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Proceedings of the .Royal Society of Edinburgh. [Sess. 
determines the exact crushing stress is not clear. The ratio of c"jc f is 
smaller the harder the stone ; experimental values vary from 065, to 043 (6,7,8) , 
c' having been measured for blocks in direct contact with the crushing platens,, 
or previously faced with thin layers of plaster of Paris, which are easily 
scraped flat and parallel, and behave as integral parts of the specimen. 
c c" . c" 
From the values of — and — already given, the calculated values of — are 
C 0 c 
found to lie between 035 and 0T5, so that the actual effect of the lead is 
less serious than it would be according to the assumed conditions. 
8. Effect of Length of Specimen upon its Apparent Strength. 
From the results given in section 3 it would appear that the crushing 
strength of a material should not be altered by the length of the test-piece, 
provided that this is short enough for no bending to take place. Published 
experimental results indicate that a greater load is required to cause rupture 
as the length of the specimen is diminished. Thus Bauschinger found, from 
careful tests on a specially fine and uniform sandstone, that a cube is about 
20 per cent, weaker than a piece of half the height, and about 7 per cent, 
stronger than a piece 14 times the height (9) . Similarly Hodgkinson, in a 
series of tests of small cast-iron cylinders, found that with a height equal 
to 1J diameter the piece was 3 per cent, weaker than when the height was 
only 1 diameter, 19 per cent, weaker than with a height of \ diameter, and 
30 per cent, weaker than a cylinder with a height equal to \ diameter (101 . 
If crushing strength is calculated as the total crushing load divided by 
the original area of cross-section of the piece, it is undoubtedly increased 
by diminishing the length of the specimen ; but if, as is more rational, the 
increase in the area of the material under load is allowed for, the case is 
different. This increase in area is greater the shorter the specimen. One 
might expect that the friction of the platens, when the specimen is relatively 
long, would not have so great an effect in the middle of the length of the 
piece as when this is short. Thus the amount of lateral extension of the 
middle of the specimen, relatively to that of the ends, would be greater 
with longer specimens. In crushing cast iron it is noticeable that a piece 
14 diameter long assumes a very distinct barrel shape towards the end of 
the test (fig. 4), while a piece only 4 diameter long, though its dimensions 
change, remains nearly cylindrical. The final maximum diameter is greater 
in short specimens than in longer ones. 
The following table gives numerical results, not previously published, 
obtained from six cast-iron bars tested some time ago for another purpose. 
