Harmonographs. I. Pendulum design

J. L. Heilbron, Electricity in the 17th and 18th Centuries: A Study in Early Modern Physics (University of California Press, Berkeley, 1979; Dover, Mineola, NY, 1999);

Elements of Early Modern Physics (University of California Press, Berkeley, 1982).

Deborah Jean

Warner

, “,” , – ().

See particularly W. D. Hackmann, “Scientific instruments: Models of brass and aids to discovery,” in The Uses of Experiment: Studies in the Natural Sciences, edited by David Gooding, Trevor Pinch, and Simon Schaffer (Cambridge U.P., Cambridge and New York, 1989), pp. 31–65;

Making Instruments Count: Essays on Historical Scientific Instruments Presented to Gerard L’Estrange Turner, edited by R. G. W. Anderson, J. A. Bennett, and W. F. Ryan (Variorum, Aldershot, Hampshire, UK and Brookfield, VT, 1993);

Thomas L. Hankins and Robert J. Silverman, Instruments and the Imagination (Princeton U.P., Princeton, 1995).

Gerard L’E.

Turner

, “,” , – ().

An entertaining selection of examples from the popular nineteenth century magazine, The English Mechanic, may also be found in Alan Sutton, A Victorian World of Science (Adam Hilger, Bristol and Boston, 1986); see particularly Chap. 3, “Philosophical Amusements, Pastimes and Hobbies.”

Greenslade has provided an extensive collection of examples from these textbooks in his series of articles in The Physics Teacher. A complete list of these (to 1994) may be found in A. P. French and Thomas B. Greenslade, Jr., Physics History from AAPT Journals II (AAPT, College Park, MD, 1995), pp. 241–242.

Other references to nineteenth century apparatus may also be found here.

Reference 3, Hankins and Silverman, pp. 113–147. See also the citations in their Ref. 6, p. 260.

Sir William Thomson (Lord Kelvin) and Peter Guthrie Tait, Treatise on Natural Philosophy (Cambridge U.P., London, 1912), Pt. I, Rev. ed.;

Principles of Mechanics and Dynamics (Dover, New York, 1962), pp. 37–38.

Reference 7, p. 38, The Oxford English Dictionary (Clarendon, Oxford, 1989), Vol. VI, 2nd ed., p. 1123,

attributes the 1867 edition of this work as the first reference to this term.

David Halliday, Robert Resnick, and Jearl Walker, Fundamental of Physics: Extended with Modern Physics (Wiley, New York, 1993), 4th ed., pp. 390–391.

S. J.

Hagen

, “,” , – ().

The description and operation of the kaleidophone has recently been provided in

Thomas B.

Greenslade

, Jr., “,” , – ().

Joseph

Lovering

, “,” (new series 8), – ().

James

Dean

, “,” , – ();

American Periodical Series (II), Reel 363 (Microfilm);

Nathaniel

Bowditch

, “,” , – ();

American Periodical Series (II), Reel 363 (Microfilm). His figure appeared in Plate III. The work of Dean and Bowditch has been described, more recently, in

A. D.

Crowell

, “,” , – ().

For further details see

Robert J.

Whitaker

, “,” , – ().

A further survey of the kaleidophone and similarly operating devices may be found in

Robert J.

Whitaker

, “,” , – ().

The vibrations of an automobile whip antenna are identical to those of the kaleidophone. These have been discussed in:

Clarence H.

Annett

, “,” , – ();

Lawrence W.

Panek

, “,” , ();

Ronald

Newburgh

and

G.

Alexander Newburgh

, “,” , – (). I am indebted to Thomas B. Greenslade, Jr. for calling my attention to these earlier references.

John Tyndall, Sound (Appleton, New York and London, 1903), 3rd ed., pp. 420–422.

A nearly identical apparatus was listed in Rudolph König, Catalogue des Appareils d’Acoustique (P. Mouillot, Paris, 1889), Cat. No. 266, 200 fr. Thomas B Greenslade, Jr. kindly called my attention to this reference.

