6 R. F. GWYTIIKR, specification of the elements of stress. 



shown to agree with the phenomena which they propose 

 to describe in natural materials. 



(iv.) I add references to papers which I have previously 

 communicated to the Society, in which I have approached 

 the point of view from which the present paper has been 

 written. 



1. Permanent Forms of Mathematical Expressions. 



Alanchesier Alemoirs, vol. xxxix. (1895), No. 8, p. 119. 



2. Rate of propagation of an Earth-Tremor. 



Manchester Aremoirs, vol. xlvi. (1902), No. 15. 



3. Conditions that Stresses should be Elastic. 



Manchester Aieinoirs, vol. Iv. (igii), No. 20. 



4. Specification of Elements of Stress. 



Manchester Memoirs, vol. Ivi. (19 12), No. 10. 



5. Specification of Elements of Stress. Part II. 



Manchester Memoirs, vol. Ivii. (1913), No. 5. 



Cartesian Coordinates. 



I. The dynamical stress equations are : 



cP dU cT ■■ 

 ex ty cz 



d[/ dO ds •■ 



+— ^ H = nV , 



dx dy dz ' 



— +5- + ^=p"' (0. 



ex cy cz 



Whatever values 11, v, w may have, we may always 

 write 



(2) 



