BULLETIN G. w. B. NO. 221.
U.'S. DEPARTMENT OF AGRICULTURE.
WEATHER BUREAU.
ATMOSPHERIC RADIATION:
A RESEARCH
AT PROVIDENCE, R. I.
SUBMITTED TO 'WILLIS L. MOORE, CHIEF U. S. WEATHER BUREAU,
BY
FRANK W. VERY.
h
WASHINGTON:
GOVERNMENT PRINTING OFFICE.
1900.
V
PHYSICS DEFT,
PHYSICS DEPT.
LETTER OF TRANSMITTAL.
UNITED STATES DEPARTMENT OF AGRICULTURE,
WEATHER BUREAU,
Washington, D. 0., January 4, 1900.
Hon. JAMES WILSON,
Secretary of Agriculture.
SIR: I have the honor herewith to transmit for publication, as a bulletin of the Weather
Bureau, a memoir by Prof. Frank W. Very on "Atmospheric Kadiatiou."
This paper gives the results of a long research carried on by Professor Very during the past
eight years. The expense of the apparatus was defrayed by Prof. James E. Keeler, Director of the
Allegheny Observatory, from funds allotted for this purpose by the Hon. J. M. Eusk on the
recommendation of my predecessor.
An examination of the manuscript will show that Professor Very has brought to bear upon
the study of this important subject a wide range of knowledge and experimental skill acquired
by his long service in connection with Prof. S. P. Laugley in researches on radiation at the Alle-
gheny Observatory. Professor Very has attacked a problem that has long been recognized as
being of fundamental importance in climatology and general meteorology. He has apparently
settled some questions that have heretofore been under discussion, but has also raised others for
future investigators to discuss.
This memoir is, therefore, to be recognized as one step of progress in our knowledge of the
subject of radiation and absorption of heat by the earth's atmosphere, and I take great pleasure
in commending it to you.
Very respectfully, your obedient servant,
WILLIS L. MOORE,
Approved : Chief United States Weather Bureau.
JAMES WILSON,
Secretary of Agriculture.
3
810833
ATMOSPHERIC RADIATION
By FRANK W. VERY.
PREFATORY NOTE.
This research was first suggested in a letter from Prof. Cleveland Abbe, of the United States
Weather Bureau, to the writer, dated November 24, 3891, in the course of which he said:
Absorption may be the absolute inverse of radiation for gases, but I don't like to assume this as to intensity, and so
I beg to know whether you and Professor Keelercau not undertake the following problem : To determine the absolute
radiation in calories from a unit mass of gas at given density and temperature and at ordinary temperatures, not
when burning, nor when electrified, but when simply heated.
Maurerhas given the only determination that I know of, but this is only computed from meteorological observa-
tions of cooling at night, and his figures demand continuation by direct experiment. He finds
6 = coefficient of radiation for air, or the amount of heat in calories that one unit volume of air
[at the level of the station where 6 = 29.5 inches; temperature = 40? Fahr.] loses by radiation in unit time
(one hour) to a surrounding surface of air whose temperature is 1 lower 0.0000418 gram calories per cubic
centimeter per hour. And again from direct radiation observations, he finds 0.000039 calories.
It ought to be possible to determine the quantity and quality of the heat radiated by a mass of warm
gas. * The stream of gas should be varied as to its diameter, so sis to determine the effect of depth from
which radiation comes. The ascending flow of warm gas can be kept steady for any length of time or cut off at
will. The black surface that serves as the basis for reference should be surrounded by a screen at 0C., so that it
can only receive and transmit or reflect the waves that belong thereto.
In regard to the direct measurement of gaseous radiations of nearly homogeneous quality at
moderate temperatures, the following was written in reply (November 27, 1891):
The problem which you suggest is an exceedingly difficult one. I should anticipate that the radiation from so
small a mass of gas as that in a transverse jet would be almost immeasurable, unless at very high temperature.
Possibly two long, diaphragmed tubes, surrounded by water jackets, and open at both ends, would answer for
ordinary temperatures when interposed in alternation; e. g. let temperature of room be + 20C., one tube being
surrounded by a freezing mixture at 20 C C., and the other by warm water at +60C. The temperature gradients
in the open tubes would be similar and are also determiuable.
In commenting on the above suggestion, Professor Abbe expressed the hope that temperatures
as low as 90 C. might be attained, but added further the important remark that "the point to
be determined experimentally is the law of radiation, transmission, and absorption as depending
upon pressure or density of the air rather than as depending upon temperature."
By the advice and consent of Professor Keeler, Director of the Allegheny Observatory,
preliminary experiments were commenced in March, 1892, with an apparatus similar to that out-
lined in the writer's letter of November 27, 1891; but as entire confidence could not be placed in
any one method, and as the complete accomplishment of the work contemplated required measure-
ments of atmospheric radiation at various pressures, a more elaborate apparatus was devised
with which experiments were begun in 1894 and continued in the intervals between other occupa-
tions until the severing of my connection with the Observatory in 1895. The reduction of the
observations begun at Allegheny was afterwards continued at Providence, R. I., and required the
further consideration of a number of obscure and troublesome details for which I did not find time
for several years, but it is hoped that the last of these difficulties has now been successfully met.
5
6
The problem has proved much more extensive than I imagined when I first undertook its
solution. It is, besides, beset with difficulties. Some of the greatest masters of science have
worked at it with only partial success, and with merely qualitative results. Professor Tyndall
rightly emphasized the necessity of a long apprenticeship in the methods and manipulations
appropriate to this study before one can be ready to appreciate the subtle sources of error to
which this particular research is open. The investigator here is dealing with the invisible and the
evanescent. In an optical apparatus, a little stray light immediately attracts attention, and we
proceed to trace it to its source with our eyes open. In our study of feeble invisible radiations,
on the other hand, we grope in the dark, and only succeed in eliminating the unwelcome
extraneous rays after innumerable trials and errors.
