438 Proceedings of the Royal Society of Edinburgh. [Sess. 
9 
as show unmistakable signs of sliding should be used for measuring the 
inclination. 
The writer has, from time to time, determined roughly the inclination 
of surfaces of sliding in a number of specimens of stone, cement, and mortar, 
and these have been supplemented by measurements made from illustrations 
of broken specimens given by various authors. Average values of these 
inclinations are : — 
Sandstone . . . 25° to 28° 
Limestone . . . 20° to 25° 
Cement . . 20° to 30° 
Mortar . . 15° to 20° 
Angles greater than these are not infrequent, but are certainly due in 
many cases to disintegration, and also to irregularities in the material. On 
the other hand, cracks parallel, or nearly so, to the direction of the applied 
crushing load are often found. These would appear to be due to the 
inability of such materials to withstand much lateral extension ; they are 
not caused by any sliding action, but are the result of the low tensile 
strength of the substance. 
The two extreme ratios of c to c, calculated from the above values of 
fi and //, are 1*5 and 3*0 nearly, showing that the end friction has a very 
considerable effect, especially on the softer and coarser materials. No 
values of the yield points of stones are known. Whether these figures 
apply with any accuracy or not to the ultimate strength of such substances 
is impossible to say at present. 
In order to obtain a clean shear a length of 2 to 4 diameters is 
necessary. Specimens of stone and concrete required for crushing tests 
are usually made in the form of cubes, and fracture takes place as shown 
in fig. 5 ; bricks are usually 9 inches by 44 inches, and 3 inches high, but 
are often halved vertically, across the long edges, before testing, in order 
to bring them within the crushing capacity of the testing machine. 
6. Wrought Iron and Mild Steel. 
These materials, when crushed, do not fracture by shearing, and they 
are not usually tested in compression except in the form of long columns, 
in which bending is of supreme importance. The determination of the 
yield point and the inclination of the lines of Liiders from short pieces, 
however, should give useful checks on the previous arguments. 
According to Morin, the value of /x for wrought iron and steel is 0T4. 
This corresponds with 0 = 8°, ^8 = 41°, nearly. If the crushing platens are 
