62 



(i) Thos9 which give the height without calculation, their conslraetion being 

 %ased on the principle of similar triangles ; euch as Christea's and Weise's Hypso • 

 ineters ; 



(li) thosa which give the anp:leg made with a horizontal line by the lines of 

 Bight to the top and haae of the tree, such as Brandis' clinometer and Abney'g level, 

 -etc. 



For measuring ^eajriis straduated rules or tapsi miy be us id. Wdere great 

 accniacy is require:), ths length of » felled tree or h^g s'louU be meas'iraJ parallel 

 to its axis and not on its slopintr surface. 'Vha seoliontl area ot a lo^ or trea o»n 

 very rarely ind-ed be obtained directly. In neaily every case the girth or diameter 

 muEt be measnied, and the area of iha section detirmlnel as if the sectijn were a. 



ciicle. Area of section = ?^-^ X (diameter).' 



Girlhr are meas^ired with tapes. It is convenient to employ tapes graduated 

 on b"th sides, one nidi for reading the girth anl the other for rea ling the correspond- 

 ing diameter. The zero end of the tape should be famished with a sharp metal 

 point, whch cnn be easi'iy fixed in the bark of the tree, so that one person may 

 %e abl« to measure any stem, no matter how thick. As a circle encloses a grea'^er 

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

 o! tre<js is seWom quite circular, the contents of a log or tree calculated directly from 



~the girth will usui<lly be in excess of the true contents. Unless the contour of 

 the log is circular, it is impossible to obtain by girth maasurament the circnmfArence 

 of the circle whidi encloses th? sime space as the section whose area is required. 

 IrregalaritieA of outline due to fluting, bark, etc., cannot, be overcome in measure- 

 ments of girth, whereaH they can more or less suooessfully be alhwea for in measur- 

 ing diameters. Ex|jeriment8 made in Baden prove that girth met'tarement yields 

 a result from 6 to 10 per cent, greater than that obtained by means of liameter 

 measur'-meiit. It is, however, obvious that, in cubing loas which depart from the 



-ojlindrical form, the measurement of ths girth is more to be relied on thin the 

 measurement of a single diametei*. When the contents of a log are to be deduced 

 from diameter measurement, that diameter should be souiibt which, considRred as 

 the diameter of a circle, gives a result, as nearly as practicable, equal to the area of 



•the section measured. When the section is elliptiform, the mean of the longest 

 and shoiiest diameterrj should be taken. 



Diameters are measured with callipers such as the instrument already described 

 ^at page 57. This instrument, it will have been noticed, resejibles in all its essential 

 : parts a shoemaker's measure. 



The sectional area or hasal area at breast height may be calculated either from 

 the diameter, <r direc'ly fiotn the girth. In terms of the diameter it is eqial to one- 

 fonrth the square of the mean of the largest and shortest diameters of the tree at 

 "that height multiplied by the value of TT or 3*1416. In t-rmn of the girth it is equal 

 to one-fourth the square of the girth divided by TT, 



The volume of the sample trees is determine!, either by felling and measuring 

 them on the ground, or by means of form factors or volume tables. I f the trees are 

 felled, two clas.-es of produce for purposes of meahureuient will be obtained : (a) 

 round timber, or the stem-wood and all strais^ht or regularly shape 1 pieoes of 

 blanches, and (i) the small wood, or smaller pieces of branobwood and rootwood and 

 all ii regular pieces. 



Several fonnu'se, approaching more or less to accuracy, have been devi^d for the 

 deferniination of the contents of round timber ; but only twj are of practical utility. 

 They are : — 



(1) volume of contents of log = half the sum of the areas of the top anl 



bottom sections x the length ; 



(2) contents = area of mid-aeciion x length. 



Both for'nnlEB contain an error, the ex'enfc of which is proportionate to the 

 timount of difference letween the area at the top and base, r^spectivelv, of the lisj, 

 that is to say, to its d gree of taper ; and this err.^r increases a* the square of thit 

 difference. The second foimula always gives too small a re»uH, the first too grea t 



