204 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



of very various proportions, therefore by this method a great num- 

 ber of tables would be required. But it can now be shown that one 

 can also manage with only one graphic table, if first we confine our- 

 selves to those cases in which the weight and pressure of the aqueous 

 vapor is small in comparison with the weight and pressure of the air, 

 and if secondly we do not require of the results any greater accuracy 

 than corresponds to the neglect of those quantities in comparison with 

 these. If we neglect \x and eas compared respectively with A andj), then 

 the form of the curves to be drawn is the same for all the absolute values 

 of /a, therefore the same curve can be used for all the different mixtures. 

 But the points at which the different stages pass into each other will be 

 located very differently for different mixtures, and special devices will 

 therefore be needed by meaus of which this point may be determined. 

 The graphic table, Fig. 28, is therefore constructed in accordance with 

 the following principles. 



The pressures are laid off as abscissas on the adopted scale for the 

 interval between 300 millimetres to 800 millimeters of the barometer ; 

 the temperatures are laid off as ordinates for the interval between —20° 

 Cels. and +30° Cels. But as we see by the diagram, a uniform increase 

 in the length of either of these coordinates does not indicate an equal in- 

 crease of pressure or of temperature; on the contrary the diagram is so 

 constructed that an equal increase of distance corresponds to an equal 

 increase in the logarithm of the pressure and in the logarithm of the ab- 

 solute temperature. The advantage of this arrangement consists in the 

 fact that thus the curves with which we have to do become, some of 

 them exact, and some of them approximate straight lines, which brings 

 an important advantage in the accurate construction and use of the 

 table. 



Now the adiabatics of the first stage (if we neglect /* with respect to A) 

 are given by the equation 



c p log T—AR log p — constant (a) 



In this diagram the logarithms are always those of the natural sys- 

 tem. With Clausius we put 



Calorie 

 c p =0.2375 Cels# degree x kilogr. 



1 Calorie 



#=29.27 



423.55 Kilogram metre 



Kilogrammetre 



Cels. degree x kilogr. 



These adiabatics appear in our diagram as straight lines. One of 

 them is distinguished by the letter alpha (a) and the whole of this system 

 may be called by this letter. The individual lines are so drawn that 



