1905-6.] A New Form of Harmonic Synthetiser. 
207 
A New Form of Harmonic Synthetiser. By J. R. Milne, 
B. Sc., Carnegie Research Fellow. (With Plate.) 
CONT 
§ 1. General Description ‘ . .208 
§ 2. Description of the Mechanism 
%ohich enables the Period 
of a Constituent Harmonic 
to be varied during motion 209 
§ 3. Description of the Mechanism 
which enables the Ampli- 
tude of a Constituent 
Harmonic to be varied 
during motion . . .210 
§ 4. Description of the Mechanism 
connected with the Pen and 
Paper .... 214 
§ 5. Certain Details of Construc- 
tion .... 215 
§ 6. Mathematical Investigation 
of the Deviation from its 
ENTS. 
| True Position of the Pen 
of an Instrument on the 
above Principle . .216 
§ 7. Expression for the Greatest 
Deviation of the Pen . 217 
§ 8. On the Necessity for finding 
the Deviation of the Pen 
with Exactness . . 21& 
§ 9. Expression for the Average 
Deviation of the Pen . 227 
§ 10. Application of the Mathe- 
matical Results to the 
Present Instrument . . 230 
§ 11. Improvements suggested 
by the Ma thematical 
Theory .... 231 
§12. Summary of the Paper . 232: 
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,* hut there were two reasons which induced 
* 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. lxv. pp. 1-70 (where also is 
given a description of Lord Kelvin’s Harmonic Analyser). ‘ ‘ On an Instrument 
for Compounding Vibrations,” Lord Rayleigh, Phil. Mag., p. 127, 1906. 
T. R. Lyle, “Preliminary Account of a Wave-Tracer and Analyser,” Phil. 
Mag., p. 549, Nov. 1903 ; and also ibid. p. 102, Jan. 1905 ; and ibid. p. 25, 
Jan. 1906. “A New Harmonic Analyser,” A. A. Michelson and S. W. 
Stratton, Phil. Mag., vol. xlv. p. 85, 1898. W. C. Baker, Note in Nature, 
p. 541, 28th Sept. 1905. 
The following references are to Harmonic Analysers: — “An Harmonic 
Analyser,” J. N. Le Conte, Phys. Rev., vol. vii. p. 27, 1898. “On a Simple 
