METEOROLOGY 13 



placed in a different category without reference to the possibiHty 

 that they may be the result of physical causes similar to those 

 responsible for sea-breezes. Sir Napier Shaw has, however, 

 attempted, in recent years, a more scientific classification, and 

 the present paper may be regarded as an extension of this 

 attempt. 



Dr. Jeffreys considers from first principles the motion of 

 air upon the rotating earth, and points out that two accelera- 

 tions and three forces have to be considered.^ The accelera- 

 tions are ; 



(i) The acceleration due to rotation of the Earth, whereby 

 air that has a velocity which is constant relative to the Earth 

 has acceleration relative to a non-rotating body. 



(2) Acceleration relative to the Earth's surface. 



These two accelerations are balanced by the forces of gravity, 

 hydrostatic pressure and friction. 



The equations of motion under these conditions are given in 

 Lamb's Hydrodynamics. After making certain simplifying 

 assumptions which can cause only errors of too small a mag- 

 nitude to matter in this enquiry, Jeffreys arrives at the follow- 

 ing equations, which are in a form suitable for the work in 

 hand : 



du ^ I hp , r^h^u 



-jr - 2 CD V cos 0= o ^ + -^T-T 



dt p R cd 02^ 



dv , a , . ^ I 8p , 8'^v 



-r. + 2 CO u cos o + 2 (o w sin (j = — ft + ^ er^ 

 dt pGi 0(f) cz^ 



dw . /I I Bp 



-y- — 2 (o V sm o = -^ — g 



dt p oz 



where w «= the angular velocity of rotation of the earth. 



d) -= the distance from the polar axis of the point ver- 

 tically below any point p. 



z «= the altitude of p. 



R -= the radius of curvature of the level surface at the 

 point vertically below _^. 



6 — the angle between the normal at p and the polar 

 axis. 



^ = the longitude of p. 



u, V and w are the component velocities of p in the 

 directions of 6, <j>, and z increasing. 



p =- the density of the air. 



p •= the hydrostatic pressure. 



K = coefficient of eddy viscosity. 



t is the time. 



1 The hydro-dynamics of this subject has, of course, received much atten- 

 tion in the past, but advances have been made in recent years in our know- 

 ledge of atmospheric friction. 



