12 



Art. 7. — K. Terazawa : 



boundary condition (25). In his book of differential equations, 

 H. Weber^^ solves the same problem by using the Cartesian 

 coordinates. But it seems that his mode of using Fourier's 

 theorem was anticipated by Lamé and Clapeyron. 



IV. Examples in the Case of Symmetry. 



§12. The solution for the case of symmetry round the origin, 

 which is discussed by Boussinesq with numerous examples, has 

 been afterwards obtained l)y Prof. Lamb in the same way as 

 adopted here. This case is implied, of course, in our solution. 

 Suppose 



(29) 



zr = 0, zd = O! 



are given at the surface ;:;=0. The corresponding solution will 

 then be obtained from (23) and (24), l)y taking only the first term 

 (m=0) in the summation. Thus 



' 



2(; + //.)./ ^ W.- 



2',, = 0, 



11^ = 



lz{k)e-'-%ßT)(U- 



(30) 



and 



2/' ■'. 



n- = -^|l(Ä:)e-'"J"o(Ä-r)MÄ'+^-|z^A-)e-''/,(Ä-r), 







J ('^> + /-<)^" •' 1^' 



)cR- 



+ 



1) Part. Diff. Gleiclmngen, vol. 2 (1912) §76-. 



