210 THE MECHANICS OF THE EAltTH's ATMOSPHERE. 



that special Gamma line tbat can be drawn through the point 4G3 

 millimetres on the isotherm 0° C. The temperature— 20 down to which 

 our table can be used is attained at the altitude 7,200 metres, and at 

 the pressure 305 millimetres, at which only two grams of water per kilo- 

 gram remain as vapor, the other nine having been condensed. If it 

 interests us to know how the density in this condition is related to the 

 density in the initial condition, we draw through the corresponding 

 points two lines parallel to the Delta line. These intersect the isotherm 

 of 0° C. at the pressures 330 and G80 millimetres. The densities are to 

 each other as these pressures, namely, as 33 to 68; and as 33 and US are 

 to 76, so they are related to the density of the air in its normal condition 

 of 0° C. temperature and 760 millimetre pressure. 



All these items are directly read off from the diagram. Errors that 

 could be injurious certainly occur only in the altitudes. These latter 

 refer strictly speaking to ascent in an atmosphere of a uniform temper- 

 ature of 0° C. But it would have been generally better to have as- 

 sumed that the temperature of the atmosphere is everywhere the same 

 as that of the ascending mass of air. The resulting error can be ma- 

 terially reduced by a very little computation. Thus we found that 

 the point where condensation began, is at the pressure 640 millimetres. 

 To this corresponds an altitude of 1,270 millimetres, provided that the 

 temperature is 0°, but in our case this is between 27° and 13°, there- 

 fore on the average about 20°. For this temperature the altitude must 

 be about - 2 a T % or -^ greater, since the density of the air is by this same 

 fraction smaller than for 0°. Therefore the altitude really lies between 

 1,350 and 1,400 millimetres. 



We must still supplement the above example by the mention of 

 special cases : 



(1) We assumed in the above that during the hail-stadium the total 

 quantity of water originally present in the air, namely, 11 grams, was 

 still contained therein. This will certainly only be an appropriate as- 

 sumption in the case of very rapid ascents. In other cases perhaps the 

 greater part of the condensed water falls as rain, and therefore only a 

 fraction of it remains to be frozen. If one has any estimate as to how 

 great this fractional part is, then the diagram will always allow us to 

 ascertain the correct conditions. Thus if in our example one had reason 

 to assume that half of the water condensed at 0° were removed, then 

 on attaining the isotherm of 0° only 8.5 grams of water per kilogram 

 of air would be present. We should then in using the auxiliary table 

 not descend to the horizontal 11, but only to the horizontal 8.5, and 

 should have started from the temperature line of 0° at the point corre- 

 sponding to the pressure 466 millimetres (instead of 4G3 millimetres) ; 

 this would have been the only difference. 



(2) If we had assumed not 50 per cent, but 10 per cent, relative hu- 

 midity in our example we should then have been able to use the Al- 

 pha line only to the dotted line 2.2. This point of intersection occurs 



