Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/27

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262

Prof. S. Arrhenius on the Influence of Carbonic Acid

where $c$ is a constant with the values $1.88$ , $1.58$ , and $1.37$ respectively for the three cases^[1]. In this way we find the following corrected values which represent the variation of temperature, if the solid ground changes its temperature 1° C. in consequence of a variation of $\beta$ as calculated by means of formula (3).

Table V. – Correction Factors for the Radiation.

$\beta =$	Solid ground, $\nu =1$ .	Water, $\nu =0.925$ .	Snow, $\nu =0.5$ .	Clouds ( $\nu =0.22$ ) at a height of.
$\beta =$	Solid ground, $\nu =1$ .	Water, $\nu =0.925$ .	Snow, $\nu =0.5$ .	0 m.	2000 m.	4000 m.
0.65	1.53	1.46	0.95	0.49	0.42	0.37
0.75	1.60	1.52	0.95	0.47	0.40	0.35
0.85	1.69	1.59	0.95	0.46	0.38	0.33
0.95	1.81	1.68	0.94	0.43	0.36	0.31
1.00	1.88	1.74	0.94	0.41	0.35	0.30

If we now assume as a mean for the whole earth ${\text{K}}=1$ and ${\text{W}}=1$ , we get $\beta =0.785$ , and taking the clouded part to be 52.5 p. c. and the clouds to have a height of 2000 metres, further assuming the unclouded remainder of the earth's surface to consist equally of land and water, we find as average variation of temperature $1.63\times 0.2385+1.54\times 0.2385+0.39\times 0.525=0.979$ , or very nearly the same effect as we may calculate directly from the formula (3). On this ground I have used the simpler formula.

In the foregoing I have remarked that according to my estimation the air is less transparent for dark heat than on Langley's estimate and nearly in the proportion 37.2 : 44, How great an influence this difference may exercise is very easily calculated with the help of formula (3) or (4). According to Langley's valuation, the effect should be nearly 15 p. c. greater than according to mine. Now I think that my estimate agrees better with the great absorption that Langley has found for heat from terrestrial radiating bodies (see p. 260), and in all circumstances I have preferred to slightly underestimate than to overrate the effect in question.

↑ $1.88=\left({\frac {288}{246}}\right)^{4}$ , $1.58=\left({\frac {276}{246}}\right)^{4}$ , and $1.37=\left({\frac {266}{246}}\right)^{4}$ . 246° is the mean absolute temperature of the higher radiating layer of the air.

[1] $1.88=\left({\frac {288}{246}}\right)^{4}$ , $1.58=\left({\frac {276}{246}}\right)^{4}$ , and $1.37=\left({\frac {266}{246}}\right)^{4}$ . 246° is the mean absolute temperature of the higher radiating layer of the air.

[1]