Brard 
Let pare ; ae: , denote the two sides of y hy. » Nf on pa f 
being in the direction From > a towards dt, One has 
(M,) + wg.) = O(M,) - oM,) ; 
gu Ol ieee dir -|¥ (m,) + Vem) . O(M)doa ; 
Let Q@ denote (Figure 5.2) the intersection of ~ with e 
Two parts )\, and pe of }> are adjacent to each other along 
The part psi corresponds to )\¢ and the part dU, t Wee - 
Hs be the determination of uw on and He Ee Let 
Ls ; cL %: VY be three vortex filaments intersecting at the same 
point, By, and located on De fas yy ; Day , respectively. 
Similarly, L f » ae ; 5 intersect RR at the same point B 
and NAG oan nes intersect R at B'. The points B and B' are 
chosen in opposite directions with respect to B°. Thus A f belongs 
to the vortex ribbon Ly, the edges of which are L rae ae, . Simi- 
larly Br belongs to the vortex ribbon L, and L3 to the vortex 
ribbon L, , the edges of L, being ~,, sf, while those of L, 
are WH, , ae . Let Mg, Mf be the intersection points with hers 
se of the curve intersecting ae at Mf. Letus define ina 
similar manner the points M, and M; on L, and Ly ,» and the 
points M, oF Mi! Aon L, and £ 
2 2 
We now suppose that Mf, M* and M5 are chosen so that 
. 
to 
i 
O 
= 
S 
to 
i 
oO 
= 
5 
td 
iN 
Ory 
(5. 15) 
n being a small length that we shall finally equate to zero. 
1214 
