226 



SCIENCE. 



[N. S. Vol. I. No. 



while heretofore all investigators deter- 

 mined the age in full years. There exists, 

 therefore, a difference of half a j'ear between 

 the period of Dr. Porter's tables and all 

 others which makes a comparison dififlcult. 

 ■ Dr. Porter bases all his discussions on 

 the assumption that all series of observations 

 of children of anj' given age are probability 

 curves, and he illustrates this point by a 

 detailed discussion of the observations on 

 stature of eight-year-old girls. In connection 

 with this subject he discusses the meaning 

 of the probable deviation, of the mean, and 

 of the average value of the series. Although 

 he employs both the mean and average 

 values, he evidently inclines toward the use 

 of the former. I will not dwell at length 

 upon the fact that whenever the curve is 

 really a probability curve the average is 

 a better value than the mean, because it is 

 more accurate, nor on the other fact that 

 the mean deviation gives a more constant 

 value than the probable deviation, and is 

 therefore the better value, as both con- 

 siderations have little practical bearing, 

 although I consider them of importance 

 from a theoretical point of view. 



It may be granted for a moment that the 

 curves are probability curves. Then there 

 remain two objections to Dr. Porter's values. 

 The one is that the difference in numbers 

 of individuals observed for each year is not 

 taken into consideration. This difference 

 in numbers has the effect that the average 

 age of all individuals whose nearest age is 

 six years will be a little more than six 

 years. These corrections amount to more 

 than 3% of the annual growth, during the 

 first and last years to even more. It af- 

 fects the annual rate of growth of stature to 

 the amount of several millimeters, the 

 weight to the amount of half a pound. 



Furthermore, Dr. Porter makes a linear 

 interpolation for determining the mean, 

 while the general curve ought to be taken 

 into consideration. The determination of 



the 50 % point of a series ought to be based on 

 the values found at two points, at least, on 

 each side. The same may be said of the 

 interpolation for all the other percentile 

 grades. The corrections made necessary by 

 these two causes are not great, but sufficient 

 to make all the millimeters and tenths of 

 kilograms inaccurate. 



A more important objection is based on 

 the fact that the observed curves are not 

 probability curves. In examining Dr. 

 Porter's curve for stature of girls of 8 years 

 of age (paper No. 4, p. 286), it will be seen 

 that in the first jjart of the table the differ- 

 ences between theorj' and observation are all 

 j)Ositive, while in the second part thej' are, 

 with one exception, all negative. When 

 the curves of stature, weight, span of arms, 

 height sitting, gii'th of chest for girls from 

 12 to 15 years of age, and for boys from 14 

 to 18 years of age are consulted it will ap- 

 pear that the asymmetry is still more 

 mai'ked. Dr. Porter himself quotes at 

 leng-th Dr. Bowditch's remarks on this asym- 

 metry (Ibid., p. 298), and calls attention to 

 the difference between mean and average. 

 These constantly occurring differences and 

 their regular distribution are the verj^ best 

 proof that the curves under consideration 

 are not probability curves. If this is the 

 case, neither the average, nor the mean, nor 

 the most fi-equent value represent the type 

 of the age to which the curve refei'S. 

 This can be determined onlj'^ by a detailed 

 examination of the causes of the asj'mme- 

 tries. 



I have stated at a former time (Science, 

 Vol. XIX., May 6, May 20, 1892) what I be- 

 lieve to be the cause of this asjTnmetry, and 

 I will revert to tliis subject after the dis- 

 cussion of one of Dr. Porter's most funda- 

 mental deductions. 



He concludes, from his data, that the 

 basis of dullness is deficient physical devel- 

 opment ; that the basis of precocity is an un- 

 usualty favorable physical development. 



