1228 



ON VOCAL SOUNDS. 



surface of the cylinder, the prolongation of its edge would cut the axis of the 

 cylinder, and Ave would have the equation — 



{lbf = d{2r-d). 



Or d 2 -2dr + {W = o (1). 



From which we deduce — 



d = r± s](r + ±b){r-\b) . . (2). 



As the equation (1) is that of an ellipse, the axes of which are 2r and r, we 

 see that the breadth and depth of the impression have the same ratio to each 

 other as an abscis to its ordinate in the above-mentioned ellipse. It is true 

 that the supposition as to the axis of the marker does not hold good as regards 

 the phonograph, as it makes an angle (a) with the tangent, but the only 

 difference which this makes is that they should be multiplied by the constant 

 term, cos a, to obtain their real value. As the marker connected with the 

 glass plate of the phonograph is constantly moving up and down, the value of 

 the angle (a) changes at each moment ; but seeing the greatest depth of the im- 

 pressions cut out on the wax surface does not exceed 0'02 mm., these slight 

 variations are of no consequence. By an elaborate and most careful system, 

 the curves, corresponding to the ordinates obtained as above, are plotted 

 out on millimetre paper, and then a magnification of about one hundred 

 is worked out. 



Discussion of examples of phonograms. — Examples of curves 

 obtained by Hermann are shown in Figs. 438 and 441. These show 



Fig. 441. — Examples of vowel curves obtained by Hermann. 



curves of the vowel A, sung on the notes e, g, c'\ of the vowel 0, 

 sung on the note c' ; and of the vowels Ae and Ao, sung on the notes 

 c and e. 



Curves of vowel tones may also be obtained on a large scale by 



