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The Tibet-III air shower array, consisting of 533 scintillation detectors,has been operating successfully at Yangbajing in Tibet, China since 1999. Usingthe dataset collected by this array from 1999 November through 2005 November,we obtained the energy spectrum of $\gamma$-rays from the Crab Nebula,expressed by a power law as $(dJ/dE) = (2.09\pm0.32)\times10^{-12} (E/{\rm 3TeV})^{-2.96\pm0.14} {\rm cm}^{-2} {\rm s}^{-1} {\rm TeV}^{-1}$ in the energyrange of 1.7 to 40 TeV. This result is consistent with other independent$\gamma$-ray observations by imaging air Cherenkov telescopes. In this paper,we carefully checked and tuned the performance of the Tibet-III array usingdata on the moon's shadow in comparison with a detailed Monte Carlo simulation.The shadow is shifted to the west of the moon's apparent position as an effectof the geomagnetic field, although the extent of this displacement depends onthe primary energy positively charged cosmic rays. This finding enables us toestimate the systematic error in determining the primary energy from its showersize. This error is estimated to be less than $\pm$12% in our experiment. Thisenergy scale estimation is the first attempt among cosmic-ray experiments atground level. The systematic pointing error is also estimated to be smallerthan $0\fdg011$. The deficit rate and position of the moon's shadow are shownto be very stable within a statistical error of $\pm$6% year by year. Thisguarantees the long-term stability of point-like source observation with theTibet-III array. These systematic errors are adequately taken into account inour study of the Crab Nebula.

Multi-Tev Gamma-Ray Observation from the Crab Nebula Using the Tibet-III Air Shower Array Finely Tuned by the Cosmic-Ray Moon's Shadow