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��AMERICAN ANTHROPOLOGIST

��[s. s., i, 1899

��243 Sioux Indians. (Adult males, 20-59 years.)

�� � �Correlated

�Correlated

� � � � �Number

�Stature:

�Length

�Breadth

�Number

�Height of race.

�Correlated

�Correlate

�of

� �of

�of

�°f

�Length of

�Breadth

�Individu-

�m

�Head.

�Head.

�Individu-

� �Head.

�Head.

�als.

� � � �als.

� � � � �(mm.)

�(mm.)

�(mm.)

� �(mm.)

�(mm.)

�(mm.)

�16

�1 600- 1649

�187.5

�I53.I

�27

�II5-II9

�191. 3

�15O.9

�49

�1650-1699

�193-3

�152.6

�71

�120-124

�I92.I

�154.8

�86

�I 700-I 749

�I94.I

�1543

�60

�125-129

�193.3

�154.6

�68

�1 750-I 799

�104.5

�155.3

�; 55

�130-134

�I96.O

�1547

�19

�1 800-1 849

�I96.5

�154.3

�1 16

�135-139

�I98.7

�155.5

� � �Number

�Breadth of

�Correlated Correlated

� � � � �of

�Face.

�Length of

�Breadth of

� � � � �Individu- als.

� �Head.

�Head.

� � � � �(mm.)

�(mm.)

�(mm.)

� � � � �8

�135-139

�187.8

�147.3

� � � � �44

�140-144

�I90.9

�1 50. 1

� � � � �85

�U5-I49

�I94.4

�152.9

� � � � �86

�150-154

�194.5

�156.5

� � � � �17

�155-159

�197. 1

�160.O

� � ��When we wish to consider the joint influences of all these causes upon either length or breadth of head, we must sub- divide each group according to the varying values of the new cause and calculate the correlated averages of the breadth of head. It will be seen at once that, in order to carry on the investigation in this manner, practically unlimited material must be available, otherwise the number of individuals in each class will be very small, owing to the great number of classes. Problems of this kind were first discussed by Francis Galton, 1 but the method of treatment has been fully developed by Karl Pearson.*

It may be well, on account of the importance of this method, to give an elementary deduction. The correlations of several organs are to be investigated, the first of which has the average value /j. The various observed values of this organ may be expressed by l x -\- x x, where x x designates the difference between an observed value and the average value. The second, third, and fourth organs have the average values, respectively, / 2, / s , / 4 ,. ..

��1 Natural Inheritance.

' Mathematical Contributions to the Theory of Evolution, ill; Philosophical Transactions of the Royal Society of London, vol. 187, pp. 253 ff.

�� �