580 i MOSSOTTI ON A PHA NOMENON 
perpendicular to it, the quantity.© will be constant in that sec- 
tion for all the threads that cross it at a perceptible distance 
from the sides of the tube. Putting then 
@+gAb=c, 
the two preceding equations become 
ghz—e=T(L+) | 
g g 
— bP as pls 4. =) 
g (A, — A) 2,4 Li ee fey J 
which are identical with those of Art. 69 de la Nouvelle Théorie 
de ? Action Capillaire. 
To these equations must be added those that exist for the 
neighbouring points. If we denote by I and I, the tensions 
that exist respectively in the two fluids in those parts of their 
surface which lie along the sides of the tube or parallel to them, 
and by » and , the angles under which these portions meet the 
concave or convex parts in which the two fluid columns termi- 
nate upwards, we shall have, in consequence of what was said | 
in § 6 of the lecture, the other two equations, 
i ore Reenter titan’? 
1 ="T; cos @, 
Treating these four equations with the same process as that em- 
ployed by Poisson*, we shall obtain the following :— 
wr styles 
* The following is the process employed by the above-named author, and 
we place it here for the reader’s convenience, 
Substitute in equations (1.) the expression for the sum of the values of the in- 
verse radii of curvature, which for cylindrical surfaces, taking axis of figure as 
the axis of x, becomes 
dz 1 dz what 
1 1 d@¢tdt de 
ety mee 
= ri 
(1+) 
where ¢ denotes the distance of the ordinate x from the axis to which it is 
parallel. Multiply both equations by ¢d¢, and we shall have 
ate? 5 
dt : 
2g 4 dt (eS a 
J/ 144% ; 
an? 
2, ae 
29 (A, — A) ft Ie wee 
j)Soyaee 
‘3 dt? 
the integrals fz td aud fix, tdt being = 0 when #= 0. 
