14 PROCEEDINGS OP THE AMERICAN ACADEMY 



3. Definitions. — In my paper* on the absolute viscosity of the 

 three states of aggregation, I defined a fluid (liquid or gas) as a 

 body which, under constant conditions of pressure, temperature, 

 and strain, shows constant viscosity as to time. In a solid, coeteris 

 paribus, viscosity markedly increases with the time during which 

 stress is brought to bear. The molecular instabilities of a liquid, 

 therefore, are supplied at the same rate in which they are used in 

 promoting viscous motion. In a solid they are used more rapidly 

 than the small rate of continuous supply. 



The point of essential concern in these definitions is the con- 

 stancy of stress, and its value below a certain critical datum. For 

 instance, if in a solid stress be increased at the (small) rate necessary 

 to insure a constant supply of instabilities, then solid viscosity will 

 also be constant, and I am by no means sure that in such a case f 

 yield points would eventually present themselves as breaks in the 

 continuity of the solid view. 



On the other hand stress may be conceived to increase so fast, 

 that even a liquid fails to present sufficient instabilities for truly 

 viscous motion. The elasticity and brittleness of many viscous 

 liquids, especially at low temperatures, is a case in point. 



4. Hardness. — Throughout my work on viscosity, X I have ad- 

 verted to the association of viscosity with zero forces acting for 

 infinite times, and of hardness with infinite forces (relatively) act- 

 ing for zero times, and have adduced many new examples showing 

 the utter distinctiveness of these two properties. The subject of 

 hardness has, however, recently taken more definite shape in the 

 researches of Auerbach,§ based on a principle due to Hertz. || 

 According to these observers, hardness is an expression for the 

 elastic limits of a body in case of contact between its plane sur- 

 face and the curved surface of some other (harder) body. Hard- 

 ness so defined admits of absolute measurement in terms of dynes 

 per square centimeter. 



5. Method of Work. — In all experiments like the present, one 

 cannot be too careful to preconsider the conditions under which the 

 results are obtained; for one is only too apt to attribute an absence 



* Phil. Mag. (5), Vol. XXIX. p. 337, 1890. Cf. p. 354. 

 t Cf. Am. Journal (3), Vol. XXXIV. p. 19, 1887. 



| Phil. Mag. (5), Vol. XXVI. p. 210, 1888. Cf. Bull. U. S. Geolog. Survey, 

 No 73, pp. 42-44, 97, 98, 1891. 



§ Auerbach, Wied. Ann., Vol. XLIII. p. 61, 1891. 

 II Hertz, Crelle's Journal, Vol. XCVI. p. 156, 1882. 



