New measurements at a centre-of-mass energy √s ≃183 GeV of the hadronic photon structure function Fγ2(x) in the Q2 interval, 9 GeV2 ≤ Q2 ≤ 30 GeV2 , are presented. The data, collected in 1997 with the L3 detector, correspond to an integrated luminosity of 51.9 pb-1 . Combining with the data taken at a centre-of-mass energy of 91 GeV, the evolution of Fγ2 with Q2 is measured in the Q2 range from 1.2 GeV2 to 30 GeV2. Fγ2 shows a linear growth with lnQ2; the value of the slope α−1dFγ2(Q2)/dlnQ2 is measured in two x bins from 0.01 to 0.2 and is somewhat higher than predicted.