MEASUREMENT OF TIMBER. 57 



with 18 inches of difference, the loss is 27 inches 

 on mean area, or 3 cubic feet in 16 feet of length, 

 and so on. 



But this difference, which is of little conse- 

 quence in ordinary timber sales, would be a matter 

 of very grave error in estimating the stock on a 

 standing forest of tapering timber, such as pines 

 or deodar for here one fells typical trees, and 

 measures the whole. In the accompanying dia- 

 gram I have endeavoured to render this clear by 

 an analysis of the formation of a tapering spar. 



In this diagram, A is a beam 50 feet long, and 

 with a side of 12 inches throughout, and conse- 

 quently contains 50 cubic feet. B is a wedge 

 reduced from the beam A, and contains 25 cubic 

 feet. C is a pyramid reduced from the wedge B 

 by the abstraction of the two pieces D, and con- 

 tains 16f cubic feet. E is a cone reduced from 

 the pyramid C by rounding off the edges, and its 

 cubic contents are to those of the pyramid as 

 7854 : 1. This relation of the cone to the pyramid 

 being an established one, it will be simpler to 

 employ the latter in looking at the problem. 



Now suppose the pyramid C were the form of 

 the sample trees felled to determine the cubic 

 contents of the forest, and the officer were to 

 proceed to determine its cubic contents in the 

 usual manner, he would measure that tree in the 



