a state that the polishing holder h is inserted into the polishing holder arm in the apparatus of the embodiment fig7 is a rear sectional view showing the state that the polishing holder is inserted into the polishing holder arm in the apparatus of the embodiment fig8 is a plan view showing a state that the polishing holder is mounted on the polishing holder arm in the apparatus of the embodiment and fig9 is a rear sectional view showing the state that the polishing holder is mounted on the polishing holder arm in the apparatus of the embodiment as shown in fig6 and fig7 the knob 29 is rotated and the long side of the key block 31 is made parallel to the polishing holder arm 14 previously to mount the polishing holder h on the polishing holder arm 14 in this state both the inside surfaces of the mounting guiding groove 36 of the polishing holder is fitted to both the outside surfaces of the polishing holder arm 14 and the polishing holder is pushed inwardly in parallel therewith until it comes into contact with the positioning pin 39 of the polishing holder arm fig8 and fig9 show the state that the polishing holder h is mounted on the polishing holder arm 14 at the time the knob 29 is rotated 90 u00b0 from the state shown in fig6 and fig7 so that the long side of the key block 31 is engaged with the peripheral groove 37 of the polishing holder h at right angles as shown in the figures with this operation the polishing holder h can be simply and securely mounted on the polishing holder arm 14 to.