CLIMATE CHANGE
`Critical Concepts in the Environment
`
`Edited by Frank Chambers and
`Michael Ogle
`
`Volume I
`
`’Global Warming’: Carbon Dioxide and Climate Change
`
`~I Routledge
`Taylor & Francis Group
`
`LONDON AND NEW YORK
`
`Lupin Ex. 1057 (Page 1 of 36)
`
`

`

`First published 2002
`by Routledge
`11 New Fetter Lane, London EC4P 4EE
`
`Simultaneously published in the USA and Canada
`by Routledge
`29 West 35th Street, New York, NY 10001
`
`Routledge is an imprint of the Taylor & Francis Group
`
`Editorial material and selection © 2002 Frank Chambers and
`Michael Ogle; individual contributors retain copyright in
`their own material.
`
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`
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`
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`
`ISBN 0-415-27656-X (Set)
`ISBN 0-4 I5-27657-8 (Volume I)
`
`Publisher’s Note
`References within each chapter are as they
`appeared in the original complete work.
`
`General Library dys~e~n
`University of Wisce~i;n,
`728 State S#eet .......
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`U.S,A.
`
`Lupin Ex. 1057 (Page 2 of 36)
`
`

`

`This material may,~be, protected by Copyright iaw (Title, 17 U~S. Code)
`
`ON THE INFLUENCE OF CARBONIC
`ACID IN THE AIR UPON THE
`TEMPERATURE OF THE GROUND
`
`Svante Arrhenius1
`
`Source: Philosophical Magazine and Journal of Science, 5th Series 41(251) (1896): 237-276.
`
`I Introduction: observations of Langley on
`atmospherical absorption
`
`A great deal has been written on the influence of the absorption of the
`atmosphere upon the climate. Tyndallz in particular has pointed out the
`enormous importance of this question. To him it was chiefly the diurnal and
`annual variations of the temperature that were lessened by this circumstance.
`Another side of the question, that has long attracted the attention of physi-
`cists, is this: is the mean temperature of the ground in any way influenced by
`the presence of heat-absorbing gases in the atmosphere? Fourier3 maintained
`that the atmosphere acts like the glass of a hot-house, because it lets through
`the light rays of the sun but retains the dark rays from the ground. This idea
`was elaborated by Pouillet4; and Langley was by some of his researches led
`to the view, that "the temperature of the earth under direct sunshine, even
`though our atmosphere were present as now, would probably fall to -200° C.,
`if that atmosphere did not possess the quality of selective absorption".~ 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.6
`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
`
`11
`
`Lupin Ex. 1057 (Page 3 of 36)
`
`

`

`’GLOBAL WARMING’
`
`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]
`The selective absorption of the atmosphere is, according to the researches
`of Tyndall, Lecher and Pernter, R6ntgen, Heine, Langley, ]~ngstr6m,
`Paschen, and others.8 of a wholly different kind. It is not exerted by the chief
`mass of the air, but in a high degree by aqueous vapour and carbonic acid,
`which are present in the air in small quantities. Further, this absorption is not
`continuous over the whole spectrum, but nearly insensible in the light part of
`it, and chiefly limited to the long-waved part, where it manifests itself in very
`well-defined absorption-bands, which fall off rapidly on both sides.9 The
`influence of this absorption is comparatively small on the heat from the sun,
`but must be of great importance in the transmission of rays from the earth.
`Tyndall held the opinion that the water-vapour has the greatest influence,
`whilst other authors, for instance Lecher and Pernter, are inclined to think
`that the carbonic acid plays the more important part. The researches of
`Paschen show that these gases are both very effective, so that probably some-
`times the one, sometimes the other, may have the greater effect according to
`the circumstances.
`In order to get an idea of how strongly the radiation of the earth (or any
`other body of the temperature +15° C.) is absorbed by quantities of water-
`vapour or carbonic acid in the proportions in which these gases are present
`in our atmosphere, one should, strictly speaking, arrange experiments on the
`absorption of heat from a body at 15° by means of appropriate quantities of
`both gases. But such experiments have not been made as yet, and, as they
`would require very expensive apparatus beyond that at my disposal, I have
`not been in a position to execute them. Fortunately there are other researches
`by Langley in his work on ’The Temperature of the Moon,’ with the aid of
`which it seems not impossible to determine the absorption of heat by aque-
`ous vapour and by carbonic acid in precisely the conditions which occur in
`our atmosphere. He has measured the radiation of the full moon (if the
`moon was not full, the necessary correction relative to this point was
`applied) at different heights and seasons of the year. This radiation was
`moreover dispersed in a spectrum, so that in his memoir we find the figures
`for the radiant heat from the moon for 21 different groups of rays, which are
`defined by the angle of deviation with a rocksalt prism having a refracting
`angle of 60 degrees. The groups lie between the angles 40° and 35°, and each
`group is separated from its neighbours by an interval of 15 minutes. Now the
`temperature of the moon is nearly the same as that of the earth, and the
`moon-rays have, as they arrive at the measuring-instruments, passed through
`layers of carbonic acid and of aqueous vapour of different thickness accord-
`ing to the height of the moon and the humidity of the air. If, then, these
`observations were wholly comparable with one another, three of them would
`suffice for calculating the absorption coefficient relatively to aqueous vapour
`and carbonic acid for any one of the 21 different groups of rays. But, as an
`
`12
`
`Lupin Ex. 1057 (Page 4 of 36)
`
`

