The concept of reduced efficiency curve and its current understanding in hydrocyclone practice, including the variability of the sharpness of classification is explained initially. A detailed mathematical analysis of Plitt - Reid function is then carried out, based on which the observed variability of the sharpness of classification is analysed and discussed. It is shown that if the geometric mean between the extreme values of the classification index, m, is taken as the constant value for the system, the errors in the predictions are least. Further, it is noted that the variation in the classification index, observed in industrial practice or as estimated from Plitt＇s equation for normal operation, is not significant enough to affect prediction of the cyclone performance. A sensitivity analysis of the more commonly used Whiten function for the reduced efficiency curve also confirms similar conclusions. As such, it is concluded that the assumption of invariance of the reduced efficiency curve with design and operating conditions of the hydrocyclone is an excellent approximation for design/selection, optimisation and control of grinding circuits. It is also shown that the principle of invariance of reduced efficiency curve is the basis for the usage of the cyclone as an on line size sensor.