, to 100, and 100 to 250, as follows:

1st. Direct comparison with the air thermometer, and also a primary

PHYSICAL LABORATORY: COMPARISONS OF STANDARDS 479

standard. This comparison is very laborious, and is not recommended
except in very exceptional cases, as more than one comparison should
be made to insure good results.

2nd. Comparison with primary standards which have been compared
many times with the air thermometer. This is recommended where an
error of y^ is of some importance.

3rd. Comparison with secondary standards which have been com-
pared many times with the primary standards, and not very often
directly with the air thermometer. This is recommended in all ordi-
nary cases, where an error of yf^ can be tolerated.

When several comparisons are made, the following intervals will be
allowed between the experiments, so that the zero reading may be
allowed to return to its primitive value.

Thermometers heated to 40 C. about 1 week.
Thermometers heated to 100 C. about 6 weeks.
Thermometers heated to 250 C. about 4 months.

The latter interval is too small for an accurate return.

For the exact details of the method of comparison, I must refer to the
above mentioned paper on the Mechanical Equivalent of Heat.

It is advisable in all cases where great accuracy is desired, that a
numbers of comparisons be made, seeing that delicate thermometers are
constantly varying through slight limits, and the average state can only
be determined by repeated experiments.

Reports. In the report of the comparison, the original readings will
be given together with the reduced ones, and the plot of the curve of
errors of the thermometer at every point. From this curve, the error
of the thermometer at any reading can be found.

It is proposed to publish at the end of the year a complete report of
all the comparisons made during the year, together with all new deter-
minations of the errors of the standards, and to send it to any address
at a price which we will hereafter announce.

Fees. The comparators allow five thermometers only to be placed in
them, of which two are our own standards in ordinary comparisons,
and one in direct comparisons with the air thermometer. Therefore,
three thermometers can be compared as easily as one in ordinary cases,
and four in direct comparisons. Hence the following system of fees
has been made out.

480 HENEY A. EOWLAND

A. When a number of Thermometers are sent
Comparison between and 40 C. for 3 or 4 thermometers.

Direct, probable error at each point =TOT $ 20

Primary Standards, probable error at each point C ^ T ^ T 11 00
Secondary Standards, probable error at each point = T f -g- 8 00

and 100 for 3 or 4 thermometers.

Direct, probable error at each point = T ^ $25 00

Primary Standards, probable error at each point = ^-3- 12 00
Secondary Standards, probable error at each point = T ^ 9 00

100 to 250 for 3 or 4 thermometers.

Direct, probable error at each point y 1 ^ $20 00

Primary Standards, probable error at each point = y 1 ^ 12 00
Secondary Standards, probable error at each point = -^ 9 00

B. For Single Thermometers

For single thermometers, the fees for the direct comparisons should
be reduced to one-third, and' for the ordinary ones to one-half the
above figures. But in this case the thermometer will have to remain
here until enough accumulate to fill the comparators.

Directions for Sending. With each thermometer, send the name of
maker, the date when made, purpose for which it is used, and the
highest temperature to which it has lately been heated, and the date
of such heating, together with the kind of comparison desired, and
whether the thermometer is generally used in the horizontal or the
vertical position.

In packing, the thermometer should be placed in a small box, which
should again be packed with straw in a larger box.

The thermometers, both during transit and while here, must be at
the owners' risk. Only sufficient fees have been charged to cover the
bare cost of the comparison, and we bear the risk of our own standards,
which are probably more valuable than any of those which will be sent
to us. But every care will be taken, and the probability of an accident
is very small.

We expect soon to be able to make other comparisons, and notice will
then be given of the fact by the issue of another circular.

ON GEISSLEK THERMOMETERS: REMARKS BY PROFESSOR
ROWLAND ON THE PRECEDING LETTER, 1 IN A COMMU-
NICATION DATED JOHNS HOPKINS UNIVERSITY, APRIL
29, 1881

[American Journal of Science [3], XXI, 451-453, 1881]

Through the kindness of Dr. Waldo, I have been allowed to see the
above and would like to give a few words of explanation.

