1896 Arrhenius (1119300), страница 3
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Theabsorption of carbonic acid first assumes a sensible value at* Langley, Ann. Ch. et 5Phys. sdr. 6, t. xvii. pp. 323 and 326, 1889,Prof. Papers, No. 15, plate 12. Lamanskyattributed his absorption-bands,which probably had this place, to the absorbing power of aqueous vapour(Pogg..Ann. cxlvi, p. 200, 1872).t It must be remembered that at this point the spectrum of' Paschen.was very weak, so that the coincidence with his figure may be accidental,248Prof. S. Arrhenius on the Influence el'Carbonic AcidX=l"5tt, after which it increases rapidly to a maximum at)~---2"6 tt, and attains a new extraordinarilyostrong maximumat X=4"6 (Lang]ey's Y).
According to AngstrSm the absorption of carbonic acid is zero at X-=0'9tt, and very weakat X-= 1"69 tL, after which it increases continuously to X=-4"6t~and decreases again to X=6'0tt. This behaviour is entirelyin agreement with the values of logx in Table II. Fromthe value zero at 40 ° (h.----l'0tt) it attains a sensible value(-0"0296) at 39°'45 (X-=l'4tt), and thereafter greater andgreater values (-0"0559 at 39°'30, and--0"1070 at 39°'15)till it reaches a considerable maximum (--0"3412 at 39 °,X-=4"3t~).
After this point the absorption decreases (at38°'45 = 5'6 ~, log x---- --0'2035). According to Table II. theabsorption of' carbonic acid at 38°'30 and 38°'15 (X----7"lttand 8"7t~) has very great °values (logx------0'2438 and--0"3730), whilst according to AngstrSm it should be insensible.This behaviour may be connected with the fact that/~ngstrSm'sspectrum had a very small intensity for the larger wavelengths. In Paschen's curve there are traces of a continuousabsorption by the carbonic acid in this whole region withweak maxima at X----5"2tt, X----5"gtt, X----6"6tt (possibly dueto traces of water-vapour), X=8"4 tt, and X=8'9 ft.
Inconsequence of the strong absorption of water-vaponr in thisregion of the spectrum, the intensity of radiation was verysmall in Lang]ey's observations, so that the calculated absorption-coefficients are there not very exact (cf. above,pp. 242-243). Possibly the calculated absorption of the carbonic acid may have come out too great, and that of thewater-vapour too small in this part (between 38°'30 and 38°'0).This can happen the more easily, as in Table I.
K and Win general increase together because they are both proportional to the "air-mass." It may be pointed out that thisalso occurs in the problems that are treated below, so that theerror fi'om this cause is not of so great importance as onemight think at the first view.For angles greater than 38 ° (X>9"5tt) we possess nodirect observations of the emission or absorption of the twogases. The sun's spectrum, according to Langley, exhibitsvery great absorption-bands at about 37°'50, 37°'25, 37 ° , and360"40°.
According to my calculations the aqueous va)poourhas its greatest absorbing power in thespectrum from 38 to35 ° at angles between 37°'15 and 3~°'45 (the figures for350"45, 35°'30, and 35°'15 are very uncertain, as they depend upon very few measurements), and the carbonic acidbetween 36°'30 and 37°'0. [Ihis seems to indicate that thefirst two absorption-bands are due to the action of water-in the Air upon the Temperature of the Ground.249vapour, the last two to that of carbonic acid.
It should beemphasized that Langley has applied the greatest diligencein the measurement or" the intensity of the moon's radiationat angles between 36° and 38° , where this radiation possessesits maximum intensity. It may, therefore, be assumed that thecalculated absorption-coefficients for this part Of the spectrumare the most exact. This is of great importance for the following calculations, for the radiation from the earth * has byfar the greatest intensity (about two thirds, cf. p.
