VOLUME OF THE STEM. 



29 



If h = the height, or length, 

 *S' = the lower section, 

 s = the upper section, and 

 s.^^^ = the middle section (Fig. 22), 

 the volume of each of the above-mentioned 

 truncated solids is, according to Simpson's 

 rule — 



6 



X h. 



This formula reduces — 



For the cylinder to V = S X It 



For the cone to V = ^^ 



Fis. 22 



And for the truncated Ap. paraboloid to T 



■ = '^xh,ov, 



By means of these formulae it would be possible to calculate 

 the volume of each part of the stem, provided its particular 

 shape had first been ascertained. This, however, would be a 

 tedious business, and it is necessary to search for a more 

 simple procedure. 



It has been found, that by far the greater portion of the 

 stem approaches in shape that of a paraboloid, and that, if 

 the stem is divided into a number of pieces of moderate 

 length, each can, without committing any appreciable error, 

 be considered as a truncated paraboloid, the volume of 

 which is — 



V =i S,n X h. 



Of these two formula, the latter is the more convenient, and 

 experience has shown, that it is even more accurate than the 

 former. 



