Forest Mensuration 3 



PARAGRAPH V. 



APOLLONIAN PARABOLOID. 



The volume v of the Apollonian paraboloid is equal to height multi- 

 plied by 1/2 sectional area, or equal to J/z of a cylinder having the same 

 height and the same basal area. 



vol. apol. = 



The volume t of the truncated Apollonian paraboloid may be ascer- 

 tained as : 



A. Height of trunk times arithmetical mean of top sectional area 



and base sectional area. 



t . apol . =h ^ll 



B. Height of trunk times sectional area in the midst of the trunk. 



t. apol. = h. sj 



PARAGRAPH VI. 



CONE. 



The volume of the ordinary cone is equal to height of cone times 1/3 

 sectional area at the base. 



h.s 

 vol. cone = 



The volume t of the truncated cone is equal to 1/3 height of trunk 

 times sum total of top sectional area si, basal sectional area 82, and V si 82 



t. cone = (Sj + s 2 + KsiSj) 



PARAGRAPH VII. 

 NEILL'S PARABOLOID. 



The volume of the Neilloid equals J4 of its height times sectional area 

 at the base. 



vol. neil. = 

 The volume of the truncated neilloid t equals 



t. neil. = y( 8l + s 2 + V ^7 [^7+ 



wherein h denotes the height of the trunk; Sj and s 2 the top sectional 

 area and the basal sectional area of the trunk. 