In reading what I had to say with respect to the Geissler thermom-
eter, the reader should remember that I was not writing on general
thermometry, but only on that part which should be useful to me in
measuring differences of temperature within the limits of and 45 C.
And so I merely made a study of thermometers, their change of zero
and other points, as it affected the problem which I had before me. I
am well aware that there are formulae for giving the changed readings
of thermometers due to previous heating, but, according to well known
principles in such cases, I preferred to eliminate such error by the
proper use of the thermometer rather than trust to an uncertain theory.

In the course of my investigation I discovered the fact that the
Geissler thermometers, especially the one I then used, departed more
from the air thermometer than any other. Now the Geissler ther-
mometer has been used for many years by physicists, principally Ger-
man, without any reduction to the air thermometer. And this correc-
tion was so great, amounting to over 0-3 C., for the specimen I used, at
the 45 point, that I thought it right to call attention to the point.
And I acknowledge that the picture was present in my mind of a physi-
cist reading a thermometer from a distance by a telescope to avoid the
heat of the body and parallax, and recording his results to thousandth
of a degree, and all this on a thermometer having an error of 0-3 C. !
As Dr. Thiesen remarks: If one is to compare his thermometer with
the air thermometer, the amount of correction is of little importance:
but departure from the air thermometer is certainly not a recommenda-
tion and, indeed, must introduce slight errors. The most accurate

1 [By Dr. M. Thiesen, replying to Rowland's criticisms of the Geissler thermometers,
as expressed in his memoir 'On the Mechanical Equivalent of Heat.']
31

482 HENRY A. ROWLAND

readings which one can make on an air thermometer will vary several
hundredths of a degree.

Hence we can never use with accuracy the direct comparison with the
air thermometer but must express the difference of the two instruments
by some formula of the form:

J = a + bt + ci 1 + &c.

Should we take an infinite number of terms this formula would ex-
press all the irregularities of our observations. But by limiting the
number of terms the curve of differences becomes smoother and
smoother and the formula expresses less and less the irregularities of
the experiment. The number of terms to be used is a matter of judg-
ment, and this point I sought to determine by the use of the observa-
tions of Eegnault and others. The rejection of the higher powers of t
is more or less of an assumption founded on the fact that we are
reasonably certain that the curve of differences between the mercurial
and the air thermometer is a smooth curve. It is evident that the
less the correction to be introduced the less the rejection of the higher
powers of t will affect our results.

We now come to my criticism of the Geissler thermometer for not
having a reservoir at the top. Dr. Thiesen has in some way misunder-
stood my principal reason for its presence. My reason was not that
" es vermindert die Schadlichkeit der im Quecksilber zuriickgebliebenen
Spuren von Luft " but that only by its use can the mercury in the bulb
be entirely free from air. Take a thermometer and turn it with the
bulb on top. If the thermometer is large, in nine cases out of ten the
mercury will separate and fall down: allow it to remain and observe the
bubble-like vacuum in the bulb. Turn the bulb in various directions so
as to wash the whole interior of the bulb, as it were, and then bring
the thermometer into a vertical position, keeping the bubble in sight.
As the mercury flows back, the bubble diminishes and finally, in a good
thermometer, almost disappears: but in most thermometers a good
sized bubble of air, in some cases as large as the wire of a pin, remains.
It is the most important function of a reservoir at the top to permit
such manipulations as to drive all such air into the top reservoir and to
make the mercury and the glass assume such perfect contact that the
bulb can be turned uppermost without the mercury separating, even in
thermometers of large size and with good generous bulbs. In many
Geissler thermometers such a test might succeed, not on account of the
freedom from air, but because the capillary tube and bulb are so small

Ox THE GEISSLER THERMOMETEKS 483

and the column so short that the capillary action is sufficient to prevent
the fall. Now I think that a thermometer in which there is this layer
of air around the mercury in the bulb must be uncertain in its action;
hence my opinion is unaltered that all thermometers in which we can-
not remove this layer or at least make certain of its absence should be
rejected.

