and Strength of Materials. 273 
from the neutral line, may be to the section of 
compression multiplied by the distance of ifs 
centre of gravity from the same line, in the 
ratio obtained from the joist; and which, 
in pine, will be nearly as 4 to 5. 
The ratio will be obtained thus—From the 
mean of our experiments on that wood, the 
depth of the section of tension to that of 
compression in a joist was as 169 to 190. 
Call these numbers the absolute depths of 
the sections, and if the breadth of the piece 
be supposed unity, they will represent the 
" E : 169 
areas likewise ; and their halves, or —;- and 
190 : 
Tae will be the distances of the centres of 
gravity of the respective sections from the 
neutral line. The ratio sought will therefore 
be expressed by 169 x as to 190 x ae or 
by (169)* to (190)*, which is as 79 to 100, 
or as 4to 5 nearly. 
In like manner, since we found the mean 
depth of the section of tension to that of com- 
pression in Dantzic fir as 23 to 25, the ratio 
above will be (23)* to(25)*, or as 17 to 20 
nearly. 
The mean of our experiments on Quebec 
oak gave 27 to 31, the ratio above will then 
be (27)? to (31)*, or 729 to 961, which is 
nearly as 3 to 4. 
Mm 
