116 REPORTS ON THE STATE OF SCIENCE. 
The value was— 
T =T;—(3'97 + 0°15) + (0°84 + 0°23) sin (nt + 173°) 
+ (0°35 + 0°15) sin (2nt + 102°), 
and the agreement between the diurnal terms in the two cases proves 
that the results are not influenced to any considerable extent by solar 
radiation. The variation at 2 km. was found to be considerably less. 
It is approximately given by 
T =T,— (9°84 + 0°23) + (0°64 4 0°31) sin (nt + 270°) 
+ (0°25 + 0:23) sin (2nt + 72°). 
The variation of the temperature in the free atmosphere is theoreti- 
cally connected with the variation of pressure. Mountain observations ' 
lead to the conclusion that the amplitude of the diurnal variation of 
pressure diminishes with height, vanishes and reappears with a change 
of phase of 180°. The semi-diurnal term, on the other hand, has its ampli- 
tude roughly proportional to the pressure, and its phase diminishes 
gradually with increasing height. 
If these conditions hold also in the free atmosphere, the phases of the 
diurnal variations of pressure and temperature ought to differ by 180° 
in the lower layers and ought to agree after the change in the pressure 
variation, 7.e., the phase of the variation of temperature ought not to 
change materially from its surface value. The observations are in fair 
agreement with this conclusion. 
The phases of the semi-diurnal variations of temperature and pressure 
ought to differ at the surface by 90° nearly, the latter (pressure) being 
the larger. In the upper layers this difference ought to diminish. 
The phase of the semi-diurnal variation of temperature found above 
is subject to a considerable probable error, but the results indicate a 
tendency in it to approach the value found for the phase of the pressure 
variation from mountain observations. Thus at Kew the phases actually 
differ by about 100°, while the phase at 1,000 m. differs by only 20°-30° 
from the phase of the variation of pressure observed at 1,000 m. in the 
Alps.2. The results for the temperature are, however, not sufficiently 
accurate to warrant conclusions as to the variation of pressure in the free 
atmosphere being drawn from them. 
V. Wind. 
The first attempt to discover the way in which the velocity of the 
wind changed with the altitude in the free atmosphere by the use of 
recording instruments appears to have been made by Archibald, whose 
results were communicated to the British Association at Montreal twenty- 
five years ago. He concluded that the velocities V, v, at heights H and 
h above the surface were connected by the equation 
V/o=(B/h)* 
where x diminished with height, but tended to a value nearly equal to }. 
} On the Pic du Midi, 2,860 m., the daily variation of pressure is given in mm, by 
Ap=0'19 sin (nt + 180°) + 0°25 sin (2nt + 124°) 
and that of temperature by 
AT=1°8 sin (nt + 251°) +0°6 sin (2nt + 80°). 
Met. Zeit., 1908. See also Hann, Lehrbruch, p. 605. 
2 Hann. Lehrbuch, p. 605. 
