18G THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



According to this solution the following gives a picture of the at- 

 mospheric circulation, which in its principal points agrees with that of 

 W. Siemens. 



(1) Currents on a spheroid without rotation. 



These currents consist of currents in the meridian, and of vertical 



movements. 



(a) The meridional current in the northern hemisphere is southerly 

 below, but northerly above, since the function cp changes its sign when 

 a increases from zero to h. It attains its largest value at 45°, and dis- 

 appears at the equator and at the poles. 



(b) The vertical circulation is zero at the earth's surface and at the 

 upper limit of the atmosphere. From the equator to 35° W north and 

 south latitudes the flow of air is positive— that is to say, ascending— 

 but in higher latitudes it is descending. Its velocity at the poles is 

 twice as great as that at the equator. 



By the comparison of the expressions for/ {a) and cp {a), it appears 

 that the former function contains the fourth powers of the small quan- 

 tities h and a\ the latter function contains their third powers. There- 

 fore, the vertical flow is to the horizontal flow, so far as magnitude is 

 concerned, as h is to 1, or as the altitude of the earth's atmosphere is 

 to the radius of the earth. From this we can scarcely assume that we 

 should be successful in the direct observation of the vertical current. 

 The great effect of the vertical current arises from this, that it rises or 

 sinks over a very extensive area. 



(2) Currents in consequence of the rotation of the earth. 



Under the assumption here made as to the distribution of tempera- 

 ture on the earth's surface, these currents consist exclusively of move- 

 ments along the parallel circles of latitude. As in the case of the two 

 terms in the component 0, so here we distinguish the two following. 



(a) The movement depending on the function g (a - ). Since this func- 

 tion is invariably negative ; therefore to begin with at the equator the 

 motion is directed toward the west. It changes its signjit latitude 35° 

 16', and then becomes a motion directed toward the east. 



(b) The second current is zero at the equator; becomes a maximum 

 at 51° 44', and is exclusively directed toward the east. Both currents 

 disappear at the poles. 



The two motions («) and (b) differ from each other fundamentally in 

 that ;' (cs) differs from zero first when a has larger values. It is there- 

 fore a current that only occurs in the higher strata of the atmosphere. 

 But thereby the function g is of a higher order than y for the small 

 quantities h and o. Therefore at great altitudes the current (b) must 

 greatly exceed the current (a) in velocity. 



The components 1« and 2a combine at the earth's surface to form the 

 regular movement of the air that we designate as the lower trade wind. 



