36G ME, S. A. HILL OX THE WINDS OF NORTHERN INDIA, AND THEIR 
Table XVI.—Comparison of Wind Velocities with Pressure Gradients over the 
Gangetic Plains. 
Maximum gradient for 60 
Month. 
Velocity in 
miles pel - diem. 
geographical mdes. 
At sea-level. 
At 10,000 feet. 
Miles. 
Inch. 
Inch. 
J annary .... 
58 - 2 
•0029 
•028 
May. 
114-4 
•0038 
•035 
July. 
95-8 
•0044 
•012 
October .... 
52-6 
•0036 
•019 
It seems probable from this Table that the high velocity for July may be attributed, 
partly at least, to the higher pressure gradient at sea-level in that month than in any 
of the others, and that the lower velocity in October than in May is the result of the 
lower gradient prevailing at high levels. The relation between the wind velocity and 
the gradients at high and low levels may be investigated as follows :— 
If v be the velocity of the wind near sea-level in miles per hour, and v that 
prevailing in a higher stratum where the gradients are the same as at 10,000 feet in 
the Table, and if x be the number of hours during which the wind from this high 
level descends to the earth’s surface, then the total distance traversed daily will be 
v'x + v (24 — x). Should the wind not descend from a level where the gradients are 
so high as those given in Table XVI,, x will not represent the true time during which 
the upper current descends, but will be longer or shorter in inverse proportion to the 
gradient. 
From Per a el’s formula for the relation between the wind velocity and barometric 
gradient, given in his work on the Movements of the Atmosphere, we get, on reducing 
to English measure, and taking the unit of distance to be one degree of the earth’s 
surface, aB = '00607 ('525 sin 6 + u) v; or, taking <f) equal to the mean latitude of 
the Gangetic plain (about 26°), and neglecting the angular velocity u, we get 
v=714aB. In arriving at this result, however, frictional retardation has been 
neglected : but, if the ratio between the actual and the theoretical velocity for a given 
gradient be called f, we may put for the actual velocity v = 714 f aB. Substituting 
for v and v in the previous formula their values thus expressed in terms of the 
barometric gradients for each of the four typical months, and assuming the probable 
values/= -4 and f = '7 since the equations are indeterminate, we get the following 
results :—■ 
Month. X. 
January. 2'.9 hours. 
May.5 - 4 ,, 
July.13 ‘9 ,, 
October.3’3 ,, 
