Scientia Sinica

12 : SCIENTIA SINICA Vol. V

ee LORE gO) ERCP | Toe oy > oS Sons Ba (59)

This presentation is not unique, since the homogeneous equations corresponding to (59) O*Fo OPo Ox Oz Oy

O7F OPo

Tid Voras ore © (60)

have non-zero solutions. Actually, the solution of (60) is

OFo Po +z Oz o = f(x+ty, x,t), (61)

where f is an arbitrary function of («+1y), z and ¢. Consequently the displacement components w and v will not be altered by adding Fo and @) to F and @.

Substituting expressions (59) fare the first two equations of (58), we

have OF OF OF OF e ies Bit oq2 — Bil gyn Pt ge + P ae + Bis wf o op op Oo? Se pee Ton Bie aa Ox2 ae BGG By z =i Basa Poa - = (0), 0 Oo O*F O°F O?F OF ez) Oy 2 {- Big sxe Ox 2 SB il ammo by? = Bae Oz ap alr PA a2 ate By3 uw} ar O op oP = Ox Besa a + Bee “Oy? + By SE — 2 ar =o: From this it follows that O°F O?F O°F O*F ae Bur aay Bia — Bsa + Oe a2 + Bis w) + : oO o? ; 6 7p , “Ft Bee qa + By, ez == [v 2 pie Ee) Ze (63) Ox Oy? Oz? Oz

where g is an arbitrary function of (x+y), z and z. But if the function f in formula (61) is so chosen that

24 2. iB SE ip SE = ola tiy, ns), (64) then by adding F, and @ to F and @, the right hand side of

equation (63) may be brought to zero. Therefore we may put g=0 without loss of generality. Thus from (63) we have