INTRODUCTION 27 



the explanation, do not exist normally, an index of 65 or one of 96 being 

 extreme. Some 50% of all skulls have indices that fall between 75 and 

 80, and consequently these are called mesocranial ("mesocephalic"). 

 Skulls below 75 are dolichocranial, and those above 80 are brachycranial. 

 The one of this illustration is dolichocranial. 



While it is usually more convenient, in using an index, to have the two 

 distances taken at right angles to each other as here, it is by no means 

 necessary, and an index may as well be used which takes two distances 



parallel to each other (as two across the face, - No. 18 



zy - zy 



under Skull, below) ; or even one that uses the whole and a part of the 



length of humerus X 100 



same line: Ex. - ^n re e Although the distance to be 



total length of arm 



reduced to a percentage is generally smaller than the one which represents 

 the 100, this also is not necessary, and there are indices where the reverse 

 is true, and where the value of the index is consequently more than 

 100. 



II. Frequency Curves 



When, after taking a large series of the same measurement in many 

 individuals, we wish to compare its distribution, that is, the frequency of 

 occurrence of each measurement, it is usual to construct a frequency 

 curve, which will show the whole result at one stroke. This is done by 

 the employment of paper with two sets of parallel rulings, at right angles 

 to each other, the so-called "cross- section paper." Spaced horizontally 

 from left to right along the bottom (or top) are placed the successive 

 measurements, while along an upright on the left is placed a series of 

 numbers, usually from 1 on, to indicate the number of individuals which 

 are included under each measurement. The result of plotting the entire 

 record out is a series of vertical columns of varying height, and the fre 

 quency curve is formed by connecting the tops of the columns. 



Example: Suppose that, as the result of measuring 36 different 

 objects, we find the result, giving each in millimeters, to be, 

 3, 5, 5, 5, 6, 4, 8, 4, 4, 6, 4, 6, 7, 3, 7, 6, 8, 10, 

 3, 4, 3, 5, 6, 5, 4, 4, 9, 5, 7, 9, 1, 6, 2, 5, 2, 5, 



As they are found to vary from 1 to 10, we may then erect as many verti- 

 cal columns, each of as many squares as there are instances of that par- 

 ticular figure, as follows : 



10 



