On Wave-Motion in an Elastic Solid. 481 



and with the corresponding notation P, Q, R ; S, T, U; for 

 stress-components (normal and tangential forces on the six 

 sides of an infinitely small rectangular parallelepiped), we 

 have 



P=(* + $n)«+(*-|n)(*+0); Q«(* + £n)/+(*-|n)(p + *)f| 



R=(A + in}0+ (*-*»)(«+/) > (3) 



S = na; T = nb; U = nc J 



Let now o- be an infinitesimal area at any point of the 

 surface S ; X, /ll, v the direction-cosines of the normal ; and 

 Xo-, Y<7, Zcr the components of the force which must be 

 applied from within to produce or maintain the specified 

 motion of the matter outside. We have 



_Y = Q^+ Sv + U\> .... (4); 



whence by (3) 



-X=(k-%n)\$ + n(2\e + fic-+vb)~) 

 -Y={k~%n)iM8+n(2fif+va + \c)l . . (5). 

 — Z= (k - §n>S + n(% + \b + pa) J 



These equations give an explicit answer to the question, 

 What is the forcive ? when the strain of the matter in 

 contact with S is given. We shall consider in detail their 

 application to the case in which S is spherical, and the motions 

 and forces are in meridional planes through OX and sym- 

 metrical round this line. Without loss of generality we may 

 take 



z = ; giving v=0, a = 0, fc = 0, Z = . . (6) 



Equations (5) therefore become 



-X=(k-%n)\8 + n{2\e + fic)\ 



-Y=(k-Zn)}A$ + n(2nf+\c)f 



§ 3. In §§ 5-26 of his paper already referred to, Stokes 

 gives a complete solution of the problem of finding the dis- 

 placement and velocity at any point of an infinite solid, 

 which must follow from any arbitrarily given displacement 

 and velocity at any previous time, if after that, the solid 

 is left to itself with no force applied to any part of it. In a 

 future communication I hope to apply this solution to the 

 diffraction of solitary waves, plane or spherical. Meantime 

 I confine myself to the subject stated in the title of the 



