28 



trees in each gradation, and, therefore, also in the who'le crop, are 

 measured as sample trees, the number of such sample trees beiug 

 therefore 



= — = say ?. 



Now as the sample trees represent the «-th portion of the whole 

 crop, not only in number but also in respect of contents and basal 

 area, we have 



A ■=> a z and C ^ c z = e ^ = c . 



As the ;?-th part of the number of trees composing' a girth 

 gradation may not be a whole number, and we cannot measure a 

 fraction of a tree, it is best, in calculating the cubical contents of 

 all the trees in a gradation, to use the last of these equalities, which 

 enables us to measure up whole stems only, and also renders it 

 unnecessary for the sample stems to be exact average stems for the 

 gradation in question. 



In practice the procedure is as follows : — 



An enumeration survey is effected in classes having a sufficiently 

 wide range of girth (say 6 inches). This being done, the 

 figure z is determined, and the number of sample stems to be mea- 

 sured for each gradation is then the nearest integer in the expression 



— . But if — is a very small fraction," as many gradations are 



lumped up together as will give one sample tree j and when this 

 is done, the basal area of the sample tree is determined in the same 

 way as when several girth-classes of the enumeration survey 

 are lumped up together to form a new girth-gradation {see the 

 figures at the bottom of the example at end of the preceding 

 section) . The girths and basal areas of all the sample stems 

 are then carefully registered, and their cubical contents accurately • 

 measured and expressed, either in one lump figure or in separate 

 figures giving the respective quantities of timber, fiie-wood, etc. 

 Lastly, the contents of all the trees in each gradation- are calculated 



