PAPER BY DR. HERTZ. 207 



These can also be read off graphically if the diagram is covered with 

 another systim of lines of equal density. We see that these Hues will 

 constitute a system of parallel degrees of density. 



Only one of these lines is in reality drawn on the accompanying 

 diagram, namely, the line marked S (delta), in order not to confuse the 

 diagram. But with the assistance of this one we can also compare the 

 densities in any two conditions d and 2 , according to the following 

 rule: From the points 1 and 2, representing these conditions on the 

 diagram, draw two straight lines, respectively, parallel to 3, until they 

 intersect the isotherm 0° C, and read off the pressures pi and ^ 2 for 

 these points of intersection. The densities for the conditions Ci and G 2 

 are in the ratio of the pressures p x : p 2 ; as is seen from the considera- 

 tions that the densities for the condition (p u 0°), and. for (p 2 , 0°) are ac- 

 cording to Mariotte's law in the ratio of p x to p 2 , and are equal to the 

 densities for the conditions C, and C 2 since they lie on the same line of 

 equal density with these. 



(3.) The difference of altitude h that corresponds under the assump- 

 tion of adiabatic equilibrium to the passage from the condition p to the 

 condition p is given by the equation 



dp. 



Up up 1 



In using this equation we take T as a function of p from the diagram 

 and then perform the integration mechanically. Actually however 

 the assumption of adiabatic equilibrum is always so imperfectly ful- 

 filled that it is not worth while to trouble about an exact development 

 of its consequences. On the other hand, for moderate altitudes, we 

 commit a relatively very unimportant error when we give T an average 

 value, and consequently consider it as constant. Within the limits of 

 the diagram T ranges only between the values 253 and 303; if there- 

 fore we give it the constant value T = 273, then the error in h will 

 scarcely exceed one-ninth of the whole value. If we are satisfied with 

 this error, then we have 



h = constant— B T log p, 



and we now can, along with the pressure, directly introduce the altitude 

 as abscissa. Consequently an equal increase in the length of the 

 abscissa will everywhere correspond to an equal increase in altitude. 

 The scale of altitudes is introduced at the base of the diagram. Its zoro 

 point is put at the pressure 760, because this is usually taken as the 

 normal pressure at sea-level. 



in. 



In order to illustrate the use of the table by an example, we propose 

 to ourselves the following concrete problem : Given a mass of air at sea- 

 level under the pressure of 750 milimetres, the temperature 27 degrees 



