We present theoretical calculations to explain the atmospheric gamma ray north-south ratios measured by us and other observers. The north-south effects is caused by the higher cosmic ray flux that strikes the Earth's atmosphere near the poles than near the equator. Primary and secondary cosmic ray integral energy distributions that vary as E-1.65 produce the gamma rays of 1--20 MeV of interest here. Gamma rays from distances north and south of the observer Compton scatter from the atmospheric nitrogen and oxygen into gamma ray telescopes flown on balloons at typical heights of 4 g/cm2 residual atmosphere. The gamma rays that originate at the longest distances from the telescopes give the largest north-south ratios. The north-south ratios, between zenith angles of 15¿ and 60¿, are greatest for the largest zenith angles and between 1.5 and 20 MeV for the largest gamma ray energies. Comparisons are made to experimental north-south ratios measured on balloons launched from Palestine, Texas, and from Alice Springs, Australia. Predictions are made for ratios at other geomagnetic latitudes and longitudes. Observers who measure backgrounds for celestial sources 180¿ in azimuthal angle from the source direction may be misled unless they correct for the north-south effect. Since neutrons of a few MeV are produced by cosmic ray collisions in the atmosphere in comparable numbers to gamma rays and their scatter path lengths are similar, we expect a neutron north-south effect comparable to that for gamma rays. ¿ American Geophysical Union 1988