134 TRANSACTIONS OF ROYAL SCOTTISH ARBORICULTURAL SOCIETY. 



which for ordinary work should be avoided ; but it is to be 

 recommended in the case of long logs of valuable timber. 



(5) Hossfeldfs rule. — This rule involves the taking of the 

 length of the log, and calculating the sectional area at the tip 

 and at one-third the length from the butt. The formula is as 

 follows : — 



y = / 3 A, + A t N )L 



and is applicable to a truncated cone or paraboloid. The 

 results obtained are accurate, especially when applied to 

 butt logs. 



6. Huber's rule. — This is the rule in general practice in 

 Europe. It is very simple, and for ordinary work sufficiently 

 accurate. It involves the taking of fewer measurements than 

 any other rule. The formula in this case is : — 



V = A m xL 



The sectional area at half the length is taken and multiplied by 

 the total length. The formula is that for the finding of the 

 volume of the frustum of a paraboloid. The results are quite 

 satisfactory, and the rule is very easily applied in field work. 



7. Smalian's rule. — This rule involves the taking of the butt 

 and tip diameters and the length. The sectional areas for the 

 butt and tip are calculated and averaged. The formula of this 

 rule is as follows : — 



V = f ^ h + ^ 



With regard to the latter two rules, Carter in his Mensuration 

 of Timber, a book issued by the office of the Inspector-General 

 of Forests, Calcutta, says : — " Both formulae contain an error, 

 the extent of which is proportionate to the amount of difference 

 between the diameters at the top and base respectively of the 

 log, that is to say, to its degree of taper, and this error increases 

 as the square of that difference. Huber's formula always gives 

 too small and Smalian's too great a result, the error of defect in 

 the one case being one-half of the error of excess in the other." 

 If, however, the diameters at butt and tip are averaged before 

 calculating the area, the result will be exactly the same as that 

 obtained from Huber's rule. 



Where a pile of logs is to be dealt with, a great deal of labour, 

 and consequently expense, is incurred in the taking down of the 



