I30 TRANSACTIONS OF ROYAL SCOTTISH ARBORICULTURAL SOCIETY- 



other is accurately measured. For instance, a log of 40 feet 

 long and 12 inches quarter-girth, gives according to quarter- 

 girth contents 40 cubic feet, whereas by true measurement the 

 log actually contains 50-88 cubic feet. If, in future, the measure- 

 ment of round timber was based on true measurement, the load 

 in every case could be taken as 50 cubic feet. 



It will be seen, therefore, that while up to the present the 

 quarter-girth system of measuring round timber has been con- 

 sidered sufficiently satisfactory for transactions between buyer 

 and seller, it has been, in fact, a compromise measure — the seller 

 losing the difference between the actual contents and quarter- 

 girth contents, and the buyer the difference between the latter 

 and the actual cubic feet of sawn timber manufactured therefrom. 

 From no point of view can this system be considered entirely 

 satisfactory. 



Indeed, no system can be so, unless it is founded on the 

 mathematical formula for obtaining the volume of the geo- 

 metrical figure most nearly approaching the form of a tree or 

 log. For this purpose the following formulas are involved : — 



Mathematical Formula for finding the Volume of certain Solids. 



1. Cylinder (Fig. 1) V = AH = area of base x height 



2. Cone (Fig. 2) V = A — = area of base x \ height 



■pj 



3. Truncated cone (Fig. 2) V = (A b + A t + ,yA b + A t ) — 



4. Paraboloid (Fig. 3) V = 



2 



5. Truncated Paraboloid (Fig. 3) V = (A b + A t ) — 



2 



6. Neiloid (Fig. 4) V = — 



4 



7. Truncated Neiloid (Fig. 4) V = A b + 4 A m + A t ) — 



6 



Mathematical Formulae for finding the area of a Circle and Ellipse. 



1. Circle. Area = 7rr 2 or 7r( — ) 



2. Ellipse. Area = Dd x 7854. 



D = Long Axis. d«= Short Axis. 



