Scientia Sinica

8 SCIENTIA SINICA Vol. V

ofA ee (vj 2) JoH(v2=%0) Jit Go—v1) Jo (36c) Oz* (vp— v1) (v1 2) (22 — V9 ) ‘ “

This system of equations is simpler than (35) in form.

Since the xy-plane is parallel to planes of isotropy, the special solution corresponding to the body forces Y may be found in the same manner.

Consider, as an example, an infinite space under a concentrate force P, at the origin. According to formula (34), we have

Bes . ze Si By, By Bog = 4 V pg?”

Jy) — (¢=0,1,2), - (37)

where

ry=Veity, 29 = 5025 21 = S12, 22> 522. (38)

ne oe : 4 : E : Substituting (37) into (36c), we obtain a Then integrating with respect

to z four times, we get

Fe Bis eee (v= 2) Ho+ (v=) Hit (vo—v1) Ae . (39) By Bag Bog 9 4 (v9— v1) (¥1— v2) (v2 v9) where : A; = oe {#1 (22?—3r*) log anaes =(= aie r) VPaae (40) s \4 V px? 2; oy J

It may be verified that expression (39) satisfies equations (36a,b). Therefore it is the required solution.

If the body forces parallel to planes of isotropy have a potential, then the calculation may be simplified greatly. In this case

= Soe ero = XS = Sa By” 1, (0) 5 (41) and system (4) is reduced to the form Oru 07x O7u 07u Oru OU Bu Ox? + Bee Oy? we Oz? + By Ox Oy + Bis OxOz Ox 0; O7u O7u O70 O70 Ow OU _

Bi Bi By + Bee Ox? + By Oy? + Buys Oz2 1 313 Bye @p (42)

o ov Ow Orw Oru

2 “ eae + Bis a ae + By, Ox? + Byg Oy? + B33 Oz? =0'.

By letting