A similar but direct ratio exists between the mean velocities and the diameters of the tubes, thus: _u_ : U :: √_d_ : √D This relation, however, is only approximately true for tubes differing greatly in diameter. The relation of the pressure to other factors is not so simply expressed. For example, in two tubes of the same length and diameter, the relation between the pressures at the ends and the mean velocity of the air may be expressed as follows: (_pₒ_² - _p₁_²)^³/² (Pₒ² - P₁²)^³/² _u_ : U :: ————————————— : ————————— (_pₒ_³ - _p₁_³) (Pₒ³ - P₁³) where _u_ and U are the respective mean velocities, _p__{0} and P_{0} the respective pressures at the initial ends of the tubes, and _p__{1} and P_{1} the respective pressures at the final ends of the tubes,—the pressures being measured above absolute zero. There are other relations that can be similarly expressed, but for them we must refer the reader to a mathematical treatise on the subject. =Moisture in the Tubes.=—When pressures of more than five pounds per square inch are used, it is not unusual to find some moisture on the interior of the tube and upon the outside of the carriers when they come out of the tube. It is seldom more than a slight dampness, or at most a degree of wetness equal to that seen on the outside of a pitcher of ice-water on a warm day. A slight amount of moisture in the tube is not objectionable, for it serves as a lubricant to the carriers; but when it is present in considerable quantity it becomes objectionable and even annoying. This moisture is brought into the tube with the air, and is deposited upon the walls of the tube when their temperature is sufficiently below that of the atmosphere. The atmosphere always contains more or less moisture in the state of vapor. The capacity of air for water-vapor depends upon its temperature, being greater the higher the temperature, but it is a fixed and definite quantity at any given temperature. When the air contains all the water-vapor it can hold at a certain temperature, it is said to be saturated. If it is not saturated, we express the amount that it contains in per cent. of the amount it would contain if it were saturated, and this is termed the “relative humidity.” For example, if the air is three-fourths saturated, we say the “relative humidity” is seventy-five; but if the temperature changes, the “relative humidity” changes also. Suppose the temperature to-day is seventy-five degrees Fahrenheit, and that the “relative humidity” is eighty, a cubic foot of air then contains 0.00107 pound of water-vapor. Now suppose this air enters a pneumatic tube and is cooled by expansion and contact with the colder walls of the tube to sixty degrees. At this temperature a cubic foot of air can contain only 0.00082 pound of water-vapor when it is saturated. Now, each cubic foot of air brought into the tube brings with it 0.00107