QUANTITATIVE ANALYSIS: APPARATUS, METHODS. 59 



from a vowel to an occlusive is not sudden. Where is the hmit to be set in 

 the case — for example — of the succession indicated by [ap]? If we say 

 "at the last vibration in the curve," then we find that a rise in the curve 

 clearly indicates the closing of the lips for the implosion of [p] while the 

 vocal bands are still sounding for the vowel. If we say " at the beginning 

 of the implosion," then we have a sonant implosion for [p]. If we deter- 

 mine to place the end of [a] at the first indication of the implosion, and the 

 beginning of [p] at the cessation of the vowel vibrations, and to call the 

 sonant implosion a glide, we get out of the difficulty in this case fairly well. 

 But in many other cases, particularly combinations of vowels and liquids, 

 no such solution is possible; one sound changes graduallj^ into another; 

 thus in the whole vowel mass, in lines 102 to 105 of the Depew plate, there 

 is not a single sudden change, and any assignment of hmits would be a 

 fiction. To the psychologist this condition is the only conceivable one. 

 In "Elements of Experimental Phonetics," Chapter XXX, the writer has 

 sketched a centroid theory of speech utterance based on these observations; 

 here it is necessary only to point out the technical difficulty in measuring. 



The amplitude of a vibration is its maximum excursion from its posi- 

 tion of equiUbrium; when a simple vibration is evenly maintained the 

 excursion is the same on both sides and the amplitude is half the distance 

 between the two extremes. Although speech curves are not evenly main- 

 tained vibrations and are not simple in form, it is sufficient for many 

 purposes to take half the vertical distance between the highest and lowest 

 points in a wave-group ; the results may be regarded as giving roughly the 

 amphtudes of the vibrations forming the groups. The technique is evident; 

 the "coordinate measurer" is specially adapted to this work. When 

 different records are to be compared the results may be divided by the mag- 

 nification of the tracing lever (p. 30) ; the results then refer to the gramo- 

 phone grooves. Nothing is known of the relation to the amplitudes of the 

 original air-vibrations. 



The study of melody is the study of the fluctuations of the pitch of the 

 tone from the glottal lips. Each explosion, puff, or vibration from the 

 glottis arouses a vibratory movement that shows itself in the speech curve 

 as a group of vibrations (p. 40); this we have called a "wave-group" or a 

 " wave. " A " wave" thus means the whole complicated group of vibrations 

 resulting from a single glottal movement. The study of melody has to do 

 with these waves or wave-groups. Confusion seldom arises, except where 

 the "wave" or "wave-group" is composed of two or three subordinate 

 vibrations of nearly equal ampUtude (Depew plate, fine 102; Cock Robin 

 plate, fines 1, 3, 7, 16); even here it is easy to pick out the stronger vibra- 

 tion that begins each group or to tell whether the groups are of twos 

 or threes by following the curve from clearly marked groups. 



