346 SEVENTH REPORT—1837. 
out of a larger body of metal than the small ones; a matter 
which we have seen greatly reduces the strength. 
Admitting, then, that the strength per square inch in each of 
the preceding cases would have been the same if the iron had 
always been of equal hardness, we must conclude that ‘the 
resistance of short cylinders of cast iron to a crushing force is 
directly as the area.”* 
If we refer to the abstract from tables 1 and 2 for the mean 
strengths per square inch, as given by the equilateral triangle, 
the square, the rectangle, and the cylinder, we shall find them 
in the latter, 99,769, 98,152, 107,971, 96,364; 
in the former, 100,416, 101,062. 
The strength, 107,971 and 101,062, as given by the prisms 
whose base is a rectangle, is the greatest ;t and this may be 
accounted for from their superior breadth to that of the other 
specimens, and consequently, from their having in them more 
of the outside and harder part of the bar, out of which they 
were cut, than the others. In the other forms the difference 
of strength is but little; and therefore we may perhaps admit 
that “* difference of form of section has no influence upon the 
power of a short prism to bear a crushing force.” 
Mode of Fracture. (See Plate.) 
When a rigid body is broken by a‘ crushing force, which is 
prevented from acting after it has effected a rupture, it will be 
found not to be crumbledor reduced to a shapeless mass, but 
to be divided according to mathematical laws, and sometimes 
into very interesting forms of fracture. The accompanying 
plate will show how the fracture was effected in a variety 
of cases, and that these were all subject to one pervading law. 
The figures in the plate are of the same size as the specimens. 
Fig. 1 represents a cylinder before it was crushed; fig. 2 
* Conceiving it desirable that this matter should be left without a doubt, 
and as Mr. Fairbairn had some very good teakwood which had been many 
years in store, 12 cylinders were turned whose diameters were ¥ inch, 1 inch, 
and 2 inches, 4 of each; the latter 8 out, of the same piece of wood; the 
height in each case was double the diameter: the strengths were as below. 
Cylinders 3 inch dia. Cylinders 1 inch dia. Cylinders 2 inches dia. 
23385 10507 38909 
2543 | Mean 9499 | Mean 89721 | Mean 
2543 | 2439 10507 | 10171 41294 | 40304 
23835 10171 . 41294 
These quantities, taking the means, are nearly as 25,100 and 400, whichis the 
ratio of the areas, and therefore the strength is nearly as the area, though this 
varies as 4 and 16 to 1. 
+ Rondelet (Zraité de ? Ari de bdtir, book 9, page 150) found that prisms of 
stone, whose base was a rectangle, as above, bore somewhat Jess than those 
with square bases of the same area. 
