310
XIX
ADIABATIC CHANGES IN MOIST AIR
assumed that the temperature of the atmosphere is everywhere
the same as that of the mass of air ascending through it. We
may considerably reduce the error due to this cause with a
very small amount of calculation. Thus we found the point
of incipient condensation to occur at a pressure 640 mm. This
corresponds to the height 1270 m. only when the temperature
is 0°.
In our case it lay between 27° and 13°, so that the
mean was about 20°. At this temperature the height is
greater by or 4 than at 0°, since the density of the air
is less by the same fraction; hence in reality the height lies
between 1350 and 1400 m.
We must now complete the example by mentioning some
special cases—
1. We assumed that during the hail stage the whole of
the original quantity of water, 11 grammes, was still contained
in the air. Now this is only true when the ascent is very
rapid; in other cases the greater part of the condensed water
will probably have been deposited as rain, and thus only a
fraction will become frozen. If we can form an estimate as
to the size of this fraction, the diagram still permits of a
determination of the correct amounts. If in our example we
had reason to suppose that one-half of the water condensed
down to 0° had been removed, then on reaching the isothermal
0° there would have been present only 8.5 grammes of water
in each kilogramme of air. Then, in using the supplementary
diagram we would have gone not as far as the horizontal line
11, but only down to the line 85; and would have left the
temperature 0° at the pressure 466 mm. This would have
been the only alteration.
2. If we had in our example assumed only 10 per cent
relative humidity in place of 50 per cent, we could have used
the line a down to the dotted line 2.2. This point of inter-
section occurs at 455 mm. and -13°6, i.e. far below zero. We
should never have had any liquid water formed at all; thus
no hail stage would have occurred, but merely a sublimation
of the water from the gaseous to the solid state. From the
point of intersection with the line 2-2 we should at once have
followed the line of the system y passing through this point.
It is of some interest to inquire how high the dew-point of
our mixture may be in its initial state of pressure and