the Laws of Viscosity. 353 



independent of the time t. Let, for the sake of brevity, 



6 -</T(^ e */T g=Bj (ll a ) 



€ -t/T^ e t,Tf =Fy (116) 



e -4^=G, (110 



6-^1^6^ = A, (12a) 



H T ^e^ = B, (12b) 



e-' T J^e^ = C , (12.) 



6-' T J^e^ = (13) 



Further, let 



nT=fr (14) 



U-h-p)T = \; (15) 



equation (11) was given by Maxwell in 1807. Using these 

 abbreviations, equations (9) and (10) may be written : — 



^x-/>=C,,e- rr -2^E-Xe, . . . (16a) 

 ri/lJ - r = Q i/!J e- t ^-'lfjiF-\e, . . . {16b} 

 p ,,- I> = C zz 6- f ^-2fiG-\e, . . . (16a) 



i-V~-= ( W e_/T — Mj (17a) 



/>,,= C- x e- rr -^B, (176) 



p^C^-W-pC (17c) 



These equations have, in our theory, the same significance 

 as that which, in the classical theory *, is possessed by the 

 known equations which give the quantities {p xx —p) &c as 

 functions of the components e, /, g, a, h, c of the velocity of 

 deformation. They contain the terms C^e - ^ &c, which do 

 not appear in the ordinary equations. Further, in these 

 equations, the functions E, F, G, A, B, C, 0, defined by (11), 



* Stokes, ' Mathematical and Physical Papers,' vol. i. p. 90, eq. (8) ; 

 Cambridge, 1880. Basset, 'A Treatise on Hydrodynamics,' vol. ii. p. 241, 

 eq. (10) : Cambridge, 1888. Lamb, 'Hydrodynamics,' p. 512, eq. (4) & 

 (5) ; Cambridge, 1895. 