More on the apparatus manufactured by [Karl] Rudolph König may be found in

Thomas B.

Greenslade

, Jr., “,” , – (), and the references therein.

Acoustical papers from various periodicals were reprinted in Rudolph Kœnig, Quelques Expériences d’Acoustique (A. Lahure, Paris, 1882). (In the spelling of König’s name I have attempted to be consistent with the original.)

Joseph Goold, Charles E. Benham, Richard Kerr, and L. R. Wilberforce, Harmonic Vibrations and Vibration Figures, edited by Herbert C. Newton (Newton & Co., Scientific Instrument Makers, London, 1909); Benham, pp. 29–33.

A list of apparatus available, with prices, is included at the end of the book. The book was reviewed by

C. V.

Boys

, “,” , (25 November ).

King and Millburn write about the firm: “[John] Newton was originally associated with William Palmer, a land-surveyor and cartographer … . His business later became successively Newton and Son and J. and W. Newton, and after his death, Newton and Co., 3 Fleet Street.” See Henry C. King and John R. Millburn, Geared to the Stars: The Evolution of Planetariums, Orreries, and Astronomical Clocks (University of Toronto Press, Toronto and Buffalo, 1978), p. 210.

William F. Rigge, S. J., Harmonic Curves (The Creighton U.P., Omaha, NE, 1926).

Thomas B.

Greenslade

, Jr., “,” , – ().

Reference 11.

Thomas B.

Greenslade

, Jr., “,” , – ().

Thomas B.

Greenslade

, Jr., “,” , – ().

Reference 14, and references cited therein.

Hubert

Airy

, “,” , – (17 August );

Hubert

Airy

, “,” , – (7 September ). Airy provides much detail regarding the adjustments of the pendulum cords, the mass of the pendulum, and the design of the pen and ink for recording the motion of the pendulum.

Charles S.

Slichter

, “,” , – (plus plates) ().

An abstract of Slichter’s work appeared in

Charles S.

Slichter

, , (3 February ). It noted: “The tracing of the pretty curves formed by compounding pendulum vibrations of different periods is a fascinating pastime of which we were beginning to believe the resources were pretty well exhausted.”

A mathematical discussion of Slichter’s paper was published by a senior student at the University of Wisconsin:

Elting H.

Comstock

, “,” , – (). Hales, unaware of Slichter’s paper at the time he performed the experiment, described a similar photographic method in 1945.

Wayne B.

Hales

, “,” , – (January, ). Hales also summarized the work of his predecessors as discussed above. He used a 12-lb ball suspended from a principal length of 325 cm.

A similar method was also described by

C. L.

Stong

, “,” , – (August, ).

Reference 10, pp. 287; 297–299. Hagen emphasized the advantages of Dobson’s pendulum were its simplicity of construction and its cost. Tisley’s commercial harmonograph was listed at 400 Marks and Browning’s version was 70 Marks.

Reference 18, pp. 68–71. Rigge’s brief, previous discussion of pendulum devices is limited and is restricted to references given in Hagen’s paper. It should be noted that Hagen, Rigge’s former professor at Georgetown University and who, in 1926, was Director of the Vatican Observatory, had encouraged Rigge to write his book. Rigge is the only author I have found who cites Hagen’s paper.

Biographical information on Hagen may be found in:

Alice

Farnsworth

, “,” , – (October, );

J.

Stein

, “,” , – (January, ).

Reference 18, pp. 68–69.

Reference 16, pp. 413–415.

S. C.

Tisley

, “,” , ().

“Tisley’s compound pendulum,” Engineering 17, 101–102 (6 February 1874). Tyndall provided a brief description of Tisley’s apparatus in his lectures on sound. He observed that “… the most instructive apparatus for the compounding of rectangular vibrations is that of Mr. Tisley,” Reference 16, p. 420.

