1896 Arrhenius (1119300), страница 2
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] 7922725'724"456691.2o9 1"291'291'271 '041"040 90'iobs....! 22"9 ]131"231"22q21 "323"1127"92~2I'2761351...... IK ...... ~ 1"46731"4023W ...... [ 075i obs.., i 11"9i3561"271'07c~12"5539K ...... ]1"28w ...... !o.81i eal¢...23"50"8618'2i1'05"821 "812"58"674382491'49l "491"491 "5080"870"890'890"822;18"918"09'29'92,20"918"612"77"838371733Ii tale...I 23"6G ......28JK ...... ! 1"4821'481'511"481"51W ......31"781 '641'781"951 "481 "8018025'224"618"327"64"83"7i ealc..., i 16"920'217"918'55"94"7542"26iobs..IG- ...... : 3022513137K ......
[ 2"262'262'262"262"262"261.081"081-'081 '081'08W ...... i 1"08 I 1 " 0 8i o b s .... [21'323'42@816"411"18"24'5i calc.,..i 21'225"91 '316"610"17'74"5494334231791"921'921'931 "921'921 '922'242'302 '24/G ......44K ...... I 205W ...... 1"932"302"242"16i o b s .... 13"412"814815"110"36'63'4i cale .... 16-219'417"314"513"03'82"94725158G ......552935in the Air upon the Temperature o/the Ground,~43different Values of K and W,caK ......W ......-o37"15.37.1"160"321"160"32i obs. ""1 68'6i calc ....
73"7G ...... 19059'57"1163Oo36"45. 3¢30. 36"15.1"18 1"18 1"20"34 0"34 0"456"2 48"3 43'450 "9 46"0 !34"9102281183~.o35"45. 35°'30. 35"15.°1'161"270'32 0'4840"7 39 036'4 31-3112251"270'4832'627"7211"270"4831"527-320o35.1"160"3219-719-354K ...... 1 "27 1"27 1"31 1"32 / 1"32 1"28 1-33 1-33 1-33 1"25W ...... 1"00 1"00 1"05 1-00 1-00 0"81 0 " 5 1 0-511 " 0 7 0"60i obs.
""] 58"9 50"3 47"9 ;41-2 !31"7 129-7 25"7 18-8 27-5 16"621"3 17"2i tale....] 53"0 51"2 47"1 39-2 !34"2 31-1 30-3 i26"8140108G ...... [ 2942519816123922205]K ...... [ 1"49W ...... [ 0"87i obs....t 43'1i ealo. '"t 55"2G- ...... / 871'480'8536"447'11491"48 1"48 1"41 1'450'890"85 O-85 0'9735 "4 31-2 28"3 24-936333"0 29"342'578127541461'411'411"410"97 0"98 0"9816'615"4 10"327"3 22"3 22"03229191"410"989"214'717K ...... / 1"48 1"48 1"48 1 "48 1"48 1"48 1"48 1"48 1"48 1"481-66 1"83 1'661"83 1 581 " 8 3 1"66W ......
] 1"66 1"58 1'66iobs .... ]47"548"7 45"8 34-5 35"0 27"5 28"7 21"4 17"4 15"432"0 23"6 23"4 17'815'411"6i ealc....] 38'243"4 42'5 33-099827967814143S- ...... / 136176131K ...... / 2'26 2'121"91 1-90 1 '91 2"09 1'911"10 1"18 1'10W ...... / 1'081"15 1"10 1'11iobs ...[44"632"0 27'8 24-7 26:6 24"5 19"0i talc..../47"133'532'8 27"4 : 26'8 23"6 21"372455863[~ ......
! 939866K1"92 2"05 2"45 2"37 2'45 2-37W2"30 1"93 2"25 2-20 2"25 2"20i obs.... 24"7 33'226"7 19-4 22"6 18-818"4 21"4 16"8i tale .... 27'131"8 23'7616365G56137771'901"90 2"121 " 1 1 1 - 1 1 1"1516'013.910"117"53720"43212"2311 " 9 7 1'971"972"33 2"33 2"3316-4 10"9 12"11'972"337"917"4328"4-1611"52212-224244Prof.
