234 Proceedings of the Royal Society of Edinburgh. [Sess. 
XVI. — A “Duplex” Form of Harmonic Synthetiser and its 
Mathematical Theory. By J. R. Milne, D.Sc. 
(Read July 5, 1915 ; MS. received July 6, 1919.) 
Introduction. 
The present paper is really a sequel to one which was published in the 
Society’s Proceedings for 1905-06 to describe an improved form of harmonic 
synthetiser, in which, by the substitution of rotary for reciprocating 
motion, all sliding parts are eliminated. Each simple harmonic unit of the 
machine consisted (see fig. 1) of a revolving crank with a pulley at its 
outer end down to which a flexible wire was led from fixed pulleys above ; 
and this takes the place of the usual mechanism, shown in fig. 2, in which 
the slider D, constrained to move in a vertical direction by the guides A 
and B, has an exact simple harmonic motion imparted to it by means of the 
pin P fixed in the revolving disc C. Lord Kelvin, in describing his 
well-known Tide-Predictor, states that he first used the plan of fig. 1, but 
subsequently altered the machine and introduced that of fig. 2 instead. 
He gives as the reason, that “ This modification, though making the 
instrument less simple, was rendered in fact necessary by the large range 
which it was proposed to give for the resultant curve, and which would 
have required inconveniently great lengths for the straight parts of 
wire between the upper and lower rows of pulleys to nearly enough 
annul the geometrical error of the simpler plan.” * 
* Proc. Inst. Civil Engineers , vol. lxv, 1881, p. 16. 
