44. CONSTRUCTION OF ISOBARIC CHARTS 



The dimension of this expression is most readily found when it is written in the fol- 

 lowing form 



846.728 fP« T dp 



£" = 2.4934 X 32.1726 x 



t/ni 



0.080 529 J„ 491.4 p 



In this expression the quantity 2.4934 is the height in feet of the mercurial column 

 for a pressure of one atmosphere, and hence it has the dimension, foot. The number 

 32. 1726 is the acceleration of gravity at sealevel at latitude 45° and has the dimension 



^. The quotient ,^r^rx-i^^,\ is the ratio of the densities of mercury and air and 



second^ ^ 0.080 529 "^ 



has the dimension zero. The two remaining quotients, ,„, , and - are also non- 



^ 491.4 p 



V 4-2 



dimensional. Therefore the dimension of the whole expression is ^r,. In order 



second 



to convert this into :, -, it must be multiplied by 0.464 876. Furthermore — may 



hour- r- ^ p •' 



be replaced by 2.302 59 d (log|j) by introducing Briggsian instead of natural loga- 

 rithms and we then write (17) in the form 



E^:=l 837.3 (< + 459.4)d(logp) (18) 



where t indicates degrees Fahrenheit, but p may be of any system of units since (/(log j;) 

 is non-dimensional. 



By treating equation (16) in a similar way we obtain 



1 r^i dr 



n ^j = p ,,/ 1 - 1 "^^ J ^0 '+«'"). (19) 



Moist air has a somewhat greater specific volume than dry air at the same tem- 

 perature and pressure ; but Ijy appl3'ing an appropriate correction to the temperature, 

 the Mariotte-Gay-Lussac law and formulas (18) and (19) can be made applicable to 

 moist air also. To determine this correction we start with the equation of condition 



for moist air, viz. : 



v{p - 0.377»/) p,v^ 

 T - T, 



where r = relative humidity and /= tension of saturated water-vapor at the tempera- 

 ture T. We have now to apply such a correction to T that the equation may be writ- 

 ten in the Mariotte-Gay-Lussac form and yet give a true value of v. We therefore 

 write 



_ «^ _ '>\ 



P ' rp — Po' f 



