30 



MEASUREMENT OF FELLED TREES. 



Accoi-ding to this method the V(jhime of the whole stem is 

 obtained by means of the following formula (see Fig. 23) : — 



Volume of stem = si Iti + ^._i /',) + «:j /'3 + • • -5 



where si, s^, s^ . . . are the sectional areas taken in the middle 

 of successive paraboloids, and lii, Jio, //3 . . . the corresponding 

 heights or lengths. If the pieces are made of equal length, 

 the above formula changes into the following : — 



h. 



Fig. 23. 



Volume of stem = (si + so + .S3 + . . .) h. 



This formula is used in all scientific investigations, and the 

 degree of accuracy, with which it works, depends on the length 

 of the pieces. 



For the purposes of determining the yield of woods and 

 for the sale of logs, the formula is further simplified by con- 

 sidering each log as one paraboloid, in other words, the 

 volume is calculated from the middle section of the log 

 multiplied by its length, according to the formula — 



where H„, represents the area of the circle, or sectional area, 

 in the middle, and H the total length of the log. Experience 

 has shown this formula to give sufficiently accurate results 

 for all practical purposes. 



The sectional area is obtained, either by measuring the 

 girth, or the diameter. If ry==girth, and fZ=diameter, the 

 section is — 



S = 



47r 



•07 9G X >f, 