S. Arrhenius on the Influence of Carbonic AcidIn this table the angle of deviation is taken as head-title.After K and W stand the quantities of carbonic acid andwater-vapour traversed by the ray in the above-mentionedunits. Under this comes after iobs. the intensity of radiation(reduced) observed by Langley on the bolometer, and afterthis the corresponding value i calc., calculated by means of theabsorption-coefficients given in Table I I . below. G is the" w e i g h t " given to the corresponding iobs. in the calculation,using the method of least squares.F o r the absorption-coefficients, calculated in this manner,I give the following table.
(The common logarithms of theabsorption-coefficients are tabulated.)TABLE II,--AbsorTtion-Coeficlents of Carbonic Acid (x)and Aqueous Vapour (y).A nofgDeviationlelog x.logy.2k.40+0.028600000-0.15061--0'1455 S27"239"4539'3039'1539"00"0296-0"0559-0'1070--0"3412--0'1105-0"0952--0"0862--0006834'529"626"427"538"4538"3038'1538"0--0'2035--0"2438--0"3760--0"1877--0"31140"2362-0"19330"319824"513.521.444.437"4537'3037'1537'0--0"0931--0'0280--0"0416--0"2067--0"1576--0"1661-0"2036--0"048459.070.075-562.936"4536"3036'1536'0--0"2465--0"2466--0"2571+ o.ooo8- o.ooooj--0'0507+00065 ]-0.0000 j--0"118456-451.439.137.9-0"1992-0"1742- 0.0628-0.1408-0.1817-0.144436.332.729.821 935'4535"3035'1585"0---0"1708-0"1652-0"0940--0"0188--00891- --The signification of these figures may be illustrated by anexample.
I f a ray of heat, corresponding to the angle ofdeviation 39°'45, passes through (he unit of carbonic acid, it de-in the Air ul~on the Temperature of the Ground.245creases in intensityinthe proportion 1 : 0"934 (log----- --0"0296),the corresponding value for the unit el: water-vapour is1:0"775 (log=--0"1105). These figures are of course onlyvalid for the circumstances in which the observations weremade, viz., that the ray should have traversed a quantity ofcarbonic acid K = 1"1 and a quantity of water-vapour W = 0"3before the absorption in the next quantities of carbonic acidand water-vapour was observed.
And these second quantitiesshould not exceed K = I ' I and W=1"8, for the observationsare not extended over a greater interval than between K = 1"1and K=2"2~ and W = 0 " 3 and W = 2 " l (the numbers for Kand W are a little different for rays of different kind). BelowA is written the relative value of the intensity of radiationfor a given kind of ray in the moonlight after it has traversedK----1 and W=0"3.
In some cases the calculation givespositive values for log x or log y. As this is a physicalabsurdity (it would signify that the ray should be strengthened by its passage through the absorbing gas), I have inthese cases, which must depend on errors of observation,assumed the absorption equal to zero for the correspondinggas, and by means of this value calculated the absorptioncoefficient of the other gas, and thereafter also A.As will be seen from an inspection of Table I., the values ofiobs. agree in most cases pretty well with the calculated valuesi talc. But in some cases the agreement is not so good as onecould wish.
These cases are mostly characterized by a small" weight" G, that is in other words, the material of observation is in these cases relatively insufficient. These casesoccur also chiefly for such rays as are strongly absorbed bywater-vapour. This effect is probably owing to the circumstance that the aqueous, vapour, in the atmosphere,..which isassumed to have vaned proportmnally to the humidity at theearth's surface, has not always had the assumed ideal anduniform distribution with the height. From observationsmade during balloon voyages, we know also that the distribution of the aqueous vapour may be very irregular, anddifferent from the mean ideal distribution.
It is also amarked feature that in some groups, for instance the third,nearly all the observed numbers are less than the calculatedones, while in other groups, for instance the fourth, thecentralT is the case. This circumstance shows that the divisionof the statistic material is carried a little too far ; and a combination of these two groups would have shown a close agreementbetween the calculated and the observed figures. As, however, such a combination is without influence on the correctness of the calculated absorption-coefficients~ I have omit~ed24:6 Prof.
S. Arrhenius on the Influence of Carbonic Acida rearrangement of the figures in greater groups, with consequent recalculation.A circumstance that argues very greatly in favour of theopinion that the absorption-coefficient given in Table II.cannot contain great errors, is that so very few logarithmshave a positive value. It' the observations of Langley hadbeen wholly insufficient, one would have expected tO findnearly as many positive as negative logarithms.
