In the previous reports, it has been shown that the current minimum I_0 required for the occurrence of magnetic flux increase is represented in the (I-H-T) space by the simultaneous equations I_0 = ξγd(T_c-T) and H_0=ξ(T_c-T)-I_g/γd. Here I_g, T_c and ξ are the characteristic constants of the superconductor measured in amp, °K and Oe/deg respectively. d is the diameter of the specimen in mm and γ seems to have a nearly constant value of 0.25 measured in amp/mm Oe, irrespective of the superconductor. It has been shown also that the formula I_0 = I_g+γdH proposed for the minimum current requirement up to that time can be derived from the above simultaneous equations after eliminating T and that these simultaneous equations are understood in a good approximation as those for the intersection of the plane I= I_g+γdH with the transition surface in the (I-H-T) space. In the present paper the experimental results on the magnetic flux increase in non-circular tin rods at the superconducting transition are reported. Under the expectation that the mysterious constant I_g should be the same in non-circular cylindrical specimens, if the paramagnetic effect should be observed in them and the current minimum should be required also for the appearance of the paramagnetic effect in them, as in the circular cylindrical specimens, measurements were done with cylindrical tin specimens of non-circular cross-sections of several types. In the specimens in which we expected the magnetic flux increase according to the proposed idea of the paramagnetic effect, we observed the magnetic flux increase and obtained the formula I_0=I_g+βH_0 for the current minimum required for the occurrence of the paramagnetic effect. Although β differs from specimen to specimen according to the shape of the specimen cross-section, the magic constant I_g proves to be the same as in the case of circular rod, irrespective of the shape of the specimen cross-section, i.e. I_g is 1.2 amp for tin