Furthermore, with respect to calibration, the reservoir is not essen-
tial to the calibration of thermometers whose range is and 100 C.
But my remarks apply better to those whose range is between and
30 C. or 40 C. Here calibration is impossible with a short column
at ordinary temperatures unless some of the mercury can be stored up
in the reservoir so as to allow the column to move over the whole scale.
And it is within this limit that thermometers are of the greatest value
in the physical laboratory.

The other defects of the Geissler thermometer, the scale which was
always coming loose, the metal cap which was never tight and always
allowe'd water to enter, the small capillary tube which wandered with
perfect irregularity from side to side over the scale, all these were so
obvious that I confined my remarks to the more obscure errors.

Furthermore, I believe there is some error in most Geissler ther-
mometers from the small size of the bulb and the capillary tube, and
this I have mentioned on p. 124 ' of the paper referred to. Pfaundler
and Platter, in a paper on the specific heat of water, in Poggendorff's
Annalen for 1870, found an immense variation within small limits. In
a subsequent paper 2 the authors traced this'error to the lagging of the
thermometer behind its true reading.

The authors used Geissler thermometers graduated to ^j- C. ! in a
series of experiments made by plunging the thermometer into water
after slightly heating or cooling the thermometer so that in one case
the mercury fell and the other rose to the required point. When the
thermometer fell about 6 or 8 C. it lagged behind 0-0654 and when
it rose 3 or 4 it lagged 0-022, making a difference of 0-087 C.! Now
my thermometers made by Baudin show no effect of this kind. They
indicate accurately the temperature whether they rise or fall to the
given point, provided the interval is not too great. The fact then
remains that a Geissler thermometer graduated to 7 V C. may be uncer-
tain to 0-087C., while a Baudin graduated to mm., one mm. being
from T V to T V C. is not uncertain to 0-01 or 0-02 C. May not the

1 [p. 393 this volume.! * Poggendorff's Annalen, cxli, p. 537.

484 HENEY A. KOWLAND

cause be found in the layer of air around the mercury of the bulb
which cannot be removed without a reservoir at the top? Or may we
not also look for such an effect from the minute size of the bore of the
capillary tube which creates a different pressure in the bulb from a
rising or falling meniscus ? Possibly the two may be combined.

PART IV

LIGHT

PRELIMINARY NOTICE OF THE RESULTS ACCOMPLISHED
IN THE MANUFACTURE AND THEORY OF GRATINGS FOR
OPTICAL PURPOSES

[Johns Hopkins University Circulars, No. 17, pp. 248, 249, 1882 ; Philosophical Magazine
[4], XIII, 469-474, 1882; Nature, 26, 211-213, 1882; Journal de Physique,
II, 5-11, 1883]

It is not many years since physicists considered that a spectroscope
constructed of a large number of prisms was the best and only instru-
ment for viewing the spectrum, where great power was required. These
instruments were large and expensive, so that few physicists could pos-
sess them. Professor Young was the first to discover that some of the
gratings of Mr. Rutherfurd showed more than any prism spectroscope
which had then been constructed. But all the gratings which had been
made up to that time were quite small, say one inch square, whereas
the power of a grating in resolving the lines of the spectrum increases
with the size. Mr. Rutherfurd then attempted to make as large grat-
ings as his machine would allow, and produced some which were nearly
two inches square, though he was rarely successful above an inch and
three-quarters, having about thirty thousand lines. These gratings
were on speculum metal and showed more of the spectrum than had
ever before been seen, and have, in the hands of Young, Rutherfurd,
Lockyer and others, done much good work for science. Many mechanics
in this country and in France and Germany, have sought to equal
Mr. Rutherfurd' s gratings, but without success.

