PRESENT STATE OF OUR KNOWLEDGE OF THE UPPER ATMOSPHERE. 117 
Berson ! found the following values for the ratio of the mean velocity 
in layers 500 m. thick to the mean wind for the day at Potsdam. The 
latter was 5°5 m.p.s :— 
Layer |0—0'|05-1-0 10-1 15 ~9-0|2:0—9'5|2:5—3:0|8—4/4—5 above 5 km. | 
| 
Ratio . rae tori( Walters 1:85 | 1:95 | 2:08 2°16 2°45) 3:05 446 | 
Ratio (2) — | 1:00 1:02 1:07 | 1:14 1:19 | 1:35 1-68) 2°45 
No. of Cases 54 54 55 49 | 41 38 36 19 10 | 
The ratio (2) is formed with the velocity in the layer 0°5-1:0 as stan- 
dard. The results show a very slow increase up to 2-3 km., after which 
the change takes place more rapidly. It appears probable that the values 
up to 3 km. are those appropriate to the pressure distribution at the 
surface, and indicate that the ratio of the gradient of pressure to the 
density remains nearly constant up to that height. The larger values 
in the upper layers show that the intensity increases with height, which 
is in accordance with the observations of temperature, since these show 
that the places with higher pressure have also higher temperature in the 
upper air. 
Gold 2 showed from a consideration of kite observations that the 
major part of the increase in the first 2,000 m. took place in the layers 
immediately above the surface. For Berlin 75 per cent. of the total 
increase occurred in the first 160 m. 
He found, too, that the velocity increased up to 500 m. almost without 
exception, but that at greater heights numerous cases occurred where 
the velocity decreased as the height increased. Thus at Oxshott, between 
500 and 1,000 m. the velocity decreased in eight cases, remained constant 
in seventeen cases, and increased in twenty-three cases out of a total 
of forty-eight, while at Blue Hill the corresponding numbers were seven, 
four, and ten out of a total of twenty-one. The change depends on the 
direction of the wind. Both at Oxshott and Berlin the velocity almost 
invariably decreased between 1°5 and 2 km. in the case of S.E. winds, 
while S.W. winds showed the greatest increase near the surface. It was 
also found that the kite observations over Berlin furnished conclusive 
evidence that the wind at 1,000 m. altitude agreed both in magnitude 
and direction with the theoretical velocity deduced from the condition 
for steady horizontal motion along the isobars, viz.— 
(w 7 sin A+ vy_ldp, (w 7 sin A)? 
ip por r 
where p is pressure, p density, v velocity of the air, ) is latitude, » the 
angular velocity of the earth about its axis, and r the radius of curvature 
of the path of the moving air. 
Egnell * deduced from the observations of clouds that the velocity 
increases with the height, so that it remains nearly inversely propor- 
tional to the density, 7.e., the velocity V is given by V = V.p./p, where 
p is density and V,, p, are the values of V and p near the surface. 
The law appears to agree moderately with the observations from pilot 
balloons. The following table gives the values of Vp in arbitrary units 
1 Wissenschaftliche Luftfahrten, II. 
2 Barometric Gradient and Wind Force, M.O., 190. 
8 Comptes rend., 1903; International Cloud Observations. Trappes. 
