HOURLY OBSERVATIONS OF AIR TEMPERATURE AND PRESSURE. 
621 
the whole period in the aggregate, in which the effects of some of the Hactuations are 
necessarily lost. For the same reason, the mean value for the year, in No. VITL, is 
not the arithmetical mean of the 12-monthly values. 
No. IX. gives the mean hourly values for each month of the year, obtained from 
the Greenwich hourly observations. This Table is extracted from the volume of 
Greenwich meteorological observations for 20 years. 
No. X. gives the corrections that should be applied to the Greenwich observations 
on account of the non-periodical variation between the initial and final midnights of 
the daily period. The nature of this correction, and how the non-periodical variation 
affects the computations of the harmonic constants, are explained in the papers before 
referred to; (Proceedings of the Royal Society, vol. 42). 
No. XI. gives the mean value for each hour and for each year, cori-ected as above, 
and the mean for the whole 20 years. 
The Tables VIII. to XI. could not be prepared in the case of tire seven observa¬ 
tories of the Meteorological Office, inasmuch as the numerical mean values of the 
hourly readings had not been obtained when the calculations now jDublished were 
carried out. 
The 20-years series for Greenwich temperature extends from 1849 to 1868, and 
that for pressure from 1854 to 1873, so that the results will only be strictly com¬ 
parable for the 15 years from 1854 to 1868. The five-year means compared with 
those for the whole series of years serve to indicate how far the mean results, obtained 
from relatively short periods, are likely to deviate from those got for long periods. 
These computations also show the degree of consistency of the computed values of the 
quantities dealt with, from year to year, and from month to month, in a considerable 
series of years. 
It is necessary to state that there has occasionally been some difficulty and uncer¬ 
tainty attending the calculation of the mean values. 
In the first place, in the series of values of the p, q coefficients, if the signs change 
periodically, as will be seen to be the case in the third and fourth orders, the 
arithmetical mean can give no true indication of the mean extent of the variations 
that have actually taken place. For instance, if the positive and negative quantities 
are in the aggregate nearly equal, the mean result would be nearly zero, though, in 
fact, the variations may have been very marked, and the positive and negative sums 
considerable. 
Again, as the several components of the diurnal curve of orders above the first are 
recurrent, there is in some cases an ambiguity arising from the difficulty of determining 
whether a change of phase in successive months takes place by occurring later or 
earlier. This, no doubt, is mainly due to the monthly periods, for which the means 
are computed, being too great to admit of following the several steps of a rapid 
■change, such as takes place about the equinoxes in the components of the third and 
fourth orders. A somewhat similar difficulty arises at times in the case of wliat may 
