QUANTITATIVE ANALYSIS: APPARATUS, METHODS. 



61 



measurements an error to one side will be compensated by a larger reading 

 for the next measurement. 



When desirable the measuring can be changed from bottoms to tops of 

 the waves, or the reverse; the middle points or any characteristic features 

 may be used. The reason is that, although each wave (that is, wave-group) 

 is the result of one glottal vibration, the groups overlap, and there is no 

 means of knowing exactly where each begins. In any case the best thing 

 to do is to pick out some characteristic feature and follow it from group 

 to group. 



A special difficulty arises from the fact that the characteristic features 

 gradually change; one fades away and another appears. For example, a set 

 of waves beginning with a fairly sharp apex may gradually develop an 

 accessory apex; the latter may finally become more prominent than the 

 other, which often ultimately disappears. In all cases of doubt it is wise to 

 measure the waves two or three times with different characteristic points. 



The wave-lengths are to be multiplied by the time equation in order 

 to obtain the period in seconds; the frequencies are found from a table of 

 reciprocals. For example, a wave-group 23.6mm. in length in the Mitchell 

 vowel record with a time equation of 1mm. = 0.0002s. indicates a period of 

 23.6 X 0.0002s. = 0.00472s., or a frequency of 1^0.00472 = 212. Since each 

 wave-group is the result of one vibration of the glottal Ups, this gives the 

 pitch of the tone from the larynx at that instant. 



A talkie of periods and frequencies is prepared to fit the measurements. 

 The first column contains the most frequent measurements in tenths of a 

 millimeter, the second the product of these by the time equation, the third 

 the reciprocals of the second. Thus for a wave-length of 50 tenths of a 

 miUimeter (first column) of a record whose time equation is 1mm. = 0.0007s., 

 the second column will show the period 50 X 0.0007s. = 0.00350s., the third 

 column the frequency 1h-0.0035= 286. The products and reciprocals can 

 be found in books of tables.* Such a table would begin as follows : 



*Zimmermami, Rechentafeln, Berlin, 1891; Ligowski, Taschenbuch der Mathematik, Berlin, 1S93; 

 Barlow, Tables, London, 1897. 



