1896 Arrhenius (1119300)
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THELONDON, E D I N B U R G H , ~.~D D U B L I NP H I L O S O P H I C A L MAGA_ZINEANDJOURNALOF SCIENCE.[FIFTH SERIES.]AP R IL1896.X X X I . On the Influence of Carbonic Acid in the Air uponthe Temperature of the Ground.By Prof. SVA~T~~RRHENIUS ~I. Introduction : Observations qf Langley onAtmospherical Absorption.AGREAT deal has been written on the influence ofthe absorption of the atmosphere upon the climate.Tyndall t in particular has pointed out the enormous importance of this question.
To him it was chiefly the diurnaland annual variations of the temperature that were lessened bythis circumstance. Another side of the question~ that has longattracted the attention of physicists, is this : Is the meantemperature of the ground in any way influenced by thepresence of heat-absorbing gases in the atmosphere ? Fourier:~maintained that the atmosphere acts like the glass of a hothouse, because it lets through the light rays of the sun butretains the dark rays from the ground.This idea waselaborated by Pouillet § ; and Langley was by some of hisresearches led to the view, that " the temperature of theearth under direct sunshine~ even though our atmospherewere present as now, would probably fall t o - - 2 0 0 ° C., ifthat atmosphere did not possess the quality of selective* Extract from a paper presented to the Royal Swedish Academy ofSciences, llth December,1895.
Communicatedby the Author.t ' Heat a Mode of Motion~ 2ad ed. p. 405 (Lend, 1865).Mdm. de l'.Ac. .R. d. 8cl. de l'Imt, de .France,t. vii. 1827.§ Compte8rendus, t. vii. p. 41 (1838).Phil. Mag. S. 5. Vol. 41. No. 251. April 1896.S238Prof. S. Arrhenius on the rnfluence o) Carbonic Acidabsorption"*. This view, which was founded on toowide a use of Newton's law of cooling, must be abandoned,as Langley himself in a later memoir showed th.~t the fullmoon, which certainly does not possess any sensible heatabsorbing atmosphere, has a "mean effective temperature "Of about 45° C.tThe air retains heat (light or dark) in two differentways.
On the one hand, the heat suitors a selective diffusion on its passage through the a i r ; on the other hand,some of the atmospheric gases absorb considerable quantitiesof heat. These two actions are very different. The selectivediffusion is extraordinarily great for the ultra-violet rays, anddiminishes continuously with increasing wave-length of thelight, so that it is insensible for the rays that form the chiefpart of the radiation from a body of the mean temperature ofthe earth $.* Langley, cProfessional Papers of the Signal Service,' No. 15.searches on Solar Heat," p.
123 (Washington, 1884)."Re-determined by Langley. Among the different formulm examined, thefollowing agrees best with the experimental results : log a = b (l/X) -t-o (1/~) ~.I have determined the coefficients of this forrnala by aid of the methodof least scluares ~ and have found-b= --0'0463,c = --0'008'204.a represents the strength of a ray of the wave-len~h k (expressed int~) after it has entered with the strength 1 and passed throuzh theair-mass I. The close agreement with experiment w-iU be seen from thefollowing table : - ~.0"358/x0"3830"4160"4400"468@5500"6150"7810"8701"011"201"502"59a 1/7"6(obs.).a l/7"s (eale.).0"9040"92O0'9350"9420"9500"9600"9680'9780"9820'9850"9870"9890"9900"9110"9230-9340"9410-9470"960O'9670"9770"9800"9840"9870"9900"993Prob. error.0'00470"00280"00170'001100018in the Air upon the "lemperature o/ the Ground.239The selective absorption of the atmosphere is~ according tothe researches of Tyndall, Lecher and Pernter~ RSntgen~Hein% Langley, ~ngs~rSm, Paschen, and others *, of awholly different kind.
I t is not exerted by the chief mass ofthe air, but in a high degree by aqueous vapour and carbonicacid, which are present in the air in small quantities.Further, this absorption is not continuous over the wholespectrum, but nearly insensible in the light part of it, andchiefly limited to the long-waved part, where it manifestsitself in very well-defined absorption-bands, which fall offrapidly on both sides t.The influence of this absorptionis comparatively small on the heat fl'om the sun, but mustbe of great importance in the transmission of rays frmnthe earth.
Tyndall held the opinion that the water-vapourhas ~he greatest influenc% whilst other authors, for instanceLecher and t)ernter, are inclined to think that the carbonicacid plays the more important part.The researches ofPaschen show that these gases are both very effective, so thatprobably sometimes the one, sometimes the other~ may havethe greater effect according to the circmnstauces.In order to get an idea of how strongly the radiation of theearth (or any other body of the temperature + 1 5 ° C.) isabsorbed by quantities of water-vapour or carbonic acid inthe proportions in which these gases are present in ore"atmosphere, one should, strictly speaking, arrange experiments on the absorption of heat from a body at 15° by meansof appropriate quantities of both gases.
