718 
MR. FAIRBAIRN’S EXPERIMENTAL INQUIRY 
That is, THE BREAKING WEIGHTS IN SIMILAR BEAMS ARE TO EACH OTHER AS THE SQUARES 
OF THEIR LIKE LINEAR DIMENSIONS. 
The method of demonstration here used in establishing this important theorem 
may be applied to any other form of beam. 
When the sections of the beams are similar, but the distance between the supports 
any quantity then we have 
W'=j.r^W (15.) 
Suppose W in equation (11.) to be determined by experiment, then we are at 
liberty to assume 
W= 
AdC 
I ’ 
where d is the depth of the beam, and C a constant determined by the assumed re- 
lation. 
From equation (14.), W'=r^'W 
=r\-r 
7'^A.rd.C 
rl 
A'd'C 
- L' • 
(16.) 
That is, THE BREAKING WEIGHTS IN BEAMS ARE FOUND BY MULTIPLYING TOGETHER THE 
AREA OF THE SECTION, THE DEPTH, AND A CONSTANT DETERMINED FROM EXPERIMENT ON 
BEAMS OF THE PARTICULAR FORM, AND DIVIDING THIS PRODUCT BY THE DISTANCE BETWEEN 
THE SUPPORTS. 
The value of 1! in this formula is not restricted to the condition of similarity. 
In experiment 12, 
Di — 3-5,D2= 1-375, D3 = 3-22, d^= 1-375, 4=3-2, W=24380-|- 80 = 24460, /=84, 
A, = 4-5x7 = 31-5, A2=]-375X-28 x 2 = -7, A3=3-22 X 1-845 X 2= 1 1-8818, 
tf,=:l-375X-3X2 = -75, a3=3-2X 1-825x2=1 1-68, 
A = A, — Aj— A 3 — tf .3 — fl3=32-5 — 25-01 =6-48, 
.'. by equation (6.), X=-0611. 
By equation (8.), Ii = 46-782. 
By equation (9.), 1=46-782 — 6-48X-061 r=46-758. 
By equation (10.), 
24460 x 84 ( 3 -. 5 -- 0611 ) , 
= 4 X 46 - 758 X 2240 =‘7 tons nearly, 
and 
Si = 17 ^ tons nearly. 
In experiment 13, W = 21715-l-80=21800 nearly, 
and 
21800 x 84 ( 3-5 + - 0611 ) 
4 x 46 ’ 7854 x 2240 
15-5 tons. 
21800 X 84 ( 3 - 5 - - 0611 ) 
4 X 46-7854 X 2240 ~ ^ ^ 