Under these circumstances, I have taken up the subject with the
resources at command in the physical laboratory of the Johns Hopkins
University.

One of the problems to be solved in making a machine is to make a
perfect screw, and this, mechanics of all countries have sought to do
for over a hundred years and have failed. On thinking over the matter,
I devised a plan whose details I shall soon publish, by which I hope to
make a practically perfect screw, and so important did the problem seem
that I immediately set Mr. Schneider, the instrument maker of the
university, at work at one. The operation seemed so successful that I

488 HENRY A. ROWLAND

immediately designed the remainder of the machine, and have now had
the pleasure since Christmas of trying it. The screw is practically per-
fect, not by accident, but because of the new process for making it, and
I have not yet been able to detect an error so great as one one-hundred-
thousandth part of an inch at any part. Neither has it any appreciable
periodic error. By means of this machine I have been able to make
gratings with 43,000 lines to the inch, and have made a ruled surface
with 160,000 lines on it, having about 29,000 lines to the inch. The
capacity of the machine is to rule a surface 6^ x 4| inches with any
required number of lines to the inch, the number only being limited by
the wear of the diamond. The machine can be set to almost any num-
ber of lines to the inch, but I have not hitherto attempted more than
43,000 lines to the inch. It ruled so perfectly at this figure that I see
no reason to doubt that at least two or three times that number might
be ruled in one inch, though it would be useless for making gratings.

*A11 gratings hitherto made have been ruled on flat surfaces. Such
gratings require a pair of telescopes for viewing the spectrum; these
telescopes interfere with many experiments, absorbing the extremities
of the spectrum strongly; besides, two telescopes of sufficient size to
use with six inch gratings would be very expensive and clumsy affairs.
In thinking over what would happen were the grating ruled on a sur-
face not flat, I thought of a new method of attacking the problem, and
soon found that if the lines were ruled on a spherical surface the
spectrum would be brought to a focus without any telescope. This
discovery of concave gratings is important for many physical investiga-
tions, such as the photographing of the spectrum both in the ultra-
violet and the ultra-red, the determination of the heating effect of the
different rays, and the determination of the relative wave lengths of
the lines of the spectrum. Furthermore it reduces the spectroscope to
its simplest proportions, so that spectroscopes of the highest power may
be made at a cost which can place them in the hands of all observers.
With one of my new concave gratings I have been able to detect double
lines in the spectrum which were never before seen.

The laws of the concave grating are very beautiful on account of their
simplicity, especially in the case where it will be used most. Draw the
radius of curvature of the mirror to the centre of the mirror, and from
its central point with a radius equal to half the radius of curvature
draw a circle; this circle thus passes through the centre of curvature
of the mirror and touches the mirror at its centre. Now if the source
of light is anywhere in this circle, the image of this source and the

GRATINGS FOR OPTICAL PURPOSES 489

different orders of the spectra are all brought to focus on this circle.
The word focus is hardly applicable to the case, however, for if the
source of light is a point the light is not brought to a single point on
the circle but is drawn out into a straight line with its length parallel
to the axis of the circle. As the object is to see lines in the spectrum
only, this fact is of little consequence provided the slit which is the
source of light is parallel to the axis of the circle. Indeed it adds to
the beauty of the spectra, as the horizontal lines due to dust in the slit
are never present, as the dust has a different focal length from the lines
of the spectrum. This action of the concave grating, however, some-
what impairs the light, especially of the higher orders, but the intro-
duction of a cylindrical lens greatly obviates this inconvenience.

