Elements

The Variation of Pressure with Height.—The variation of pres sure in the vertical is given by = —gp. This equation is readily derived by the consideration of the vertical forces acting on a cube, two of whose faces are horizontal. It may be written in the form These equations form the basis of barometric altimetry.

The Reduction of Pressure to Mean Sea Level.

When the pressure is measured at a station z metres above mean sea level, it is reduced to mean sea level by the addition of an amount equivalent to the weight of a column of air extending from the level of observation down to mean sea level; it being assumed that the mean vapour pressure through this column is equal to the vapour pressure at the point of observation, and that the mean temperature can be computed from the temperature at the level of observation, together with a lapse rate of o.5° C per ioo metres. Moreover it is found that if the height of the sta tion does not exceed 5oo metres results well within the as signed limit of accuracy are obtained when we ignore the humid ity of the air, and the variations of gravity with latitude and height, and adopt the dry bulb reading at the time of observation as the mean temperature of the column. For fuller details of these methods see Computer's Handbook, Section I.

Adiabatic Changes in Ascending or Descending Dry Air.—Let the state of the atmosphere be specified by the vari ables p, p, T, at height z, and let p', p', T' denote the state of any displaced mass when it is at height z. The accented letters will therefore refer to air which has been displaced from its normal environment. We denote specific heat of air at constant volume by and at constant pressure by cp. Let v'= I, = specific volume of the moving air. In moving from height z to height z-}-dz, the loss of heat is equal to the work done by the moving mass in expanding against the action of the pressure due to the environment : Adiabatic Changes in Moist but Unsaturated Air.—The argu ment used above is applicable to moist unsaturated air, pro vided we give to R and the appropriate values. The adiabatic lapse rate is given by g- where c'p is now interpreted as the spe c; cific heat of the mixture of air and water vapour; but since the water vapour only accounts for a small fraction of the constitu tion of normal air, c'p cannot differ by an appreciable amount from cp, and the lapse rate for unsaturated air is only slightly less than that of dry air.

Adiabatic Changes in Saturated Air.

When saturated air rises through its environment the cooling produced by expansion causes condensation, and the latent heat so liberated becomes available for maintaining the temperature of the air. Let the air be composed of x kg. of water vapour to i kg. of dry air. When (z +x)kg. of the mixture rises from a height z to height z+dz, a quantity dx of water vapour condenses, and an amount rdx of latent heat is liberated, and used in heating the mixture and the resulting water-drops. It will be assumed that the heat ing of the water-drops may be neglected. In practice most of the condensed water is eliminated, and the neglect of the heating of water-drops is in any case justified.

Near the ground has the value of o.56° C per ioo metres. dz The saturated adiabatic lapse rate increases slowly with height, and at very low temperatures at which x has become very small, it approaches asymptotically the value of the dry adiabatic lapse rate.

The values of the adiabatic lapse rate for saturated and un saturated air are of fundamental importance in meteorology. The mean lapse rate observed in the atmosphere is slightly greater than the saturated lapse rate, indicating stability for dry air, but instability for saturated air. In these conditions any mass of saturated air which rises becomes increasingly warmer than its environment at the successive levels which it attains.

Further, saturated air which is caused to descend immediately ceases to be saturated, and its temperature rises at the unsatu rated or dry adiabatic lapse rate. Thus damp winds which rise over mountain ranges descend on the other side as very warm dry winds (fohn winds). The physical process involved in the con sideration of the saturated adiabatic lapse rate is not in reality an adiabatic process, since, as we have seen, it is not reversible. For this reason it is frequently referred to as a pseudo-adiabatic process.