Methane mixing ratios in trapped air in the Dye 3 Greenland ice core decrease from 1.25 ppmv below the firn-ice transition (~90 years B.P.) to a baseline value of 0.70 ppmv at a depth of ~250 m (~500 years B.P.). Below this level to a depth of 1950 m (~27,000 years B.P.) the mixing ratio appears to be constant at the base-line level, an in agreement with data of Robbins et al. (1973) on 700--2470 year-old Antarctic ice. The uniformity of these CH4 mixing ratios in both hemispheric ice caps and over some 26 millennia indicates that, whether or not the absolute values correctly reflect the true atmospheric mixing ratios vs. time, the atmospheric CH4 mixing ratios were nevertheless essentially constant over this range of time. Above 250 m depth the trapped-air CH4 mixing ratios increase linearly up to ~100 m depth, and then increase sharply just below the firn-ice transition. The mixing ratio vs. age trajectory is strongly offset from the estimated atmospheric record of the past 15 years, but when corrected for the ~90 year difference in age of air and ice at firn closure, the ice-core data track quite precisely into the recent atmospheric record. Thus we believe that these data correctly reflect past CH4 atmospheric mixing ratios. The increase in atmospheric methane concentration begins at ~1580 A.D. and amounts to ~0.40 ppmv by 1918, and ~0.90 ppmv by 1980; the equilibrium greenhouse warming associated with this increased CH4 concentration is about 0.23 ¿C over the past 400 years, and at the current rate of increase the warming due to CH4 is about 38% of the CO2 warming effect.