Convection Currents in the Atmosphere. 119 



II. The Periodic Motion of the Atmosphere. 



The equations of motion of the atmosphere are assumed 

 to be 



Dt p 0% o ox 



whe 



Dv v 1 op ,j ^ . 1 7 o$ 



Dt poy o oy 



Bw 1 Bp . , n , . 1 7 o$ 



vt poz 3 c^' j 



(1) 



re 



, ^ <^ ch/- . 



6 "a* + By + 3*' (2) 



and & is the kinematic coefficient of pseudo-viscosity. It has 

 been shown by G. I. Taylor to be equal to the ratio of eddy 

 conductivity to heat capacity per unit volume in the case of 

 an eddying fluid with no vertical motion apart from eddy 

 motion. 1 assume this to be the case in general. The true 

 kinematic viscosity is not equal to the quantity that Fourier 

 denotes by K/CD, or the ratio of true conductivity to heat 

 capacity per unit volume ■ the latter is indeed / times the 

 former on the kinetic theory of gases, where / is about 2*5. 

 Both are, however, very small in comparison with the 

 eddy viscosity. For instance, Taylor gives * for his z*/4:t 7 

 which is my k, values ranging from 0*57 x 10 3 to 3*4 x 10 3 , 

 whereas the true kinematic viscosity for air is 0*017 at 0° C. 

 The eddies therefore produce overwhelmingly the greater 

 part of both the effective conductivity and the effective 

 viscosity, and we are justified in putting k in the terms 

 depending on both of these in the equations. 

 The equation of continuity is 



'—J-& (*> 



But, by Charles's law, 



p = p a /(l + aV), (4) 



where p Q is the undisturbed density and a. the coefficient of 

 expansion. 



Then neglecting V 2 , we have 



*='■& (5> 



* Phil. Trans, vol. ccxv. A. p. 10 (1915). 