The final apparatus for work at various pressures frequently gave trouble by springing leaks
when heated j and the possibility of contamination of the air column by evaporation or combus-
tion of organic substances prevented the employment of elevated temperatures. Moreover, it
was especially desired that the temperatures should not greatly exceed those of the ordinary
atmospheric range. Hence the radiations measured have been of small magnitude, requiring a
sensitive measuring apparatus, and attention to many minute details inevitable in measurements
of this character. I shall not trouble the reader with a recital of all the difficulties encountered;
but, in order that the meaning and value of the results may be quite clear, it will be necessary to
consider the theory of some parts of the apparatus carefully.
MEASURING INSTRUMENTS.
THE BOLOMETER.
The measurements of radiation have all been made with a bolometer constructed after Lang-
ley's earlier plans, in which the exposed face is composed of very thin strips of blackened platinum,
arranged in two series, those in the rear occupying the positions of the apertures in the front
series. The unexposed member is of nearly identical resistance and is divided into two parts, one
on each side of the central member, which receives the radiation coining through the graduated
apertures of the bolometer case. The electric current passes to and fro along the strips which are
held separate and insulated by grooves in the disk of an ebonite holder, a disposition which is
objectionable, as I shall show presently, but which does not prevent the instrument from being
used for certain classes of relative measurements, where the accompanying conditions do not
vary much.
The bolometer battery consisted of eight gravity cells arranged in one series, the current
being reduced to its working strength by interposing resistance between the battery and the
Wheatstone's bridge, of which the bolometer forms a part.
When a bolometer of two nearly equal arms is used, it is desirable, in order to secure the
most sensitive combination, that the balancing arms of the Wheatstone's bridge should be of
greater resistance than the bolometer arms, in case all of the resistances can not be made equal.
Since in the bridge used by me, choice could be made between balancing resistances of 1, 10, or
100 ohms, the bolometer arms being a little over 31.5 ohms, at 20 C., or with connections about
32 ohms in all, the normal arrangement of the bridge is with balancing arms of 100 ohms. But
on several occasions the bridge, being used for different purposes, was inadvertently left with
balancing arms of only 10 ohms. It becomes necessary, therefore, to reduce these measures to
normal sensitiveness of a 100 : 32 bridge.
According to theory, the current through the galvanometer is, by Kirchhoff's law:
C = E -( r * r *~ r ^
where
D = r 5 r 6 (r { + r t + r. } + r 4 ) + r 5 (r t -f r ;j ) (r. z + r 4 ) + r ti (r { -f r t ) (r 3 + r,) + r^ (r 2 -f r 4 ) + r 2 r 4 (r, -f r 3 ).
In the normal arrangement (1), and the exceptional or insensitive arrangement (2), the
currents in consecutive experiments were :
Measured battery current = 0.026 ampere.
" " ' " =0.032 "
(1)
(2)
The extra resistance (-K), plus that of the bridge, was:
(1) R + % (r, + r 3 ) = 266 ohms.
(2) J R + (r' 1 +r 3 )=221
Assuming the electromotive force of one gravity cell to be 1.1 volt, the total resistance of
eight cells, plus an extra resistance of 200 ohms, plus the bridge, should have been :
(1)
>- 6 + -R +
+ r 3 ) =
= 338.5 ohms.
whence the apparent resistance of the battery was:
(1)
(2)
For eight cells, 72.5 ohms; for one cell, 9.2 ohms.
" " " 54.0 " ; < " " 6.9 "
According to this, the diminution of the external resistance from 266 to 221, or by 17 per
cent., increased the current by 23 per cent., the battery resistance at the same time diminishing by
25 per cent. It is possible that a portion of the change was in the potential of the battery, and
both voltage and resistance may have been lower than the values given; but for the purposes of
a test, the resistances may be taken as stated, and assuming further that the exposed arm of the
bolometer has its resistance increased by radiation by 0,005 ohm, I proceed to calculate the current
through the galvanometer in each of the two arrangements of the bridge. The resistances at
20C. are those of the Elliott coils, graduated according to British Association units, of which
1 = 0.989 of the the accepted legal ohm.
(1) n = r 2 = 100, r 3 = 32.005, - 4 = 32, r 5 = 20.5, r 6 = 272.5.*
(2) r'i = r' 2 = 10, r 3 = 32.005, r 4 = 32, r 5 = 20.5, r' 6 = 254.
D = (20.5 x 272.5 x 264.005) + (20.5 x 132.005 x 132) + (272.5 x 200 x 64.005)
+ (100 x 32.005 x 132) + (100 x 32 x 132.005) = 6 165 159.
D ;2) = (20.5 x 254 x 84.005) + (20.5 x 42.005 x 42) + (254 x 20 x 64.005) + (10 x 32.005 x 42)
+ (10 x 32 x 42.005) = 825 609.
Computed ratio of galvanometer currents:
5( 2)
= 1.339 +
The' theory was tested by exposing the bolometer to radiation from blackened screens
containing boiling water, and water at the temperature of the room (about 30 C.) with the
followin results:
(1) n = r a = 100 ohms.
(2) r / 1 = r / 2 = 10 ohms.
Temperature of screens.
Deflection
Temperature of screens.
Deflection.
99. 1
366 div
99. 1
232 div.
29. 4
364
30. 2
232
0T
9Q9
Excess, 69. 7 C.
