118 THE RATE OF GROWTH [ch. 



will represent a vibration which is gradually dying out ; the ampli- 

 tude of the sine-curve will gradually diminish till it disappears ; 

 in short, our phenomenon is simply expressed by what is known 

 as a "damped sine-curve." Exactly the same thing occurs in 

 man, though neither in his case nor in that of the fish have we 

 sufficient data for its complete illustration. 



We can demonstrate the fact, however, in the case of man by 

 the help of certain very interesting measurements which have 

 been recorded by Daffner *, of the height of German cadets, 

 measured at half-yearly intervals. 



Growth in height of German military Cadets, in half-yearly 

 periods. {Dajfner.) 



Increment in cm. 



In the accompanying diagram (Fig. 30) the half-yearly incre- 

 ments are set forth, from the above table, and it will be seen that 

 they form two even and entirely separate series. The curve 

 joining up each series of points is an acceleration-curve; and the 

 comparison of the two curves gives a clear view of the relative 

 rates of growth during winter and summer, and the fluctuation 

 which these velocities undergo during the years in question. The 

 dotted Hne represents, approximately, the acceleration-curve in 

 its continuous fluctuation of alternate seasonal decrease and 

 increase. 



In the case of trees, the seasonal fluctuations of growthl admit 



* Das Wachstum des Menschen, p. 329, 1902. 



f The diurnal periodicity is beautifully shewn in the case of the Hop by Joh. 

 Schmidt (C E. du Laboratoire de Garlsberg, x, pp. 235-248, Copenhague, 1913). 