`

`THE INFLUENCE OF CARBONIC ACID IN THE AIR
`
`inspection of the 24 different series of observations will readily show, this is
`not the case. The intensity of radiation for any group of rays should always
`diminish with increasing quantity of aqueous vapour or carbonic acid tra-
`versed. Now the quantity of carbonic acid is proportional to the path of the
`ray through the atmosphere, that is, to the quantity called "Air-mass" in
`Langley’s figures. As unit for the carbonic acid we therefore take air-mass =
`1, i.e. the quantity of carbonic acid that is traversed in the air by a vertical
`ray. The quantity of aqueous vapour traversed is proportional partly to the
`"air-mass," partly to the humidity, expressed in grammes of water per cubic
`metre. As unit for the aqueous vapour I have taken the quantity of aqueous
`vapour that is traversed by a vertical ray, if the air contains 10 grammes per
`cubic metre at the earth’s surfacea°. If we tabulate the 24 series of observa-
`tions published by Langley in the work cited with respect to the quantities of
`carbonic acid and aqueous vapou~:, we immediately detect that his figures run
`very irregularly, so that very many exceptions are found to the rule that the
`transmitted heat should continuously decrease when both these quantities
`irtcrease. And it seems as if periodic alternations with the time of observa-
`tion occurred in his series. On what circumstance these alterations with the
`time depend one can only make vague conjectures: probably the clearness of
`the sky may have altered within a long period of observation, although this
`could not be detected by the eye. In order to eliminate this irregular vari-
`ation, I have divided the observations into four groups, for which the mean
`quantities of carbonic acid (K) and of water-vapour (W) were 1.21 and 0-36,
`2.2! and 0"86, 1"33 and 1.18, and 2.22 and 2.34 respectively. With the help of
`the mean values of the heat-radiation for every group of rays in these four
`groups of observations, I have roughly calculated the absorption coefficients
`(x and y) for both gases, and by means of these reduced the value for each
`observation to the value that it would have possessed if K and W had been
`1"5 and 0-88 respectively. The 21 values for the different rays were then
`summed up, so that I obtained the total heat-radiation for every series of
`observations, reduced to K = 1.5 and W = 0-88. If the materials of observa-
`tion were very regular, the figures for this total radiation should not differ
`very much from one another. In fact, one sees that observations that are
`made at nearly the same time give also nearly equal values, but if the obser-
`vations were made at very different times, the values differ also generally very
`much. For the following periods I have found the corresponding mean values
`of the total radiation:--
`
`Period.
`
`1885. Feb. 21-June 24
`1885. July 29-1886. Feb. 16.
`1886. Sept. 13-Sept. 18
`1886. Oct. 1 I-Nov. 8
`1887, Jan. 8-Feb. 9
`
`Mean
`value,
`4850
`6344
`2748
`5535
`3725
`
`Reduction
`factor.
`1.3
`1.00
`2.31
`1.15
`I’70
`
`13
`
`Lupin Ex. 1057 (Page 5 of 36)
`
`

