128 TRANSACTIONS OF ROYAL SCOTTISH ARBORICULTURAL SOCIETY. 



One-fourth of the girth of the log is measured in inches, then 

 squared and multiplied by the length of the log in feet and 

 divided by 144 to obtain the volume in cubic feet. 



In order to test this formula, take as an example a perfectly 

 cylindrical log, 10 feet long by 48 inches in circumference. 

 The mathematical formula for obtaining the volume or contents 

 of a cylinder is equal to the area of one end multiplied by the 

 perpendicular height to the other end, or : — 



V = AH 

 where V = Volume; A = area of base ; H = height. 



The area of the base of a cylinder being a perfect circle is 

 calculated from the formula 7rr 2 = 3-1416 x (radius) 2 

 or 7854 D 2 = 7854 x (diameter) 2 



The circumference = Dtt = diameter x 3-1416. 



In the example given, therefore, 



If the circumference = 48 



then the quarter-girth or &= 12 

 4 



Diameter or M _ _z — _ 15-272 

 77 3-1416 



and radius = 7-636 



Sectional area = 7rr 2 = 3*1416 x 7-636 x 7-636 



= 183-180 square inches 



= 1-272 square feet. 



The contents or volume of the cylinder, therefore, will be — 



V = AH 



V = 7rr a x H 



= 1*272 x 10 



= 12-72 cubic feet. 



Measuring the same cylinder by the quarter-girth system 

 we get — 



v-(*y x JL 



W '44 

 48 48 10 



~ 4 4 144 

 = 10 cubic feet 



showing a loss of 2*72 cubic feet, equal to 21-38 per cent. 



It does seem strange that this method of measuring round 

 timber, which shows such a large percentage of error, should 



