97 
1919 - 20 .] The Daily Temperature Curve. 
the twelve equations and the sum be taken, the result is 6 = 0*08. I adopt 
0*05 (see § 7). Hence a = 0*680, 6 = 0*050, a = 0*2561, log e~^= —0*0364 t, 
lo ge~' rt = —0*2589 t. It appears from the last paragraph in section 2 that 
the values of a and 6 at night and day need not be the same. The day 
curves demand a small positive value of 6, since otherwise f (cf. § 7), which 
is proportional to (ql'+p'l), would be negative. 
c 0 and the constants of integration are determined in the manner set 
forth in section 8. In deriving their values I have used, in formula (II), 
t — t s instead of t, thus counting the hour angles from sunset. 
(10) The Tables. — Table I contains the observed average hourly 
temperatures as already stated in section 4. 
Tables II and III give the results of the various calculations for the 
month of June, as an illustration of the method. 
Table IV contains the values of the constants c 0 and of the constants 
of integration, c x and c r These constants, together with the cloud-factor 
(§ 5), vary during the year, while the other constants (§7) maintain their 
values throughout the year. 
c 0 of the day curves exceeds the minimum temperature, while 
c 0 of the night curves is smaller than the minimum temperature. This 
discrepancy suggests that c 0 is actually not a constant, but varies with a 
daily period. To take this into account a third differential equation has 
to be added to formulae (3) and (4), which would, however, be a serious 
complication of the problem. The representation of the observations, as it 
is, is quite satisfactory. 
The constants of integration also differ for day and night curves even 
though the same values of the constants a and 6 be used and the hour 
angles be counted from the same zero. It appears to me that the cause 
must be sought in the differential equation, which does not take all the 
agencies into account. 
Table V gives a comparison of the observed and calculated tempera- 
tures. In the bottom line the average departures are given, which range 
between 0°T8 in May and 0°*04 in November for the day curves, and are 
less than 0°*05 for ail the night curves. The departures of the calculated 
temperatures are systematic, and largest near sunrise and sunset. As for 
the large departures of the night curves in December and January, it will 
be seen by reference to Table I that the temperatures begin to rise several 
hours before sunrise. This again proves that the differential equation (I) 
does not perfectly represent the case. At the same time the agreement 
between calculated and observed figures is quite satisfactory for the 
purpose for which the work has been undertaken. 
VOL. XL. 
7 
