4 GwVTHER, Conditions of Stresses in a Heavy Body. 



removed, we deduce from statical considerations that 

 the alteration of vertical stress across every horizontal 

 section is equal to the weight of the body. The conse- 

 quences ma)' be that rupture takes place, or that the 

 strains exceed the elastic limit, but if there is justification 

 for believing that the strains are small and within the 

 elastic limit, we proceed to equate the stresses to the 

 corresponding functions of the strain and obtain the dis- 

 placements in the bod}'. 



If, again, we consider a massive structure built up 

 /;/ situ, the cases may vary greatly from, say, the substance 

 of the Earth to the greater or less structures raised by 

 human hands. The materials may be complex and of 

 very various characteristics. For the purpose of my argu- 

 ment I shall imagine a concrete wall built in courses of 

 equal heights and so constructed as to allow us to assume 

 a complete bond between the courses. 



The material of each course is initially in a fairly 

 liquid state able to run under hydrostatic pressure. As it 

 sets it develops in some way a capacity to exert other 

 stresses than hydrostatic pressure and finally becomes a 

 solid mass. 



As the wall is built up additional stresses are caused 

 in each course by the weight of the superincumbent 

 courses. Finally, we have a wall in which the stresses 

 vary periodically (in the Fourier sense). There appears 

 no justification for claiming that the stresses are elastic 

 stresses, or have the character of such stresses. If, 

 however, we could remove the original structural stress 

 in each course from the whole system of stresses, we 

 might fairly assume the character of elastic stresses for 

 the remaining portion of the stress system. 



Mathematically, this process now suggested is not 

 greatly different from that employed in the first simple 



