THEORY OF CYCLONES — VON BEZOLD 355 



which equation can be still further simplified in special cases since 

 we can consider <p to be constant and put 



k sin f = K. 



The first fofin of this equation could also have been deduced 

 directly from the fundamental equations of Guldberg and Mohn, 

 giving attention of course to the algebraic signs 12 here adopted. 



The second form is more convenient for application to special 

 cases drawn from the synoptic weather charts especially when in 

 place of tan a we introduce the value 



h dr 

 l° T dh 



For definite values of pressure and temperature the heights h can 

 be taken directly from tables which give the heights of columns of 

 air corresponding to a pressure of i mm , such as Table V of Mohn's 

 "Grundzuge," whilst the distances of the isobars corresponding to 

 differences of pressure of i mm are measured directly on the weather 

 chart. 



Suppose, for instance, we wish to determine the inclinations of 

 the isobaric surfaces for northern England, for points between 

 Shields and Bradford, from the weather chart of October 14, 1881, 

 as published in Sprung's Lehrbuch, Plate VII; we first find for h the 

 value 1 1.4 meters, for the pressure 73o mm and the temperature 

 io° C. then prevailing; for the distance between the isobars 72 5 mm 

 and 7S3 mm we find 180 kilometers and therefore / = 18 kilometers 

 or 18,000 meters for the distance between 729 and 730 or between 

 730 and 73i mm , whence follows 



tg a = UA = tg 0° 1' 36". 

 18000 



This example is interesting in that it shows very clearly how 

 remarkably slight in general is the inclination of the isobaric sur- 

 faces, since even for the great atmospheric disturbances that pre- 

 vailed in that region on that day one must go northward 18 kilo- 

 meters in order to experience a change of pressure equal to that 

 found by rising vertically only 12 meters. 



If now we seek to draw some general conclusions from equa- 

 tion (9) then we perceive, first of all, that it is essential to theexist- 



12 Sprung: Lehrbuch, p. 119, equation (5). 