OO 1
367
Excess, 68. 9
Ml>W
235
364
233
362
231
365
231
363
230
363
230
361
230
Mean deflection
= 364.2
Mean deflection
=231.6
>- 6 is supposed to include the extra resistance It.
8
Galvanometer deflection for 1 of temperature-excess :
(1) 5.225 div. (2) 3.361 div.
Ratio of observed galvanometer currents:
^5 (l) 1 - r -
r\ i \ J..OOO
^5 (2J
To bring the computed value into agreement with theobser\ed, a battery resistance of nearly
1,000 ohms would be required; but this is entirely inadmissible, since any bad connection would
have reduced the current and the galvanometer deflection, both of -which were such as to give
customary values in the normal reduction. For constant battery current the ratio of galvanometer
currents with the two arrangements should be:
C ( } 03^
-~. = 1.339 x = 1-648 (computed)
x =1.913 (observed)
Using the observed factor, observations with insensitive condition of the bridge are brought
into fair agreement with normal measures, but the computed factor gives discordant results.
There can be no doubt, therefore, of the substantial accuracy of the observed ratio. A study of
these discrepancies has elucidated some obscure points in the theory of the bolometer, which I
will indicate.
The sensitiveness of a bolometric apparatus is a complex of many factors. It depends upon
the resistance of the bolometer, the material of its strips, and the rate at which the metal varies
in resistance with changes of temperature, the absorbent quality of the surface for rays of various
wave-lengths, the area exposed to radiation, the^ thickness of the strips, the resistance and form
of the galvanometer coils, the strength of the magnets forming the needle, the ratio of their mass
to the other parts of the needle, their dimensions and position in reference to the galvanometer
coils, the astaticism and damping of the needle, the torsion of its suspending fiber, the strength
of the external magnetic field, the arrangement of the Wheatstoue's bridge, the strength of battery
current employed, and the excess to which the bolometer strips are heated by the current. The
last is a very important factor, and is probably responsible for the greater part of the discrepancy
between incomplete theory and observation in the preceding example. The theory of the bolo-
meter, in fact, can not be reduced to a simple case of Wheatstone's bridge, unless all of the factors,
with the exception of the trifling change of resistance produced by the radiation to be measured,
have remained constant.
Prof. Harry F. Eeid, in his "Theory of the bolometer" (Am. Journ. of Sci., ser. 3, vol. 35, p.
160, Feb., 1888), has given a formula for the bolometer with its whole surface blackened :
in which 6 is the galvanometer deflection, D the galvanometer constant, a the ratio of the
resistance of the bolometer strips at the temperature t -\- 1 to their resistance at temperature /,
H the intensity of normal radiation per unit of area expressed in thermal units, a the relative
absorbent power, of the bolometric surface exposed to radiation, m the loss of heat by combined
radiation and convection (conduction being assumed negligible) in thermal units for the unit of
time and unit surface of the strips, i the ratio of the resistance of the exposed part of the strips
to the entire arm of the Wheatstone's bridge of which they form a part, A the total length in
series of the exposed part of the bolometer strips, ft the width of an individual strip, and t l t
the excess of temperature of the strips due to the battery current which enters as the square root
of this quantity, the current being here stated in thermal units, and the galvanometer constant
also having reference to these units. The formula also relates to the most efficient arrangement
of the bridge resistances, but small variations from this ideal are of minor importance, the main
point being that the bolometer arms shall have, as nearly as possible, equal resistances, and be
inclosed in a common chamber which can be kept at a nearly constant temperature.
9
Professor Reid says (p. 165-166) :
Since the resistance of the strip does not enter the equation, it is of no importance so long as the fonr arms of
the bridge and the galvanometer all have the same resistance ; but this should not be so small as to decrease materially
the value of i, or to make the galvanometer connections an appreciable fraction of the resistance in the galvanometer
branch. /I and ft only occur multiplied together and under the radical sign ; other things being equal, S varies as the
square root of the exposable area of the strip. For a given area it does not matter, then, whether the strip be made
of a single broad piece of platinum or of several narrow pieces arranged side by side and connected in series. This
however, is subject to the limitations mentioned in regard to the resistance of the strip. The thickness of the
strip does not occur in the expression above; we have supposed the strip flat and so thin that the edges are only a
very small fraction of the surface and the heat lost by conduction negligible. As long as these are true the actual
thickness of the strip is unimportant, (ti t ) is the increase in the temperature of the strip above the case due
to the current passing through it ; for a particular bolometer it is proportional to the square of the current.
The equation is not of general applicability, and some of the assumptions made in deducing
it are not warranted by facts of observation. Thus experiments which I have made, some of
which will be described presently, prove that conduction of heat can not be neglected in platinum
two or three microns thick, such as is used in bolometers. Again, the relation between the heat
generated by the current and the temperature of the strip, deduced " according to Kewton's law
of cooling, which is sufficiently accurrate for the small change in temperature under considera
tion,"' in Professor Reid's estimation, is shown by observation to require a more complex expres-
sion, the loss of heat from thin strips being largely produced by convection, which is not nearly
proportional to excess of temperature , even though this be small.
In the derivation of the above equation the galvanometer resistance has been assumed equal
to that of one arm of the bolometer; but, as shown by Schwendler (Phil. Mar/. (4), vol. 33, p. 29, 1867),
the neglect of the space occupied by insulating material has led to an error in this customary
allowance, and Mr. F. A. Laws (Phys. Rev., vol. 5, p. 300, 1897) shows by trials of various windings
that in a properly wound galvanometer the galvanometer resistance should be more nearly one-half
that of one of the bridge arms if the maximum deflection is required. However, we are not
concerned so much with those factors which influence the galvanometer constant as with those
which enter into the variable bolometric effect.
