752 PROFESSOR FLEEMING JENKIN AND J. A. EWING ON THE 
curves, after analysis, were built up again graphically by synthesis of their 
constituent simple harmonic waves, and this process always gave an accurate 
reproduction of the original. 
We have paid but little attention to the phases of the constituent tones. 
They did not appear to follow any simple rule. One and the same voice singing 
the same vowel at the same pitch on different occasions, although generally 
adhering to one wave-form, sometimes gave a changed phase relation of 
approximately the same constituents. On this account we have not taken the 
trouble to calculate the phase relation except in a few cases, but have confined 
our attention to the much more important peculiarity, the amplitude of the 
tones. It may be observed that the experiments have given thorough confir- 
mation of HELMHoLTz’s discovery that vowel quality is not dependent on 
phase relation, so long as the constituent tones are unchanged. 
To satisfy ourselves that the curves obtained were not affected to any 
practical extent by the particular form of instrument employed, we made 
numerous experiments with varied discs, springs, and mouthpieces, as well as 
with several different thicknesses of tinfoil, the result being to prove that the 
curves were so little affected by the special conditions of the apparatus, that 
they might be considered as giving a true and consistent record of the essential 
characteristics of the sound. 
Having said so much by way of preface as to the mode of obtaining and 
analysing the curves, we now pass on to speak of the result. The experiments 
were chiefly directed to the two sounds 6 and @ (the vowels in “oh!” and 
“food ”). Several very different voices were employed. Voice No. 1 was a 
powerful baritone, with a very considerable range and good musical training. 
No. 2 was a high set and somewhat harsh voice of limited range, and without 
musical trainng. No 3 was a rich and well-trained bass voice of a man of 
eighty. Nos. 4 and 5 were somewhat alike, being voices of moderate range and 
power, and with some musical training; No. 5 was the stronger of the two. 
No. 6 was a powerful bass. Generally the vowel sounds were sung in tune with 
notes given by a piano, and when not otherwise described, it is to be under- 
stood that the pitch was determined in this way. In other cases, which will be 
named when they occur, the sounds were spoken or sung at random, and the 
pitch was determined afterwards by measuring the lengths of the curves. 
Figure 1* (Plate XX XVI.) gives the wave-forms for a series of 6’s sung by 
voice No. 1. The pitch on which the vowel was sung is denoted by the letter 
alongside the curve. In naming pitches we have adopted the usual notation, in 
which ¢’ has 256 complete vibrations per second, and c” 512. A rise in the 
curve, as printed here, corresponds with a hollow in the tinfoil. The arrow 
pointing from right to left shows the direction in which the tinfoil passed under 
* These figures have been reproduced by a photo-lithographic process. 

