Assuming that the atmosphere at the surface of Mars consists of ⅕ oxygen and ⅘ other gases, as nitrogen, etc., the composition of the atmosphere to great heights is calculated, just as was done for the earth, from the actions of gas diffusion and gravity. The electron density in the atmosphere of Mars due to the ultraviolet light of the sun is found to have a maximum value of 1.1 ×105at a height of 440 km above the surface on a summer day, and 0.55×105at 310 km on a winter day: On a summer day the skip distances for 100, 80, 60 and 50-meter waves are 0, 730, 1410 and 2240 km, respectively, and the shortest wave for reliable long distance wireless communication over the surface of Mars is about 47 meters. Winter and night values of these quantities are greater. Because of the skip distances for waves below 100 meters, it would seem that conditions on Mars are not very advantageous for short-wave communication, and it may be conjectured that no wireless apparatus exists there for waves below 100 meters. Waves longer than about 100 meters will not pierce through the atmosphere of the earth. These calculations, apart from other considerations, support the conclusion that only a very optimistic experimenter would look for successful wireless communication between the earth and Mars.