392 Mr. A. Mallock [May 27, 



stituting a bar of the same dimensions, but well annealed, it will be 

 seen that the same deflection is shown. Using a similar bar of 

 wrought iron, the deflection is only a little greater. 



The limits of elasticity are of course widely different in all 

 three cases. 



In engineering and structural work it is the limits of elasticity 

 which are important to designers rather than the elasticity itself, for 

 it is on these limits that the strength of materials depends. The 

 elasticity enters into calculations of the reaction of springs, in which 

 is included the deflection of loaded structures, such as girders and 

 bridges ; for all structures, whether meant to be rigid or not, are in 

 effect springs with longer or shorter periods of vibration. It is the 

 strain limits, however, of the materials, and not their elasticities, 

 which decide what loads can be safely borne. 



When a material is strained beyond its elastic limits it either 

 takes a permanent set or is ruptured, and the manner in which set or 

 rupture occurs gives rise to such qualifications as hard, soft, brittle, 

 tough, malleable, ductile, friable, plastic, etc. 



The behaviour indicated by these adjectives can be explained by 

 the relative differences between the volume elasticity and rigidity in 

 conjunction with the limits of strain which either kind of elasticity 

 will withstand. 



When a substance is said to be hard or soft (in the metallurgist's 

 sense) it is implied that the rigidity is great or small. For the 

 mineralogist hardness has another meaning, and refers to the pro- 

 perties of a surface as opposed to that of a volume. If one material 

 will scratch another, the one which is scratched is considered the 

 softer of the two, and by this test a rough and arbitrary scale of 

 mineralogical hardness has been established, ranging from diamond 

 at one end to talc at the other. 



I believe that this sort of surface hardness is analogous to surface 

 tension, for it is hardly to be thought that the causes which produce 

 surface tension in fluids cease to operate in the case of solids. On 

 this view hardness of this sort might be defined as the limit of 

 tangential strain at a surface which can be borne without rupture. 

 This may be very different from the strains which can be borne 

 in the interior. For example, diamond is the hardest substance 

 known in the mineralogical sense, but it can be easily crushed by 

 hard steel, showing that one, at any rate, of the strain limits for 

 diamond is less than it is for steel. 



A body is brittle if, whether hard or soft, the limits both for 

 volume extension and rigidity are small, and the characters of the 

 fractured surface will often help to determine which of these limits 

 is the greater ; but it would take too long to enter into the details 

 of the subject at this time. 



Malleability implies that the material can be worked without 

 rupture under the hammer ; ductibility, that it can be drawn out 



