126 



SCIENCE 



[N. S. Vol. XLI. No. 104T 



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 

 different species, sizes and ages. If a tree 

 resembled any geometric body, such as a 

 truncated cone, or an Appolonian para- 

 boloid, it would be a simple matter to deter- 

 mine 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 practise of determining the 

 contents of trees either in board measure 

 or in cubic feet is to measure a large num- 

 ber 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, how- 

 ever, 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 meas- 

 urement of hundreds of thousands of trees. 

 The measurement of the taper of a large 

 number 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 dis- 

 covery of this very simple relation provides 

 for the first time a basis for the construc- 

 tion of a universal volume table. The 

 mathematicians of the earlier period sought 

 in vain to find a formula by which the cubic 

 contents of a tree could be expressed. What 

 the mathematicians failed to develop by 

 the deductive method, foresters have found 

 by the inductive method. With a reliable 

 table for converting cubic measure into 

 board measure for trees of different sizes 

 the universal volume table expressed in 

 cubic feet could be translated into a uni- 

 versal table expressed in board feet, which 

 is the measure peculiar to this country. 



There is another contribution of which I 

 am somewhat hesitant to speak for it is not 

 a contribution to pure science, if by sci- 

 ence is meant only the physical or natural 

 sciences. Since, however, it touches the 

 interests of a large number of people, I 

 may be forgiven if I say a few words about 

 it. It is a contribution to what one econ- 

 omist has aptly called the "science of social 

 engineering." The transfer of the forest 

 reserves in 1905 to the Department of Agri- 

 culture marked a new departure in the na- 

 tional economic life. It recognized the new 

 principle that the nation's resources should 

 be managed by the nation and directly in 

 the interests of the whole people; it recog- 

 nized that these resources should be devel- 

 oped collectively rather than individually 

 and indirectly. Nearly ten years have now 

 passed since the inauguration of this policy. 

 The record of what has been accomplished 

 and the manner in which many of the prob- 

 lems have been approached and solved must 

 unquestionably be considered a contribu- 

 tion to the methods by which similar prob- 

 lems may be handled by the nation in the 



