SCHNEIDER'S FORMULA 445 



same for both periods. This, however, is a wrong assumption 

 if the width of the annual rings be the same all the way up 

 the stem. For, in such a case, if the height be the same, the 

 form factor must be greater ; and conversely, if the form factor 

 be the same, the height must be greater. 



The application of the formulae as above described will, 

 on an evenly tapering tree, only give correct results if the 

 width of the recent annual rings at half-way up the stem is 

 in reality one-half of the width of such rings at ground level. 

 But this should never be the case with trees that are growing 

 under correct sylvicultural management. In trees approach- 

 ing maturity the annual rings will usually be widest at the 

 top of such part of the bole as is clean and free from branches, 

 and therefore in the case of well -grown timber it is obvious 

 that the percentage as indicated by the formulae, when 

 measurements are taken at breast high, is far too small. 



Now, the assumption of the same height growth in trees 

 approaching maturity will not materially affect the result ; 

 the chief error lies in the assumption of the same form factor. 



In the application of Schneider's formula this error may 

 be corrected by multiplying the percentage as indicated at 



breast high by 



Diameter at breast high 



Diameter at half-way up any evenly-tapering tree' 



if the width of the rings at half-way up be taken as the 

 average width over the stem. 



But the diameter half-way up the stem is an unknown 

 quantity ; it is, however, equal to 



A/(Diameter at breast high) 2 x form factor. 

 Therefore, if 



p = percentage as indicated at breast high by Schneider's formula, 

 D = diameter at breast high, 



the true percentage increment is equal to 



D 



<h x - 



^/D 2 x form factor (for total contents) 



This method for correcting the percentage, as indicated 

 at breast high, is also applicable to Pressler's formula, if a 



