EXAMPLES OF VOWEL ANALYSIS. 149 



the same distance apart (the horizontal distances being 4.7, 4.6, 4.9, 4.4, 

 5.3, 4.1), we can perhaps neglect the small divergence and apply the rule 

 given on page 137, finding that the axis lies at 4.2mm. below the tangential 

 line. The axis need not be drawn; it is sufficient to make all measurements 

 from the tangential fine and subtract 4.2mm. 



To analyze the curve a number of ordinates must be measured. The 

 decision concerning the number should be intelligently made. With 12 

 ordinates only 6 partials are obtained, with 24 only 12, with 36 only 18, 

 etc. The choice of the number of ordinates is determined by the number 

 of partials which it is desired to obtain, or which the curve is accurate 

 enough to justify. The evident smoothness of the curve indicates that 

 if very high partials are present they must be of such small amplitude 

 that they can hardly be detected. We will therefore not undertake the 

 very great labor (at least two days of work) involved in using 72 ordinates, 

 l)ut will confine ourselves to 36. We shall then obtain the first 18 partials. 



The third step is to measure the length of the wave. The ocular 

 scale is moved till its vertical fine is cut by the curve at 4.2; the reading 

 of the horizontal micrometer screw is noted. The vertical line is then 

 made to traverse the whole length of the wave until the curve again for 

 the last time cuts it at 4.2. The length of the wave in this case was found 

 to be 28.4mm. Since the time equation for this record is 1mm. = 0.0002s., 

 the period of the wave is 0.00o68s., and its frequency 176.1. 



Since the length of the wave is 28.4ram., the 36 equidistant ordinates 

 must be at 0.79mm. apart. We place the vertical hue of the scale at 

 the beginning of the wave and note the reading. The horizontal microm- 

 eter screw is then moved 0.79mm. and the reading is again taken, etc. 

 In this way the 36 readings are obtained from which the ordinates are 

 obtained by subtracting the reading of the axis, namely, 4.2. The ordi- 

 nates in thepresentcaseareO, 2.2,3.7,4.2,3.2, 1.8, —0.3, —2.1, —3.7, —4.1, 

 -3.4, -1.4, 0.9, 2.2, 3.2, 3.2, 2.8, 2.0, 0.6, -0.8, -2.2,-2.9, -2.7, -1.7, 

 - 0.2, 1.0, 1.6, 1.6, 1.3,0.7,0.0, -0.9, -1.8, - 2.4, - 2.3, - 1.6mm. Adding 



these ordinates and dividing by 36 we obtain -^ =0.02, that is, the axis 



of the curve practically coincides with the axis found by using the maxima 

 and minima; it lies, namely, at 4.2mm. below the tangential line. To 

 detect mistakes in measurement the 36 values are plotted on milUmeter 

 paper; the resulting curve is found to agree with the original. 



To perform a simple harmonic analysis the 36 values are written 

 in the first column of the analysis sheet and are then multiplied by the 

 cosines (p. 90). This gives the table found on page 148. It is convenient 

 to write + values in black and —values in red. 



