16 MENSURATION AND INCREMENT [CH. 



the past rate of growth by comparing its present volume with 

 its recorded volume in the past, but it is of course most unlikely 

 that such past measurements will often be available. It will 

 therefore be necessary generally to estimate the volume incre- 

 ment of the standing crop by means of the ascertained volume 

 increment of an average sample tree, which, growing in a fully- 

 stocked close-canopied crop, may be taken as representative of 

 the entire crop. 



It is obvious that our sample tree must represent all the 

 general conditions of growth which govern the individual stems 

 forming the crop, with a given degree of density, and growing 

 in close cover, because a tree growing in a free and isolated 

 position with an unrestricted amount of growing space in which 

 to spread itself, will develop in a very different way from a stem 

 grown in close cover. Then we have to remember that the 

 determination of the past rate of increment, although unlike 

 the estimation of future increment, which is necessarily more or 

 less speculative, it rests on actual existing data, is complicated 

 by the fact that a certain number of stems disappear out of the 

 crop year by year, or are removed by thinnings, and that the 

 stems remaining give us practically no information on this point. 



The first thing to be done in any case is to consider the best 

 means of ascertaining the rate of volume increment of a sample 

 tree, which depends on its rate of growth in height, its form 

 factor, and its rate of growth in basal area, which in turn is 

 proportional to the square of its girth, diameter or radius. This 

 volume increment may be expressed either in cubic feet, or else 

 as a percentage. With reference to the volume of the wood- 

 capital producing it, the increment of a whole crop is stated as 

 so much per acre per annum. 



14. Increment of felled trees. Stem-analysis. 



In the case of felled trees, or of a sample tree which can be 

 felled and cut up in order to measure its past-rate of growth in 

 height and in radius, the rate of growth is ascertained by 

 counting and measuring the annual rings. 



The most complete investigation of this kind is effected by 

 making what is called a stem-analysis, which is a rather intricate 



