398 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
The experiments in Table II., upon pillars shorter than these, are not in sufficient 
variety to enable us satisfactorily to pursue the comparison ; and if we attempted one 
between the strengths of the short pillars in that Table, as, for instance, those of one- 
third, or one-fourth the length of those above, we should find the value of n very low, 
on account of the crippling or other great change which we have seen (Art. 6) that 
pillars sustain by the weight, when they are made shorter than about thirty times the 
diameter. 
Strength as dependent on Length. 
26. In order to obtain the power of the length, to which the strength of pillars of 
the same diameter is proportional, considering this as some inverse power x, we will 
determine its value from the first and second Tables, beginning with Table I., in which 
the lengths vary as widely as eight and sixteen to one ; and we shall take the values 
from the whole range in that Table. 
27- Here we find that a pillar of half an inch diameter and 605 inches long, was 
broken with 143 lbs., and one of the same diameter and 3’78125 inches, the one-six- 
teenth of the former length, required 15107 lbs. to break it. Proceeding in the man- 
ner adopted before, we have, 
1* : 16 r : : 143 : 15107- 
Whence we obtain x = L6807- 
In this comparison I shall assume all the pillars which were cast from the same 
models, to be equally thick, neglecting occasional slight differences in their dia- 
meters. 
28. Pillars with their Ends rounded. 
Diameters of cylinders 
considered equal. 
Lengths of which the 
strengths are compared. 
Values of x. 
Mean values of x. 
inch. 
•50 
inch. 
•50 
inches. 
60-5 
inches. 
and 30*25 
1*914'| 
•50 
•50 
60*5 
15-125 
1-867 1 
1-799 
•50 
•497 
60-5 
7-5625 
1-734 f 
•50 
•50 
60-5 
3-78125 
1-681 J 
•77 
•77 
60-5 
30-25 
1-805^1 
•77 
•76 
60-5 
15-125 
1-782 j 
•77 
•77 
60-5 
7-5625 
1-626 y 
1-702 
•77 
•76 
30-25 
15-125 
1-758 | 
•77 
•77 
30-25 
7-5625 
D537J 
•99 
•99 
60-5 
30-25 
1-682 1 
1-685 
•99 
•99 
60-5 
15-125 
1-688 / 
1-29 
1-29 
60-5 
30-25 
1-595 
1-595 
1-52 
1-52 
60-5 
30-25 
1-583 
1-583 
