2-M 
MR. W. H. BARLOW ON THE RESISTANCE OF FLEXURE 
Adopting therefore the second method, let 1 to m represent the ratio oif to : 
then /=^<p 5 
and 
7W<p-f-<P -pv^ — F; 
or 
r- 
DS 
F' 
•m + 
m’’ 
m 
which ought to be a constant quantity in all the experiments. 
We cannot obtain the deflections at the line of rupture, but they may be assumed 
to be proportional to the deflections with ^^ths of the breaking weights in each case. 
Now the value of F in the solid beam was found to be 41,709 lbs. ; and the value 
of f, from the experiments on direct tension, was 18,750 lbs. : and as in the solid 
beam f-\-<p=F, 
(p will be 22,959 lbs., 
and the ratio of p to ywill be as 1 to '81. 
For the purpose of comparison, I have deduced the value of /“and p, in solid beams, 
from the experiments of Mr. Hodgkinson on ten different descriptions of metal ; the 
results of which are given in the following Table : — 
Description of iron. 
Transverse 
strength of bar 
1 inch square 
and 54 inches 
between the 
supports. 
Tensile strength 
per square inch. 
Value 
from the formula 
Value of <p from I 
the formula I 
31 
lbs. 
lbs. 
lbs. 
lbs. 
Carron iron No. 2, cold blast 
476 
16,683 
38,556 
21,873 
Carron iron No. 2, hot blast 
463 
13,505 
37,503 
23,998 
Cari’on iron No. 3, cold blast 
446 
14.200 
36,126 
21,926 
Carron iron No. 3, hot blast 
527 
17,755 
42,687 
24,932 
Devon iron No. 3, hot blast 
637 
21,907 
43,497 
21,590 
Buffery iron No. 1, cold blast 
463 
17,466 
37,503 
20,037 
Buffery iron No. 1, hot blast 
436 
13,434 
35,316 
21,882 
Coed-Talon iron No. 2, cold blast 
413 
18,855 
33,453 
14,598 
Coed-Talon iron No. 2, hot blast 
416 
16,676 
33,696 
17,020 
Low Moor iron No. 3, cold blast 
467 
14,535 
37,827 
23,292 
Means 
464 
16,502 
37,616 
21,114 
The mean ratio of p to/in these metals appears to be as 1 to *78. The metal used 
in my experiments was a mixture consisting of two-thirds of South Staffordshire 
No. 3, hot blast pig, and one-third old metal recast. As compared with Mr. Hodg- 
kinson’s experiments, its strength accorded nearly with that of the Carron iron 
No. 3, hot blast. 
The mean ratio of p to f, obtained from Mr. FIodgkinson’s experiments, being as 
1 to ‘78, and from the experiments herein detailed being as 1 to ‘81, we may con- 
sider/ to be four-fifths of p ; and therefore 
m = '8. 
