396 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
1*765 
hince — 77 - 
'50 
3-530 
1 
we have 
and 
whence 
1 " 
3-53” : : 143 : 15560, 
15560 
3*53 re = 
143 
Log. 
n 
15560 
143 
= 3718. 
Log. 3-53 
I insert below values of n , thus obtained, from the first and second Tables ; and 
from the square pillars and those with discs, in Tables III. and IV., beginning with 
long pillars with their ends rounded. 
23. In Table I., comparing the strength of a pillar of 
•50 in. diameter, and 60^ ins. long, with that of 77 in* diameter, gives /? = 3 - 928 
•50 in. diameter, and 60^ ins. long, with that of '99 in. diameter, gives n = 3788 
•50 in. diameter, and 60^ ins. long, with that of 129 in. diameter, gives n — 3*889 
•50 in. diameter, and 60^ ins. long, with that of T52 in. diameter, gives n = 3*894 
•50 in. diameter, and 60^ ins. long, with that of 1765 in. diameter, gives n = 3718 
•50 in. diameter, and 60| ins. long, with that of T94 in. diameter, gives n — 3741 
77 in. diameter, and 60^ ins. long, with that of 1*765 in. diameter, gives n — 3*609 
77 in. diameter, and 60^ ins. long, with that of T94 in. diameter, gives n = 3*654 
•50 in. diameter, and 30^ ins. long, with that of T29 in. diameter, gives n — 3*656 
*50 in. diameter, and 30| ins. long, with that of 1*52 in. diameter, gives n — 3*687 
77 in. diameter, and 30| ins. long, with that of 1*52 in. diameter, gives n = 3*63 7 
*99 in. diameter, and 30^ ins. long, with that of 1*52 in. diameter, gives n = 3*902 
*50 in. diameter, and 15^ ins. long, with that of *76 in. diameter, gives n = 3*768 
*50 in. diameter, and 15^ ins. long, with that of *99 in. diameter, gives n — 3*425 
Mean value of n — 3*736 
In this comparison I have excluded all pillars, the length of which was not greater 
than about fifteen times the diameter. In pillars shorter than in about this propor- 
tion, a great change doubtless takes place by degrees in their elasticity, and their 
strength is much reduced. This remark is intended to be understood only of pillars 
with rounded ends : in those with flat ends, the same change, we have seen, begins to 
take place when the length of the pillar is less than thirty times the diameter. As 
this change in the elasticity of pillars must be produced by the same weight (the dia- 
meter being supposed constant), the relative strength of pillars with rounded and with 
flat ends, to resist the change, must depend upon the laws that regulate their ultimate 
strength ; and we have seen that a pillar with rounded ends will bear the same as one 
of double the length with flat ones. In the experiments, Table III., on square bars 
