30 Mr. E. Gold : Relation between Periodic Variations of 



The terms in cos at, sin at do not affect the diurnal and 

 semi-diurnal oscillations except in the neighbourhood of 

 lat. 30° and the poles, where a = n and 2n respectively. 

 The effect of the Earth's rotation on air moving in latitude <f> 

 is to produce a periodic variation of period 2ir/a. Near 

 lat. 30° and at the poles the values of the period are 24 and 

 12 hours respectively, so that in these cases the effect of a 

 force having a diurnal or semi-diurnal period would be 

 unusually exaggerated. Neglecting these terms and sub- 

 stituting for Ej, E 2 the values taken above, we get 



u= - 14 sin <ft ^4^ S 2 2 |sin (nt+Xj-ll-S (2 + 3 cos 2 <£) sin (2nt 4-2\ 2 ), 



r- 



56 sin <b cos <f> 

 1— 4cos 2 <£ 



cos (nt + X^ + 57*5 cos 9 cos (2nt + 2X 2 )> 



The Earth's rotation produces no effect, therefore, on the 

 phases of the semi-diurnal components, but it increases the 

 amplitudes. Thus in spite of the decrease in the amplitude 

 of the semi-diurnal pressure variation as latitude increases, 

 the resulting variation in wind velocity increases. North 

 of lat. 42° the amplitude of v is slightly greater than 

 that of u f or the semi-diurnal component. For the diurnal 

 component the amplitude of u is always greater than that 

 of v. 



The infinite values for u and v at latitude 30° are of course 

 impossible in the actual case. They indicate either that the 

 form we have chosen for E : is inadmissible, or that the 

 neglect of the vertical motion and of friction is no longer 

 permissible. 



Margules determined the form of Ej so that the motion 

 remained finite near latitude 30°, but his value gives too 

 large values to E x in higher latitudes; his values for latitude 

 45° are more than double the equatorial values. A simple 

 form for E x which makes u, v finite for lat. 30° is 

 d (sin <f> — | sin 3 </>). It is clear that whatever form we 

 determine for E x to satisfy this condition must be such that 

 E x diminishes with the latitude in the neighbourhood of 

 lat. 30°, and E must therefore have its maximum value N. 

 of lat. 30° N. This does not agree with observation, and it 

 follows that the vertical motion or friction, or both, cannot 

 be neglected in the neighbourhood of lat. 30°. 



