The energy at which ions trapped in a static quadrupole magnetic well begin to exhibit nonadiabatic behaviour in their single-particle motion has been determined for mirror ratios from 1.4 to 8.1. The analyzed data are derived partly from digital-computer orbit calculations and partly from experiment. These data are fitted well, for mirror ratio >or=1.6, by the equation (obtained from simple theoretical considerations and approximations) W_max (keV)=((8.5*10^-4)(Z²/A)(B_ML)²)/(R(R-1)³), where L^-2=l_z^-2+l_r^-2(R-1)^-1. The effective mirror ratio, R, is B_M divided by the magnetic field at the centre of the well. The parameters l_z and l_r are the distances (in centimeters) from the centre to the B_M constant-magnetic-field contour, along and perpendicular to the magnetic axis, respectively. The investigated particles either reflect at closed contours of constant magnetic-field magnitude or are constrained by the field lines to reflect in regions where the contours approximate sections of closed magnetic-field surfaces. The calculated trajectories pass through the central region of the well and represent the first trapped particles in a closed-contour system to become nonadiabatic as the energy is increased. The fitted data extend over a range of almost 2000 in energy, a factor of 6 in l_z, and from 1.5 to 3.2 in the ratio l_z/l_r.