2 Art. 7. — K. Terazawa : 



be extremely unsuited for obtaining physical results, seems now to 

 have gained practical importance. 



§2. The present paper deals with the problem in the case in 

 which the bomidary is subjected to any given normal pressure, by 

 generalizing the method adopted by Lamb.^^ In the first two 

 sections the general solution of the problem is obtained in the type 

 of the Bessel-Fourier expansion of a function. The third section 

 discusses several examples in the case of symmetry about an axis 

 normal to the boundary, and forms the main part of this communi- 

 cation. Most of these special examples have been investigated by 

 the autliors above cited: the behaviour at the surface especially; 

 and yet it ]jiay be worth while to discuss them again more closely, 

 referring especially to the beha^■iour inside the boundary. 



The last section is added as an appendix, supplying the 

 general solutions corresponding to several boundary conditions, 

 excepting that of normal pressure, in the case of symmetry about 

 a normal to the boundary. 



§3. The results of tliese special examples applied to find the 

 limit of rupture of a foundation over which a heavy load is 

 distributed. Strictly speaking, ]jy applying the mathematical 

 theory of elasticity, we can treat of rupture only, for some kmds of 

 brittle solids like cast iron, in which tlie linear relation of stress 

 and strain holds and, moreover, the strains are so small that their 

 squares are negligible up to the point where rupture takes place. 

 For a ductile material, such as mild steel, and for an imperfectly 

 elastic material, like cen:ient or sandstone, we must bear in mind 

 that the theoretical results indicate only roughly the state of stress 

 when, in the first case, it begins to take permanent set, and, in 

 the second case, when it breaks. 



§4. Another application will be found in a problem of 

 geophysics. In his elaborate observations on the lunar deflection 

 of gravity, Dr. 0. Hecker has pointed out that the force acting on 

 the pendulum at Potsdam is a large fraction of the moon's force 

 when it acts towards the east or west than when it acts towards the 



1) Though the writer had not read his paper until the work was almost finished. 



