63 



(ii) those which give the angles made with a horizontal 

 line by the lines of sight to the top and base of 

 the tree. 



"For measuring lengths graduated rules or tapes may be 

 used. "Where great accuracy is required, the length of a 

 felled tree or log should be measured parallel to its axis 

 and not on its sloping surface. The sectional area of a 

 log or tree can very rarely indeed be obtained directly. 

 In nearly every case the girth or diameter must be mea- 

 sured, and the area of the section determined as if the 

 section were a circle. Area of section=-^^-^ (diameter)^. 



Girths are measured with tapes. It is convenient to 

 employ tapes graduated on both sides, one side for reading 

 the girth and the other for reading the corresponding 

 diameter. The zero end of the tape should be furnished 

 with a sharp metal point, which can be easily fixed in the bark 

 of the tree, so that one person may be able to measure any 

 stem, no matter how thick. As a circle encloses a greater 

 area than any other plane figure of equal perimeter, and as 

 the sectional outline of trees is seldom quite circular, the 

 contents of a log or tree calculated directly from the girth 

 will usually be in excess of the true contents. Unless the 

 contour of the log is circular, it is impossible to obtain by 

 girth measurement the circumference of the circle which 

 encloses the same space as the section whose area is required. 

 Irregularities of outline, due to fluting, bark, etc., cannot be 

 overcome in measurements of girth, whereas they can more 

 or less successfully be allowed for in measuring diameters. 

 Experiments made in Baden prove that girth measurement 

 yields a result from six to ten per cent, greater than 

 that obtained by means of diameter measurement. It is, 

 however, obvious that, in cubing logs which depart from the 

 cylindrical form, the measurement of the girth is more to be 

 relied on than the measurement of a single diameter. When 

 the contents of a log are to be deduced from diameter mea- 

 surement, that diameter should be sought which, considered 

 as the diameter of a circle, gives a result as nearly as practic- 

 able equal to the area of the section measured. When the 

 section is elliptiform, the mean of the longest and shortest dia- 

 meters should be taken. 



The mean of these diameters D and d is -^ and the area of the section is 

 then assumed to be JLx ^?5^. Now, as the real area of the ellipse is Z. Dd. the 



4 * 



