ON THE STRENGTH OF PILLARS. 
387 
in green (moist) sand, which rendered the operation of casting less troublesome ; and 
it was conceived that the mode of casting would make little or no difference in the 
strength, a conjecture which was proved afterwards to be correct. I have not given 
here an explanation of these or the other tables, as it is hoped they will be understood 
by inspection. The forms of the fractures of many of the pillars, particularly those 
in Tables I. and II., are given in conjunction with the drawings of the pillars in 
Plate XV. The position of the neutral line was sought for with great care, and is 
inserted in the tables wherever it could be obtained with any degree of certainty. 
Conclusions from the First and Second Tables. 
5. The experiments in the second table were undertaken after those in the first 
were nearly completed ; for I found, by a trial or two, that a pillar with flat ends was 
much stronger than one of the same diameter and length with its ends rounded. To 
ascertain, therefore, the ratio of the strength in the two cases, and whether it was con- 
stant under all changes of dimension, it became necessary to make the second table to 
include most of the lengths and diameters of the former ; and, indeed, other considera- 
tions made me reduce the lengths in it, till the pillars broke by crushing without flexure. 
Taking, then, the mean breaking weights of pillars from the same models in the first 
two tables of experiments, and neglecting the small differences in the measured dia- 
meters of the castings, we have the ratio of the strengths as in the following abstract. 
Abstract from Tables I. and II., &c. 
Pillars with rounded ends. 
Pillars with flat ends. 
Ratio of breaking 
weights of pillars 
with rounded and 
flat ends, the dia- 
meters being consi- 
dered equal. 
Length. 
Mean dia- 
meter. 
Number of 
experiments 
deduced from. 
Breaking 
weight. 
Mean dia- 
meter. 
Number of 
experiments 
deduced from. 
Breaking 
weight. 
Weight which 
would crush 
tire cylinder. 
inches. 
inch. 
lbs. 
inch. 
lbs. 
lbs. 
60-5 
•50 
2 
143 
•51 
2 
487* 
22430 
1 : 3-405" 
60-5 
•77 
2 
780 
•77 
2 
2456 
51130 
1 : 3-148 
60-5 
•99 
2 
1902 
•997 
3 
6238 
85721 
1 : 3-279 
co 
60-5 
1-29 
2 
5707 
1-29 
3 
16064 
143508 
1 : 2-815 
60-5 
1-52 
2 
10861 
1-56 
3 
28962 
209869 
1 : 2-667 
30-25 
•50 
3 
539 
•50 
1 
1662 
21559 
1 : 3-083 
c3 
30-25 
•77 
1 
2726 
•77 
3 
8811 
51130 
1 : 3-232 
Pi 
30-25 
•99 
2 
6105 
1-01 
4 
20310 
87971 
1 : 3-326 
15-125 
•50 
3 
1904 
•51 
3 
6764 
22430 
1 : 3-552 J 
I 
20-166 
•767 
2 
6602 
•777 
3 
15581 
52064 
1 : 2-3600 
20-166 
1-01 
2 
15737 
1-022 
2 
31804 
90074 
1 : 2-0210 
15-125 
•76 
3 
9223 
•775 
4 
21059 
51797 
1 : 2-2833 
7-5625 
•497 
3 
5262 
•50 
3 
11255 
21559 
1 : 2-1389 
15-125 
•99 
3 
19752 
1-000 
2 
40250 
86238 
1 : 2-0378 
10-083 
•76 
3 
17506 
•768 
4 
25923 
50865 
1 : 1-4808 
7-5625 
•77 
2 
22948 
•777 
3 
32007 
52064 
1 : 1-3947 
3-7812 
•50 
2 
15107 
•52 
3 
24616 
23319 
1 : 1-6294 
* This pillar had discs on the ends. 
6. The preceding abstract contains the results of experiments with pillars varying 
in length, from 121 times the diameter, down to 7\ times ; and we see, from the last 
3 d 2 