`

`’GLOBAL WARMING’
`
`In order to reduce the figures of Langley to comparability with one
`another, I have applied the reduction factors tabulated above to the observa-
`tions made in the respective periods. I have convinced myself that by this
`mode of working no systematic error is introduced into the following
`calculations.
`After this had been done, I rearranged the figures of Langley’s groups
`according to the values of K and W in the following table. (For further
`details see my original memoir.)
`in this table the angle of deviation is taken as head-title. After K and W
`stand the quantities of carbonic acid and water-vapour traversed by the ray
`in the above-mentioned units. Under this comes after i obs. the intensity of
`radiation (reduced) observed by Langley on the bolometer, and after this
`the corresponding value i calc., calculated by means of the absorption-
`coefficients given in Table II. below. G is the "weight" given to the corres-
`ponding i obs. in the calculation, using the method of least squares.
`For the absorption-coefficients, calculated in this manner, I give the follow-
`ing table. (The common logarithms of the absorption-coefficients are
`tabulated.)
`The signification of these figures may be illustrated by an example. If a ray
`of heat, corresponding to the angle of deviation 39°-45, passes through the
`unit of carbonic acid, it decreases in intensity in the proportion 1 : 0.934
`(log=-0"0296), the corresponding value for the unit of water-vapour is 1 :
`0"775 (log= -0"1105). These figures are of course only valid for the circum-
`stances in which the observations were made, viz., that the ray should have
`traversed a quantity of carbonic acid K = 1. I and a quantity of water-vapour
`W = 0"3 before the absorption in the next quantities of carbonic acid and
`water-vapour was observed. And these second quantities should not exceed
`K = 1.1 and W = 1-8, for the observations are not extended over a greater
`interval than between K = 1.1 and K = 2.2, and W = 0.3 and W = 2-1 (the
`numbers for K and W are a little different for rays of different kind). Below
`A is written the relative value of the intensity of radiation for a given kind of
`ray in the moonlight after it has traversed K = 1 and W = 0-3. In some cases
`the calculation gives positive values for log x or log y. As this is a physical
`absurdity (it would signify that the ray should be strengthened by its passage
`through the absorbing gas), I have in these cases, which must depend on
`errors of observation, assumed the absorption equal to zero for the corres-
`ponding gas, and by means of this value calculated the absorption-coefficient
`of the other gas, and thereafter also A.
`As will be seen from an inspection of Table I., the values of i obs. agree in
`most cases pretty well with the calculated values i calc. But in some cases the
`agreement is not so good as one could wish. These cases are mostly charac-
`terized by a small "weight" G, that is in other words, the material of observa-
`tion is in these cases relatively insufficient. These cases occur also chiefly for
`such rays as are strongly absorbed by water-vapour. This effect is Probably
`
`14
`
`Lupin Ex. 1057 (Page 6 of 36)
`
`

