oo 
Nits ZEILON, 
4. Letting now o’ and 9" denote the extreme densities of the 
fluid, we put 
cx malesu MS 0) 
for the upper fluid, and 
for the lower fluid. On the hypothesis of slight diffusion, d and « are 
then quantities which are everywhere sensibly zero, except in the 
/ " do de do 
neighbourhood of y = 0. Writing respectively TE and "E for dz B 
iransform our equations by partial integration, so that for instance B") 
is transformed into: 
2! 
, sinh k(y — A") EUN | " ] 
RITU RIS —he zm | e (cosh k(y — 2) + ...)| dz 
8) ea = 
A' 
EIE E [a (cosh k(h" — 2) + en) dz , 
sinh ky 
sinh kA", 
0 
whereas by the similar ealeulus the equation €) reduces to: 
9) ol. coth. A) 16” icoth RE zs (oo) A Al 
/ 
where: 
= 
1 i d , OM ; 
= — xi] p le (cosh k(h' + 2) — ky? sinh k(k' + 2))| der, 
A 
[41 | " N d 11 \ | I 2) 11 ) 
Jl Tesıh ur, ae |e(cosh k(h" — 2) + iy sinh k(h" — 2))| OWE - 
If here d and « are identically zero, we have the case of an 
abrupt change of density at y = 0, equal to e’—o", and 9) then 
gives a vale V?, determined from Stokes’ law: 
9g Q coth kh'- o" coth kh" 
i Seesen, 