The beautiful simplicity of the fact that the line of foci of the dif-
ferent orders of the spectra are on the circle described above leads
immediately to a mechanical contrivance by which we can move from
one spectrum to the next and yet have the apparatus always in focus;
for we only have to attach the slit, the eye-piece and the grating to three
arms of equal length, which are pivoted together at their other ends
and the conditions are satisfied. However we move the three arms the
spectra are always in focus. The most interesting case of this contriv-
ance is when the bars carrying the eye-piece and grating are attached
end to end, thus forming a diameter of the circle with the eye-piece at
the centre of curvature of the mirror, and the rod carrying the slit
alone movable. In this case the spectrum as viewed by the eye-piece
is normal, and when a micrometer is used the value of a division of its
head in wave-lengths does not depend on the position of the slit, but
is simply proportional to the order of the spectrum, so that it need be
determined once only. Furthermore, if the eye-piece is replaced by a
photographic camera the photographic spectrum is a normal one. The
mechanical means of keeping the focus* is especially important when
investigating the ultra-violet and ultra-red portions of the solar
spectrum.

Another important property of the concave grating is that all the
superimposed spectra are in exactly the same focus. When viewing
such superimposed spectra it is a most beautiful sight to see the lines
appear colored on a nearly white ground. By micrometric measurement
of such superimposed spectra we have a most beautiful method of
determining the relative wave lengths of the different portions of the
spectrum, which far exceeds in accuracy any other method yet devised.
In working in the ultra-violet or ultra-red portions of the spectrum we

490 HENRY A. EOWLAND

can also focus on the superimposed spectrum and so get the focus for
the portion experimented on.

The fact that the light has to pass through no glass in the concave
grating makes it important in the examination of the extremities of
the spectrum where the glass might absorb very much.

There is one important research in which the concave grating in its
present form does not seem to be of much use, and that is in the exami-
nation of the solar protuberances; an instrument can only be used for
this purpose in which the dust in the slit and the lines of the spectrum
are in focus at once. It might be possible to introduce a cylindrical
lens in such a way as to obviate this difficulty. But for other work on
the sun the concave grating will be found very useful. But its principal
use will be to get the relative wave lengths of the lines of the spectrum,
and so to map the spectrum; to divide lines of the spectrum which are
very near together, and so to see as much as possible of the spectrum;
to photograph the spectrum so that it shall be normal; to investigate
the portions of the spectrum beyond the range of vision; and lastly to
put in the hands of any physicist at a moderate cost such a powerful
instrument as could only hitherto be purchased by wealthy individuals
or institutions.

To give further information of what can be done in the way of grat-
ings I will state the following particulars :

The dividing engine can rule a space 6| inches long and 4 inches
wide. The lines, which can be 4^ inches long, do not depart from a
straight line so much as nnnnnr inch, and the carriage moves forward in
an equally straight line. The screw is practically perfect and has been
tested to nnmnj" inch without showing error. Neither does it have any
appreciable periodic error, and the periodic error due to the mounting
and graduated head can be entirely eliminated by a suitable attachment.
For showing the production of ghosts by a periodic error, such an error
can be introduced to any reasonable amount. Every grating made by
the machine is a good one, dividing the 1474 line with ease, but some
are better than others. Eutherfurd's machine only made one in every
four good, and only one in a long time which might be called first-class.
One division of the head of the screw makes 14,438 lines to the inch.
Any fraction of this number in which the numerator is not greater
than say 20 or 30 can be ruled. Some exact numbers to the millimetre,
such as 400, 800, 1200, etc., can also be ruled. For the finest definition
either 14,438 or 28,876 lines to the inch are recommended, the first for
ordinary use and the second for examining the extremities of the

GRATINGS FOR OPTICAL PURPOSES 491

spectrum. Extremely brilliant gratings have been made with 43,314
lines to the inch, and there is little difficulty in ruling more if desired.
The following show some results obtained:

Flat grating, 1 inch square, 43,000 lines to the inch. Divides the
1474 line in the first spectrum.

Flat grating, 2X3 inches, 14,438 lines to the inch, total 43,314.
Divides 1474 in the first spectrum, the E line (Angstrom 5269-4) in
the second and is good in the fourth and even fifth spectrum.

Flat grating, 2X3 inches, 1200 lines to one millimetre. Shows very
many more lines in the B and A groups than were ever before seen.