`

`Table I Radiation (i) of the full moon for different values of K and W.
`
`400" 39°’45" 390"30" 39°’15" 390" 380.45. 380.30, 38°.15. 38°. 370.45. 37~.30. 370.15. 370, 360.45. 360.30. 36".15. 36°. 35°.45. 35°,30. 35°.15. 35°.
`K
`1-16
`1"12
`1.16 1"13
`1-16
`1-13
`1.16 1.13
`1-16
`1.13
`W
`0.32
`0-269 0"32 0-271
`0"32 0.271
`0"32 0-271
`0-32
`0-271
`iobs.
`28-7 26’6
`27’0 26.4
`24-8 24-8
`I2.6 20.I
`43"8
`65-9
`icalc. 27-0 34.5
`29-0 25-7
`24"4 23.5
`12-5 19,4
`40"8
`58-0
`G
`79
`27
`75 56
`69
`53
`35
`43
`121
`140
`1-29
`1"29
`0-86
`1.04
`18-2 11.0
`21.8
`12.5
`74
`38
`
`1-16
`0-32
`74-4
`68-8
`206
`
`1-16
`0-32
`68.6
`73.7
`190
`
`1-16
`0"32
`59
`57"1
`163
`
`1.18
`0.34
`56,2
`50,9
`118
`
`1-18 1"27
`0-34 0"48
`48"3
`43-4
`46.0
`34-9
`102
`28
`
`1-27
`1.26
`0.90 0-96
`5.8
`3-7
`8-6
`12.8
`24
`13
`
`1"29
`0-86
`14-0
`26.1
`57
`
`1 "27
`1.07
`32.0
`42.1
`139
`
`1.27
`1"27
`1-27
`1.31
`1"32
`1-00
`1,00
`1.00
`1"05
`1"00
`52"3
`58-9
`50"3
`47.9
`41"2
`52-7
`53-0
`51.2
`47-1
`39,2
`261 294 251 205 140
`
`1-32
`1.00
`31"7
`34.2
`108
`
`1.16 1-27
`0.32 0-48
`40-7 39.0
`36.4 31.3
`112
`25
`1.28 1"33
`0.81 0-51
`29-7
`25~7
`31.1
`30.3
`98
`16
`
`1-27
`0.48
`32.6
`27.7
`21
`
`1,33
`0.51
`18.8
`26-8
`12
`
`1"27
`0-48
`31"5
`27-3
`20
`
`1-33
`1"07
`27-5
`21.3
`39
`
`1"16
`0-32
`19.7
`19.3
`54
`
`1-25
`0-60
`16-6
`17.2
`22
`
`K
`W
`iobs.
`icale.
`G
`
`1.28
`1"27
`0.81
`1-07
`22.9 31-2
`23-1
`27,9
`76
`I35
`
`1-29 1-29
`0"86 I’04
`26"7 21.3
`25-4 21"2
`109 73
`
`1.46
`K
`1,40
`1-39 1-49
`W
`0.75
`0,823 0.78 0-87
`iobs.
`11.9 28,2
`23.0 18.9
`icalc. 23,6 29.4
`25-4 20,9
`G
`28
`28
`25 38
`K
`1.48
`1.52
`W
`1-80
`2,03
`iobs.
`25,2 27,6
`icalc.
`16-9 21-4
`G
`30
`22
`
`1.48 1.51
`1-78 1-64
`24.6 18-3
`20"2 17.9
`51 31
`
`1.48
`1.78
`27.6
`18-5
`37
`
`1-51
`1.95
`4-8
`5-9
`5
`2"26 2"26
`2"26 2-26
`1"08 1"08
`1-08
`1-08
`20-8 16.4
`II’1
`8.2
`21-3 16.6
`10.1
`7-7
`43 34 23
`17
`
`m
`
`K
`2.26
`2"26
`W
`1-08
`1.08
`iobs.
`21.3 23’4
`icalc. 21.2 25"9
`G
`44
`49
`
`K
`W
`iobs.
`icale.
`G
`
`2.03
`1.93
`13"4
`16-2
`55
`
`1-92
`2,30
`12.8
`19"4
`29
`
`1-92 1,93
`2"24 2"16
`14.8 15-1
`17"3 14.5
`35
`47
`
`1"92
`1.92
`2-24 2-30
`10"3
`6.6
`13,0
`3-8
`25
`15
`
`1.49
`1-49
`0.89 0-89
`18.0
`9-2
`18-6
`12-7
`37
`17
`
`1.50
`1.49
`0.82 0-89
`9.9
`14-4
`7.8
`10.8
`33
`28
`
`1.49
`0.87
`34.8
`43.2
`70
`1.52
`2-03
`45-5
`28.2
`37
`
`2"26
`1,08
`36-I
`33.9
`75
`
`1.50
`0-82
`24-6
`24.4
`81
`1.48
`1-80
`17-6
`12.0
`21
`
`2-27
`1"06
`17"3
`14.7
`37
`
`2-37
`2"20
`7.9
`6"1
`26
`
`2.27
`1-06
`47.1
`48-3
`112
`
`2.26
`1-08
`44-6
`47.1
`93
`
`2"12
`1-91
`1.90
`1-15
`1.10
`1"11
`32.0 27.8
`24,7
`33"5
`32.8
`27,4
`98
`66
`58
`2-45 2"37
`2"25
`2,20
`26.7
`19.4
`23-7
`18.4
`77
`63
`
`1"91
`1-10
`26-6
`26.8
`63
`
`2"45
`2-25
`22.6
`21"4
`65
`
`1"92
`2"05
`2-30
`1-93
`20-8
`31"5
`23-4
`35-1
`47 129
`
`1.92
`2"05
`2-30
`1-93
`24-7
`33.2
`27.1
`31"8
`56 137
`
`1.50
`1.49
`1-48
`1.48
`0-84
`0.87
`0-85
`0-85
`46.6
`43.1
`36-4 35.4
`55.2
`55-2 47-I
`42.5
`15I
`87
`149
`146
`1.48
`1"48
`1-48
`1-48
`1’67
`1-66
`1"58
`1"66
`43-9
`47.5
`48 "7
`45.8
`40"2 ,38,2
`43.4
`42"5
`119 136
`176
`131
`
`1,48
`0.85
`31,2
`36-3
`127
`1.48
`1.66
`34,5
`33,0
`99
`
`1-41
`0.97
`28.3
`33-0
`54
`1"48
`1-83
`35"0
`32.0
`82
`
`1-45
`1-41
`0-89 0.97
`24.9
`16-6
`29.3 27.3
`78
`32
`1-48 I "48
`1,66 1.83
`27-5 28-7
`23"6 23"4
`79
`67
`
`1-41
`0.98
`15.4
`22.3
`29
`1.48
`1.58
`21"4
`17.8
`81
`
`1.90
`1.11
`16-0
`17-5
`37
`
`1.41
`0.98
`10.3
`22.0
`19
`1"48
`1"83
`17.4
`15-4
`41
`
`1"90
`1-15
`13-9
`20-4
`32
`
`2.09
`1.91
`1.18
`1"I1
`24-5
`19-0
`23"6 21-3
`72
`45
`
`2.37
`1.97
`1"97
`1"97
`2.20 2-33
`2-33
`2-33
`I8.8
`16-4
`I0-9
`12"I
`16.8
`17-4
`11.5
`12-2
`61
`32 22 24
`
`1.41
`0.98
`9-2
`14-7
`17
`1-48
`1.66
`15"4
`11-6
`43
`
`2-12
`
`10"1
`12"2
`31
`
`1-97
`2-33
`7"9
`8-4
`16
`
`1-48
`1-80
`3.7
`4.7
`4
`
`1.51
`1.95
`3-6
`6"6
`3
`2-26 2"26
`1-08
`1.08
`4-5
`3-5
`4.5
`5"1
`9
`7
`1-92 2’45
`2.24 2"25
`3"4
`3-4
`2-9
`2’6
`8
`10"
`
`