The excess of temperature (ti 1 ), which in a given bolometer depends mainly on the battery
current, varies with the square of the current and inversely as the section of the strip. It is
therefore a function of ft, the breadth, and 6, the thickness of the strip. But if tf oc V A. ft(t\ t ) y
the substitution of the relation, ^ / ex, in this variable relation gives:
# oc V
and other things being equal, that bolometer which is subdivided into the largest number of
strips, or has the largest ratio between A. and ft, should give the greatest galvanometer deflection.
Possibly this might actually be the case in a vacuum, but in air more than one cause interferes
with its realization. To keep the thin metal strips from undesired electric communication an
ebonite holder with interlocking grooves has been used in the instrument belonging to my outfit.
The heat retained by the nonconducting holder and by impeded convection very nearly neutralizes
any gain that might result from the subdivision. But the theory does not yield readily to pure
mathematics, and I proceed to experiments which throw some light on the activities in play in a
working bolometer.
The measures in the following table were made several years ago by Professor Reid and
myself, and were laid aside as hopelessly discrepant; but with further experience I am able to
explain the discordances, and to show that they contain the key to a fuller theory of the actual
instrument. The experiments were made on a nearly constant source of radiation with a single
bolometer, varying the battery current and the aperture in order to get some knowledge of the
connection between A. x ft and t\ t . The quantity (2 v) is the battery current, given first as
originally read in divisions of the arbitrary scale of the battery galvanometer, and afterwards in
amperes as corrected by the calibration of the scale. The constant of this galvanometer is
1 div. = 0.000 33 amp. near 100 div. T is the excess of temperature of the radiator. The other
symbols are as already defined. The seventh column gives values reduced to uniform battery
current and the eighth to full aperture.
10
TABLE 1.
1
2
3
4
5
c
7
8
&
.0335
For aper-
{
A/3
T
2w
s
f
lif
ture of ii
8fj. mm.
C.
div. amp.
div.
,=0. 60
8.64
81.0
60 =0.0214
72.5
0. 895
1.383
,=0. 60
8.64
81.7
82 =0.0279
85,2
1.043
1.234
,=0. 60
8.64
83.7
166 =0.0480
157.9
1.886
1.301
1.340
,=0. 60
8.64
82.6
180 =0. 0508
176.4
2.138
1.388
!=0. 60
8.64
81.5
196 =0. 0537
185.4
2.275
1.396
.7=0. 38
5.40
81.1
115.5=0.0366
81.2
1.001
0.902
1. 4251
is=0. 38
5.40
80.4
126 =0.0391
92.2
1.147
0.972
1. 536J
*j=0. 25
3.60
79.9
160 =0. 0467
77.7
0.972
0.685
1.6441
3=0. 25
3.60
79.4
173 =0. 0493
98.4
1.239
0.832
1.997/
The exposed parts of the bolometer strips constitute 62.4 per cent, of the whole, or allowing
for the resistance of the connections, 60 per cent, of the total resistance of the bolometeric arm
of the Wheatstone's bridge is exposed in condition v The mean currents giving unit deflection
per degree of temperature-excess are given in the second column of the next table.
TABLE 2.
Exposed part.
Battery cur-
rents.
Equally effi-
cient cur-
t
2
rents = 2v X i
Ampere.
Ampere.
i 1= =0. 60
0. 0252
0. 01512
f 2 =0. 38
0. 0353
0. 01341
i.,=0. 25
0. 0434
0. 01085
When the aperture of the inner bolometer chamber is reduced, a larger battery current is
required to give a constant galvanometer deflection, but a current which is smaller than the
inverse proportion of the aperture. The smaller exposed area is therefore more efficient for the
unit of battery current, and the reason of this seems to be because the central part of the strips,
heated by radiation, are adjoined, in the case of the smaller aperture, by larger portions of free
strips at a slightly lower temperature, into which the heat can pass by conduction to be dissipated
through a larger surface, but at a lower excess of temperature. One might hesitate to predict
whether the larger surface or the lower excess would have the predominating influence, although
in general two units of surface radiate less than one unit at twice the excess of the two, and
the experiment decides in favor of this view, for the losses are less when the heat is distributed
to a relatively wider area, so that a smaller current is then needed to produce a given deflection.
Let i be the area of the fully exposed bolometer strips, 2 , the area of the central part when
the aperture of the bolometer chamber is reduced, and Ha^ Ha 2 , the heat received from radiation
in the two conditions. Owing to the slight thermal conductivity of the ebonite holder, the heat
developed by the current in the covered parts of the bolometer raises the temperature of the ends
of the strips excessively, the heat from the covered ends being partly dissipated by conduction to
the freely exposed parts, where it passes off by radiation and convection. The distribution of
temperature in the shielded strip is therefore something like the curve in fig. 1, the ends (e) being
at a higher temperature than the middle (w), and the flow of. heat being in the direction of the
arrows.
11
If c" is a current larger than c 7 , the excess of temperature of the strips at the ends under
these respective currents will be:
while unless conduction more than compensates for the relatively greater loss by radiation and
convection at the higher excess, the corresponding quantity in the middle of the strips will be:
(2)
and in any case
(ti - t ) e > (t, - t ) m , (3)
the subscript e and m denoting end and middle positions.