Flat grating, 2 X 3 inches, 14,438 lines to the inch. This has most
wonderful brilliancy in one of the first spectra, so that I have seen
the Z line, wave-length 8240 (see Abney^s map of the ultra-red region),
and determined its wave-length roughly, and have seen much further
below the A line than the B line is above the A line. The same may
be said of the violet end of the spectrum. But such gratings are only
obtained by accident.

Concave grating, 2X3 inches, 7 feet radius of curvature, 4818 lines
to the inch. The coincidences of the spectra can be observed to the
tenth or twelfth spectrum.

Concave grating, 2X3 inches, 14,438 lines to the inch, radius of cur-
vature 8 feet. Divides the 1474 line in the first spectrum, the E line
in the second, and is good in the third or fourth.

Concave grating, 3 X 5 inches, 17 feet radius of curvature, 28,876
lines to the inch, and thus nearly 160,000 lines in all. This shows
more in the first spectrum than was ever seen before. Divides 1474
and E very widely and shows the stronger component of Angstrom 5275
double. Second spectrum not tried.

Concave grating, 4 X 5f inches, 3610 lines to the inch, radius of cur-
vature 5 feet 4 inches. This grating was made for Professor Langley's
experiments on the ultra-red portion of the spectrum, and was thus
made very bright in the first spectrum. The definition seems to be
very fine notwithstanding the short focus and divides the 1474 line with
ease. But it is difficult to rule so concave a grating as the diamond
marks differently on the different parts of the plate.

These give illustrations of the results accomplished, but of course
many other experiments have been made. I have not yet been able to
decide whether the definition of the concave grating fully comes up to
that of a flat grating, but it evidently does so very nearly.

30
ON CONCAVE GEATINGS FOE OPTICAL PUEPOSES *

[American Journal of Science [3], XXVI, 87-98, 1883 ; Philosophical Magazine
[5], XVI, 197-210, 1883]

GENERAL THEORY

Having recently completed a very successful machine for ruling
gratings, my attention was naturally called to the effect of irregularity
in the form and position of the lines and the form of the surface on
the definition of the grating. Mr. C. S. Peirce has recently shown, in
the American Journal of Mathematics, that a periodic error in the
ruling produces what have been called ghosts in the spectrum. At first
I attempted to calculate the effect of other irregularities by the ordi-
nary method of integration, but the results obtained were not commen-
surate with the labor. I then sought for a simpler method. Guided by
the fact that inverse methods in electrical distribution are simpler
than direct methods, I soon found an inverse method for use in this
problem.

In the use of the grating in most ordinary spectroscopes, the tele-
scopes are fixed together as nearly parallel as possible, and the grating
turned around a vertical axis to bring the different spectra into the
field of view. The rays striking on the grating are nearly parallel,
but for the sake of generality I shall assume that they radiate from a
point in space and shall investigate the proper ruling of the grating
to bring the rays back to the point from which they started. The wave
fronts will be a series of spherical shells at equal distances apart. If

J An abstract of this paper with some other matter was given at the Physical
Society of London in November last, the paper being in my hand in its present shape
at that time. As I wished to make some additions, for which I have not yet had
time, I did not then publish it. I was much surprised soon after to see an article
on this subject which had been presented to the Physical Society and was published
in the Philosophical Magazine. The article contains nothing more than an exten-
sion of my remarks at the Physical Society and formula; similar to those in this
paper. As I have not before Ihis published anything except a preliminary notice of
the concave gratings, I expected a little time to work up the subject, seeing that the
practical work of photographing the spectrum has recently absorbed all my time.
But probably I have waited too long.

