424 
MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
1260 lbs ; and from a mean between three other experiments, a pillar of the same 
length and 1*015 inches diameter had its greatest resistance overcome by 15480 lbs. 
Since 1 .^ - = we have, putting n for the power, l n : T9519" : : 1260 : 15480. 
Whence reducing, and taking the logarithms, we obtain n = 3*75073, which is 
nearly the same as the mean from the cast-iron pillars with rounded ends (Art. 23.). 
Computed Strength of Wrought-iron Pillars long enough not to he crushed , as in Art. 
59. and 60., hy the weight which would overcome their greatest resistance. 
63. We have seen, from the last article, that the strength of cylindrical pillars 
whereof the length is constant, varies nearly according to the same power of the dia- 
meter as that in cast-iron ones. But where the diameter is constant, the strength 
is inversely as the square of the length, nearly. 
Whence if, in round or square pillars, we put d for the diameter, or side of the 
square, l for the length, h the breaking weight, a, a! constant quantities, and adopt 
the powers of d , which were used for cast iron, we shall have (Arts. 36. 38.) 
* «d 376 
b - e ’ 
in pillars with rounded ends ; 
1 a! d 3-55 
b - f > 
in pillars with flat ends. 
From the pillars in Table XII. we obtain as below: 
ft. ins. lbs. 
From those 7 6§ long, with rounded ends, a = 97049 
From those 5 0^ long, with rounded ends, a = 94648 
i 
Mean value of a — 95848 
ft. ins. lbs. 
From those 7 6f long, with flat ends, a! = 281464 
From those 5 0^ long, with flat ends, a' = 307770 
Mean value of a! = 299617 
Here the length is taken in feet, and the diameter in inches. 
Timber. 
64. To find n the power of the diameter, or of the side of a square, to which the 
strength is proportional, the length being constant, and the pillar so long as not to be 
crushed (Arts. 59. 60.) with the breaking weight. For this purpose Table XIII. will 
supply us with the results of six experiments upon pillars of Dantzic oak, 46*1 inches 
long. Whence it appears that a pillar T02 inch square was broken with a mean 
weight = 1754 lbs., and one 1*50 inch square with 7888 lbs. 
