Causes and Effects of Variation in the Range of Teynperature. 347 
That is to say, the ratios of the ampUtudes are greater when a — /3 is 
greater. 
The ampUtudes ih, in Tables 5 and 6, may be approximately repre- 
sented by the formula — 
?ti = '42(M-m). 
From some points of view the harmonic constants look better when 
computed for the "temperature variability," i.e., for the curve of change 
of temperature from hour to hour, than they do when they are computed 
for the hourly temperatures. The harmonic constants in the diurnal 
curves of temperature variability, or, if we prefer to call it so, in the 
A0/A^ curve — w^here d is the temperature and t the time counted from 
midnight— are given in Tables 7 and 8. The angles V^, V2, V3, in this 
case of course differ by 7r/2 from those of Tables 5 and 6. The ratios of 
the amplitudes of temperature variability to those of temperature, for both 
greater and lesser ranges of temperature, are approximately — 
w, = 3'8; 2^2-1-9; = 1-3. 
The respective ratios of the amplitudes of temperature variability for the 
greater ranges of temperature (a) to the amplitudes for the lesser ranges 
(/3) are the same as those of temperature. 
One advantage of working out the harmonic constants for the varia- 
bility is that they bring into strong relief the fact that the phase times of 
the three principal waves, given in Tables 7 and 8, group themselves 
closely about the phase time of the 12 -hour wave of pressure. In fact, all 
three of the variability component waves come to a maximum within 
about an hour or less of the time of a maximum of the pressure wave in 
question. This near coincidence of phase times in the first place, next 
the tendency which the phase times of the first and second harmonic 
components of temperature variability as well as the second component 
of barometric pressure show to come earlier in the day during the spring 
and early summer months ; thirdly, the greater magnitude of the ampli- 
tude of the variability curve as well as of the second harmonic component 
of pressure at the same period ; these go to support the idea that the 
12-hour pressure wave arises initially as the result of the variation of 
temperature from instant to instant, and not as a result of temperature 
alone. Obviously the mere expansion of the air upwards could have no 
effect upon the pressure beneath, excepting by virtue of the reaction 
downwards, and this last must be greatest when the upward acceleration 
of the air is a maximum, i.e., when dQjdt is a maximum. 
* See a remarkable paper by Halm published in the Journal of the Scottish Meteoro- 
logical Society, Third Series, No. XXII., 1906. Also Sutton, " The Diurnal Variation of 
Barometric Pressure," Report S.A.A.A.S., 1906. Hann has yet another able paper, 
" Ueber die Zerlegung des komplexen taeglichen Ganges der Temperatur und des Luft- 
druckes in eine ganz- und eine halbtaegige Welle," in Met. Zeit., July, 1911. 