ON CONCAVE GRATINGS FOR OPTICAL PURPOSES 493

these waves strike on a reflecting surface, they will be reflected back
provided they can do so all in the same phase. A sphere around the
radiant point satisfies the condition for waves of all lengths and thus
gives the case of ordinary reflection. Let any surface cut the wave
surfaces in any manner and let us remove those portions of the surface
which are cut by the wave surfaces; the light of that particular wave-
length can then be reflected back along the same path in the same
phase and thus, by the above principle, a portion will be sent back.
But the solution holds for only one wave-length and so white light will
be drawn out into a spectrum. Hence we have the important conclu-
sion that a theoretically perfect grating for one position of the slit and
eye-piece can be ruled on any surface, flat or otherwise. This is an
extremely important practical conclusion and explains many facts which
have been observed in the use of gratings. For we see that errors of
the dividing engine can be counterbalanced by errors in the flatness of
the plate, so that a bad dividing engine may now and then make a
grating which is good in one spectrum but not in all. And so we often
find that one spectrum is better than another. Furthermore Professor
Young has observed that he could often improve the definition of a
grating by slightly bending the plate on which it was ruled.

From the above theorem we see that if a plate is ruled in circles
whose radius is r sin [JL and whose distance apart is dr / sin //, where Ar
is constant, then the ruling will be appropriate to bring the spectrum
to a focus at a distance, r, and angle of incidence, //. Thus we should
need no telescopes to view the spectrum in that particular position of
the grating. Had the wave surfaces been cylindrical instead of spher-
ical the lines would have been straight instead of circular, but at the
above distances apart. In this case the spectrum would have been
brought to a focus, but would have been diffused in the direction of
the lines. In the same way we can conclude that in flat gratings any
departure from a straight line has the effect of causing the dust in the
slit and the spectrum to have different foci, a fact sometimes observed.

We also see that, if the departure from equal spaces is small, or, in
other words, the distance r is great, the lines must be ruled at distances
apart represented by

r sin n

in order to bring the light to a focus at the angle p. and distance r, c
being a constant and x the distance from some point on the plate. If
f* changes sign, then r must change in sign. Hence we see that the

494 HENKY A. ROWLAND

effect of a linear error in the spacing is to make the focus on one side
shorter and the other side longer than the normal amount. Professor
Peirce has measured some of Mr. Eutherfurd's gratings and found that
the spaces increased in passing along the grating, and he also found
that the foci of symmetrical spectra were different. But this is the
first attempt to connect the two. The definition of a grating may
thus be very good even when the error of run of the screw is consider-
able, provided it is linear.

CONCAVE G-KATINGR

Let us now take the special case of lines ruled on a spherical surface;
and let us not confine ourselves to light coming back to the same point,
but let the light return to another point. Let the co-ordinates of the
radiant point and focal point be y<=0, x = a and y = 0, x*+- a, and
let the centre of the sphere whose radius is p be at x r , y'. Let r be the
distance from the radiant point to the point x, y, and let R be that from
the focal point to x, y. Let us then write

2b = R -f re,

where c is equal to 1 according as the reflected or transmitted ray is
used. Should we increase b by equal quantities and draw the ellip-
soids or hyperboloids so indicated, we could use these surfaces in the
same way as the wave surfaces above. The intersections of these
surfaces with any other surface form what are known as Huyghens'
zones. By actually drawing these zones on the surface, we form a
grating which will diffract the light of a certain wave-length to the
given focal point. For the particular problem in hand, we need only
work in the plane x, y for the present.

Let s be an element of the curve of intersection of the given surface
with the plane x, y. Then our present problem is to find the width of
Huyghens' zones on the surface, that is ds in terms of db.

The equation of the circle is

(x-xy + (y-y'? = f>*
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 '

2 A more simple solution is the following: _ mnst be constant in the direction

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~ ~^~~

\ _<r

Making x = 0, y = 0, y' = 0, x' p,

we have x" x f " I x //2 x /// ~i\

~ ' ~ P ~ + ~ = '

_n cos p + cos v _ 2Rr cos a cose

r cos" v + R cos 2 u r cos 2 v + R cos 2 u '

Ox CONCAVE GRATINGS FOR OPTICAL PURPOSES

497

Whence the focal length is

pR cos'

COS a COS p COb v

For the transmitted beam, change the sign of R. Supposing p, R and v
to remain constant and r and // to vary, this equation will then give the
line on which all the spectra and the central image are brought to a
focus.

