GENERAL MEETING. 29 
out them there is no harmony. This is also apparent from the well- 
known rule in thorough-bass that a third with its fundamental 
note is to be treated as a complete chord. Now it happens, in 
dividing the octave by equal temperament into 12 equal parts, 
that a major third is nearly 4 and the minor third nearly 3 of 
these, and thus we obtain not only tolerable fifths, but also tolerable 
, thirds, and the requirement of thirds for harmony is approximately 
fulfilled. They are still better fulfilled, of course, if we divide the 
octave into 41 or 58 parts, as Mr. Doolittle has shown. As to the 
seventh harmonic, Poole and Helmholtz rightly hold that it should 
be and is used by instruments which can temper. It is obviously 
the fourth element of the chord of the dominant G, B, D, F, the F 
being the seventh harmonic to the G two octaves below (nearly 
so in equal tempcrament and exactly in natural harmony), and 
this chord in modern music forms the opposing harmony to the 
tonic chord C, E, G, in major, and C, E flat, G, in minor. Instru- 
ments with fixed tones like the piano-forte have to use equal tem- 
perament, and thus virtually reject all natural harmony except the 
octave. This defect is generally inappreciable in very slow move- 
ments, but may be noticed by a very cultivated ear. 
Other remarks were made by Messrs. CLARKE, Mussry, and 
HARKNESS. 
Mr. H. FarquHar read a 
REVIEW OF THE THEORETICAL DISCUSSION IN PROF. P. G. TAIT’S 
“ PNCYCLOPZDIA BRITANNICA” ARTICLE ON MECHANICS. 
[ Abstract. ] 
This article covers seventy-four quarto pages in the last edition 
of the Encyclopedia, and gives a thorough mathematical treatment 
of the subject. No innovations calling for comment—unless an 
extended use of the “fluxional” notation for derivative functions 
be so regarded—appear until near the end, where two and a half 
pages are devoted to a disproof of the objective reality of force, 
and an advocacy of the disuse of the term in scientific writing. 
The character of the publication, and the eminence of the author 
in mathematics and physics, entitle his arguments to a careful 
examination. 
