BRIGGS: THE LIVING PLANT AS A PHYSICAL SYSTEM 99 



V = Ur-h (11) 

 or, since by assumption h = ar 



V = i 7r«r 3 (12) 

 The rate of growth would be 



dV „dr / 10 v 



= irar 2 — (13) 



dt dt 



hence the necessary condition for a uniform growth rate is that 



— = cr~ (14) 



dr 



where c is a constant. 



Let us now examine Huntington's data for the Sequoia by 

 i± 



plotting ~- against r 2 . If a portion of the resulting graph is a 

 ar 



straight Jine, the growth-rate during the corresponding period 

 will be constant, subject of course to the assumption made re- 

 garding the form of the tree. This graph is presented in figure 

 4. It will be seen that the growth-rate decreases for values of 

 r- up to 30,000 cm 2 , corresponding to trees about 1200 years 

 of age. For values greater than this, however, the relationship 

 is approximately linear, i.e., the growth-rate is constant within 

 the errors of the determinations. The oldest trees included in 

 these measurements were over 3000 years of age. Since the 

 birth of Christ, therefore, these giant trees have been growing 

 at a practically uniform rate, save as that rate has been modi- 

 fied by weather conditions. 



Gas exchange between the leaf and the air. We pass now to a 

 consideration of some of the physical processes within the plant. 

 We shall first consider the path by which carbon dioxide enters 

 the leaf. The rate of assimilation of carbon-dioxide by an ac- 

 tive leaf in bright sunlight is very great. In fact Brown and 

 Escombe have found that a Catalpa leaf in bright sunshine will 

 absorb carbon-dioxide at a rate one-half as fast as it would if the 

 lower surface of the leaf were covered with a film of caustic pot- 

 ash solution constantly renewed. The stomatal openings in the 



