TBANSACTIONS OF SECTION A. 619 



6. The Direction of tlie Upper Currents over the Equator in connection ivith 

 the KraJcatoa Smoke-stream. By Professor E. Douglas Akchibald. 



The object of this communication is to show that the results of an examination 

 of the data regarding- the stream of volcanic dust, &c., which issued from Krakatoa 

 on August 26 and 27, 1883, are not at variance with what can be legitimately 

 deduced from the general theory of atmospheric circulation, as well as with what 

 is at present known from observation regarding the gradients and velocity of the air 

 in the neighbourhood of the equator. 



The results of the Krakatoa inquiry necessitate the existence of a constant cur- 

 rent over, and in the neighbourhood of, the equator, at a height of from 80,000 to 

 120,000 feet, and of a velocity of from 75 to 80 miles an hour. 



1. In order to test the probability of this hypothesis reference is made to the 

 general theory and to the equation for the poleward gradient 



Tx = 2VEa) sm (f) + '^ ^ ^ + --J^ + Fn 



as given in Sprung's * Lehrbuch.' 



Where Tn = gradient towards the north. 



£0 = earth's angular velocity of rotation. 



Ve = velocity towards the east. 



Vjj = velocity towards the north. 



(f> = latitude. 



F„ = friction term. 



R = radius of the circle of latitude. 



t = time. 



Now in the neighbourhood of the equator the term 2Veo) sin cj) vanishes, and at 



a great height F^ becomes very small. Also —~, representing a term depending 



on rapid changes of velocity, becomes very small. The air at the higher levels 

 near the equator may thus move from W. to E., or E. to W., with considerable 

 velocity without any sensible gradient. The possibility of its moving rapidly in a 

 meridional direction is omitted, since, the equator being an axis of symmetry with 

 respect to the adjacent regions, there is no reason why the air should move across 

 it towards one pole more than the other. 



2. It is ne.xt shown that if the air is initially moving at the higher levels from 

 E. to W. there is no theoretical cause which would turn it from this course in the 

 neighbourhood of the equator, since the radius of the inertia curve in which the air 



V 



over a rotating sphere tends to move, viz. : becomes very large in this 



2a)Sm(f) 



region, and ultimately oo .it the equator itself. 



The deviating influence of inertia relative to the earths surface would only 

 begin to make itself felt at some distance from the equator, and the air moving 

 from E. to W. would gradually curve round through S.E. to S., and finally to 

 S.W., the direction which the upper current, as exhibited by the motions of the 

 upper clouds, is known to have at the borders of the trade zone. 



3 The ffeneral tendency of the lower air in the region of the trades to move 

 from some easterly to some westerly points and rise in the neighbourhood of the 

 equator would favour the upper air moving in the same direction, since the former 

 in rising would communicate its westward component to the latter. 



4. The curves of barometric pressure calculated by Professor Sprung from data 

 furnished by Professor Ferrel for a mean longitude at 



(a) Sea level 



(b) 6,558 feet 



(c) 1.3,116 feet 



show that the gradient over the neighbourhood of the equator and for 20° on either 

 side is very small, and that thus the air would not have a tendency to stream 

 towards the poles and so acquire a AY. to E. motion until it had arrived at some 

 distance from the equator. 



