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238

Prof. S. Arrhenius on the Influence of Carbonic Acid

absorption"^[1]. This view, which was founded on too wide a use of Newton's law of cooling, must be abandoned, as Langley himself in a later memoir showed that the full moon, which certainly does not possess any sensible heat-absorbing atmosphere, has a "mean effective temperature" of about 45° C.^[2]

The air retains heat (light or dark) in two different ways. On the one hand, the heat suffers a selective diffusion on its passage through the air; on the other hand, some of the atmospheric gases absorb considerable quantities of heat. These two actions are very different. The selective diffusion is extraordinarily great for the ultra-violet rays, and diminishes continuously with increasing wave-length of the light, so that it is insensible for the rays that form the chief part of the radiation from a body of the mean temperature of the earth^[3].

↑ Langley, 'Professional Papers of the Signal Service,' No. 15. "Researches on Solar Heat," p. 123 (Washington, 1884).
↑ Langley, "The Temperature of the Moon." Mem. of the National Academy of Sciences, vol. iv. 9th mem. p. 193 (1890).

↑ Langley, 'Prof. Papers,' No. 15, p. 151. I have tried to calculate a formula for the value of the absorption due to the selective reflexion, as determined by Langley. Among the different formulæ examined, the following agrees best with the experimental results: –

\log a=b(1/\lambda )+c(1/\lambda )^{3}

.

I have determined the coefficients of this formula by aid of the method of least squares, and have found – $b=-0.0463$ , $c=-0.008204$ .

$a$ represents the strength of a ray of the wave-length $\lambda$ (expressed in $\mu$ ) after it has entered with the strength 1 and passed through the air-mass 1. The close agreement with experiment will be seen from the following table: –

$\lambda$ .	$a^{1/7.6}$ (obs.).	$a^{1/7.6}$ (calc.).	Prob. error.
0.358 $~\mu$	0.904	0.911
0.383	0.920	0.923	0.0047
0.416	0.935	0.934
0.440	0.942	0.941
0.468	0.950	0.947	0.0028
0.550	0.960	0.960
0.615	0.968	0.967
0.781	0.978	0.977
0.870	0.982	0.980	0.0017
1.01	0.985	0.984
1.20	0.987	0.987
1.50	0.989	0.990	0.0011
2.59	0.990	0.993	0.0018

[1] Langley, 'Professional Papers of the Signal Service,' No. 15. "Researches on Solar Heat," p. 123 (Washington, 1884).

[2] Langley, "The Temperature of the Moon." Mem. of the National Academy of Sciences, vol. iv. 9th mem. p. 193 (1890).

[p238-3] Langley, 'Prof. Papers,' No. 15, p. 151. I have tried to calculate a formula for the value of the absorption due to the selective reflexion, as determined by Langley. Among the different formulæ examined, the following agrees best with the experimental results: – $\log a=b(1/\lambda )+c(1/\lambda )^{3}$ .

I have determined the coefficients of this formula by aid of the method of least squares, and have found – $b=-0.0463$ , $c=-0.008204$ .

$a$ represents the strength of a ray of the wave-length $\lambda$ (expressed in $\mu$ ) after it has entered with the strength 1 and passed through the air-mass 1. The close agreement with experiment will be seen from the following table: –

$\lambda$ . $a^{1/7.6}$ (obs.). $a^{1/7.6}$ (calc.). Prob. error.

0.358 $~\mu$ 0.904 0.911

0.383 0.920 0.923 0.0047

0.416 0.935 0.934

0.440 0.942 0.941

0.468 0.950 0.947 0.0028

0.550 0.960 0.960

0.615 0.968 0.967

0.781 0.978 0.977

0.870 0.982 0.980 0.0017

1.01 0.985 0.984

1.20 0.987 0.987

1.50 0.989 0.990 0.0011

2.59 0.990 0.993 0.0018

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