HOURLY OBSERVATIONS OP AIR TEMPERATURE AND PRESSURE, 
631 
On the other hand, while sunset in December is rather more than three hours 
before the tune of mean temperature, in June it is about half-an-hour after that time. 
Also it will be found that in January whereas the temperature is above the mean 
of the whole 24 hours for not more than 8f hours, in June it is above the mean for 
nearly 12 hours. 
It may here be pointed out that the rationale of some of the empirical rules for 
obtaining the mean daily temperature, from a limited number of observations made at 
certain stated hours, is supplied by reference to the harmonic expressions for the 
hourly deviations of the temperature from the mean of the whole day. 
In the first place it is obvious, that by adding together the harmonic expressions 
for any two hours, twelve hours apart, the whole of the odd components disappear, > 
and that the sum is twice the mean value added to twice the sum of the even com¬ 
ponents of the selected pair of hours, which are respectively equal to one another. 
Disregarding the components above the fourth order, as may be done in practice, if 
the hours selected be such that the component of the second order is zero, which will 
be the case when the hours correspond to 45° fi- or 135° then half the sum of 
the observed temperatures at the selected pair of hours will be equal to the true daily 
mean added to the value of the component of the fourth order for the selected hours, 
which at English stations will hardly amount to so much as half a degree Fahrenheit. 
At Greenwich it will be found that in January the mean of observations at 4.30 a.m., 
and 4.30 p.m., or at 10.30 a.m., and 10.30 p.m., difter by less than 0°J from the true 
mean, and a similar result will be obtained in June by taking the mean of observations 
at 3 A.M. or 9 a.m., and at the corresponding afternoon hours. 
For like reasons it will be seen that by taking the mean of observations at any four 
hours, at equal intervals of six hours, not only wdl the whole of the odd components 
disappear, but those of the second order also, so that the result will only differ from 
the true mean by the amount of the component of the fourth order for the selected 
hours. As the fourth component disappears at hours when i 22|° equals 0° or 180°, 
the hours at Greenwich which will give the best result will be found to be 2, 8, 14, 
and 20, or 5, 11, 17, and 23. 
Again, if the mean of any three hours, at equal intervals of eight hours, be taken, 
it wiU be seen that the sums of the first, second, and fiourth components disap])ear, 
and that the result will only differ from the true daily mean by the amount of the 
third component for the selected hours, which at English stations will hardly exceed 
three-quarters of a degree. The best result will be obtained when the selected 
hours correspond to pg A 30° = 0°, or 180°, when the tlilrd component becomes zero, 
and at Greenwich for the greater part of the year this condition will be nea.rly 
complied with by the hours 3, 11, and 19, or 7, 15, and 23. 
It will be readily understood that the true reason for such close approximations 
being so easily obtained, is the great preponderance of the first and second components 
of the temperature variation over all the rest. 
