Our knowledge of wind eddies in the atmosphere has so far been confined to the observations of meteorologists and aviators. The treatment of eddy motion in either incompressible or compressible fluids by means of mathematics has always been regarded as a problem of great difficulty, but this appears to be because attention has chiefly been directed to the behaviour of eddies considered as individuals rather than to the average effect of a collection of eddies. The difference between these two aspects of the question resembles the difference between the consideration of the action of molecule on molecule in the dynamical theory of gases, and the consideration of the average effect, on the properties of a gas, of the motion of its molecules. It has been known for a long time that the retarding effect of the surface of the earth on the velocity of the wind must be due, in some way, to eddy motion; but apparently no one has investigated the question of whether any known type of eddy motion is capable of producing the distribution of wind velocity which has been observed by meteorologists, and no calculations have been made to find out how much eddy motion is necessary in order to account for this distribution. The present paper deals with the effect of a system of eddies on the velocity of the wind and on the temperature and humidity of the atmosphere. In a future paper the way in which they are produced and their stability when formed will be considered.