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MR. HODGKINSON’S EXPERIMENTAL RESEARCHES 
through imperfect fixings, or some other cause, are capable of moving at the top. It 
applies, too, if I am not mistaken, to the experiments upon timber by Girard*, whose 
pillars rested upon a flat surface at the bottom, but turned with a joint at the top, or 
were moveable there in the direction of the length of the lever. But when the pillars 
were so placed as to have their least dimensions in that direction, they broke with the 
mean weight, as above defined, instead of the full weight, which they were expected 
to bear, as will be evident from a careful inspection of M. Girard’s plates attached to 
the work. 
18. In all the previous experiments, where the pillars were uniform and the same 
at both ends, the fracture took place in the middle, or very near to it. This, as might 
be expected, was not the case where one end was flat and the other rounded ; in that 
case the pillar broke at some point nearer to the rounded end, the piece broken off 
being always a little more than one-third of the whole length. The excess, however, 
above one-third was so small, that I conceive this division would be absolutely that 
to which the material would tend, provided it were incompressible, and if the pillar 
were better fixed at the flat end, and more free to move at the rounded one. 
With this view, two pillars, each thirty inches and a quarter long, and one inch in 
diameter, were formed with broad discs on one end, and rendered as nearly pointed 
at the other as was consistent with their bearing the pressure. 
The result of the experiment upon these was this : the part broken off from one 
was 10‘42 inches, and from the other 10'30, whilst the one-third part of the whole 
length was 10‘08 inches. I was led to conceive the division above (one-third) not 
improbable, since it had been shown before, that a pillar with flat ends, or with discs 
upon them, bore the same as a pillar of half the length with rounded ends ; and as 
the pillars above had a disc on one end, and were rounded at the other, they might 
divide themselves so that the part with the flat end might be twice as long as that 
with the rounded one. 
The results of my experiments on wrought iron, which is the only material besides 
cast iron in which I have examined the matter, give the division so as to make the 
piece, near to the rounded end, more in excess above one-third of the whole length 
than in cast iron ; the experiments, however, were made upon pillars too short to try 
the matter quite satisfactorily. This deviation, if the above views are correct, may 
perhaps be attributed to the greater compressibility of wrought iron than of cast, as 
compared with their powers of resisting tension. A better material to try it would 
be stone. 
] 9. We have now seen, that when uniform pillars are so placed that one end is 
fixed and the other moveable, the point of greatest strain is at one-third, or a little more, 
of the whole length of the pillar from the moveable end. We might, therefore, eco- 
nomise the metal by increasing the thickness in that point, and reducing the strength 
as we recede both ways from it. 
* Traite Analytique cle la Resistance des Solides. 
