Similarly equation (11) of the former paper becomes here d 'dt{u(u2+v2+w2)+u(352+n2+52) } +6p1⁄23u: +2pn2u +2p5u From (5), (6), and from (8) in the former paper we obtain ди дх ду дго ละ + (3u2 + v2 + w° +35+ n2 + 53) 3 (pE3) + 2uv: ду (7) ઠ =2pu +(3u2+v2+w2+3§2+n2 + 52)pX+2uvpY +2uwpZ, δε Pat (p2) If the disturbance is not a very violent one, the first, the fourth, and the fifth member on the left-hand side may be omitted. Hence an equation which (under somewhat particular assumptions) was given by Maxwell. Let us write D2=§3 (§2+n2+52) — §2 . (352 +n2+52) ; . . Now this equation would lead at once to results contrary to experience, as shown by Maxwell, unless D=0; accordingly the first term on the right-hand side may be dropped. And if §2, 72, and 52 can be replaced each with sufficient approximation by (+2+), we shall have an approximate equation which is of secondary importance only in the subsequent calculation. 3. Let us now proceed to prove our principal equation. Putting in (1) Q=(u+)2 and again Q=u+§ and multiplying by 2u we obtain (without neglecting any term) the symbols L, M, N being defined as follows: SE L=p { (55+n2+53) °F 2 + ( F2+5m2+52)2 +(F+n2+552)}. (21) ди δε ди M=(55a+n2+53) (pë3du +p5n+55) д д (ρηζ2) ду д д + (E2 + y2+55) (+ (PES) + 3 (pn5") + (p)). (23) We easily find, to a first approximation, L=0, and дргу (24) aprz N=3(E +5°+5%) (@pr2+dpry + pre); (25) thus equation (20) becomes дх . δε (E2+n2+52)2 { de +p (++)}; (27) ди (28) If we make 3p=p(2+n2+52) and introduce Lord Rayleigh's Dissipation Function F defined as follows :— F= (pp2) √x +(p−pn2) v + (p−p52) д до де ду ди + + Returning to (29), multiplying by dx dy dz and integrating throughout the volume occupied by the medium, д St. A dx dy dz=− д д + 8. W { pr = 3 (5 + n2 + 5) + pr, 3 y (F +72 + 5) Jx Here the direction-cosines of the normal to the element ds of 4. In order to interpret equation (32) let us adopt a some- ¥ S(Cq)=(C'g'+C"q"+C""q""), C', C", and C being the components of C, and q', q′′, and q′′ and the total kinetic energy of such currents per unit volume is N being the number of molecules per unit volume. Calling 5. The energy of motion of the heat-energy is susceptible of several kinds of variation, from various sources, to which the consecutive terms of the right-hand side of (32) refer. The first term represents the loss by convection across the surface; the second the gain due to viscosity; the third expresses the reversible effect of the mean pressure doing work. The fourth term relates to the communication of heat through the surface, since pr, pry, and pr, are the values of the total component fluxes of energy. In order to find the meaning of the fifth term, let us substitute for the differential coefficients values from (12) and two other equations which can be written down from symmetry; then that term will be and represents therefore the source of variation due to inter- |