The core of fig 15 is the field in the upper right where the system with 3 colored spheres is shown in 4 states. They are just at the loacations for the displacement of (a,b) = (1,1); (3,1); (3,3); (3;1). These are the locations which were used in the calculation example.
With the general description of figure 14 a movement between any two points of the plane for a and b can be described. So the sinusoidal movements of the experiment with a phase shift of 90° can be described as the the circle in the plane a,b.
For the calculation the circular movement is split into small fractions and the the functions for the movement of Xs are applied.
The blue curve on the left shows Xs(b)/a. Its value states which fraction of the movement of sphere A gives the movement of the barycernter Xs. The value of this function Xs(b) depends on the value of b, which means how far sphere B is stretched out from sphere C.
For confirmation: If b is large, the value of Xs(b) is very small. This means the spheres B and C are separate and have twice the flow rsistance of A. If A moves, it moves twice as fast in the opposite direction of B and C. The result is no movement of the barycenter. On the other hand if b is small, the flow rsistance of B and C is smaller than two times the flow resisitance of A and with any movement of A the barycenter moves (pushing away B and C almost as far as A moves to the opposite side).
The blue curve at the bottom is just complementary, showng Xs(a)/b the movement of the barycenter for the movement of B.
