F. Boas to K. Pearson, 26th Feb. 1899.- External URL
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Sent From (Definite): Franz Uri BoasSent To (Definite): Karl PearsonDate: 26 Feb 1899
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Holder (Definite): University College London: Special Collections
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Sent fromFranz Uri Boas
26 Feb 1899
Description:
‘Dear Professor Pearson,
Your publication on correlation and regression of 1896 has increased my interest in these questions very much, and I have had opportunity to investigate a number of questions from this point of view. You may be aware that the subject of correlation of organs had attracted my attention a number of years ago, but my method of treatment was a very imperfect one.
...
It weems to my mind that, in the case of correlation of organs at least, your theory requires a certain modification. Professor [Hermon Carey] Bumpus of Providence, R.I. pointed out to me, that when the correlation between two organs is slight, there is a tendency for extremes in one organ to be associated with increased variability in other organs. That is to say the reduction of variability in our array is not σ(1-22) but contains a term of the first variable. It seems very plausible that the coefficients x11 x12... (Equation I p. 262) should depend upon the values of y, or in words, that the organization of any individual should depend upon the form of its organs. This would necessitate the introduction of numbers of higher orders in the equations.
By the application of the method outlined above, it is easy to give approximations for curves that would comply with these conditions. It seems to me that such conditions can easily be incorporated by comparing the algebraic equations resulting from various assumptions. I will not enter into this subject, but will say a few words on the constancy of the coefficient of correlation in local races. The great differences that you obtained for Janvians[?], Egyptians, etc. in the case of the cephalic index is very puzzling to me. I have, since a long time, suspected that these differences are due to the intermarriage of different races. This result has been borne out very well in an investigation on full blood and half blood Indians in such a way, that I find increased correlation wherever the measurements of the component elements differ...
In all these cases it seems necessary to include terms of higher order in the treatment, since the coefficient of correlation depends upon it. This must be expected, if the mixture of races tends to produce regression to parental forms, as is the case in many instances. The anthropometric material that I have been able to investigate suggests that in pure races Galton’s function is constant, but I am far from certain that this is universally true. At the present time, when I find very low or very high values as compared to the more frequent value, I am inclined to suspect mixture.
I have not investigated many cases of heredity, but it would not seem unlikely that similar conditions may prevail. The whole subject is certainly one of the greatest importance and I am certain that your investigation will revolutionize biological methods, once their significance has been recognised.
Yours very truly,
Franz Boas.’
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Sent toKarl Pearson
26 Feb 1899
Description:
‘Dear Professor Pearson,
Your publication on correlation and regression of 1896 has increased my interest in these questions very much, and I have had opportunity to investigate a number of questions from this point of view. You may be aware that the subject of correlation of organs had attracted my attention a number of years ago, but my method of treatment was a very imperfect one.
...
It weems to my mind that, in the case of correlation of organs at least, your theory requires a certain modification. Professor [Hermon Carey] Bumpus of Providence, R.I. pointed out to me, that when the correlation between two organs is slight, there is a tendency for extremes in one organ to be associated with increased variability in other organs. That is to say the reduction of variability in our array is not σ(1-22) but contains a term of the first variable. It seems very plausible that the coefficients x11 x12... (Equation I p. 262) should depend upon the values of y, or in words, that the organization of any individual should depend upon the form of its organs. This would necessitate the introduction of numbers of higher orders in the equations.
By the application of the method outlined above, it is easy to give approximations for curves that would comply with these conditions. It seems to me that such conditions can easily be incorporated by comparing the algebraic equations resulting from various assumptions. I will not enter into this subject, but will say a few words on the constancy of the coefficient of correlation in local races. The great differences that you obtained for Janvians[?], Egyptians, etc. in the case of the cephalic index is very puzzling to me. I have, since a long time, suspected that these differences are due to the intermarriage of different races. This result has been borne out very well in an investigation on full blood and half blood Indians in such a way, that I find increased correlation wherever the measurements of the component elements differ...
In all these cases it seems necessary to include terms of higher order in the treatment, since the coefficient of correlation depends upon it. This must be expected, if the mixture of races tends to produce regression to parental forms, as is the case in many instances. The anthropometric material that I have been able to investigate suggests that in pure races Galton’s function is constant, but I am far from certain that this is universally true. At the present time, when I find very low or very high values as compared to the more frequent value, I am inclined to suspect mixture.
I have not investigated many cases of heredity, but it would not seem unlikely that similar conditions may prevail. The whole subject is certainly one of the greatest importance and I am certain that your investigation will revolutionize biological methods, once their significance has been recognised.
Yours very truly,
Franz Boas.’
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