116 Mr. H. Jeffreys on Periodic 



It', then, the suffix refer to the land, 1 to the ocean, and 

 2 to the atmosphere, we have 



^X? _& v 2 V = with Y = ^> on the boundary, . . (4) 

 ^Xl — ^V^^O with Yj = 0> on the boundary, . . (5) 



ot 



^ _/c 2 V 2 V 2 -:P^-^ + (Q + X^)6-^ with V 2 = <l> 

 " on the lower boundary. (6) 



Further, [K 2 ^- s -K„^°] = -F overland, . (7) 



Tk^-K^^-F oversea. . (8) 



But if the amount of heat crossing unit area at fhe upper 

 limit of the atmosphere per unit time be H, we have 



H-I + „(S + S±»). .... m 



and H is independent of the position on the earth, 

 involving only the time, 

 a is the specific heat, and p the density of the air. 



The Effect of the Distribution of Land and Sea. 



We need to consider the effect of the unequal heating of the 

 atmosphere over land and sea on the motion of the air. For 

 this purpose we consider the surface to be divided up into an 

 infinite series of strips, parallel to the axis of ?/, and each of 

 width I. Alternate strips are respectively land and water. 

 Those from x = 2nl to (2n + l)l are taken to be land, and 

 from x—(2n — 1)1 to 2nl to be sea, where n is any integer, 

 positive or negative. From the symmetry of the system we 

 see that scalar quantities like pressure and temperature can 

 be expanded in a Fourier series of sines and cosines of 

 multiples of irxjl. Further, as the system is symmetrical 

 about the plane a?=^l, we see that we can only have sines of 

 odd multiples and cosines of even multiples of irx\l. 



We are considering only one period at a time, and there- 

 fore assume that every variable term is proportional to 

 exp L<yt, where 7 is a real constant. 



At a point sufficiently far from the coast the temperature 



