364 SEVENTH REPORT—1837. 
submitted to tension. The deflections from equal weights are 
nearly the same, whether the rib be extended or compressed, 
(as was shown by Duleau in experiments upon triangular bars 
of malleable iron,) but the ultimate strengths, as appears from 
above, are widely different. 
It is to be hoped that the observations made above will ob- 
viate objections which have been offered against a form of cast 
iron beam arrived at by the writer, ina paper alluded to above. 
From this paper it appeared that a beam bore the greatest 
weight from the same quantity of metal when the strengths of 
its bottom and top ribs were as 6 or 63 to 1, and this was found 
in the subsequent experiments of the writer to be nearly the 
ratio of the tensile to the compressive strength of the iron. 
To ascertain the correctness or otherwise of the assertion of 
Emerson, so often shown to be true in theory, that if a small 
portion be taken from the vertex of a beam whose section is a 
triangle, the part will be stronger than the whole, castings 
were formed both from the hot and cold blast iron (experi- 
ments 8, 9, 10, in the one, and 8, 9, in the other). They were 
all from the same model and ground to the exact size, and the 
part taken off in the frustums was j5th of the whole height 
of the triangle. The breaking weights of the whole triangle, 
in the hot blast iron were 672 and 812 lbs., mean 742 lbs. and 
of the frustum 728 lbs. In the cold blast iron the whole tri- 
angle was broken with 815 lbs., and the frustum with 677. 
The difference in the transverse strengths of the hot and cold 
blast Carron irons, No. 2, is very small, the ratio between them 
being 99 to 100. (See recapitulation at the close of this re- 
port.) We may therefore assume their strengths to be the 
same, and taking an arithmetic mean between all the strengths 
we have strength of triangle 766 Ibs., strength of frustum 
702 lbs. ‘The frustum is therefore weaker than the triangle. 
It is often asserted by practical men that if the hard skin at 
the outside of a cast iron bar be removed, its strength, com- 
paratively with its dimensions, will be much reduced; to try 
this, four bars, 14 inch square each, were made, two of hot and 
two of cold blast ; they were then planed in the middle to one 
inch square nearly : their results are in experiments 11 and 12 
in Table 1, and 10 and 11 in Table 2. Their strengths were 
fully equal to those of bars 1 inch square, which were cast with 
them but not inserted. 
It is generally admitted that the strength of a rectangular 
beam, whose length and breadth are given, is as the square of 
the depth. To ascertain how far this important law agrees 
with experiment, castings were formed both in the Carron and 