`

`’GLOBAL WARMING’
`
`Table H Absorption-coefficients of carbonic acid (x) and aqueous vapour (y).
`
`Angle of Deviation.
`
`log x.
`
`40°
`
`39"45
`39"30
`39’ 15
`39"0
`38"45
`38- 30
`38" 15
`38"0
`37"45
`37"30
`37"15
`37"0
`
`36"45
`
`36.30
`
`36.15
`
`36"0
`35.45
`35"30
`35" 15
`35"0
`
`0"0000
`[+0-0286
`-0"0296
`-0’0559
`-0’ 1070
`-0’3412
`-0-2035
`-0"2438
`-0-3760
`-0"1877
`-0"0931
`-0"0280
`-0-0416
`-0"2067
`
`-0"2466
`[-0"2465
`-0.2571
`
`-0. i652
`{-0"1708
`-0"0940
`-0" 1992
`-0" 1742
`-0.0188
`-0"0891
`
`log y.
`
`-0"1506 }
`-0"1455
`-0" 1105
`-0"0952
`-0"0862
`-0"0068
`-0"3114
`-0"2362
`-0" 1933
`-0"3196
`-0" 1576
`-0"1661
`-0-2036
`-0"0484
`
`-0"0000
`+0"0008)
`-0.0507
`
`-0.0000
`+0"0065)
`-0" 1184
`-0.0628
`-0" 1408
`-0-1817
`-0" 1444
`
`A.
`
`27-2
`
`34"5
`29"6
`26"4
`27"5
`24"5
`13" 5
`21 ’4
`44"4
`59"0
`70"0
`75-5
`62"9
`
`56-4
`
`51.4
`
`39"1
`
`37"9
`36"3
`32"7
`29"8
`21 "9
`
`owing to the circumstance that the aqueous vaponr in the atmosphere, which
`is assumed to have varied proportionally to the humidity at the earth’s sur-
`face, has not always had the assumed ideal and uniform distribution with the
`height. From observations made during balloon voyages, we know also that
`the distribution of the aqueous vapour may be very irregular, and different
`from the mean ideal distribution. It is also a marked feature that in some
`groups, for instance the third, nearly all the observed numbers are less than
`the calculated ones, while in other groups, for instance the fourth, the con-
`trary is the case. This circumstance shows that the division of the statistic
`material is carried a little too far; and a combination of these two groups
`would have shown a close agreement between the calculated and the
`observed figures. As, however, such a combination is without influence on
`the correctness of the calculated absorption-coefficients, I have omitted
`a rearrangement of the figures in greater groups, with consequent
`recalculation.
`A circumstance that argues very greatly in favour of the opinion that the
`absorption-coefficient given in Table II. cannot contain, great errors, is that so
`very few logarithms have a positive value. If the observations of Langley had
`been wholly insufficient, one would have expected to find nearly as many
`
`16
`
`Lupin Ex. 1057 (Page 8 of 36)
`
`