:Now thereare only three such cases, viz.,/'or carbonic acid at "m angleof 40 °, and for water-vapour at the angles 36G'45 and36°'15. The observations for 40 ° are not very accurate,because they were of little interest to Langley, the corresponding rays not belonging to the moon's spectrum but onlyto the diffused sunlight from the moon.
As these rays alsodo not occur to any sensible degree in the heat from a bodyof 15 ° C., this non-agreement is without importance for ourproblem. The two positive values for the logarithms belonging to aqueous vapour are quite insignificant. They correspondonly to errors of 0"2 and 1"5 per cent. for the absorption ofthe quantity W = 1, and fall wholly in the range of experimental errors.It is certainly not devoid of interest to compare theseabsorption-coefficients with the results of the direct observations by Paschen and /~ngstrSm*.
In making this comparison, we must bear in mind that an exact agreementcannot be expected, for the signification of the above coefficients is rather unlike that of the coefficients that are ormay be calculated from the observations of these two authors.The above coefficients give the rate of absorption of a raythat has traversed quantities of carbonic acid (K----1"1) andwater-vapour (W = 0"3); whilst the coefficients of Paschen and/~ngstrSm represent the absorption experienced by a ray onthe passage through the first layers of these gases. Insome cases we may expect a great difference between thesetwo quantities, so that only a general agreement can belooked for.According to Paschen's figures there seems to exist nosensible emission or absorption by the aqueous vapour atwave-lengths between 0"9/~ ami 1"2 ~ (.corresponding to theangle of deviation 4:0°). On the other hand, the representation of the sun's spectrum by Langley shows a great many• I)aschen, Wied.
Ann. 1. p. 409, 1893 ; li. p. 1, lit. p. 2C9, and liii.p. 334, 18941 especiallyvol. 1.otab. ix. fig. 5, curve 1 for carbonic acid,cltrve 2 for aqueous vapour. AngstrSm,JBihan# till ~. lZet.-Ak, ltandlingar, Bd. xv. Afd. 1, No. 9, p. 15, 1889; Ofverslgt af K. Fet.oA~.2Srhandl.
1889, No. 91 p. 553,in the Air upon the Temperature of the (_4round.24:7strong absorption-bands in this interval, among which thosemarked p, o'~ % and (~ are the most prominent*, and theseabsorption-bands belong most probably to the aqueous vapour,That Paschen has not observed any emission by water-vapourin this interval may very well be accounted for by the factthat his heat-spectrmn had a very small intensity for theseshort-waved rays.
But it may be conceded that the absorptioncoefficient for aqueous wlpour at this angle in Table lI. isnot very accurate (probably too great), in consequence of thelittle importance that Langley attached to the correspondingobservations. After this occurs in Langley's spectrum the.great absorption-band ~ at the angle 39"45 (A.= 1"4/2), wherein Paschen's curve the emission first becomes sensible(logy=--0"1105 in Table II.). At wave-lengths of greatervalue we find according to Pasehen strong absorption-bandsat A.=l"83k* (!2 in Langley's spectrum), i.e.
in the neighbourhood of 39°'30 and at X= 2"64/2 (Langley's X) a little abovethe angle 39°'15. In accordance with this I have foundrather large absorption-coefficients for aqueous vapour atthese angles (logy=-0"095"2 and --0"0862 resp.). From~=3"0/2 to h.=4"7/z thereafter, according to Pasehen theabsorption is very small, in agreement with my calculation(fogy= --0"0068 at 39 °, corresponding to X=4"3/2). Fromthis point the absorption increases again and presents newmaxima at X=5"5/2, X= 6"6 /~, and X=7"7/~, i.e.
in thevicinity of the angles 38°'45 (~.=5"6/2) and 38°'30 (X=7"1#).In this region the absorption of the water-vapour is continuous over the whole interval, in consequence of which thegreat absorption-coefficient in this part (log y=--0"3114 and--0"2362) becomes intelligible. In consequence of the decreasing intensity of the emission-spectrum of aqueous vapourin t)aschen's curve we cannot pursue the details of it closely~but it seems as if the emission of the water-vapour would alsobe considerable at X=8"7/~ (39c'15)~ which corresponds withthe great absorption-coefficient (logy=--0"1933) at thisplace. The observations of Paschen are not extended further,ending at X= 9'5/2, which corresponds to an angle of 39°'08.For carbonic acid we filld at first the value zero at 40 °, inagreement with the figures of Paschen and ~ngstrSmt.
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