During exposure of the central part of a strip to radiation, conduction from the sides in that
part must be diminished or reversed. Since the temperature-excess imparted by u given quantity
of heat is smaller when the initial temperature is greater, > .t { must be less at the ends than at
the center of the strip, and less at the middle for the greater current; also the mean t 2 <i, or the
mean excess of temperature produced by radiation received, must be less for the fully exposed
than for the centrally exposed strip; consequently, A L and A 2 being lengths of the exposed part of
the strips for full and for partial exposure, and the temperature varying symmetrically in the two
halves of a strip,
For the currents c' and c" the deflections are approximately:
X (a a, c 1 }
(A A being a small element of length, a the coefficient of change of resistance with temperature)
^V-^A)
' - X (a 02 C')
2 ^2
^-'OMA) m
) V>
<J" 2 ex ^ ' - x (a 02 c 7 ')
in which
Observation shows that
fi'i 4- o i c' <C <5 7 2 4- o 2 c 7 (9)
( y// l 4. , C " < <5 8 _L. a,, C " (10)
tf'i 4- a, c 7 > tf 7/ ! 4- o t c 77 (11)
<5' 2 4- 2 C' < <y /7 2 4- 2 C" (12)
Hence, within specified limits,
^JL / < L. < ^. < ^. i (13)
12
Inequality (11) is a consequence of the unequal distribution- of the temperature-excess
developed by the battery current in the strips, and the law of increase of this excess at
the preponderant ends, given by (1). Inequality (12), dealing with a part of the strips where
temperature is fairly equable, is a consequence, as will be shown presently, of the great
influence of convection in cooling, and the rapid rate at which convection increases with the
temperature-excess in masses of matter of the form and temperature considered here. Inequality
(13) expresses the fact, which has been demonstrated in the experiment already given, that
bolometers of reduced aperture are relatively more efficient.
Bolometers used with full aperture, if of the same general construction, are as a rule more
efficient per unit of area when the number of strips and the total area are smaller.
Determinations of the battery current required to produce a nearly constant deflection on
an approximately constant source of radiation with three different bolometers, constructed with
various arrangements of strips, but all having grooved ebonite holders, gave me the results in
the next table.
TABLE 3.
(Deflections similar.)
Number of strips in each arm n
1
5
23
Length of strips exposed A
8. 5 mm.
48. ram.
184. mm.
Resistance of bolometer B
9. 2 ohm.
14. 7 ohm.
82. 1 ohm.
Fraction of resistance exposed i
0.38
0.60
0.63
Area exposed A/3
1.62 sq. mm.
8. 64 sq. mm.
42.3 sq. mm.
Section of strips /36
0. 000209 sq. mm.
0. 000504 sq. mm.
0. 000322 sq. mm.
Thickness of strips 6
0. 0011 mm.
0. 0014 mm.
0. 0028 mm.
Battery current (2) giving uniform")
(150. 5 div.
60. div.
13.0 div.
deflection . J
|=0. 0447 amp.
0. 0214 amp.
=0. 0055 amp.
Deflection (mean of 10 observations) S
73. 4 div.
72. 6 div.
75. 8 div.
Probable error of 1 observation
^0. 63 per cent.
-4^0. 42 per cent.
-J-0. 28 per cent.
Excess of temperature of radiant] ^
82 C.
80 G C.
78 C.
source
s
Deflection per degree -T-F,
0. 895 div.
0. 908 div.
0. 972 div.
Heat developed by battery-current, computed!: n A t
2.71
1.00
as proportional to (2v)' 2 R
Deflection per degree per sq. mm. exposed!
0. 552 div.
0. 105 div.
0. 023 div.
area J
Deflection per degree per mm. of A
0. 1053 div.
0. 0189 div.
0. 0053 div.
Ratio of efficiency per mm. of A
19.9
3.6
1.0
Ratio of efficiency per sq. mm. of A/? 24.
4.6
1.0
Ditto, computed for constant current on erro-\ 034
neous assumption S oc 2v J
1.176
1.000
In the next table, further measures, made with the same bolometers by Professor Reid and
myself, give a comparison of deflections on a nearly constant source of radiation with approxi-
mately constant battery current.
TABLE 4.
(Currents similar.)
Number of strips in each arm n
1
5
23
Length of strips exposed A
8.5 mm.
48. mm.
184. mm.
Battery current 2 v
168. div.
166. div.
157. 5 div.
Deflection (mean of 7, 16 and 10 obser-1
91. div.
157. 9 div.
327. 2 div.
vations) J
Probable error of one observation
^0. 85 per cent.
-j-0. 44 per cent.
^0. 33 per cent.
Excess of temperature of radiant!
source J
75. 5C.
83. 7 C.
78 C '. 4C.
Deflection per degree
1.205 div.
1. 886 <liv.
4. 173 div.
Heat developed by battery current,!
1 00
1. 56
7.85
computed as proportional to (2v)' 2 B \
X. \J\J
Deflection per degree per sq. mm. ex-1
0. 744 div.
0. 218 div.
0. 099 div.
posed area J
Deflection per degree per mm. of A
0.1418 div.
0. 0393 div.
0. 0227 div.
Ratio of efficiency per mm. of A
6.25
1.73
1.00
Ratio of efficiency per sq. mm. of A/2
7.52
2.20
1.00
13
The relative efficiency of unit area of the bolometer is diminished by the use of an excessive
battery current, which evolves so much heat that it can not be dispersed rapidly enough in the
rather limited chamber of the bolometer case to prevent undue increase of the primitive excess
(<! < ), thereby diminishing the increment (<z <i), due to radiation. A comparison of the relative
efficiencies, given in the last lines of Tables 3 and 4, and of the heat developed by the battery
current, shows that whereas, with equal currents, the single-strip bolometer is actually about
seven and one-half times as efficient as the 23- strip instrument, the heat being nearly eight times
as great in the latter, reduction of observations made with unequal currents makes the computed
efficiency of the single-strip instrument for equal currents only about three times that of the other,
when the heat in the single strip is over seven times as great as in the 23-strip bolometer.
