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It is suggested that microscopic vortex rings (MVR) play an important role inthe \lambda-transition in helium-II and substantially determine the value ofT_{\lambda}. For very thin films of He-II, with thickness d less than the sizeof the smallest MVR, the rings do not fit in and, therefore, do not exist insuch films. Consequently, for superfluid films of He-II, a peculiarity in theform of a smoothed-out jump should be observed in the curve T_{m}(d) at thevalues of thickness approximately equal to the size of the smallest MVR, d= 3 -9 A (T_{m} is the temperature of the maximum of the broad peak on the curve ofthe dependence of the specific heat on temperature). The absence of a similarpeculiarity will be an evidence that MVR do not influence the values ofT_{\lambda} and T_{m}, and do not play any key role in the \lambda-transition.The currently available experimental data are insufficient for revealing thepredicted peculiarity.

Possible experiment for determination of the role of microscopic vortex rings in the \lambda-transition in He-II