Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/6

And it seems as if periodic alterations with the time of observation occurred in his series. On what circumstance these alterations with the time depend one can only make vague conjectures: probably the clearness of the sky may have altered within a long period of observation, although this could not be detected by the eye. In order to eliminate this irregular variation, I have divided the observations into four groups, for which the mean quantities of carbonic acid (${\text{K}}$) and of water-vapour (${\text{W}}$) were $1.21$ and $0.36$, $2.21$ and $0.86$, $1.33$ and $1.18$, and $2.22$ and $2.34$ respectively. With the help of the mean values of the heat-radiation for every group of rays in these four groups of observations, I have roughly calculated the absorption coefficients ($x$ and $y$) for both gases, and by means of these reduced the value for each observation to the value that it would have possessed if ${\text{K}}$ and ${\text{W}}$ had been $1.5$ and $0.88$ respectively. The 21 values for the different rays were then summed up, so that I obtained the total heat-radiation for every series of observations, reduced to ${\text{K}}=1.5$ and ${\text{W}}=0.88$. If the materials of observation were very regular, the figures for this total radiation should not differ very much from one another. In fact, one sees that observations that are made at nearly the same time give also nearly equal values, but if the observations were made at very different times, the values differ also generally very much. For the following periods I have found the corresponding mean values of the total radiation: –

Period.	Mean value.	Reduction factor.
1885. Sept.Feb. 21–​1886.June  Feb. 16.24 ......	4850	1.30
1885. Sept.July 29–​1886. Feb. 16.	6344	1.00
1886. Sept. 13–​1886.Sept.  Feb. 16.18 ......	2748	2.31
1886. Sept.Oct. 11–​1886.Nov.  Feb. 16.08 ......	5535	1.15
1887. Sept.Jan. 08–​1886.Feb.  Feb. 16.09 ......	3725	1.70

In order to reduce the figures of Langley to comparability with one another, I have applied the reduction factors tabulated above to the observations made in the respective periods. I have convinced myself that by this mode of working no systematic error is introduced into the following calculations.

After this had been done, I rearranged the figures of Langley's groups according to the values of ${\text{K}}$ and ${\text{W}}$ in the following table. (For further details see my original memoir.)