44 CANADIAN FORESTRY ASSOCIATION 



work of the other four and keep the topographical and sylvicultural notes, the pro- 

 gress of the party is much more rapid and the accuracy of the work is increased. 



THE RELATION OF DIAMETER TO VOLUME. 



A careful study of the shapes of the trunks of forest grown trees shows; (1), 

 That each species has a characteristic shape or "form," and (2), That there is a 

 tolerably constant relationship existing between its diameter at breast height 

 and its volume. 



The method of determining this relationship for any given species is to select 

 a large number of sound trees having the typical shape of forest grown trees, 

 whose diameters range from a few inches up, measure their diameters at breast 

 height to the nearest tenth of an inch, fell them, cut them into ten foot lengths, 

 until a diameter of three, or four inches is reached and measure to the nearest tenth 

 of an inch the average diameters at the ends of the logs; first outside the bark 

 and then inside the bark. Frojn the measurements thus obtained we then compute 

 to the nearest hundredth part of a cubic foot, the total volume of each log," of the 

 stump and of the unused top ; also the volume of the wood inside the bark for the 

 different sections of the tree. The object of making two sets of measurements and 

 calculations is to be find what percentage the solid wood inside the bark is of the 

 total volume. Several mathematical formulae have been devised for the compu- 

 tation of these volumes, but are of too technical a nature to be dealt with in such 

 a paper as this. Having found the volumes of all the trees analyzed, the next step 

 is to plot, on cross-section paper, the breast high diameter of each tree as a hori- 

 zontal distance and its volume as a vertical distance. From the points thus located 

 we can then draw a curve showing the relationship that exists between the volume 

 of an average tree and its diameter at breast height. The accompanying diagram 

 shows such a curve based upon the analysis of sixty-six aspen, measured last sum- 

 mer in the Riding Mountain Forest Reserve. Some of the technically trained for- 

 esters present will probably object to my basing a diameter-volume curve upon 

 the analysis of so few trees. The explanation is that we have only made a start 

 in the work of studying the growth of these species. Next year more stem ana- 

 lyses will be made, which, with those already obtained, will give a fair average for 

 aspen, balm, white spruce and Jack pine. 



To find the number of cubic feet of wood per acre for any given species, we 

 first find out from the tally sheets how many trees of each diameter class there are 

 per acre, multiply by the volumes indicated by the diameter-volume curve of the 

 species under consideration, and add together the products. In the case of trees 

 less than a foot in diameter it is found that a standard cord of stacked wood con- 

 tains only about ninety cubic feet of solid wood; hence if our figures indicate 1080 

 cubic feet of wood per acre,we say that there are twelve cords to the acre. Where 

 the trees are large enough for saw timber we may scale the logs down to any given 

 diameter, by whatever log rule is in use in the district, and then construct a curve 

 showing the relationship between the breast high diameters of the trees and their 

 merchantable contents in board feet. Our next diagram shows a curve of this 

 nature, which naturally falls away below the total volume curve; (1), Because 

 of the volume lost in the tops not large enough to make sawlogs; (2), The volume 

 of the stumps; (3), The volume of the bark (about 15% for spruce), and (4), The 

 loss due to sawdust, sla.bs, edgings and trimmings. 



