404 THE GRAMMAR OF SCIENCE 



of life, and its mean value lies between .4 and .5.^ We 

 shall speak of this result as the law of gi'owtJi of like 

 pai'ts. 



Beyond this law for the growth of like parts, we 

 require to investigate a law for growth giving the change 

 with age. For without very precise attention to age we 

 cannot predict much as to evolution ; type, variation, and 

 correlation all change with the age of the individual, and 

 this change may be just as much due to growth as to 

 a selective death-rate. For example, it is quite obvious 

 that the mean weight and mean length of new-born babies 

 differ from those of adults of say 20 to 22, but the babies 

 have quite a different variation and a higher correlation 

 for the two characters than the adults. Is this due to a 

 selective death-rate, or merely a phenomenon of growth ? 

 Clearly the period of life of any class must be stated, and 

 we must not form our numerical specification of a form 

 of life on individuals of widely different ages. Let me 

 illustrate this. 



Suppose we measure the stature of 1000 English boys 

 of I I years of age, and again the stature of the same lOOO 

 boys at 1 3 years of age ; obviously the type will have 

 changed, the boys will be taller ; further, the variation 

 will have changed — as a matter of fact we shall expect 

 to find them less variable. But if a boy of 1 1 years 

 who was 5 3 inches becomes at 13 years 5 5 inches, 

 should we expect a second boy of i i years who was also 

 5 3 inches to have also become 5 5 inches at 1 3 years ? 

 By no means ; he may have become 56 inches or only 

 54.5 inches, for all boys do not grow at the same rate. 

 What then have we got ? If we take all the boys of 1 1 

 years of age who were 5 3 inches, they will form an 

 " array " of boys at i 3 years, with an average height of 

 5 5 inches say, but scattered about this height with a 

 definite standard deviation less than that of all boys of 13. 



^ The theory of this particular numerical value I do not here discuss. I 

 state the law as a probable one only, because I have only verified it at present 

 for comparatively few forms of life ; but even if only approximately true, it 

 will serve to illustrate the sort of quantitative law we are seeking. 



