132 TRANSACTIONS OF ROYAL SCOTTISH ARBORICULTURAL SOCIETY. 



example, a circle (Fig. 6) with diameter 12 inches, has an area 

 of 785 square feet, and an ellipse, with axes 15 ins. x 9-6 ins., 

 encloses the same area, but the circumference of the circle is 

 37*69 inches, whereas that of the ellipse is 39*175 inches. 

 Moreover the greater the difference between the long and short 

 axes the greater will the error be in calculating the area from 

 a girth measurement. Diagrams Nos. 7, 8 and 9 show various 

 sections, with the areas calculated from girth and diameter 

 measurements. 



In each case the area was first found by making use of the 

 "Planimeter," after which the areas were calculated from the 

 average of two diameters taken at right angles to each other, 

 and from the girth measurement. 



From the results given, it will be seen that whenever the 

 section deviates from the form of a true circle the most accurate 

 result is obtained by calculating from diameter or calliper 

 measurements. Schlich refers to this point in his Manual of 

 Forestry as follows : — "Generally, the sections of trees approach 

 the shape of an ellipse, the greater axis of which lies in the 

 same locality, as a rule in a constant direction. Where trees 

 are much exposed to wind, the greater axis lies generally in the 

 direction of the prevailing wind ; in Western Europe, therefore, 

 from west to east, or from south-west to north-east. The 

 inaccuracy caused by measuring the girth and calculating 

 therefrom the sectional area, has been found to amount on 

 an average to about 7 per cent. Where only one diameter is 

 measured, the error may be the same or even more ; where 

 two diameters at right angles are measured, and the mean 

 taken, the error generally does not exceed 2 per cent, of the 

 true amount." 



Before considering what system of measurement should be 

 adopted in future in our country, the following rules should be 

 examined : — 



Various Methods of Cubing Logs. 



1. The Hoppus quarter-girth method has already been 

 described. It is generally used in Britain, but gives very 

 inaccurate results, being 21 '5 per cent, in error. 



xL 



Formula = V = 



144 