On the other hand, -the probable errors of single observations maintain much the same
relation when the order of excessive heating by the current is reversed. The deflections with
uniform current are by no means inversely proportional to the exposed areas, as the last line of
Table 4 shows, the deflection per square millimeter being much greater for the smaller instru-
ments; but this can not be due entirely, or mainly, to diminished values of t } # for the smaller,
as compared with the larger instruments, for otherwise there should be a reversal of efficiency
when the order of excessive heating is reversed, and at least some change in the relation between
probable errors.
One other factor remains to be considered the form of the bolometer. It is evident that
a large part of the heat in the strips is removed by convection, and that convection is much
impeded in the double-layer, alternate-aperture, gridiron -pattern, or multiple-strip bolometer,
while in a single strip instrument, or one of few and narrow strips, the adherent sheaths of heated
air slip from the metal much more readily. The primitive excess of temperature is much less,
therefore, in the simpler bolometer, and the excess imparted by radiation is greater. It is difficult
to give a mathematical expression for this factor, but the experiments described in the foregoing
pages indicate its importance. The removal of hot air by convection is not a perfectly continuous
process, but an alternation of instants of quiescence, during which heat accumulates, and the
establishment of miniature whirlwinds, by which the hot air is swept away. The irregularities
thus produced account for the larger probable errors in those instruments where convection is
least impeded. If the battery current is reduced until the probable error for one observation is
the same in every case, there is little difference between the deflections from single-strip and
multiple-strip bolometers of the same metal.
In the next experiment the mean temperature of excess of the bolometer strips (T), corre-
sponding to (t l t ) m Professor Eeid's formula, was calculated, by Callendar's formula* for
platinum resistance, from the measured resistances, when different currents (C 1 ) were used.
TABLE 5.
Current C.
Temperature
excess (T).
C*
09
T
T-z
Ampere.
C.
Ci 0.0011
T t 0.0
C. 2 = 0.0119
r= 0.6
1.000
1.000
C 3 = 0.0279
T 3 = 3.6
5.497
6.000
C. ( = 0.0427
T 4 = 10. 4
12. 875
17. 333
C-, = 0.0505
T, = 15. 8
18.008
26. 333
The last two columns show that the mean temperature-excess increases more rapidly than the
square of the current, indicating that the confinement of parts of the circuit and the impeding of
convection are responsible for the departure.
Returning now to the experiments described on page 7, et seq., the following temperature-
excesses are indicated for the bolometer, by the measures in Table 5:
(1) Battery current, G\ 0.026 amp., temperature-excess, T l = 3.0 C.
(2) " " C z 0.032 amp., " " T 2 = 5.0 C.
* R = 1 + 0.00346 T. (See La Lumitre Electrique, January 8, 1887, p. 78.) Measurements of the resistance of the
same bolometer at constant temperatures, in summer and winter, agreed well with this law.
14
The heat generated by the current in the second case is to that in the first as (0.032) 2 :
(0.026) 2 = 1.515.
The temperatures maintained are in the ratio: 5.0: 3.0 = 1.67.
The ratio for the central part of the strips where the radiation is received, will be smaller
than this, as has been pointed out before (inequality 3) ; but this will not affect the argument, since
the diminution of the temperature-ratio is accompanied by an increase of the factor for convection.
A comparison of the loss of heat from thin strips and from the spherical bulb of a small
thermometer is instructive. Experiment has shown that the thermometer at corresponding
temperature-excesses
T! = 3.0, cools 0.71 per minute.
T 2 = 5.0, cools 1.24 per minute.
The dimensions and water-equivalent of the thermometer bulb were such that these repre-
sent, respectively,
0.001032 small calories per sq. cm. per sec.
and 0.001802 " " " " "
The platinum in one arm of the bolometer had a water-equivalent of about 0.00002 gram, and
the heat developed in it by the current was:
(1)
Q9 vx 1 A9
x 0.026 x 10-' ) 2 x ~ 1= = 0.00129 calory per sec.
4.2 x 10'
(2)
X 0.032 x 10- 1 ) 2 x
v.,
j *
= 0.00195
The cooling in the two cases must have been :
(1)
n on 1 QK
= 97.5 " "
0.00129 .
T> = 64.o per sec.
0.00002
0.00195
0.00002
which, as the temperature-excesses are so much smaller, shows that the strips lose the greater
part of their heat in a small fraction of a second. The total area (both sides) of the platinum
being about 0.6 sq. cm., the losses are
(1) 0.00215 small calory per sq. cm. per sec.
(2) 0.00325 " " " " ' "
taking place partly by radiation through the limited aperture of the ebonite frame holding the
strips, and partly by convection from a surface whose ratio to the volume is about 3,000 times
as great as that of the thermometer bulb. In the thermometer I have determined the loss by
convection as a percentage of the total loss, getting the values in the following table:
TABLE 6.
T.
Convection.
T.
Convection.
o
Per cent.
C
Per cent.
1
6.5
9 24.8
2
11.0
10 25. 8
3
14.5
11 26. 7
4
17.0
12 27. 4
5
19.2
13 28.
6
21.0
14 28. 6
7
22.5
15 29. 2
8 23.7
16 29. 8
By the measurements of Dr. J. T. Bottomley * on the emissivity of wires in vacuum and in
air, it is evident that, in a wire 0.2 mm. thick at temperature-excesses of 150 and 200 C., con-
' Phil. Trans. Royal Soc. London, 1887 (A), p. 429.
15
vectiou is about fifty times as groat as radiation, which is probably clue to the readiness with
which successive sheaths of heated air slip off from such a surface. Suppose the thickness of the
air sheath to be ten times that of the wire, air to the depth of 2 mm. being heated by molecular
interchange. The adhesion between the two must be very slight, but increases with the diameter
of the wire.
