582 MOSSOTTI ON A PHANOMENON 
These two equations differ from the corresponding equations 
obtained by Poisson, as we have not made use of an equation 
which he denotes by F — F’= K in Art. 69 of his Théorie de 
l’ Action, &c., and which we consider inadmissible in these cases. 
4. Let us apply the obtained equations to the experiments ; 
made by natural philosophers, that is when one of the two fluids 
wets the sides of the tube all round, in which cases alone can we, 
I think, easily obtain constant effects. I therefore observe, that 
if the upper fluid wets the sides, its internal surface being every- 
where in contact with the lower fluid, the tension in the surface 
downwards. Substituting these values of x under the integrals i in equations (3.), 
and effecting the integrations, we shall obtain as two equations 
g {ch pe beat +2er=0 
gf, —a{@, + y,) e+ str — axis y? } +ee2+2aeT,=0; 
and in consequence of equations (4.) these will become 
27 ep 2aTtgatyete(r—eji—s7} =0 
: sa + 2aT,+9(A, —a{netiti-a—sr'} =o. 
/ 
Assuming the radius « very small when I and I, are not supposed very 
small, we shall obtain approximately 
i =-7 +i Tr+— 2__ 2 Tse 
yore an eA 3 7 ) 3 } 
eg ane ihe (4, — A) a T T2 = T?—L3)i— 73 
aT at ot {b+ ely 12) 2 sf. 
If now we denote by x #”¢ the volume of the upper fluid, which ought to be . 
given, we shall have 
ac af*atdt— 2 fx tat; 
or by equations (8), 
Pee oF ft een ee ) ne Y -=) 
Te BAe UA gee 
whence we get 
aa i—A 2 — — 
c=ge if a (T (A, — 4)—T,4). 
Substituting this value of ¢ as well as those of = and sa in equations (4.), we 
2h 
shall finally obtain , 
A Cg 2 
eg Rt ea T+ +h 4{Tr+2cr_rmyt_ ih 
A See ane 
he Sega ttt ge{trt pry gr}, 
which are the same as the equations in the text. 
