﻿relative to a Rotating Earth, 61 



example, we may take the case of a uniform east or west 

 wind over a considerable region. In this case 



u = c, r = 0, w = 0, . . . . (35) 



and the pressure distribution consistent with this motion is 

 represented by 



k log /3 = 2 Or (cos </> z — sin (j>y) — gz + k\ogp , . (36) 



where p Q refers to the density of air at the reference point 0. 

 The isobars at the Earth's surface are in this case a uniform 

 system running due East and West. 

 A similar case is that given by 



u=0, v = cx + d, 20 = 0, . . . (37) 



which represents a wind towards the North, while the corre- 

 sponding pressure distribution is that represented by 



k log p = O sin (/> (ex 2 + 2dx) —gz + h log p . . (38) 



The isobars are again a system of straight lines, but runnino- 

 north and south, and uniformly spaced when c = 0. 

 In a similar manner we find that 



u = c 1 , v = c 2 , iu = 0, . . . . (39) 



corresponds to a system of straight isobars represented by 



k \ogp = 2Q sin cf) {c^x — c^y) + 2Q cos<f> .c^—gz + k log/j . (40) 



The isobars are again lines of flow of the air, as in each case 

 considered above. 



The case of motion corresponding most closely to a 

 cyclonic or anticyclonic circulation is that discussed in an 

 earlier paper *, represented by 



it=—<o(y-(3z); v = co l i-; iv = 0. . . (41) 

 In this case 



Q _ 2fl cos <j) 



^- w + 2min^,' < 42 ) 



and the pressure distribution is that represented by 



^log^ = i(a) 2 4-2a>f2sin</,){.r 2 -r( i/ -/3c) 2 }--^- f ^log /0o . 



. . . (43) 

 The term fr^- must be small in order that the continuity 

 equation may be fulfilled. 



* Phil. Mag. vol. xli. April 1921 ; vol. xlii. July 1921. 



