242 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Hence the greatest error occurs when 
r 2 - 2 xr cos 0 = 0, 
i.e. when cos 9 = ~, 
2x 
and therefore e = r/4tx. 
If, then, the value of e be given, this determines x, the necessary size of 
the unit. In the present example e = '002, and r* = 5/4 = 1*25 inches; for 
it must be remembered that in practice the wire AB in fig. 3 is double, 
as shown in fig. 1. 
Hence x = 13 feet, a result which is in very striking contrast with the 
former for the Duplex Unit. 
Related Matters. 
For a description of the method employed for varying the amplitude 
of each harmonic unit during the running of the machine, and for various 
practical details, reference should be made to the former paper. 
Summary. 
The present paper is a continuation of one published thirteen years 
ago describing a new form of harmonic synthetiser. The object is to 
show that by a slight alteration the simple form of mechanism proposed 
by Lord Kelvin in 1881, but afterwards rejected by him on acount of 
“ obliquity error,” can be made quite satisfactory. 
The Author wishes to express his indebtedness to the Trustees of the 
Moray Fund of Edinburgh University for a grant, and to the Carnegie 
Trust for the Universities of Scotland for defraying the expense of the 
illustrations. 
(. Issued separately January 29, 1920.) 
