The author discusses the compatibility equation of critical multipliers $\lambda_{cr}$, deduced in Note I. He furnishes coefficient expressions, minima evaluations for calculus of the $\lambda_{cr}$ and the tables of entire parameters couples $(m, n)$ concurring to the minimum for circular cylindrical tubes of dimensions $L$ (Length), $a$ (Radius), $h$ (Thickness) such that $a/L = 0,1 (0,1) 0,6$; $50 h/a = 0,2 (0,2), 1,6$.