Scientia Sinica

10 SCIENTIA SINICA 3 Vol -V

tae) =(|Ty m0) de, (48) the first two equations of (47) may be rewritten in the forms

oO? O7u 07u 670 eo? a Bi at a> Beg wana) + By a azz Tn Bid emeene A saree 0 — at,

Oy? Ox Oy (49) O7u 07u O70 O¢u 0? a, _ Bo Gay t+ Basa + Bu or Tt Bas ae 1 Bis Gye (w Bat) =0. In order to satisfy these two equations, we may put ___oF pee OE * Ox Oz * Oy Oz (50) ay By es O*F = vi EF 2 af By; oT Bis Bys 2 Biz; Oz?

The last equation of (47) is reduced to the equation satisfied by the stress © function F:

Zee =) ( 2 a oie =F Bis [#4 2 (vi+ 7 ef )\V1* 3 "Be Bake to 2. J + 233 mc — as) =| = (0). (51)

This equation has the same form as equation (10). Hence its solution can

be obtained by the method described in SIII.

When the temperature distribution is steady, and when there is no thermal source inside the body, the problem may be simplified greatly. In this case, the temperature T satisfies the equation

OL OnLy i Ott

Ox2 te Oy? a2 Oz? ea (52)

where s is a constant depending on the ratio of the coefficients of thermal conductivity of the body. A special solution of system (47) may be put in the form

BT OP v=kh, oP w=; se (53)

Ox

where 4, and 4, are constants to be adjusted. Substituting these expressions