But such experimentshave not been made as yet, and, as they would require veryexpensive apparatus beyond that at my disposal, I have notbeen in a position to execute them. Fortunately there areother researches by Langley in his work on ~ The TemperatureFor ultra-violet rays the absorption becomes extremely great inaccordance with facts.As one may see from the probable errors which I have placed alongsidefor the least concordant values and also for one value (1"50~), wherethe probable error is extremelv small, the differences are just of themagnitude that one might expect iu an exactly fitting formula. Thecurves for the formula and for the experimental values cut each other atfour points (1/k=2'43, 1'88, 1'28, and 0'8"2 respectively). From theformula we may estimate the value of the selective reflexion for thoseparts of the spectrtlm that prevail in the heat from the moon and theearth (an~le of d~viation=38 -36 °, X----104-24'4~) We find that theabsorption from this cause varms betweeea 0"5 and 1 p.
c. for ale-mass 1.This insensible action, which is wholly covered by the experimentalerrors, I have neglected in the following calculations."Vide Wiakeima.nn, I-[aadb~ch der Physik.T Cf., e.g.~ Trabert~ MeteorologlseheZeitschrlft, Bcl,it. p. 238 (1894).$2240Prof. S. Arrhenius on the Tnfluence of Carbonic Acidof the Moon,' with the aid of which it seems not impossibleto determine the absorption of heat by aqueous vapour andby carbonic acid in precisely the conditions which occur inout" atmosphere. He has measured the radiation of the fullmoon (if the moon was not full, the necessary correctionrelative to this point was applied) at different heights andseasons of the year.
This radiation was moreover dispersedin a spectrum~ so that in his memoir we find the figures forthe radiant heat from the moon for 21 different groups ofrays, which are defined by the angle of deviation witha rocksalt prism having a refracting angle of 60 degrees.The groups lie between the angles 40 ° and 35 °, and eachgroup is separated from its neighbours by an interval of 15minutes. ~ow the temperature of the moon is nearly thesame as that of the earth, and the moon-rays have, as theyarrive at the measuring-instrmnents~ passed through layers ofcarbonic acid and of aqueous vapour of' different thicknessaccording to the height of the moon and the humidity of theair.
If, then, these observations were wholly comparable withone another, three of them would suffice for calculating theabsorption coefficient relatively to aqueous vapour andcarbonic acid for any one of the 21 different groups of rays.But, as an inspection of the 24 different series of observationswill readily show, this is not the case. The intensity ofradiation for any group of rays should always diminish withincreasing quantity of aqueous vapour or carbonic acidtraversed.
Now the quantity of carbonic acid is proportionalto the path of the ray through the atmosphere, that is, to thequantity called " Air-mass" in Langley's figures. As unitfor the carbonic acid we therefore take air-mass=l, i.e. thequantity of carbonic acid that is traversed in the air by avertical ray. The quantity of aqueous vapour traversed isproportional partly to the "all-mass," partly to the humidity,expressed in grammes of water per cubic metre. As unit forthe aqueous vapour I have t~lken the quantity of aqueousvapour that is traversed by a vertical ray, if the air contains10 grammes per cubic metre at the earth's surface*.
If wetabulate the 2~ series of observations published by Langleyin the work cited with respect to the quantities of carbonicacid and aqueous vapour, we immediately detect that hisfigures run very irregularly, so that very many exceptionsare found to the rule that the transmitted heat shouldcontinuously decrease when both these quantities increase.* This unit nearly corresponds to the mean humidity of the air (seeTable VI. p. 264).in the Air upon the Temperature of the Ground.241And it seems as if periodic alterations with the time ofobservation occurred in his series. On what cireumsL~ncethese alterations with the time depend one can only makevague conjectures : probably the clearness of the sky mayhave altered ~ ithin a long period of observation~ although thiscould not he detected by the eye.
In order to eliminate thisirregular variation, I have divided the observations into fourgroups, for which the mean quantities of carbonic acid (K)and of water-vapour (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 thehelp of the mean values of the heat-radiation for ever)- groupof rays in these four groups of observations, I have roughlycalculated the absorption coefficients (x and 2/) for bot.h gases,and by means of these reduced the value for each observationto the value that it would have possessed if K and W hadbeen 1"5 and 0"88 respectively. The 21 values for thedifferent rays were then summed up, so that I obtained thetotal heat-radiation for every series of observations, reduced toK = 1 " 5 and W~-0"88.
If the materials of observation werevery regular, the figures for this total radiation should notdiffer very much from one another. In thct, one sees thatobservations that are made at nearly the same time give alsonearly equal values, but if the observations were made at verydifferent times, the values diflhr also generally very much.For the following periods I have found the correspondingmean values of the total radiation :-1885.1885.1886.1886.1887.Period.Feb.
21--JuneJuly 29-1886.Sept. 13-Sept.Oct. 11-:Nov.Jan. 8-Feb.Mean24 ......Feb. 16.18 ......89 ......value,48506344274855353725Reductionfactor.1"31"002"311"151"70In order to reduce the figures of Langley to comparabilitywith one another, I have applied the reduction factorstabulated above to the observations made in the respectiveperiods. I have convinced myself that by this mode ofworking no systematic error is introduced into the followingcalculations.After this had been done, I rearranged the figures ofLangley's groups according to the values of K and Win the following table. (For further details see my originalmemoir,)242Prof. S. A r r h e n i u son the Influence of Carbonic AcidTABLE I.--Radlation (i) of the Full Moon foro40.0039"45. 3~39"15039.O138.45. t 38"30.°11611131116...... / 1 - 1 6 / 1 . , 2~ 1.13w ....../[°"32 0 . 2 6 9 ,2 0.271 0'32 0"271 0"32ob~. .../ 28.7 126-6 2 ~26.4 24"8 248 12'6i cale...,~l 27"0 [34"5G ......
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