22 



Art. 7. — K. Terazawa : 



§20. To fix matters, suppose an isolated mountain or a high 

 tower of uniform density with a circular base standing on the 

 ground; the surface of the mountain or the other being given by 

 the other by the equation 



mVi^ 



(wVr + (w^-l)rf2 



(53) 



This equation is so adjusted that the height at the centre is h 

 and that at the point r=mh is hjn. We shall make the rough 

 assumption that each point on the surface of the ground is pressed 

 normally downwards with a pressure given by the product of the 

 specific gravity and the height of the mountain at that point. Tlie 

 quantity «, used in the above, is now 



a = 



mh 



V;i^"-1 



In the annexed diagram, the upper curves are supposed to 

 represent the profiles of mountains and the inner ones those of 

 columnar buildings such as chimneys or monuments, the height 

 being taken as unity, and m and n chosen properly. 



If we denote the specific gravity of the mountains or other 

 bodies by w, then the total amount of pressure will be 



n 





The maximum of the greatest principal stress becomes 



N. 



= —wh, 



(54) 



