92 



The J'ournal of Forestry. 



mathematical ratio given ; or we might start with the diameter and 

 use the Archimedean formula, W of the square of the diameter will 

 equal the area of the circle. For my own part, I rather lean to this 

 last method, first — because the sum is fairly simple and yet tolerably 

 exact ; and secondly, because the diameter is more obvious to the eye , 

 and a knowledge of it gives the inexperienced a more vivid idea of 

 the size of the tree than a knowledge of the circumference only. For 

 my own part, I confess I always find it necessary when hearing or 

 reading of such and such a large tree being of such and such a cir- 

 cumference, to reduce this to its diameter, in order to give myself an 

 exact picture of its size. 



The diameter, I might add, is easily obtained by an instrument, as 



-^1- s^nd tizi^n^ 



shown in the accompanying engraving — A B C is a T square ; A B 

 being marked out into feet and inches. D E is a sliding joint, 

 moving perpendicularly to A B. " 



I am having an instrument made on this principle for my own use 

 when travelling abroad. A common walking-stick is split down the 

 middle, and opens out to a T square, marked in feet and inches. It is 

 without the sliding rule D E, but the eye will be sufficient for 

 ordinary purposes of observation. When alone, even if provided with 

 a tape, it is more convenient practically to take the diameter than the 

 circumference of a large tree ; and the instrument which takes it has 

 the advantage of being useful and not incommodious as well. 



I need hardly add, by way of conclusion, that we can infer the 

 dimensions of the quarter girth from our knowledge of the diameter 

 as well as from our knowledge of the circumference. Taking the 

 latter roughly to represent 3| diameters, the ratio of the quarter-girth 

 to the diameter is as 11 to 14; and the difference between a result 

 obtained by the quarter-girth on this datum, and that obtained by the 

 method of Archimedes is precisely this: that according to the 

 ordinary method the area of the circle is equal to the square of i|- of 

 the diameter, but according to the method of Archimedes it is equal 

 to 



^ of the diameter squared. 