By far the most interesting case is obtained by making

since these values satisfy the equation. The line of foci is then a
circle with a radius equal to one-half p. Hence if a source of light

FIG. i.

exists on this circle, the reflected image and all the spectra will be
brought to a focus on the same circle. Thus if we attach the slit, the
eye-piece and the grating to the three radii of the circle, however we
move them, we shall always have some spectrum in the focus of the
eye-piece. But in some positions the line of foci is so oblique to the
direction of the light that only one line of the spectrum can be seen
well at any one time. The best position of the eye-piece as far as we
consider this fact is thus the one opposite to the grating and at its
centre of curvature. In this position the line of foci is perpendicular
to the direction of the light, and we shall show presently that the
spectrum is normal at this point whatever the position of the slit, pro-
vided it is on the circle.

Fig. 1 represents this case; A is the slit, C is the eye-piece, and B is
the grating with its centre of curvature at C. In this case all the con-
ditions are satisfied by fixing the grating and eye-piece to the bar BC
32

498 HENRY A. ROWLAND

whose ends rest on carriages moving on the rails AB and AC at right
angles to each other; when desired, the radius AD may be put in to hold
everything steady, but this has been found practically unnecessary.

The proper formula? for this case are as follows: If ^ is the wave-
length and w the distance apart of the lines of the grating from centre
to centre, then we have

1 _ IN _ sin v

~~d~ %w~ ~T~

where N is the order of the spectrum.

w sin v

/ =

Now in the given case p is constant and so NX is proportional to the
line AC. Or, for any given spectrum, the wave-length is proportional
to that line.

If a micrometer is fixed at C we can consider the case as follows :

1 )N
-tf ^^(sin^ + sinv),

d). w

7i~ = ~W cos /*
a/i N

If D is the distance the cross-hairs of the micrometer move forward
for one division of the head, we can write for the point C

A., = I-

and for the same point ft is zero. Hence

But this is independent of v and we thus arrive at the important fact
that the value of a division of the micrometer is always the same for
the same spectrum and can always be determined with sufficient accu-
racy from the dimensions of the apparatus and number of lines on the
grating, as well as by observation of the spectrum.

Furthermore, this proves that the spectrum is normal at this point
and to the same scale in the same spectrum. Hence we have only to
photograph the spectrum to obtain the normal spectrum and a centi-
meter for any of the photographs always represents the same increase
of wave-length.

It is to be specially noted that this theorem is rigidly true whether
the adjustments are correct or not, provided only that the micrometer
is on the line drawn perpendicularly from the centre of the grating, even
if it is not the centre of curvature.

Ox CONCAVE GRATINGS FOE OPTICAL PURPOSES 499

As the radius of curvature of concave gratings is usually great, the
distance through which the spectrum remains practically normal is very
great. In the instrument which I principally use, the radius of curva-
ture p, is about 21 feet 4 inches, the width of the ruling "being about 5-5
inches. In such an instrument the spectrum thrown on a flat plate is
normal within about 1 part in 1,000,000, for 6 inches and less than 1 in
35,000, for 18 inches. In photographing the spectrum on a flat plate,
the definition is excellent for 12 inches, and by use of a plate bent to 11
feet radius, a plate of 20 inches in length is in perfect focus and the
spectrum still so nearly normal as to have its error neglected for most
purposes.

Another important property of the concave grating is that all the
superimposed spectra are in focus at the same point, and so by micro-
metric measurements the relative wave-lengths are readily determined.
Hence, knowing the absolute wave-length of one line, the whole spec-
trum can be measured. Professor Peirce has determined the absolute
wave-length of one line with great care and I am now measuring the
coincidences. This method is greatly more accurate than