118 REPORTS ON THE STATE OF SCIENCE. 
(metres per sec. x pressure in metres x T/T) deduced from ten sets of 
_ observations at Munich ! of which seven reached 12 km :— 
Height . : 3 1 3 5'5 8— LO 12 km. 
Vp 2 : ye tao) 48 45 53 45 37 
Observations made by Cave * in July 1908 furnish in the same units 
at the same heights the following values :— 
Vp eee eo Eah? | bbs) 89); Ob tee toO. ae 
Vp(May 1909) . 85 54 36 36 ° 33 ~~ 19 
The second row gives values from seven ascents in May 1909. 
The law implies that the mean gradients of pressure have the same 
value in the upper air as near the surface, and this can be the case only 
if the mean temperature over high pressure is greater than it is over the 
low pressure, 7.e., if the horizontal gradients of pressure and temperature 
are in the same sense. It was seen from the results for temperature that 
this was the case. It remains to be seen if the observed difference of 
temperature is sufficient to make the gradient of pressure constant. 
If p and p + 6 p are the pressures at two places at the surface, then 
the corresponding pressures at a height z are pe~",(p +6 p) e~“**” 
where u = (% = = Se T being temperature, and H the height of 
the homogeneous atmosphere, 8 km. nearly. 
If the difference of pressure is the same as at the surface 
e~“dp—pe“du=Sdp, ie, 8 p=—pe-“(l—e ")-18u. 
But 
HT? Er 
where ¢, is approximately the mean value of 5 T. 
Put T=T, (1—az) and a H =} corresponding to a constant 
vertical fall of temperature at a rate of 5°-7 C. per km. 
Then u = — (a H)™ log (1 — az) 
du= — 7, (a H) (l—az)7 
ew= (1 = a. 2)° 
The condition cannot be satisfied exactly at all heights with such 
a distribution, but if ¢, be determined so that it is satisfied at a height 
H, say, it will be approximately true for intermediate heights, and the 
value of ¢, will indicate if the condition is likely to be satisfied, regard 
being paid to the results of observations. 
Ii z=H,«oH =}, T)=273 
the condition 6 p= pe-“ (1 —e-“) 1 8u becomes 
__ 748 p 
du — (Me oT_ (ee 
t, 
P 
Thus if 6 p = 20 mm., t, = 2° C nearly. 
Now the actual mean difference in temperature up to 8 km. between 
regions where pressure > 770 mm. and regions where it < 750, is ap- 
proximately 4° C. or practically double the amount necessary to make 
V p constant. The value of V p ought, therefore, to be greater at 8 km. 
than near the surface. The results indicate that this is the case, and they 
show, further, that V p diminishes at greater heights. But this is entirely 
in accordance with the results for temperature, which showed that 6 T, 
’ Registrierballonfahrten, 1907-08.  * Quar. Jour. R. Met. Soc., 1908. 
° Weekly Weather Report, 1909. 