I have been unable to determine the convective ratio for a bolometer, but it is probably
safe to assume that it is intermediate between that of a wire of diameter the same as the width of
a single bolometer strip (about 0.2 mm.), and a thermometer bulb. Simply as an illustration, we
may suppose the convection ratio is seven times as great as for a bulb. For small excesses, the
radiation may be taken proportional to the rise of temperature, and increasing the convection ratios
in the preceding table in the proportion 7: 1, we have:
(1) T! = 3.0
(2) T- 2 = 5.0
Radiation + convection = 1.00 + (7 x .145 x 1.00) = 2.015.
Radiation + convection = 1.67 + (7 x .192 x 1.67) = 3.914.
Ratio of total losses = = 1.942.
2.01o
In (2) the temperature being 67 per cent, greater than in (1), the losses are 10.3 per cent.
greater than a simple proportion to the losses at the lower temperature, and the rise of tempera-
ture produced by a constant radiation is correspondingly less effective in changing the resistance
of the bolometer, which may be expressed in terms of galvanometer current by multiplying the
computed relative efficiency of the two arrangements of the bridge (p. 7) by 1.163, giving the
corrected ratio
_^il) = 1.339 x 1.163 = 1.557,
^5 (2)
which is not far from the observed ratio, 1.555, now finally adopted. For equal currents this ratio
becomes 1.9 L, and by this factor all deflections taken with the insensitive arrangement of the
bridge have been multiplied.
The value assumed for the convection ratio, according to this test, is slightly too large; but
in any case it can not be quite correct, since no allowance has been made for thermal conduction
in the thin strips. I am not able at present to give an estimate of this factor, but the following
experiment makes its existence probable in metal as thin, or very nearly as thin, as that used
for bolometers.
I first heated the front surface of a sheet of platinum, 4 /u thick and blackened on both sides,
by radiation from a lamp, and measured the increment of radiation from the rear surface of the
platinum by means of a bolometer which was, of course, completely shielded from the direct rays
of the lamp. Xearly two minutes were consumed in reaching a maximum deflection. Fearing
some secondary effect, due to the gradual heating of the perforated screens which limited the
bundle of rays falling on the platinum, the experiment was modified as follows: The sheet of
blackened platinum covered the aperture of the bolometer case and was in turn protected by a
double cardboard screen with 2-cm. circular apertures centrally situated. A sunbeam of 5.7 cm.
circular section, kept fixed by a heliostat, fell upon a concave mirror of 150 cm. focus, and the
solar image was formed upon the center of the platinum foil. As before, the radiation from the
rear surface of a sheet of platinum, receiving heat from the front by direct radiation on a very
small part of its area, was to be measured. The sky was quite clear the time from 11 to 12 a. m.
All exposures were made by withdrawing a distant screen placed in the path of the sunbeam.
The results contained in the following table show that much the larger part of the heat, being of
course that of the small area embraced in the solar image, is obtained within the first ten
seconds. The subsequent progressively diminishing increments can not be attributed to any
heating of the bolometer case, since the insertion of a neutral screen behind the platinum made
very little change in the deflection.
16
TABLE 7.
PLATINUM HEATING IN SUNSHINE.
s
10 s
20 s
30'
40'
50'
60'
70
80'
90' 100'
3i.' 120-
183
193
187.4
193
204
196.8
203
215
205.2
208
223
212.6
213
228
216
215
231
220.6
216.5
233
221.8
217. 7 217. 5
234. 7 236. 3
223. 5 225. 4
219.0
239.1
225.1
227.7
219.5 220
238. 9 239. 1
224.4 225.6
Mean.
187.8
197.9
207.7
214.5
219.0
222.2
223. 8 225. 3 226. 4
i
227. 6 228. 2
PLATINUM SHADED COOLING.
220
239.1
225.6
49
53
49.8
40
42
40.7
28
29
27.1
19.6
21
18.5
14.4
15
13.1
11.4
11.2
10.3
8.2
8.3
7.7
6.0
5.3
5.3
3.9
3.9
3.5
2.4
2.2
1.9
0.8
1.1
0.4 !
Mean.
50.6
40. 9 28.
19.7 14.2 11.0 8. 1 ; 5.5
3.8
2.2
0.8 i
Two minutes are consumed in attaining the maximum radiation, and tbe same in cooling.
The whole of this retardation is not to be attributed to the slowness of conduction in the thin
metal. A portion of the effect is due to the time required to establish a heat gradient in the air
near the heated strip. The temperature acquired by the thin, blackened platinum in full normal
sunshine is such as could be developed by the sun's rays in less than one tenth of a second if all
were absorbed. The same radiation is capable of heating an air layer around the platinum 4.5
mm. deep to the same temperature as the platinum in the same time, and there must be perpetual
transfer of heat from the metal to some such layer of air in a bolometer exposed to full sunshine,
since more heat is lost by convection than by radiation. How much of the heat in the experiment
just described has been transferred from the focus to surrounding parts by conduction, and how
much to parts above the focus by convection, can perhaps be determined in a repetition by
mapping the distribution of heat in the foil, using a bolometer case of very small angular aperture.
It is evident from the foregoing studies that the thin metal strips of a bolometer had best be
supported by stout metal arms at a distance from all insulating or obstructing partitions. Such
an instrument has not been used in the present measures, but it is hoped that by keeping the
conditions nearly the same, the results may still be capable of statement in terms of absolute
measurement.
The actual bolometer used exposes a surface of 19.0 sq. mm., divided into fifteen strips, the
total exposed strip-length being
A = 15 x 5.1 = 76.5 mm.