The advertising section of Nature is a useful source of information on instrument makers and some of their products. The firm of “Tisley and Spiller” first published an announcement of their anticipated opening in October, 1872: “Tisley and Spiller, Scientific Instrument Makers, 172 Brompton Road, S.W. Will shortly open the above premises for the Manufacture and Sale of Philosophical Apparatus, with the most modern Improvements in Electricity, Magnetism, Spectrum Analysis, &c.” Nature (London) 6, ci (24 October 1872). And in December they announced that they “Have opened the above premises for the Manufacture and Sale … .” Nature (London) 7, xx (5 December 1872).

In January, 1874 the first announcements were made regarding Tisley’s pendulum: “Tisley’s Compound Pendulum Apparatus, With Pens, Ink, &c, for drawing Lissajous’ Curves (as produced by Wheatstone’s Kaleidophone) on Cards, or on blackened Glass for the Lantern, and packed in strong Deal Cabinet (3 ft. 1 ft. 1 ft.) which also serves as a Stand for the instrument to work on.” The price was given as £10. Also advertised were attachments for projection, specimen curves, and “Educational Set of Acoustic Apparatus, For performing many of the experiments, included in the course of Lectures recently given by Dr. Tyndall at the Royal Institution,” The firm is now referred to as “Tisley and Spiller, Opticians, etc.” Nature (London) 9, xci (22 January 1874).

In March the wording was changed to announce: “Tisley’s Pendulum Apparatus, With Tracer, &c., for drawing Lissajous’ Curves on Cards, or blackened Glass for the Lantern;… .” Nature (London) 9, clx (19 March 1874).

By 3 May 1877 the advertisement, in addition to advertising “Prof. Dewar’s New Electrometer” and a table polariscope, read: “Tisley’s Pendulum Apparatus, for drawing Lissajous figures (graphic drawings of the Musical Intervals) on card or on blackened glass; with Optical Arrangement for projecting them on the screen in the process of formation. (Most attractive for Class Demonstration) £14 14s.” Nature (London) 16, vii (3 May 1877).

Two weeks later the company now offered “Tisley’s Harmonograph, For drawing Lissajous’ and Meide’s figures (graphic drawing of Harmonic Vibrations) on card or on blackened glass—most attractive for Class Demonstration—from £3 10s to £21.” Nature (London) 16, xxii (17 May 1877). This also seems to be the first use of the term, “harmonograph,” that I have been able to find. Its use here predates the first reference to the term cited in The Oxford English Dictionary by nearly two years. The Oxford English Dictionary (Clarendon, Oxford, 1989), Vol. VI, 2nd ed., p. 1125. The definition given there is: “An instrument for tracing curves representing sonorous vibrations.”

On 31 January 1878 “S. C. Tisley & Co.” advertised this apparatus for the last time. Nature (London) 17, cx (31 January 1878). The following week it was replaced by “The Phoneidoscope, An Instrument for Observing the Colour-Figures of Liquid Films Under the Action of Sonorous Vibrations,” Nature (London) 17, cxviii (7 February 1878).

Under the name, “Tisley & Spiller,” the firm published an advertisement for the last time on August 23, 1877: Nature (London) 16, cliii (23 August 1877). The following week it was listed as “S. C. Tisley & Co., Opticians,” Nature (London) 16, clxiv (30 August 1877).

Queen’s new form of Tisley’s compound,” J. Franklin Inst. 108, 268–271 (October, 1879).

This design seems to include a gas light source. A description of this design, its use, and an identical picture is included in J. A. Zahm, Sound and Music (A. C. McClurg, Chicago, 1892), pp. 408–411; this is the source of Fig. 5.

Nature (London) 17, 394–395 (14 March 1878). The firm seems to have continued until 1884 when “S. C. Tisley & Co., Manufacturing Opticians and Scientific Instrument Makers” announced that: “Messrs. S. C. Tisley & Co. have great pleasure in informing Scientific Gentlemen that they have made arrangements with Mr. J. W. GAMMAGE … to take the Management of the above business.” Nature (London) 29, cxcviii (17 April 1884).

