Using the strain seismograms of the New Guinea earthquake of 1938 and the Kamchatka earthquake of 1952, the decrement of the G wave in the mantle of the earth was determined from the comparison of the amplitude of Fourier components, which are obtained by analyzing the G phases at different epicentral distances. The value of 1/Q thus obtained is a little larger than that given by M. Ewing and F. Press using mantle Rayleigh waves, but is not much different. The phase velocity was also calculated using the argument of the Fourier transform. The dispersion curves obtained from (G1 and G3), (G2 and G4) of the New Guinea earthquake and (G1 and G3) of the Kamchatka earthquake agree quite well, giving a nearly constant group velocity 4.4 km/sec. as was anticipated. Theoretical consideration of the distribution of shear velocity that serves as the wave channel for the guidance of the G wave was given, and the shear velocity was calculated applying the method of T. Takahashi to the dispersion curve derived from the condition of constant group velocity, which is a direct consequence of the fact that the G wave shows almost no dispersion. The Vs(z)/V0 curve which was derived theoretically agrees well with the curve given by the distribution of shear velocity of Jeffreys-Bullen in the range between one and several hundred kilometers.