[For part I see the authors in Proc. R. Soc. Lond., Ser. A 431, No.1883, 509-518 (1990; Zbl 0719.33001).]
L. Lorch and P. Szego have established some monotonicity results on the inflection points , . of Bessel function of the first kind. They proved that increases with and that increases on , for . In the present paper the authors prove that increases with for . Their results together with Lorch and Szego results show that increases with , for any . The authors obtain the results with a sophisticated use, with error estimates, of asymptotic approximations. Some of these approximations are due to Olver.