268 ANNUAL EEPOET SMITHSONIAN INSTITUTION, 1915. 



tensity of transpiration. The mechanical properties of wood come, 

 therefore, within the control of the forester who raises and cares for 

 the forest. 



There is another field of scientific endeavor in which foresters 

 in this country may claim some credit. This is in the field of forest 

 mathematics. One unfamiliar with forest growth can hardly realize 

 the difficulties in the way of measuring the forest crop, the amount 

 of wood produced in a forest composed, for instance, of many dif- 

 ferent species, sizes, and ages. If a tree resembled any geometric 

 body, such as a truncated cone, or an Appolonian paraboloid, it 

 would be a simple matter to determine its contents by applying the 

 formula for such body. But a tree's form does not coincide with 

 that of any known geometric body, so that it would seem that the 

 only possible way of determining the contents of the trees forming 

 a forest would be by measuring each single tree. Evidently this 

 would be an entirely impracticable task. 



The common practice of determining the contents of trees either 

 in board measure or in cubic feet is to measure a large number of 

 trees of a given species in a given locality and apply the average 

 figures to the trees of the same diameters and heights within that 

 locality. Since there are, however, a great many species of trees 

 in this country some of which have a very wide geographic range, 

 this method necessarily involves the preparation of a large number 

 of local volume tables and hence the measurement of hundreds of 

 thousands of trees. The measurement of the taper of a large num- 

 ber of trees has shown that there are certain critical points along 

 the stem of a tree the ratio between which expresses the form of the 

 tree in a sufficiently accurate manner. It was found that trees hav- 

 ing the same total height, the same diameter breast high (4^ feet 

 from the ground) and the same ratio between the diameter at half 

 the height of the tree and the diameter breast high, must invariably 

 have the same cubic contents irrespective of the species of the tree 

 or the region in which it grows. Thus whether it be a Scotch pine 

 of northern Sweden, a yellow pine of Arizona, a mahogany of the 

 Tropics, or a scrubby birch of the Arctic Circle, the volume of the 

 tree may be expressed by means of one simple relationship. The 

 discovery of this very simple relation provides, for the first time, a 

 basis for the construction of a universal volume table. The mathe- 

 maticians of the earlier period sought in vain to find a formula by 

 which the cubic contents of a tree could be expressed. AVhat the 

 mathematicians failed to develop by the deductive method, foresters 

 have found by the inductive method. With a reliable table for con- 

 verting cubic measure into board measure for trees of different sizes, 

 the universal volume table expressed in cubic feet could be translated 