J. H. Pepper, Cyclopaedic Science Simplified (Frederick Warne, London, 1877), 4th ed., pp. 562–565.

This edition is the first to discuss and describe Tisley’s apparatus. The diagram of the apparatus (p. 563) is the same as that printed in Engineering, Ref. 31, and in Greenslade, Ref. 19, p. 257.

Gaston Tissandier, Popular Scientific Recreations in Natural Philosophy, Astronomy, Geology, Chemistry, Etc. (Ward, Lock, and Co., London, 1883), p. 175.

Reference 35, p. 176.

I.

Bernard Cohen

, “,” , – (January, ). His diagram is essentially identical to that provided by Tissandier.

Reference 37, p. 228.

Greenslade, who has studied and photographed this apparatus, notes that “… the weight of the second pendulum can be raised at a steady rate by what I think is a clockwork mechanism. Furthermore, the rotating table provides two more SHMs parallel to the original two, since a circle is a Lissajous figure.” Personal correspondence, 13 March 2000. See also Ref. 19, p. 258.

Herbert C. Newton, “Simple Harmonographs,” Ref. 17, pp. 4–8.

This is the same as the diagram reproduced by Greenslade, Ref. 19, p. 257. It also illustrates the discussion of the harmonograph (attributed to Tisley and Tissandier) in Joseph Frick, Dr. J. Fricks Physikalische Technik;…, Erster Band, Zweite Abteilung (Friedrich Bieweg und Sohn, Braunschweig, 1905), 7th ed., p. 1322.

An illustration of the same apparatus, on display in the Science Museum, London, may be found in John van Riemsdijk and Paul Sharp, In the Science Museum (Her Majesty’s Stationery Office, London, 1968), pp. 77–78.

Reference 17, “Descriptive and Practical Details as to Harmonographs,” pp. 39–50.

The “Sympalmograph” appeared in the following announcement in Nature (London) 16, 691 (21 June 1877):

THE SYMPALMOGRAPH. A NEW PENDULUM APPARATUS FOR DRAWING LISSAJOUS SOUND CURVES. With this Apparatus the relations of Sounds to each other are shown graphically. The curves are of great beauty and variety; they may be applied to decorative purposes. Price of the Apparatus complete, in Case, £3 10s. 0d. A Pamphlet on the Sympalmograph and Lissajous Curves, with Specimen and Diagrams, sent for Seven Stamps. JOHN BROWNING, OPTICAL AND PHYSICAL INSTRUMENT MAKER TO THE ROYAL OBSERVATORY, ETC. 63 STRAND, W.C., LONDON.

I have been unable to obtain a copy of this pamphlet. Some years later, Benham wrote a thorough description for the construction of a sympalmograph by the home craftsman in

Charles E.

Benham

, “,” , (26 July ). This article is the source of the definition of the term in The Oxford English Dictionary (Clarendon, Oxford, 1989), Vol. XVII, 2nd ed., p. 450. The definition given is: “… an apparatus for exhibiting the combination of vibrations, consisting of a double pendulum the two parts of which can be caused to vibrate in different directions and at varying rates, with a style attached so as to trace the resulting curves on a prepared surface.”

Reference 17, pp. 51–61.

I.

Bernard Cohen

, , – (22 March ).

Archibald

Williams

, “,” [], – (April, ).

The Oxford English Dictionary (Clarendon, Oxford, 1989), Vol. VI, 2nd ed., p. 1125. The definition given is: “A figure or curve drawn by a harmonograph.”

Charles

E. Benham

, “,” , new series , – (June, ).

For many years Benham (1860–1929) was editor of the Essex County Standard, Colchester. He was a prolific writer on a variety of subjects including many scientific topics. A brief biographical sketch is in “Obituary: Mr. C[harles] E[dwin] Benham,” The Times (London), 3 April 1929, p. 17.

