CUBIC FEET. 



B. M. 



72.2 



251 



75-8 



257 



68.6 



237 



70.9 



245 



74.1 



256 



72 .0 



248 



433-6 



1,494 



72.3 



272 



112,788 



424,320 



80 REPORT OF THE 



Six sound, straight trees, then, of about those dimensions, are selected in the 

 forest, felled, measured, and the volumes tabulated as shown below. There will be 

 a difference in the form of the trees though their diameters and heights may be the 

 same, and, hence, their volumes will differ. The total area of the sample trees, 

 divided by their number, will give the average volume, and this, multiplied by the 

 number of trees of the stand, will give the volume of the stand : 



SAMPLE TREES. 



No. I, ------- - 



No. 2, .--.--.. 



No. 3, - 



No. 4, - - - 



No. 5, - - - - - -• - - 



No. 6, - - ' - - - - . ■ . 



A^olume of the six trees, - = . 



Average volume, --.-.. 

 Volume of 1,560 trees, _ . . . 



When the basal area a of the sample tree is exactly — , the simple formula, 



n 



V = V X 11 is always used for reckoning the volume. But if the basal area is not 



A 



— , it is evident that multiplying the volume of the sample tree by the number of 



trees multiplies also the error. The formula V = v — may then be used. 



a 



This very simple and convenient method was introduced into Germany by 

 Huber in the year 1824 and was recommended later by Carl Heyer. Still it is not 

 sufficiently accurate. By other methods discussed in this paper much better 

 results can be obtained with but very little more work. 



The method depends upon the principle that the sample tree presents not only 

 the mean cross area but also the mean height and form factor of the stand. That 

 these conditions may be satisfied the following equalities must exist : 



A H F =^ n^ay h^ f^ + n.^ a.^ k^ /, -+- 7/3 a-^ //g /s H 



But since A = n^ a^ -\- ti^ ^2 + ''3 <^3 H 



Then HF=h,f, + hf, + 7/3/3 + 



This is seldom true for a Avhole stand but only for sizes that lie close together ; 

 and, therefore, the measurement of a stand by means of one arithmetical mean 

 sample tree cannot give accurate results. 



