1896 Arrhenius (1119300), страница 4
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The table hastwo headings, one which runs horizontally and represents thequantity of aqueous vapour (W), and another that runs vertically and represents the quantity of carbonic acid (K) in theatmosphere.TinL~ I I I . ~ The Transparency of a given AtmosphereforHeat ~'om a body of 15 ° (2.ttoOc02.i03.0.5.1"0:37"234"731"527"023"520"115"810"96"62'90"8835"032"729"625"322018'814"710"26'12"50'8130"71"5.2"0.3"0.23"922"219"916"714"412"39"3 ,6"3 i3'51'5046119 "317"815"913"111"09"37"14"82"~1"00"324-f).
I 6-0.10-0.iL_11"2"53"54610204026"928"6 25"125'9 22"621"919"119'016"616'314"212'710"88"77"35 '24"32'2 ~ 1"80'670"56i10"79"78"47"415"63"71"80'750"245'34"23"11"91'00"390"128"98"O6"94"23"32'00"20 I0"070"02Quite different f,'om this dark heat is the behaviour of theheat from the sun on passing through new parts of the earth'satmosphere. The first parts of the atmosphere exert withoutdoubt a selective absorption of some ultt'a-red rays, buL assoon as these are extinguished the heat seems not to diminishas it traverses new quantities of the gases under discussion.This can easily be shown for aqueous vapour with the help ofLangley's actinometric observations from Mount~fin Campand Lone Pine in (2olorado*.
These observations wereexecuted at Lone Pine from the 18th of August to the 6th ofSeptember 1882 at 7h 15 m and 7h 45 TM A.~., at 11 h 4 5 m A.M.and 12 ~ 15 m P.~., and at 4 h 15 m and 4 h 45 mP.~. At MountainC a m p the observations were carried out from the 22nd to the25th of August at the same times of the day, except that onlyone obserxation was performed in the morning (at 8h 0'=).
[have divided these observations into two groups for eachstation according to the humidity of the air. In the followinglittle table are quoted, first the place of observation, and afterthis under D the mean date of the observations (August 1882),under W the quantity of water, under I the radiation observedby m e a n s o f the actinometer, under I1 the second observationo f t h e s a m e quantity.Langley, ' Researches on Solar Keat,' pp. 94, 98, and 177.252Prof.
S. Arrhen~us on the Influence of Carbonic AcidMorning.Noon.Evening,D. W. I. 11.. W. I. 11.D. W.I.L~,o J'29'3 0'61 1'42~: 1'55~~ J'23"6 0"46 1"6921"715, "[26"60'51 1'417 1"351 ]Pine. [ 2I'1 0"8~ 1"458 l"583.f [ 26"9 0"59 1"699 1"721 [ f 23"2 0"74 1"4°.81"359fMountain jr 23"5 0"088 1"790"[ f 22"5 0'182 1"904 1'873~ J 24"5 0205 1"701 1"641]Camp.
[23'5 0"]53 1'749f. [24'5 0"2i5 1"890 1"917.( [ 22"5 0"32 1"601 1'527fAt a very low h~lmidity (Mountain Camp) it is evident thatthe absorbing po~ er of the aqueous vapour has an influence,fol:the figures for greater humidity are (with an insignificantex,eption) inferior to those for less humidity. But for theobservations from Lone Pine the contrary seems to be true.I t is not permissible to assume that the radiation can bestrengthened by its passage through aqueous vapour, but theobserved effect must be caused by some secondary circumstance. Probably the air is in general more pure if thereis more water-vapour in it than if there is less.
Theselective diffusion diminishes in consequence of this greaterpurity, and this secondary effect more than counterbalancesthe insignificant absorption that the radiation suffers from theincrease of the water-vapour. It is noteworthy that Elsterand Geitel have proved that invisible actinic rays of veryhigh refrangibility traverse the air much more easily if it ishumid than if iris dry. Langlcy's figures demonstrate meanwhile that the influence of aqueous vapour on the radiationfrom the sun is insensible as soon as it has exceeded a valueof about 0"4.Probably the same reasoning will hold good for carbonic acid, for the absorption spectrum of both gases is of thesame general character.
Moreover, the absorption by carbonic acid occurs at considerably greater wave-lengths, andconsequently for much less important parts of the sun'sspectrum than the absorption by water-vapour*. It is,therelbre, justifiable to assume that the radiation from thesun suffers no appreciable diminution if K and W increasefrom a rather insignificant value ( K = 1, W =0"4) to higherones.Before we proceed further we need to examine anotherquestion.
Let the carbonic acid in the air be, for instance,the same as now ( K - - 1 for vertical rays), and the quantityof water-vapour be 10 grammes per cubic metre ( W = 1 forOf. above, pages 246-'2487 and Langley's curve for the solar spectrum, Ann. d. Ch. et d. Phys. sgr. 6, t. xvii. pp. 3"23 and 3"26 (1889)Prof. Papers,' No. 15, plate 12.in the Air upon the Temperature oat"the Ground.253vertical rays). Then the vertical rays from the earth traversethe quantities K---1 and W - - 1 ; rays that escape under anangle of 30 ° with the horizon (air-mass-~2) traverse thoquantities K ~2, W - - 2 ; and so forth.
