THE MEASUREMENT OF TIMBER. I35 



pile, and measuring each individual log. In many such cases 

 it is easy to get the tip and butt measurement, and therefore by 

 adopting this system a sufficiently satisfactory result would be 

 obtained. 



In order to compare the results obtained from these various 

 rules, take a log 36 feet in length, perfectly circular in section 

 and with an even taper from butt to tip. Let the diameter at 

 the butt be 18 inches and at the tip 6 inches, then the diameter 

 at the middle will be 12 inches, and that at a third length from 

 butt 14 inches. The cubic contents of the log according to the 

 various rules described will be as follows : — 



Sectional Cubic 



Area, Sq. Ft. Contents. 

 i. Hoppus Quarter-Girth Rule : 



V = M£ xL = 9-4»*9-42 6 = . 6l6 6= 6 



144 144 



Custom-house Quarter-Girth Rule: 



V = ^ xLs= 9-42x 9 - 4 2 x 8 . g6o 



I][ 3 IJ 3 



3. Fifth Girth Rule : 



(IT 



V = 2 W, x L= 2 * 7-538 x 7-538 X36 = . 7 8 9 x 36 = 28-404 

 144 144 



4. Newton's Rule : 



, r (A b + 4A m + A t ) L 735 - i3i , c c c 



y = \ b — 5_m 1/ x _ too — o_ x 6 = .g 5I x 36 = 30-636 



6 144 6 x 144 



5. Hossfeldt's Rule : 



_. (3Al+A t ) L 400-088 .0 (■ r r 



V = — — a x = ^ x t.6 = '85 1 x 36 = 30-636 



4 144 4x144 



6. Huber's Rule : 



V = ^x L= II3 '° 97 X 36 = -785x36 =28-260 

 144 144 



7. Smalian's Rule: 



,. (A b +A t ) L 282-743 rOC C 



V = i— 5 'J-x = '-^ x 36= -981 x 36 = 35-316 



2 144 2 x 144 



It will be seen from the above that the results vary according 

 to the number of cross-sections taken. The greater the number 



