12 PHYSICS OF THE AIR
pressure merely requires measuring the loss of pressure due to absorption of the vapor in a closed space, for which there are several devices;1 or, as more commonly practiced, finding the dew point and referring it to a table of predetermined saturation pressures. Similarly, the difference between the current and dew-point temperatures is sufficient to determine, from suitable tables, the relative humidity.
The dew point may be found by any one of several slightly different methods, all of which have for their basis the determination of that temperature at which moisture just begins to collect on a cooling surface. A thin-walled silver tube, burnished on the outside, is an excellent vessel for the cooling mixture. The temperature of the liquid, if well stirred, and that of such a tube will be very nearly the same; and, besides, the dulling of the surface promptly reveals the slightest condensation.
It "should be noted, however, that if carefully taken the observed temperatures of the silver hygrometer will be slightly below the actual "dew point." This is because the initial deposit is in the form of minute droplets, whose vapor pressure is greater than that of a flat surface at the same temperature, in accordance with the equation,2
A 2Tf>»
R(pw "" Pv)
which may be derived as follows:
Let R be the radius of a capillary tube standing in a vessel of water (Fig. 6); h the height of the water in the tube when saturation is attained and all air removed; T the surface tension; pw the density of the water; pv the average density through h of the saturated vapor; and g the gravity acceleration. Then, obviously,
and
Ap = Pvgh,
being the difference between the vapor pressures at the inner and outer surfaces.
Hence
, Ap 2T , A 2TPv
* - and Ap = ^—^_.
pvg R(pw — Pv)g K R (pv
At ordinary temperatures and for droplets whose radii are 10~4 cm. (a possible size) the temperature depression, or error, amounts roughly to 0.02° C. According to the equation, the error obviously might have any value, though actually it seems always to be small; that is, this, too, like many other physical equations, has its limitations.
ISHAW, A. N., Trans. Roy. Soc. Canada, 10; 85, 1916.
2THOMSON, SIR WILLIAM, Proc. Roy. Soc. Edin., 7, 63, 1870; Phil. Mag. 42; 448, 1871.