Assuming the fluid motion to be potential and two-dimensional, the local velocities over an aerofoil section satisfy, after Prager⁽²⁾, the integral equation (1). The parameter of this Fredholm's type of integral equation has the value 1, which is just a characteristic constant for the kernel. Therefore if we change the equation into a system of simultaneous linear equations such as (3), replacing the integrals by summations by means of Simpson's or other rule, the determinant defined by the coefficients of the left hand sides of (3) in the limiting case where the numbers of the terms and the equations are infinite, becomes zero. This holds for the case with finite number of unknowns within the limit of error due to the replacement of the integrals by the summations. Since we can, in such a case, give the value of one of the unknown quantities arbitrarily, the number of solutions is infinite. This means that the type of flow is indefinite, unless the circulation round the aerofoil is defined. We may assume that the circulation may exist such that the trailing edge to be a stagnation point. Then, substituting v=0 at the trailing edge, omitting one of the equations (3), we can obtain uniquely the remaining unknowns by the remaining equations such as (4). Of course the solution thus obtained satisfies the omitted equation. The pressure distribution over the aerofoil is calculated from this velocity distribution by aid of the Bernoulli's theorem.
For aerofoil sections of multiple contours, the integral equation to be solved is (5) or (6), according to the number of contours. The number of v to be taken arbitrarily is the same as the number of contours, or in other words, one stagnation point on each contour is presumably determined. The method of solution is similar to that for single contour.
For the simultaneous equations with so many unknowns as more than twenty, the successive approximation method as tried by v. Kármán⁽³⁾ is used with advantages.

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