`

`THE INFLUENCE OF CARBONIC ACID IN THE AIR
`
`positive as negative logarithms. Now there are only three such cases, viz., for
`carbonid acid at an angle of 40°, and for water-vapour at the angles 36°-45
`and 36°. 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 only to the diffused sunlight from the moon. As these
`rays also do not occur to any sensible degree in the heat from a body of 15°
`C., this non-agreement is without importance for our problem. The two posi-
`tive values for the logarithms belonging to aqueous vapour are quite
`insignificant. They correspond only to errors of 0.2 and 1.5 per cent. for the
`absorption of the quantity W=I, and fall wholly in the range of experimental
`errors.
`It is certainly not devoid of interest to compare these absorption-
`coefficients with the results of the direct observations by Paschen and
`/kngstr6m.1~ In making this comparison, we must bear in mind that an exact
`agreement cannot be expected, for the signification of the above coefficients
`is rather unlike that of the coefficients that are or may be calculated from the
`observations of these two authors. The above coefficients give the rate of
`absorption of a ray that has traversed quantities of carbonic acid (K=I-1)
`and water-vapour (W=0-3); whilst the coefficients of Paschen .and/~ngstr6m
`represent the absorption experienced by a ray on the passage through the
`first layers of these gases. In some cases we may expect a great difference
`between these two quantities, so that only a general agreement can be
`looked for.
`According to Paschen’s figures there seems to exist no sensible emission or
`absorption by the aqueous vapour at wave-lengths between 0"9/z and 1"2/~
`(corresponding to the angle of deviation 40°). On the other hand, the repre-
`sentation of the sun’s spectrum by Langley shows a great many strong
`absorption-bands in this interval, among which those marked p, o, x, and q~
`are the most prominent,~2 and these absorption-bands belong most probably
`to the aqueous vapour, That Paschen has not observed any emission by
`water-vapour in this interval may very well be accounted for by the fact that
`his heat-spectrum had a very small intensity for these short-waved rays. But it
`may be conceded that the absorption-coefficient for aqueous vapour at this
`angle in Table II. is not very accurate (probably too great), in consequence of
`the little importance that Langley attached to the corresponding observa-
`tions. After this occurs in Langley’s spectrum the great absorption-band ~g at
`the angle 39.45 (L = 1"4 /z), where in Paschen’s curve the emission first
`becomes sensible (!og y = -0.I 105 in Table II.). At wave-lengths of greater
`value we find according to Paschen strong absorption-bands at L = 1.83/t (~
`in Langley’s spectrum), i.e. in the neighbourhood of 39°-30 and at ~, = 2.64/t
`(Langley’s X) a little above the angle 39°. 15. In accordance with this I have
`found rather large absorption-coefficients for aqueous vapour at these angles
`(log y = -0.0952 and -0.0862 resp.). From L = 3"0/,t to ~, = 4.7/~ thereafter,
`according to Paschen the absorption is very small, in agreement with my
`
`I7
`
`Lupin Ex. 1057 (Page 9 of 36)
`
`

