PAPER BY DR. HERTZ. 209 



temperature 13.3. The altitude at which we now find ourselves corre- 

 si)onds to the lower limit of the formation of clouds, and is about 1,270 

 metres. lu order to follow the conditions further we draw a curve of 

 the Beta {fi) system through the point of intersection. 



This curve is inclined much more slowly toward the axis of abscissas 

 than the Alpha line hitherto used, therefore the temperature now 

 changes with the altitude much more slowly than before, which is due 

 to the evolution of the latent heat of the aqueous vapor. We have now 

 risen 1,000 metres since the commencement of condensation, but the tem- 

 perature has sunk only to 8.2°, or only 0.51 o to each 100 meters. We 

 now iind ourselves on the dotted line 8.9, and perceive that 8 9 grams 

 of water are still in the state of vapor ; that therefore in this first 1,000 

 metres of the cloud layer 2.1 grams of water have been condensed per 

 kilogram of air. We attain the temperature zero degrees C. at the 

 pressure 472 millimetres, and at the altitude 3,750 meters, whereas if 

 the air has been dry, and we had not been obliged to leave the Alpha 

 line, this temperature would have been attained at an altitude of 2,G00 

 metres. It now appears that by this time 4.9 grams of water, or 0.45 per 

 cent, of the total contents, have been condensed, and during further ex- 

 pansion this portion begins to freeze and form hail [the reader will re- 

 call that although 45 per cent, has been condensed into visible cloud, 

 yet it has not separated from its original air and been precipitated as 

 rain, but is still rising with the air and of course cooling- with itj. But 

 the temperature can not sink further until the last particle of water is 

 frozen, and we therefore must retain the temperature d^ uniformly dur- 

 ing a certain distance of further ascent. 



In order to ascertain this distance we make use of the auxiliary 

 diagram between the scale of altitude and the larger diagram, we 

 pass down the isobar 472 millimetres to the dotted line of this diagram; 

 we draw through this intersection a line parallel to the inclined 

 line of the auxiliary table, and go along this line until we reach that 

 horizontal line that is characterized by the number 11, or the total 

 weight of the contained water, and which we easily interpolate between 

 the engraved lines 10 and 15. As soon as we have attained this line 

 we read ofl" the pressure p = 463 millimetres, and turn back to the larger 

 diagram. At the i^ressure thus found the process of freezing is fin- 

 ished, and the layer within which it all takes place has a thickness of 

 about 150 metres. It must surprise one that, according to the dotted 

 line, the quaniitv of water in the form of aqueous vapor has again in- 

 creased a little during the process of freezing. But this is quite cor- 

 rect ; in fact, the volume has increased without lowering the temper- 

 ature. We leave the temperature 0° C. at the pressure 4G3 millimetres. 

 The water which hereafter is precipitated passes directly over into the 

 solid condition. Since there is now but little water as aqueous vapor, 

 therefore the temperature again begins to sink more rapidly with the 

 altitude. We ascertain the different conditions in that we make use of 

 80 A 14 