Reference 17, pp. 61–79.

Joseph Goold, “Vibration-Figures: Their Production & Constitution in Nature and in the Workshop,” Ref. 17, pp. 97–159 plus plates. Benham’s “Miniature Twin Elliptic Pendulums” were available from Newton and Co. for £2 15s; Goold’s “Twin Elliptic Pendulum” for £3 3s.

Reference 35, pp. 177–179.

Rev. John

Andrew

, “,” , – (). Andrew is the source of the definition in The Oxford English Dictionary (Clarendon, Oxford, 1989), Vol. XI, 2nd ed., p. 469.

S. J.

M[ichael] J. Hoferer

, “,” , – (1 April ).

This paper was reprinted in George M. Hopkins, Experimental Science: Elementary Practical and Experimental Physics (Munn, New York, 1911), Vol. II, 27th ed., pp. 420–428.

An abstract of a four pendulum apparatus had been published earlier in

S. C.

Tisley

, “,” , – (). I have found nothing further on this design.

H. Martyn Cundy and A. P. Rollett, Mathematical Models (Clarendon, Oxford, 1961), 2nd ed., pp. 248–251.

Reference 51, pp. 242–245; 246–248.

Reference 22.

A. D. Bulman, Model Making for Young Physicists (John Murray, London, 1963), pp. 42–46;

reprinted as Model-Making for Physicists (Crowell, New York, 1968), pp. 86–94.

C. L.

Stong

, “,” , – (May ).

R. L.

Doan

, “,” , – (May, ).

A similar, but slightly more elaborate design, was listed in 1949 Catalog: Scientific Apparatus, Chemicals, and Supplies (W. M. Welch Scientific Company, Chicago, 1949), p. 56; Cat. No. 834, $35.00.

E. G.

Plasterer

, “,” , – (April, ).

Wallace A.

Hilton

, “,” , – (January, ).

Leonard Rose Ingersoll, A Laboratory Manual of Experiments in Physics (McGraw–Hill, New York, 1925), p. 164.

Ingersoll refers to Duff, who provides examples of the curves to be drawn and who refers to the Y-suspended pendulum. A. Wilber Duff, ed., A Text-Book of Physics (Blakiston’s Son, Philadelphia, 1921), 5th ed., pp. 179–181.

Leonard Rose Ingersoll and Miles Jay Martin, A Laboratory Manual of Experiments in Physics (McGraw–Hill, New York, 1942), 5th ed., pp. 224–225.

Leonard Rose Ingersoll, Miles Jay Martin, and Theodore Alton Rouse, A Laboratory Manual of Experiments in Physics (McGraw–Hill, New York, 1953), 6th ed., pp. 173–175.

S.

Tolansky

, “,” , – ().

Reference 62, pp. 268–270.

Reference 62, pp. 271–274.

Reference 62, p. 274.

R. H.

Romer

, “” , – ().

Reference 66, p. 1116.

Harry F. Meiners, ed., Physics Demonstration Experiments, Mechanics and Wave Motion Vol. I (Ronald, New York, 1970), pp. 347–348.

Robert L. Weber, ed., More Random Walks in Science (IOP, London, 1982), pp. 82–86.

The title was: “The future European harmonic pendulum: Report of a working party appointed by The Arts Research Council.” This was reprinted from Orbit, Journal of the Rutherford High Energy Laboratory, Didcot, England, December, 1964, p. 8.

A detailed account of early scientific instruments at Harvard was given some years ago by I. Bernard Cohen, Some Early Tools of American Science (Harvard U.P., Cambridge, MA, 1950;

Russell & Russell, New York, 1967). This is to be supplemented by David P. Wheatland, The Apparatus of Science at Harvard: 1765–1800 (Harvard U.P., Cambridge, MA, 1968).

