VOLUME OF THE STEM. 



31 



According to this method the volume of the whole stem is 

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



Volume of stem = s l l^+s^h^+Ss h. 3 +. . ., 



where s lt s 2 , s s . . . are the sectional areas taken in the middle 

 of successive paraboloids, and h l9 h 2) h s . . . the corresponding 

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

 the above formula changes into the following : 



Volume of stem = (s 1 4-S2+ s 3 + ) '& 

 This formula is used in all scientific investigations, and the 



I*,, jfc^..- **.:. * 2 -->;.,- 



Fig. 23. 



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 



V=S m xH, 



where S m represents the 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 g = girth, and d = diameter, the section 

 is : 