The different rays thate m a n a t e f r o m a p o i n t of the e a r t h ' s surface suffer~ therefor%a different a b s o r p t i o n l t h e g r e a t e r , the m o r e the p a t h of t h er a y declines from the v e r t i c a l line. I t m a y t h e n be askedhow l o n g a p a t h m u s t the total radiation make, t h a t theabsorbed fraction of it is the same as the absorbed fraction o ft h e total mass of r a y s t h a t e m a n a t e to space in differentdirections. F o r t h e e m i t t e d rays we will suppose t h a t thecosine law of L a m b e r t holds good.
W i t h the aid of Table I I I .we may calculate the absorbed fraction of any ray~ and thenstun up the total absorbed heat and determine how great afraction it is of the total radiation. In this way we find forour example the path (air-mass) 1"6L In other words, thetotal absorbed part of the whole radiation is just as great asif the total radiation traversed the quantities 1"61 of aqueousvapour and of' carbonic acid. This nmnber depends upon thecomposition of the atmosphere, so that it becomes less thegreater the quantity of aqueous vapour and carbonic acidin the air.
In the following table (IV.) we find this numberfor different quantities of both gases.TABLE IV.--Mean path o/the Earth's rays.CO20"3.0"5.2.3.0"67109 -5 -7-]1"641"571"5311'66l'65l'611"551"511"51"621"611"571"511"47,)1"581'571"521"461'432"51"561'541"501"451"4131"521"511'471"441'403"51"481'481'451"42If the absorptioa of the atmosphere approaches zer% thisnumber approaches the value 2.Phil. 3fag. S. 5.
Vol. 41. :No, 251. April 1896.T25~Prof. S. Arrhenius on the Influence of Carbonic AcidI I I . Thermal Equilibrium on the Surface and in theAtmosphere of the Earth.As we now have a sufficient knowledge of the absorptionof heat by the atmosphere, it remains to examine how thetemperature of the ground depends on the absorptive powerof the air. Such an investigation has been already performedby Pouillet~, but it must be made anew, for Pouillet usedhypotheses that are not in agreement with our presentknowledge.In our deductions we will assume that the heat that is conducted from the interior of the earth to its surface may bewholly neglected.
I f a change occurs in the temperatureof the earth's surface, the upper layers of the earth's crust willevidently also change their temperature ; but this later process will pass away in a very short time in comparison withthe time that is necessary for the alteration of the surfacetemperature, so that at any time the heat that is transportedfrom the interior to the surface (positive in the winter, negative in the summer) must remain independent of the smallsecular variations of the surface temperature~ and in thecourse of a year be very nearly equal to zero.Likewise we will suppose that the heat that is conductedto a given p]ace on the earth's surface or in the atmospherein consequence of atmospheric or oceanic currents, horizontalor vertical: remains the same in the course of the time considered, and we will also suppose that the clouded part of thesky remains unchanged.
It is only the variation of thetemperature with the transparency of the air that we shallexamine.All authors agree in the view that there prevails an equilibrium in the temperature of the earth and of its atmosphere.The atmosphere must, therefore, radiate as much heat tospace as it gains partly through the absorption of the sun'srays, partly through the radiation from the hotter surface ofthe earth and by means of ascending cm'rents of air heatedby contact with the ground. On the other hand, the earthloses just as much heat by radiation to space and to theatmosphere as it gains by absorption of the sun's rays. Ifwe consider a given place in the atmosphere or on the ground,we must also take into consideration the quantities of heatthat are carried to this place by means of oceanic or atmospheric currents. For the radiation we will suppose that* Pouillet, ComTtesrendus~t.
vii. p. 41 (1838).in the Air upon the Temperature of the Ground.255Stefau's law of radiation~ which is now generally accepted,holds good, or in other words that the quantity of heat (W)that radiates from a body of the albedo (l--v) and temperature T (absolute) to another body of the absorption-coefficient/9 and absolute temperature 0 isW = v / ~ ( T 4 - 0'),where 7 is the so-called radiation constant (1"21.10 -15 persec. and cm.:). Empty space may be regarded as having theabsolute temperature 0%Provisionally we regard the air as a uniform envelope ofthe temperature 0 and the absorption-coefficient a for solarheat; so that if A calories arrive from the sun in a column of1 cm.
2 cross-section, aA are absorbed by the atmosphere and( 1 - - a ) A reach the earth's surface. In the A calories thereis, therefore, not included that part of the sun's heat whichby means of selective reflexion in the atmosphere is thrownout towards space. Further~ let /9 designate the absorptioncoefficient of the air for the heat that radiates from the earth'ssurface ; /9 is also the emission-coefflcient of the air for radiation of low temperature~strictly 15°; but as the sl~eetraldistribution of the heat varies rather slowly with the temperature,/3 may be looked on as the emission-coefficient also atthe temperature of the air.
Let the albedo of the earth'scrust be designated by (I--v), and the quantities of heat thatare conveyed to the air and to the earth's surface at the pointconsidered be M and N respectively. As unit of time wemay take any period: the best choice in the following calculation is perhaps to take three months for this purpose. Asunit of surface we may take i cm.
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