TRANSACTIONS OF THE SECTIONS. 
61 I 
for the neutral line is found to shift when the elasticity becomes 
defective, or perhaps earlier ; and therefore its place is difficult 
to be found in some bodies, as, for instance, cast iron, at the 
breaking point. In that metal we cannot discover it by inspec¬ 
tion after fracture, as in timber. 
Cast iron, however, affords a more simple rule for its ultimate 
strength, in some forms, as will be seen afterwards. Mr. 
Hodgkinson commenced the research for this rule, and the 
other objects of the paper, by seeking in that metal for the re¬ 
lative extensions and compressions of a bent piece, under equal 
weights, through the whole range up to fracture. For this pur¬ 
pose he got several castings moulded, such that a cross section 
D-E 
of each was in the form DCE c and the castings seve¬ 
ral feet long. During an experiment, one end of the casting 
was fixed in a wall, and weights to bend it hung at the other. 
It was so fixed as to be easily removed, in order that the casting 
might be turned the other side upward, as the intention was 
alternately to compress and extend the vertical rib C of D C E. 
When the rib was upwards, the deflection arose from its ex¬ 
tension, and when downwards, from its compression. 
The corresponding results from equal weights are placed in 
order as below: 
Extensions 37 . . 61*.. 96 .. 86 .. 156 . . 165 .. 172 .. 203 
Compressions 34 .. 53 .. 97*.. 84 . . 135 . . 163 .. 167 .. 186 
From this comparison it appears that the extensions are 
greater than the compressions, by equal weights, whether the 
elasticity be perfect or not; the first four pairs of experiments 
having been made before the elasticity could have been much 
injured, and the other four nearly at the breaking point. Still 
the difference between the extensions and compressions is so 
small, that their equality seems to be a law of nature ; the de¬ 
viations arising only from imperfect elasticity. 
In every instance the casting broke by tension ; viz. by tearing 
asunder the vertical rib, that rib being upwards, thus I 
The rib never showed any sign of being crushed when it was 
compressed, though sustaining a weight which would have torn 
it asunder when stretched. To try, then, the effect of a greater 
weight, it was increased, in one instance, to double what would 
have broken the casting the other way up. Still the rib was 
not crushed; and, after sustaining the weight for many hours, 
the piece seemed only to have lost a little of its elasticity. 
To set this matter in a still clearer point of view, two castings 
were taken of the same form as the preceding, and apparently 
precisely alike; they were placed between two props, upwards 
O Q o 
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