ON THE STRENGTH OF PILLARS. 
403 
Short Pillars. 
39. The mean value 98922 lbs. would be too great, if used for calculating, by the pre- 
ceding formula, the strengths of solid round pillars, which are shorter than about 30 
times the diameter. I shall, therefore, insert below the values of x, from the shorter 
pillars in Table II.; together with the particulars of the experiments from which they 
were derived. 
Putting these in a line with the real breaking weights, and the number of tons per 
square inch, upon the section of the pillars, I will endeavour to show the cause of the 
falling off in strength. 
No. of 
experi- 
ment. 
Diameter. 
Length of pillar. 
Breaking 
weight. 
Tons per square 
inch, the crush- 
ing weight being 
49 nearly. 
Value of a? from 
w l 1 ' 7 
formula „ — 
d 3 ° 5 
Ratio of diameter 
to length. 
1 
inch. 
•777 
inches. 
20-166 

feet. 
1-6805 
lbs. 
15581 
14-7 
lbs. 
92224 
1 : 25-95 
2 
.50 
12-1 
1-0083 
7195 
16-4 
85467 
1 : 24-20 
3 
•50 
10-083 
= 
•84028 
8931 
20-3 
77817 
1 : 20-166 
4 
1-022 
20-166 
— 
1-6805 
31804 
17-3 
71154 
1 : 19-732 
5 
•775 
15-125 
— 
1-2604 
21059 
19-9 
77141 
1 : 19-516 
6 
•785 
12-1 
= 
1-0083 
24287 
22-4 
46207 
1 : 15-414 
7 
•50 
7-5625 
= 
•6302 
11255 
25-6 
60133 
1 : 15-125 
8 
1-00 
15-125 
= 
1-2604 
40250 
22-9 
59516 
1 : 15-125 
9 
•768 
10-083 
= 
•84028 
25923 
25-0 
49224 
1 : 13-129 
10 
•777 
7-5625 
= 
•6302 
32007 
30-1 
35757 
1 : 9-733 
11 
•50 
3-7812 
Z = 
•3151 
17468 
39-7 
28725 
1 : 7-562 
12 
•52 
2 
zz : 
•16666 
22867 
48-1 
11080 
1 : 3-846 
13 
•52 
1 
zn 
•08333 
24616 
51-74 
1 : 1-923 
40. The second, third, and fourth columns in this abstract give, as will be seen, 
the dimensions and breaking weight of the pillars, each result being generally the 
mean from several experiments. The fifth column gives the number of tons which 
the breaking weight is upon the area of the section ; the sixth, the value of x , or the 
strength of a pillar, one foot long and one inch diameter, as calculated from each 
result by the formula before used (Art. 38.). The last column gives the number of 
times which the length exceeds the diameter. 
If there were no falling off in the strength of these pillars through crushing, as 
before mentioned (Art. 6. 7 .), we know that the value of x would be constant, and 
nearly equal to the mean value, 98922 lbs. ; which applies, as we have seen, to cast- 
iron pillars flat at the ends, of which the length is not less than about 30 times the 
diameter. But we see, from the abstract above, that in pillars whose length is about 
15 times the diameter, the value of x, which being obtained from the breaking weight 
must fall with it, is reduced to 46207, 60133, 59516, mean 55285 ; being somewhat 
more than 49461, the half of the general mean. In pillars whose length is 7'56 times 
the diameter, or a little more than a quarter of 30 times the diameter, the strength is 
reduced to 28725, whilst the fourth of the general mean is 2473 1 . Pillars whose length 
is about 20 times the diameter, or two-thirds of 30 times, we see give the value of x 
77817, 71154, and 77141, whilst two-thirds of the general mean is 65948 lbs. 
3 f 2 
