and Soft States in Metals. 259 
4, In reviewing the researches on the subject of hardening 
and annealing, it is found that, with very few exceptions, they 
have had special reference to these phenomena as they occur 
in iron and steel. This has naturally resulted from the great 
importance of these materials in engineering and construction, 
but there can be no doubt that from the point of view of a 
broad study of the subject, this choice of the material for 
investigation has to some extent been unfortunate, inasmuch 
-as the properties of iron and its alloys are very much more 
complicated than those of any other metal in ordinary use. 
In a steel containing a minute percentage of carbon it is 
possible to identify five or six primary constituents whose 
appearance depends almost entirely on the heat treatment to 
which the specimen has been subjected. In addition to this, 
it is believed that iron itself can appear in two or three 
allotropie modifications, each of which has its definite trans- 
formation temperature. The student of this subject is 
therefore confronted with a set of complicated problems, 
the elements of which it has been all but impossible to isolate 
from each other. 
5. For the study of the phenomena which are to be here 
discussed, it has appeared to me desirable to detach these 
phenomena as far as possible from complications of the kind 
above referred to. With this object, while the metals and 
-other substances examined have been of many widely different 
types, the ultimate reference has always been made to those 
in which the behaviour is simple as well as characteristic. 
6. At an early stage in this study I was led to the con- 
-clusion that nothing was to be gained by attempting to stretch 
-our ideas of the crystalline state so that room might be found 
within, that state for all the varied phenomena presented in 
the meshanical and thermal treatment of metals. A crystalline 
aggregate must owe its origin to some inherent quality of its 
molecules in virtue of which they take up and retain fixed 
positions with reference to each other. The molecular theory of 
magnetism supplies an illustration of a simple form of polarity 
in which the molecules are arranged end to end to form strings 
or rows. The compounds of the asymmetric carbon atom 
supply a more complete illustration of the direct influence of 
the molecular polarity on the form of the crystal ; for here 
the definite space relations of the molecule find their counter- 
part in the geometrical form of the crystal. The strictness of 
these molecular and geometrical relations must be regarded as a - 
characteristic feature of the crystalline state. 
7. Up to its limit of elasticity a crystal may be strained 
without its ceasing to be a cryaiels but when this limit is 
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