`

`’GLOBAL WARMING’
`
`calculation (log y = -0.0068 at 39°, corresponding to 2. = 4.3 #). From this
`point the absorption increases again and presents new maxima at 2. = 5.5 p,
`2. = 6-6 p, and 2. = 7-7 lz, i.e. in the vicinity of the angles 38°.45 (2. = 5.6
`and 38°.30 (2. = 7-1 /~). In this region the absorption of the water-vapour
`is continuous over the whole interval, in consequence of which the great
`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 vapour in Paschen’s curve we cannot pursue the details
`of it closely, but it seems as if the emission of the water-vapour would also
`be considerable at 2. = 8.7 # (39°.15), which corresponds with the great
`absorption-coefficient (log y =-0"1933) at this place. The observations of
`Paschen are not extended further, ending at 2. = 9"5/z, which corresponds to
`an angle of 39°.08:
`For carbonic acid we find at first the value zero at 40°, in agreement
`with the figures of Paschen and Angstr6m.13 The absorption of carbonic
`acid first assumes a sensible value at 2. = 1.5 /t, after which it increases
`rapidly to a maximum at 2. = 2"6 p, and attains a new extraordinarily
`strong maximum at 2. = 4.6 (Langley’s Y). According to Angstr6m the
`absorption of carbonic acid is zero at Z = 0"9 p, and very weak at 2. = 1.69
`y, after which it increases continuously to 2. = 4’6 p and decreases again to
`2. = 6.0/~. This behaviour is entirely in agreement with the values of log x
`in Table II. From the value zero at 40° (2. = 1.0 p) it attains a sensible
`value (-0.0296) at 39°’45 (2. = 1.4 p), and thereafter greater and greater
`values (-0’0559 at 39°.30, and -0.1070 at 39°.15) till it reaches a consider-
`able maximum (-0.3412 at 39°, 2. = 4.3 p). After this point the absorption
`decreases (at 38°.45 = 5.6/~, log x = -0.2035). According to Table II. the
`absorption of carbonic acid at 38°-30 and 38°.15 (2. = 7.1 # and 8.7 #) has
`very great values (log x = -0"2438 and -0-3730), whilst according to
`Angstr6m it should be insensible. This behaviour may be connected with
`the fact that Angstr6m’s spectrum had a very small intensity for the larger
`wavelengths. In Paschen’s curve there are traces of a continuous absorp-
`tion by the carbonic acid in this whole region with weak maxima at 2. =
`5.2/z, 2. = 5.9/~, 2. = 6.6 p (possibly due to traces of water-vapour), 2. = 8.4
`y, and 2. = 8.9 F. In consequence of the strong absorption of water-vapour
`in this region of the spectrum, the intensity of radiation was very small in
`Langley’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
`the water-vapour too small in this part (between 38°.30 and 38°.0). This
`can happen the more easily, as in Table I. K and W in general increase
`together because they are both proportional to the "air-mass." it may be
`pointed out that this also occurs in the problems that are treated below, so
`that the error from this cause is not of so great importance as one might
`think at the first view. ’
`
`18
`
`Lupin Ex. 1057 (Page 10 of 36)
`
`

`

`THE INFLUENCE OF CARBONIC ACID IN THE AIR
`
`For angles greater than 38° (L > 9"5 kt) we possess no direct observations
`of the emission or absorption of the two gases. The sun’s spectrum, accord-
`ing to Langley, exhibits very great absorption-bands at about 37°’50, 37°’25,
`37°, and 36°’40°. According to my calculations the aqueous vapour has its
`greatest absorbing power in the spectrum from 38° to 35° at angles between
`37°-15 and 37°-45 (the figures for 35°’45, 35°’30, and 35°’15 are very
`uncertain, as they depend upon very few measurements), and the carbonic
`acid between 36°.30 and 37°’0. This seems to indicate that the first two
`absorption-bands are due to the action of water-vapour, the last two to that
`of carbonic acid. It should be emphasized that Langley has applied the
`greatest diligence in the measurement of the intensity of the moon’s
`radiation at angles between 36° and 38°, where this radiation possesses
`its maximum intensity. It may, therefore, be assumed that the calculated
`absorption-coefficients for this part of the spectrum are the most exact. This
`is of great importance for the following calculations, for the radiation from
`the earth~4 has by far the greatest intensity (about two thirds, cf p. 250) in
`this portion of the spectrum.
`
`II The total absorption by atmospheres of
`varying composition
`
`As we have now determined, in the manner described, the values of the
`absorption-coefficients for all kinds of rays, it will with the help of Langtey’s
`figures15 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 specified
`quantities of carbonic acid and water-vapour. To begin with, we will execute
`this calculation with the values K = 1 and W = 0.3. We take that kind of ray
`for which the best determinations have been made by Langley, and this lies in
`the midst of the most important part of the radiation (37°). For this pencil
`of rays we find the intensity of radiation at K = 1 and W = 0-3 equal to 62"9;
`and with the help of the absorption-coefficients we calculate the intensity for
`K = 0 and W = 0, and find it equal to 105. Then we use Langley’s experi-
`ments on the spectral distribution of the radiation from a body of 15° C.,
`and calculate the intensity for all other angles of deviation. These intensities
`are given under the heading M. After this we have to calculate the values for
`K = 1 and W = 0.3. For the angle 37° we know it to be 62"9. For any other
`angle we could take the values A from Table II. if the moon were a body of
`15° C. But a calculation of the figures of Very~6 shows that the full moon has
`a higher temperature, about 100° C. Now the spectral distribution is nearly,
`but not quite, the same for the heat from a body of 15° C. and for that from
`one of I00° C. With the help of Langley’s figures it is, however, easy to
`reduce the intensities for the hot body at 100° (the moon) to be valid for a
`body at 15° (the earth). The values of A reduced in this manner are tabulated
`below under the heading N.
`
`19
`
`Lupin Ex. 1057 (Page 11 of 36)
`
`