While the harmonograph is not specifically addressed, an introduction to some of the problems that might be encountered in its analysis may be found in Arnold Sommerfeld, Mechanics Lectures on Theoretical Physics Vol. 1 (Academic, New York, 1952). See particularly his discussion of the “simple pendulum,” pp. 87–90; the “compound pendulum,” pp. 91–93; and the “double pendulum,” pp. 111–114 and 195–196. The “double-elliptic” harmonograph is a form of a double pendulum. However, Sommerfeld’s analysis deals only with the specific case in which a large (nearly) point mass is suspended from a support by a massless string, and a much smaller mass is suspended from this mass by a string of nearly equal length.

Reference 12, p. 298.

Giorgio Tabarroni, “Righi, Augusto,” Dictionary of Scientific Biography (Scribner’s, New York, 1970), Vol. 11, pp. 460–461.

Augusto

Righi

, “,” , – ();

Augusto

Righi

, , – ();

Augusto

Righi

, , – ().

Nature (London) 58, 488–489 (15 September 1898).

This summary seems to be based on a report to the Bolgona Academy of Sciences and published in Augusto Righi, “Appar. per la composiz. d. oscillaz. di 2 pendoli,” Memorie della Accademia delle Scienze dell’ Instituto di Bologna 6, 12 pp. (1897). I have not seen this paper.

Reference 16, p. 422.

J. H. Poynting and J. J. Thomson, A Text-Book of Physics: Sound (Charles Griffin, London, 1927), 9th ed., pp. 74–79.

Reference 77, p. 79.

Arthur Taber Jones, Sound: A Textbook (Van Nostrand, New York, 1937), p. 130

Reference 62, p. 267.

J. Dennis Lawrence, A Catalog of Special Curves (Dover, New York, 1972), p. 178.

A. K.

Dewdney

, “,” , (May, ).

P. H. Sydenham, Measuring Instruments: Tools of Knowledge and Control (Peter Peregrinus, Stevenage, UK, 1979), p. 78.

Reference 19, p. 256.

Crowell, Ref. 13.

M. J.

Lissajous

, “,” , – ();

M. J.

Lissajous

, “,” , – ();

M. J.

Lissajous

, “,” , – ();

M. J.

Lissajous

, “,” , – ();

M. J.

Lissajous

, “,” , ();

M. J.

Lissajous

, “,” , – ().

J.

Lissajous

, “,” , – ().

An excerpt of this paper, translated by Harry B. Miller, may be found in: J. Lissajous, “Memoir on the optical study of vibratory motion,” in Acoustical Measurements: Methods and Instrumentation, edited by Harry B. Miller (Hutchinson Ross, Stroudsburg, PA, 1982), pp. 6–23.

John

Tyndall

, “,” , – (). Tyndall provided a clear summary of the experiments performed by Lissajous in the lecture.

The award citation is printed in: “Prix Lacaze, Physique,” C. R. Acad. Sci. 79, 1607–1610 (1874).

A biography of Lissajous (1822–1880) may be found in Sigalia Dostrovsky, “Lissajous, Jules Antoine,” Dictionary of Scientific Biography (Scribner’s, New York, 1970), Vol. 8, pp. 398–399.

F.

Melde

, “,” , – ().

Ferdinand

Lippich

, “,” , – ().

Reference 74.

J. W. Strutt and Lord Rayleigh, The Theory of Sound (Macmillan, London, 1894; Dover, New York, 1945), Vol. I, Rev. ed., pp. 26–35.

A. P. French, Vibrations and Waves (Norton, New York, 1971), pp. 29–39.

Edward F.

Fahy

and

Frank G.

Karioris

, “,” , – ().

Frank G.

Karioris

, “,” , – (May, ).

B. A.

Smith

, “,” , – (January, ).

Mu-Shiang

Wu

and

W. H.

Tsai

, “,” , – ().

Thomas B.

Greenslade

, Jr., “,” , – (September, ).

E. Y. C.

Tong

, “,” , – (November, ).