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



where 



_ -ifoX. + ftY.) 



tan vn- a3 ( a Y 2 _2nX 2 ) + /3 2 (aX 2 -2nY 2 ) 



tan ^- a2 (2«Y 2 -aX 2 )+/3 2 (2 rt X 2 -aY 2 )' 



and the values of ^r 1? -^r 2 are chosen in the same manner as 

 those of U 2 - 



The effect of friction is, therefore, to change both the 

 phase and the amplitude of the motion. The amplitude is 

 always diminished if «j, /3 1? a 2 , /3 2 are positive, i. e. if the 

 amplitudes of the variations of pressure always increase 

 towards the equator. Trabert * treated l/n as a small quantity 

 and obtained approximate results for u, v according to 

 which the amplitude is always increased by friction of this 

 type. 



At the equator v = 0. The amplitude of the diurnal term 



/ Z 2 \» 

 u x is diminished in the ratio 1 : I 1 H — % I owing to the 



friction, and the phase is increased by tan -1 -. The ampli- 



(k 2 \l 

 1+ a-~2), and the 



phase increased by tan -1 ~ . 



At lat. 30° the diurnal terms no longer become infinite. 

 The denominator X x 2 - Y x 2 is always a real positive quantity 

 for all latitudes. For the form of E x chosen abovca 



«!=^-Csin(£, /3i = -n- C sin <f) cos </>, 



so that we may write 



w= sr Csm ^ > |_ — — x*-y 2 — J sm ( ni+ ^i + ^i)» 



v ~ ~R m ^ C0S ^ 1_ X 2 — Y 2 J C0S ^ x 2 ^' 



_ -?(X 1 + 2Y 1 cosc/)) 



_ ;(2X 1 cos0 + Y 1 ) 

 tan ^ 2 ~ nYiCl-4 cos 2 tf>)' 



* ifcfe^. Ze#. 1903, pp. 554, 555, note. The error appears to arise 

 through the omission of the term 2lio sin (j)W in the equation for S. 



