The average quantity of heat received by the arctic regions as a whole per unit surface to that received at the equator, as we have already seen, is as 5·45 to 12, assuming that the percentage of rays cut off by the atmosphere is the same at both places. In this case the mean annual temperature of the arctic regions, taken as a whole, would be about −69°, did those regions depend entirely for their temperature upon the heat received directly from the sun. But the temperature would not even reach to this; for the percentage of rays cut off by the atmosphere in arctic regions is generally believed to be greater than at the equator, and consequently the actual mean quantity of heat received by the arctic regions will be less than 5·45−12ths of what is received at the equator. In the article on Climate in the “Encyclopædia Britannica” there is a Table calculated upon the principle that the quantity of heat cut off is proportionate to the number of aërial particles which the rays have to encounter before reaching the surface of the earth—that, as a general rule, if the tracts of the rays follow an arithmetical progression, the diminished force with which the rays reach the ground will form a decreasing geometrical progression. According to this Table about 75 per cent. of the sun’s rays are cut off by the atmosphere in arctic regions. If 75 per cent. of the rays were cut off by the atmosphere in arctic regions, then the direct rays of the sun could not maintain a mean temperature 100° above that of space. But this is no doubt much too high a percentage for the quantity of heat cut off; for recent discoveries in regard to the absorption of radiant heat by gases and vapours prove that Tables computed on this principle must be incorrect. The researches of Tyndall and Melloni show that when rays pass through any substance, the absorption is rapid at first: but the rays are soon “sifted,” as it is called, and they then pass onwards with but little further obstruction. Still, however, owing to the dense fogs which prevail in arctic regions, the quantity of heat cut off must be considerable. If as much as 50 per cent. of the sun’s rays are cut off by the atmosphere in arctic regions, the amount of heat received directly from the sun would not be sufficient to maintain a mean annual temperature of −100°. Consequently the arctic regions must depend to an enormous extent upon ocean-currents for their temperature. _Influence of Ocean-currents shown by another Method._—That the temperature of the arctic regions would sink enormously, and the temperature of the equator rise enormously, were all ocean-currents stopped, can be shown by another method—viz., by taking the mean annual temperature from the equator to the pole along a meridian passing through the ocean, say, the Atlantic, and comparing it with the mean annual temperature taken along a meridian passing through a great continent, say, the Asiatic.