Langley revisited

by Hans Erren, Posted 11 August 2003, Revision 10 September 2003, 2nd Revision 28 December 2003, 3rd Revision 25 March 2004.

Allegheny Moon it’s up to you
Please see what you can do


Goal of this paper
Dispersion of a rock salt prism
The Allegheny observations of 9 February 1887
Reconstructing the Allegheny observations using modtran3

Goal of this paper

The key paper on global warming written by Svante Arrhenius [1] in 1896 relies on the infrared observations of the moon as published by Langley in 1890[2]. The paper of Langley contains errors that were corrected in 1900 by Langley and Abbot[3] but this was after Arrhenius published his theory.
I recalibrate Langley's original data with modern observations and standard atmospheric models using modtran3 online radiation code[4].

An omission that has to be emphasised, is that Langley left Frank W. Very out as co-author in his publication of 1890 [2]; Very is the leading observer and processor of all lunar data in this work, and Langley acknowledges his error on page 212:

fig 1: Langley acknowledges Frank W. Very

Dispersion of a rock salt prism

Langley and Very use rocksalt (NaCl) prisms to create an infrared spectrum, as glass gets opaque at infrared wavelengths. Here is the setup of the instruments.

fig 2: Instrumental setup from plate 4. M=Mirror, S=Slit, L=Lense(2x), P=Prism, B=Bolometer

The angle of deviation d can be obtained by applying Snell's law on the prism geometry.

d = q +arcsin(n sin(A-arcsin((sinq )/n)))-A               (1)

where n = refractive index, A = prism top angle and q = minimum deviation angle.

A and q are observational values but the refractive index n beyond wavelengths of about 5 micron, was not exactly known in 1890. Langley and Very relied on an extrapolation of near infrared values and made a large error in the mid infrared. It was only the work of Paschen which showed that the refractive index curved back in the mid infrared. This was acknowledged by Langley and Abbot in 1900, but this was after Arrhenius had published his work in 1896. A comparison of refractive indices is shown in an adaptation from plate 20 in Langley and Abbott.

fig 3: Langleys refractive index measurements and his extrapolation in 1886 (both highlighted in orange) compared with later work. (Adapted from plate 20 in Langley and Abbot 1900)

The fitting curve in figure 3 is from Ketteler, using Langley and Abbot values (page 261),

fig 4: Langley and Abbot values for Ketteler's dispersion formula.

Note, however, the following typographical errors:

fig 5: The corrected Ketteler dispersion formula.

The corrected formula is also fitting modern data.

fig 6: Modern values[5] of refractive index compared with Ketteler.

Applying Ketteler on equation (1), yields the deviation angle as function of wavelength (neglecting the refractive index of air). As comparison the old theory of Cauchy is given which yields good fit in the visible part but is useless in the infrared, as Langley found out in 1886. Also Langley's 1886 extrapolation is given.

fig 7: NaCl prism deviation according to Cauchy, Langley and Ketteler (= Langley 1900).

The extrapolation of Langley was much used, although Langley himself had warned about it in earlier work. Here is his footnote 2 on page 255 of Langley and Abbot 1900:

fig 8: Langley regretting people running away with his extrapolation.

Langley's 1886 extrapolation error has a long life: Due to Arrhenius, Ramanathan and Vogelmann[6] in 1997 assumed that Langley observed well up to 30 micron (which btw is physically impossible as NaCl becomes opaque at 20 micron [5]).

The Allegheny observations of 9 February 1887

The data that Svante Arrhenius used, were all taken at the Allegheny Observatory in Pittsburgh, Pennsylvania, USA, longitude 80° 00' 35.16" W, latitude 40° 27' 41.6" N and altitude 380 m. The observatory is in the center of a coal mining area.

The first mistake that needs to be put aside, is the impression that the data in Arrhenius 1896 are true lunar spectra. The data used by Arrhenius are moon minus sky observations. For lunar work the bolometer was working at the very detection limit of the instrument, and the raw lunar spectra show a tremendous amount of instrument noise. Here are e.g. the raw bolometer readings of 9 February 1887.

fig 8: Raw bolometer readings of 9 february 1887.

