280 On the Transverse Strain, 
adsl are oT ees a)) (Art. 15th, ) 
where a is the depth of tension, b the breadth 
of the piece, d its whole depth, v and w the 
indices of extension and compression, and s 
L and C as before.— Assuming C = unity, we 
have then s =8000ibs, a, from the last ex- 
ample, = 5:6 inches, b — 12,d— 12, L— 120; 
v, fromthe mean of our experiments on ex- 
tension, ‘97, and w, from those of compres- 
sion, = ‘895 (articles 25 and 28) which 
substituted in the formula give 
8000 12xK5:6/ 5°6 1895 
120 2:97 ' 1-972: 7X Db05 4))= =177438.6 
pounds = the resistance at the end, and 
17743'6X 2 =35487ibs. = the true weight on 
the middle, and which differs from 35840, 
the result of the pEpeeding example, only 
353 pounds, or less than -2, part of the whole 
weight ; and if we have assumed the value 
of s too small, the difference will not be 
much greater. Hence then the error arising 
from supposing the extensions and compres- 
sions to be as the forces, is too trifling to be 
worthy of notice in a thing so anomalous as 
timber. 
Example 4th. Suppose the beam, whose 
strength is required to be cylindrical, as for 
instance, the body of a tree? 
