No CrossRef data available.
Article contents
A New Form of Harmonic Synthetiser
Published online by Cambridge University Press: 15 September 2014
Extract
The author has designed and constructed an instrument for the purpose of drawing the curve which is the summation of a number of simple harmonic curves; and as the apparatus has been found to work very satisfactorily in practice, it seems worth while to publish a description of the machine, especially in view of its numerous applications. Various forms of harmonic synthetiser are already in existence, but there were two reasons which induced the author to add another to their number. In the first place, it was desired to ascertain whether results of a high degree of accuracy could not be obtained from an apparatus of quite inexpensive design; and in the second, to construct a machine in which both the amplitude and periodic time of each of the simple harmonic constituents might be varied at will while the instrument is in motion.
- Type
- Proceedings
- Information
- Copyright
- Copyright © Royal Society of Edinburgh 1906
References
page 207 note * The following papers may be consulted :—“Tide Predicting Machine in use at Nat. Ph. Lab.,” Great Trigonometrical Survey of India, vol. xvi.; also Proc. of Institution of Civil Engineers, vol. Ixv. pp. 1–70 (where also is given a description of Lord Kelvin's Harmonic Analyser). “On an Instrument for Compounding Vibrations,” Rayleigh, Lord, Phil. Mag., p. 127, 1906.Google ScholarLyle, T. E., “Preliminary Account of a Wave-Tracer and Analyser,” Phil. Mag., p. 549, Nov. 1903CrossRefGoogle Scholar; and also ibid. p. 102, Jan. 1905; and ibid. p. 25, Jan. 1906. “A New Harmonic Analyser,” Michelson, A. A. and Stratton, S. W., Phil. Mag., vol. xlv. p. 85, 1898.CrossRefGoogle ScholarBaker, W. C., Note in Nature, p. 541, 28th Sept. 1905.Google Scholar
The following references are to Harmonic Analysers:—“An Harmonic Analyser,” Le Conte, J. N., Phys. Rev., vol. vii. p. 27, 1898.Google Scholar “On a Simple Form of Harmonic Analyser,” Yule, G. V., Phil. Mag., vol. xxxix. p. 367, 1895.CrossRefGoogle Scholar “Harmonic Analyser,” Rowe, Geo. H., Electrical World and Engineer, p. 587, 25th March 1905.Google Scholar Three papers by Prof. SirThomson, W., Proc. Roy. Soc, pp. 266, 269, 271, 1876.Google Scholar “On an Integrating Machine having a New Kinematic Principle,” Prof. Thomson, James, Proc. Roy. Soc., vol. xxiv. p. 262, 1876.Google Scholar “On a New Harmonic Analyser,” Prof. Henrici, O., Phil. Mag., vol. xxxviii. p, 110, 1894.CrossRefGoogle Scholar “Ueber Instrumente zur harmonischen Analyse,” Henrici, O., Catalogue Munich Mathematical Exhibition, 1892–1983.Google Scholar
page 209 note * Proof may be found in any work on Mechanism, e.g. in that by S. Dunkerley, p. 23 (edition 1905).
page 212 note * The matter is fully discussed in Dunkerley's, S.Mechanism, p. 97 (edition 1905).Google Scholar
page 218 note * The diameter of the small pulleys is 1 inch, which is also the distance between the upper pair; and these are both distant about 30 inches from the lower pulley, whose circle of rotation is ½ inch in diameter. Such being the dimensions of the -machinery, we are probably led into no appreciable error by having to substitute the above approximate statement for the exact one, which is too complicated to be used.
page 223 note * The termination of the hyperbolic branch at its points of contact with the two straight lines, i.e., at the points the abscissæ of which are respectively 
is simply because, as explained above, (12) is physically meaningless beyond these limits. As negative values of p are also meaningless in the present connection, all that lies on the left of the 6 axis has been omitted from the figure.
page 226 note * The angle is to be taken between 0 and π.
page 226 note † The angle is to be taken between π and 2π.