406 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
values of n (Art. 23 to 25.). We may also see its effects in the comparison between 
the strengths of pillars T29 diameter, and between those of T56, in the abstract 
(Art. 5.). In each of these cases the pillars were of the same diameter nearly; but 
as the breaking weights were, from another cause, very different, the comparative 
strength was considerably lower than in the pillars of smaller diameter. This falling 
off in the strength of large pillars of equal lengths arises principally from this circum- 
stance, that the strength to resist flexure increases as a power of the diameter some- 
what under the fourth ; and the resistance to crushing only as the second. Thus the 
pillars of greater diameter require a much greater load upon the same area of section 
to break them than those with smaller diameters. The position of the neutral line 
is therefore different, and the area of the part submitted to tension reduced ; the pillar, 
therefore, becomes more flexible, and consequently weaker. 
Some small part of this falling off in the strength of larger pillars might be ac- 
counted for by the softer quality of cast iron when cast in large masses ; but other 
materials exhibit the same diminution of strength, and the cause above is sufficient 
to account for it. 
Tabulated results of the formula y = , , 3 ■ 
u 0 + %c 
Diameter 
of pillar. 
Length of 
pillar. 
Value of b. 
Value of c. 
Breaking 
weight. 
Calculated breaking 
weight from fonnula 
for y. 
inches. 
inches. 
lbs. 
lbs. 
lbs. 
lbs. 
•50 
12-1 
8327 
21559 
7195 
7328 
•50 
10-083 
11353 
21559 
8931 
8872 
•50 
7*5625 
18515 
21559 
11255 
11508 
•50 
3-7812 
60155 
21559 
17468 
16992 
•777 
20-166 
16713 
52064 
15581 
15604 
•775 
15-125 
27005 
51797 
21059 
21241 
•785 
12-1 
41300 
53142 
24287 
27043 
•768 
10-083 
52096 
50865 
25923 
29363 
•777 
7-5625 
88547 
52064 
32007 
36130 
1-022 
20-1666 
44218 
90074 
31804 
35631 
1-000 
15-125 
66746 
86238 
40250 
43797 
The formula for y gives results agreeing moderately well with the strengths of 
pillars decreasing in length, both here and in the experiments on hollow pillars, as 
will be seen further on (Art. 52.). 
Similar Pillars. 
d 3 ' 76 
44. We have found the strengths of solid pillars of cast iron to vary as -jT anc ^ 
^ 3'55 
nearly ; when they are not shorter than from fifteen to thirty times the diameter, 
according as the ends are rounded or flat (Art. 36 to 38.). 
In the research for these numbers I have been led to conclude, that, if the material 
had been incompressible, the 376 and 3*55 would each have become 4, and the 17 
d A 
have been 2 (Art. 24. 33.). In that case the strength would have varied as which is 
