96 Proceedings of Royal Society of Edinburgh. [sess. 
An analysis may be made by Prof. Hermann’s “Schablonen ” 
in much shorter time and much more smoothly than in the 
ordinary manner. It does not generally take more than an hour or 
two. It is true that the ratio of the ordinates to their abscissae in 
the curves obtained in this way, in some cases, differs widely from 
the real one, but this obviously does not matter for harmonic analy- 
sis. For the study of the curve itself the adopted dimensions were 
very convenient and useful. The curve with its real ratio of height 
and length would be wholly unfit for examination. 
The length of the periods of vowels uttered by myself was about 
-i- of the circumference of the cylinder, which generally had a 
value of 173-174 mm. The length of such a period being conse- 
quently about 1 *93 mm., its greatest height did not even reach 
0*02 mm.; so that in a curve drawn on a hundred times magnified 
scale, the largest underwave would not even have a height of 
2 mm. 
The calculations of the value of a and b, a 2 and b 2i etc., and of 
the amplitudes of the harmonic constituents Ja 2 + b 2 , Jaf + bf, 
etc., were not made, as Prof. Hermann advises, on the centi- 
meter-paper itself, but on a separate sheet of paper, which was 
kept together with the sheet containing the numbers, so that it 
was possible to correct any mistakes afterwards. Since the centi- 
meter paper (which is rather expensive) contains thirty-four vertical 
columns, and since every analysis requires eleven of these, one 
sheet of it is sufficient for three analyses, if the calculations are 
made on a separate paper. 
Up till now I have made about 350 Fourierian analyses, most of 
them from vowel curves. 
The values of the amplitudes of the partials obtained were 
generally reduced in such a way that the amplitude of the funda- 
mental tone Ja l + b 1 was taken as unit. It is a curious fact 
that the amplitude of the fundamental tone, when vowel sounds 
are subjected to analysis, is by no means greater than that of the 
partials, in most cases even much smaller. Especially in spoken 
vowels the amplitude of the fundamental tone is relatively small. 
This explains the fact that it is almost impossible to estimate 
the pitch in which a vowel is spoken by simply hearing it. 