`

`’GLOBAL WARMING’
`
`Angle 40°.
`3.4
`M
`N
`3.1
`
`39-45.
`tl.6
`10-1
`
`39"30,
`24,8
`11-3
`
`39.15,
`45-9
`13.7
`
`39.0.
`84-0
`18-0
`
`38,45,
`121.7
`18.1
`
`38"30.
`161
`11"2
`
`38.15.
`189
`19"6
`
`38"0.
`210
`44.4
`
`37.45.
`210
`59
`
`37"30.
`188
`70
`
`Angle
`M
`N
`
`37°.15. 37.0.
`147
`105
`75.5
`62’9
`
`36.45. 36-30. 36-15, 36.0.
`99
`60
`51
`103
`37-9
`56.4
`51.4
`39,1
`
`35.45. 35-30. 35.15. 35-0.
`65
`62
`43
`39
`39.2
`37.6
`36"0
`28"7
`
`Sum.
`2023
`743.2
`
`P.e.
`100
`37.2
`
`For angles less than 37° one finds, in the manner above described, numbers
`that are a little inferior to the tabulated ones, which are found by means of
`the absorption-coefficients of Table II. and the values of N. In this way the
`sum of the M’s is a little greater (6"8 per cent.) than it would be accordingto
`the calculation given above. This non-agreement results probably from the
`circumstance that the spectrum in the observations was not quite pure.
`The value 37.2 may possibly be affected with a relatively great error in
`consequence of the uncertainty of the M-values. In the following calcula-
`tions it is not so much the value 37.2 that plays the important part, but rather
`the diminution of the value caused by increasing the quantities K and W. For
`comparison, it may be mentioned that Langley has estimated the quantity of
`heat from the moon that passed through the atmosphere (of mean com-
`position) in his researches to be 38 per cent.17 As the mean atmosphere in
`Langley’s observations corresponded with higher values of K and W than K
`= 1 and W = 0.3, it will be seen that he attributed to the atmosphere a greater
`transparence for opaque rays than I have done. In accordance with Langtey’s
`estimation, we should expect for K = 1 and W = 0-3 a value of about 44
`instead of 37.2. How great an influence this difference may exert will be
`investigated in what follows.
`The absorption-coefficients quoted in Table II. are valid for an interval of
`K between about 1-1 and 2-25, and for W between 0.3 and 2-22. In this
`interval one rfiay, with the help of those coefficients and the values of N
`given above, calculate the value of N for another value of K and W, and so in
`this way obtain by means of summation the total heat that passes through an
`atmosphere of given condition. For further calculations I have also computed
`values of N for atmospheres that contain greater quantities of carbonic
`acid and aqueous vapour. These values must be considered as extrapolated.
`In the following table (Table III.) I have given these values of N. The hum-
`.bets printed in italics are found directly in the manner described, those in
`ordinary type are interpolated from them with the help of Pouillet’s
`exponential formula. The table has two headings, one which runs horizon-
`tally and represents the quantity of aqueous vapour (W), and another that
`runs vertically and represents the quantity of carbonic acid (K) in the
`atmosphere.
`Quite different from this dark" heat is the behaviour of the heat from the
`sun on passing through new parts of the earth’s atmosphere. The first parts
`of the atmosphere exert without doubt a selective absorption of some ultra-
`red rays, but as soon as these are extinguished the heat seems not to diminish
`
`20
`
`Lupin Ex. 1057 (Page 12 of 36)
`
`

`

`THE INFLUENCE OF CARBONIC ACID IN THE