U=-a 



128 Convection Currents in the Atmosphere. 



Case 2. Small island. X large compared with v and 



(cy/k)K 



L - 7^(& - y ) + ^ (18) 



~ = - {(3 + H ^-+ (?*- MHi J o(^>^ 



. . . (19) 



. . . (20) 

 V = (66-^ + ^- A *)Jo(Xr)^ (21) 



It is no longer true that p' —ga ; in other words, in 

 problems dealing with small islands the neglect of the 

 vertical velocity is not justifiable. The largest term in 

 p' is —2p ct(g/X)be~ A2 J (\r)e l y t . Thus, the maximum pressure 

 coincides with the minimum temperature. 



Summary. 



1. In land-masses of continental dimensions the customary 

 neglect of the velocity in the equation of vertical motion is 

 justifiable for harmonic disturbances with a period of a year. 

 If the diameter of an island be between about 10 km. and 

 1000 km. the same will hold good for a daily period. In 

 such a case, all heating being supposed done by eddy 

 currents, the pressure would reach its maximum an eighth 

 of a period after the temperature maximum, and the maxi- 

 mum outward wind-velocity at a small height would occur a 

 quarter of a period after the temperature minimum. In the 

 case of an annual period an amplitude of 1° C. in the tempe- 

 rature variation would give rise to one of about 0'42 mm. in 

 the pressure variation ; this agrees with the facts of obser- 

 vation within the limits of variation of the eddy viscosity. 



2. Daily motion cannot penetrate far into the interior of a 

 large continent. 



3. In the case of a small island it is no longer justifiable 

 to neglect the vertical velocity. When it is very small the 

 pressure maximum and the maximum outward velocity occur 

 at the same time as the temperature minimum when the heat 

 is supposed supplied from the earth's surface. In order that 

 this may hold it is, however, necessary that the island should 

 not be more than 0*1 km. in diameter for a daily period, and 

 2 km. for an annual one. 



