276 Experiments on the Strength of Wood. [ApPRIL, 
The next set of experiments were made to find how much the 
strength of timber is increased by augmenting the depth and 
breadth, and what law this increase of dimensions follows. Several 
pieces of red fir were taken, each piece five feet long, and varying 
from 2, 21, 21, and 3 inches, in breadth and thickness. The mean 
strength of the first was 129 lb.; the second, 193 lb.; the third, 
259 lb. ; the fourth, 367 lb.; and the fifth, 440 Ib. 
To find the law of the increase of strength, try in what powers 
of thickness the several weights or resistances of the wood are, by 
comparing every two experiments; first 129 with 193, and then 
with 259, &c. and so on till every combination of two has been 
compared. This may be done by the following theorem :— 
T" : ¢":: W:w. T and ¢ representing the thickness of the timber, 
W and w the weights employed to break it, and m the exponent 
Log. W — Log. w 
Log. T — Log. i 
By applying this rule to all the numbers above, the several values 
of m, or exponent of the power, are as follows :— 
sought; m = 
129 &193 | 3°4206 
3°1236 | 193 &259 | 2-7917 
3°2833 367 | 3°2026 | 259 &367 | 3°6569 
; 2°0260 440 | 2°8645 440 | 2:9438 | 367 & 440 | 2:0849 
The imperfections of the different pieces of wood cause these 
various values of m from 36569 to 2:0849. Add the 10 exponents 
together, and divide the sum by 10; the quotient 303979 may be 
considered as the mean value of m. The nearest calculated expo- 
nent to this is 3°0260, found from the numbers 129 and 440; 
which shows that the strength of timber increases in somewhat 
greater proportiaa-than the cube of the thickness, 
Assuming, therefore, either of these two numbers, 440 and 129, 
and their respective thickness, three and two inches, and computing 
the weights answering to either thickness, the unavoidable irregu-~ 
larities in the experiments will be corrected, and the strength 
brought into a regular series. Computing in this way, they come 
out as follows :— 
T = 3 Log. 0°4771213 
t = 2 Log. 0:3010300 
0°1760913 Log, 1:2457347 
3°0398 Log. 0°4828450 
1°7285797 Nat. Numb, 0°53528 
AAV Log. 2°6434527 
2°1081727 Nat. N. 128°28 Jb. 
which is the corrected strength answering to two inches. By pro- 
ceeding in a similar manner with the other thicknesses, the cor- 
rected series will be as set down in the following table :— 
6 
od 