What is evident from this dataset is that the absolute value of the bolometer readings are very erratic. A measuring sequence has the following steps:

A series is a set from high deviation angle to low deviation angle and back. On 9-10 February 1887 four series were observed:

The following observation times were recorded, airmass and zenithangle are derived from online ephemeris for 9 and 10 Feb 1887

date		time (EST)	zenithangle	airmass	Series	
9-Feb-1887	20:30		81.04		6.183	I	
		20:48		77.80		4.635	I	
		21:05		74.72		3.747	I	
		21:20		72.02		3.210	II	
		21:42		68.06		2.661	II	
		21:45		67.52		2.602	II	
		22:00		64.86		2.343	II	
		22:20		61.34		2.078	II	
		22:48		56.54		1.810	III	
		23:00		54.54		1.720	III	
		23:15		52.09		1.625	III	
10-Feb-1887	0:00		45.29		1.420	IV	
		0:12		43.65		1.381	IV	
		0:30		41.38		1.331	IV	

Only when a reduction is made, the data are starting to make sense. The following graph shows a reduction moonC-(skyB+skyD)/2 of all four series. The effect of decreasing airmass is prominent in the observations.

fig 9: Reduced bolometer readings (moon-sky) of 9 february 1887.

Reconstructing the Allegheny observations using modtran3

For starters here is a recent "lunar infrared spectrum"

click to enlarge
fig 10: High resolution calibrated atmospheric spectrum using the moon as light source. With permisson of J. Notholt, Institute of Environmental Physics, University of Bremen, Germany.

The radiation code of Modtran3 to calculate infrared atmosphere spectra was put online by David Archer and Ray Pierrehumbert[4]. Frank Very only recorded the ground temperature within the observatory. Outside recorded temperatures in Pittsburgh were obtained by James Keeler and published in Arrhenius 1896(german version), p.8 [9]. For Feb 9 the readings were:

Frank Very 
Allegheny observatory
time 19:30
dry bulb 		16 °C
wet bulb 		11.2 °C
RH 	56%
pH2O 	1006 Pa	7.546 torr

James Keeler 
time 22:00
dry bulb 38.8 F	3.78 °C
wet bulb 36.4 F	2.44 °C
RH 	80%
pH2O 	639 Pa	4.79 torr

To create a moon sky residual the following steps were taken.

Below are standard atmospheres (summer and winter) from modtran 3, the importance of water vapour modeling is evident.

fig 11: summer and winter spectra from modtran3

The next step is to compare modtran with Allegheny, for this the wavelength in the modtran data was mapped to deviation angle using Ketteler's formula. The amplitude of the Allegheny data was scaled with an arbitrary factor of 1/7000

fig 12: standard modtran3 spectra compared with Allegheny observations

Figure 12 depicts vertical rays (zenith angle 0 = airmass 1 for standard atmospheres. In figure 13 the parameters are set to match temperature and humidity of James Keeler, also the influence of varying airmass on the spectra is shown.

fig 13: modtran3 Airmass 6 (zenith angle 81.04 degrees) and Airmass 1 (zenith angle 0 degrees) compared with Allegheny observations

The data lower than 6 micron (dispersion angle 38 to 41 degrees) is due to solar NIR emission scattering from the moon. Compare e.g. with the apollo 14 rock samples at the Aster spectral library The statement of Baliunas and Soon [8] that Langley's data go up to only 3 micron could be based on Solar spectra by Langley (see Langley and Abbot for a nice example)



I thank Hartwig Volz for advise on Kirchoff's law, and Justus Notholt for providing me with modern lunar data.


[1] Svante Arrhenius, 1896(1), On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, The London, Edinburgh, and Dublin Philosophical Magazine and Jounal of Science [fifth series] April 1896. vol 41, p237-275, Online scanned document (Warning, 27.1 Mb pdf)
[2] Samuel P. Langley (and Frank W. Very),1890 , The Temperature of the Moon, Memoir of the National Academy of Sciences, vol. iv. 9th mem. 193pp .
[3] Langley & Abbot, 1900, Annals of the Astrophysical Observatory of the Smithsonian Institution, Volume I, Online scanned document
[4] David Archer and Ray Pierrehumbert, [undated] , MODTRAN3 Atmospheric Radiation Code, University of Chicago Department of the Geophysical Sciences,
[5]Data source for NaCl optical properties:;;
[6] Ramanathan, V. and A.M. Vogelmann.(1997) Greenhouse effect, atmospheric solar absorption and the Earth's radiation budget: From the Arrhenius/Langley era to the 1990s. AMBIO, 26(1):38-46
[7] Dick Manning and Al Hoffman (Words and Music), (ca 1956), Allegheny Moon, Artist: Patti Page (peak Billboard position # 2 in 1956),
[8]Sallie Baliunas and Willie Soon , (1999) Cutting Edge: Pioneers in the Greenhouse Effect, World Climate report, vol 4 no 19
[9] Svante Arrhenius, 1896(2), Ueber den Einfluss des Atmosphärischen Kohlensäurengehalts auf die Temperatur der Erdoberfläche, Bihang till Kongliga Svenska Vetenskaps-Akademiens Handlingar, Stockholm 1896, Band 22 Afd I N:o 1, p1-101.

see also:
Arrhenius original tables:
Arrhenius was wrong:
this page: