40 GROWTH 



qualitative aspects of growth and the general mechanisms of 

 growth in words. We now proceed to a consideration of the 

 quantitative aspects of growth and aging, that is, a consideration 

 of growth and senescence which can be represented by numeri- 

 cal values and curves. Before presenting these curves it seems 

 desirable to say a few words in explanation concerning the 

 general spirit in which the curves were prepared. 



The curves were prepared, first, in order to give a quantita- 

 tive picture of the changes with age as contrasted to the qualita- 

 tive ideas one obtains from a verbal description, and, second, in 

 order to obtain the laws of growth. Now, in a scientific sense, a 

 law is usually a mathematical formula which describes quanti- 

 tatively a large number of phenomena, thus recognizing their 

 essential similarity. The meaning of the idea of law may be 

 best illustrated by reference to Newton's law of gravitation. 

 Newton's law of gravitation is merely a statement of the fact 

 that the force of attraction between two bodies is proportional 

 to the product of their masses, and inversely proportional to the 

 square of the distance between them. This statement is pre- 

 sented in the form of the formula 



in which F is the force of gravitation, M and M', the masses 

 of the bodies, and d the distance between the bodies. G is a 

 proportionality constant known as the constant of gravitation. 



This formula represents a great law because it shows the ele- 

 ment of sameness in such diverse phenomena as the fall of the 

 apple, the movement of the tides, and motions of the heavenly 

 bodies. Thus, by the discovery of this law, a great many appar- 

 ently unrelated phenomena were shown to be the consequences 

 of the same force — the force of gravitation. This formula does 

 not, however, explain the ultimate nature or meaning of the 

 force of gravitation. This is true of most other scientific laws — 

 they represent the quantitative aspects of the phenomena in a 

 generalized form; they show by their form the similarities be- 