250) in thisportion of the spectrum.II. The "lbtal Absorptio~ I~!!Atmospheres of VaryingComposition.As we have now determined, in the manner described, thevalues of the absorption-coefficients for all kinds of rays, itwill with the help of Langley's figures ~ be possible to calculate the fraction of the heat from a body at 15 ° C. (the earth)which is absorbed by an atmosphere that contains specifiedquantities of carbonic acid and water-vapour. To begin with,we will execute this calculation with the values K = I andW = 0 ' 3 . We take that kind of ray for which the best determinations have been made by Langley, anti this lies in the midstof the most important part of the..
radiation (37 v). For thispencil of rays we find the intensity of radiation at K = 1 andW=0"3 equal to 62"9; and with the help of the absorptioncoefficients we calculate the intensity tbr K = 0 and W = 0 ,and find it equal to 105. Then we use Langley's experimentson the spectral distribution of the radiation from a body of15° C., and calculate the intensity for all other angles of deviation. These intensities are given under the heading 3I. Afterthis we have to calculate the values for K = I and W=0"3.For the angle 37 ° we know it to be 62"9.
For any otherangle we could take the values A from Table II. if the moonwere a body of 15° C. But a calculation of the figures ofVery:~ shows that the full moon has a higher temperature,about 100° C. Now the spectral distribution is nearly, butnot quite, the same for the heat from a body of 15° C. andfor that from one of 100° C. With the help of Langlev'sfigures it is, however, easy to reduce the intensities for (hehot body at 100° (the moon) to be valid for a body at 15°* After having been sifted through an atmosphere of K=I'I andW=O'3.~f ' Temperature of the Moon,'plate 5.The Distributionof the Moons Heat~ Utrecht Societyof Arts andSc.
The Hague, 1891.250Prof. S. Arrhenius on the L~aence of Ca'rboJdc Acht(the earth). The values of A reduced in this manner aretabulated below under the heading N.Angle...40°. 39"45. 39'30. 39"15. 390. 38"45. 38"30. 38"15. 38'0. 37"45. 37"30.~[ ...... 3"4 11"6 24"8 45"9 84'0 121'7 161189 210210188N ...... 3"110'111"313"7 18'018"111"21 9 " 6 44"4 5970Angle...37°'15. 37'0.
36"45. 36"30. 36"15. 36"0. 35"45. 35"30. 35'15. 35"0. Sum. P.~..]~[ ...... 147 105 1039960 5165624339 2023 100N ...... 75"5 62'9 56"4 5l'4 39"1 37"9 39"2 37"6 36"0 28"7 743"2 37"2For angles less than 37 ° one finds, ill the manner abovedescribed, nmnbers that are a little inferior to the tabulatedones, which are found by means of the absorption-coefficientsof Table II. and the values of N. In this way the sum of theM's is a little greater (6"8 per cent.) than it would be according to the calculation given above. This non-agreementresnIts probably from the circumstance that the spectrmn inthe observations was not quite pure.The value 37"2 may possibly be affected with a relativelygreat error in consequence of the uncertainty of the M-values.In the following calculations it is not so much the value 37"2that plays the important part~ but rather the diminution ofthe value caused by increasing the quantities K and W.
Forcomparison, it may be mentioned that Langley has estimatedthe quantity of heat from the moon that passed through theatmosphere (of mean composition) in his researches to be 38per cent.* As the mean atmosphere in Langley's observations corresponded with higher values of K and W than K - - 1and W = 0 " 3 , it will be seen that he attributed to the atmosphere a greater transparence for opaque rays than I havedone. In accordance with Langley's esthnation, we shouldexpect for K----1 and W----0"3 a value of about 44 instead of37"2. How great an influence this difference may exert willbe investigated in what follows.The absorption-coefficients quoted in Table II. are valid foran interval of K between about l ' l and 2"25, and for W between0"3 and 2"2"2. In this interval one may, with the help of thosecoefficients and the w~lues of N given above, calculate the valueof 1N~ for another value of K and W, and so in this way obtainby means of summation the total heat that passes through anatmosphere of given condition.
For further calculations Ihave also computed values of N for atmospheres that containgreater quantities of carbonic acid and aqueous vapour. Thesevalues must be considered as extrapolated. In the followingtable (Table I I I . ) I have given these values of ~T. Thenmnbers printed in italics are found directly in the manner* Langley, ~Temperature of the Moon,' p. 197.in the A~r upon tlte ~mperature of the Ground.251described, those in ordinary type are interpolated from themwith the help of Pouillet's'exponential formula.
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