The methods used in standardizing the instrument will be described under the head of
" Screens."
THE GALVANOMETER.
The astatic reflecting galvanometer has a resistance of 20.5 ohms at 20 C. Its chief pecul-
iarity is the needle, which is provided with hollow, cylindrical magnets of very hard steel, arranged
in four groups of five each, on opposite sides of a straight, supporting, hollow glass fiber. Each
group consists of one magnet 9.5 mm. long, two magnets, each 8.5 mm. long, and two of 6.0 mm.
length, arranged symmetrically on pieces of mica, the cylinders being fastened by shellac and
kept from contact with each other by minute bits of paper. The magnets are all of one diameter,
1.3 mm., and the weights of the various parts of the needle are as follows:
nags.
Twenty hollow cylindrical magnets 219. 2
Concave mirror of platinized glass 63.
Glass fiber (139 mm. long) 32.1
Copper suspension ring 2.
Mica, paper, and shellac 17. 3
17
In order to balance the mirror, attached to the west face of the upper system, and make the
supporting glass fiber hang centrally in its well, a platinum vane, pointing east, was attached at
the lower end of the glass fiber, bringing up the total weight of the needle to a little over 350
milligrams.
The rigidity of the needle is sufficient to resist the very slight strain experienced .during
an ordinary free deflection, but accidental maladjustment has sometimes to be corrected, and the
method used in astaticizing may be of interest to those who work with similar instruments.
In a system as delicately constructed as this is, a slight knock or pressure is liable to disturb
the parallelism of the planes of the upper and lower systems. Hence, if the upper and stronger
system, indicated by the full line (NS) in fig. 2, has its plane displaced, so that its north-seeking
poles lie on the east side of a vertical plane through the lower system (N'S 1 ), there is a resultant
magnetism at right angles to the mean plane of the system, and with its north-seeking poles on
the east side of that plane. This resultant, combined with the original residual of the partially
astatic system, turns the normal to the mirror (P) to the south of the west point. Some care is
necessary, therefore, to secure an approach to astaticism and at the same time to keep the mean
plane of the system in the magnetic meridian. The following mode of astaticizing has been found
advantageous, and, with care, can be applied without dismounting the delicately suspended
needle.
The upper system having the greater capacity for retaining magnetism, whatever diminution
of magnetism is necessary has been made on this system. The lower system is first magnetized to
saturation by a large magnet. Next the magnetism of the upper system is brought to a slight
excess by making judicious passes with the large magnet at a distance of 1 cm. or less. Finally,
the magnetism of the upper system is diminished very gradually by stroking the individual
magnets with minute bits of magnetized needles set in marked wooden handles, the free north-
seeking or south-seeking poles projecting slightly.
Suppose that, the normal to the mirror pointing west, the upper system is stroked on its east
side by the little magnets.
(1) Strengthening south-seeking poles inclines normal north.
(2) Strengthening north-seeking poles inclines normal south.
(3) Weakening south seeking poles inclines normal south.
(4) Weakening north-seeking poles inclines normal north.
In case the relative position of the planes has been very much disturbed by these gentle
strokings, if, for instance, the normal to the mirror turus strongly to the south after weakening the
south-seeking poles of the upper system, it may be necessary to strengthen the south-seeking poles
of the lower system by the large magnet: or if the reverse disturbance of the planes has occurred
and the normal inclines strongly to the north, the north-seeking poles of the lower system may
have to be strengthened. The reasons for the above rules will be evident from the figure. Thus
in the application of (3) pressure from the east at 8 opens the angle between the planes of the
system, as in fig. 2. The resultant systems, N'S and N8 r , are developed, which tend to set in the
plane of the meridian. At the same time the directive force of NS has been weakened. In (4)
pressure being applied on the east side of ^V, the opening of the angle between the planes of N8
N'S' is the opposite of that in fig. 2, and the resultant magnetic systems, SN', S'N, having their
south- seeking poles on the east side of the mean plane, tend to rotate P to the north, the directive
12812 Bull. G 2
18
force of N8 being diminished as before. In (1) the pressure tends to open out the angle as in
fig. 2 and swing P to the south, but the directive force of NS being increased, tends in the
opposite direction, and it might not be certain which would prevail. The rule, however, is the
result of experience.
A single hollow cylindrical magnet 10 mm. long, suspended by a very fine quartz fiber,
made a half vibration in 0.286 sec. (specific inagetism = 135 0. G. S. units per gram of steel).
The average of a system of ten magnets, as prepared for the galvanometer was 0.386 sec.
(square = 0.149). In 1892 the astatic condition of the needle was such as to give a half
vibration in 10 seconds, which in 1894 had diminished to 8 seconds, no retouching having been
made during the interval. The ratios
0.149 :10 2 = 1 :671
0.149: 8 2 = 1:429
would represent the relative directive powers of the partially astatic system at these dates, were
it not that the magnetic moments are not inversely proportional to the squares of the times of
vibration in a needle as heavily damped as this. The weight of the magnets being about 0.2
gram, and specific magnetism 800 Gaussian units ( : '- per iiigr. of steel ), or 80 C. G. S.
SGC
units per gram of steel, the magnetic moment, if all the magnets pointed one way, would be
0.2 x 80 = 16 C. G. S.
Astaticized, if the law of inverse squares of the times were followed, the magnetic moments
would be
(1892) 16 -^ 671 = 0.0238 C. G. S.
(1894) 16 -i- 429 = 0.0373
the ratio of which is
0.0238 -j- 0.0373 = 0.638.
But the galvanometer constant, determined by an entirely independent method, does not differ
much from inverse proportionality to the times of vibration, the field magnetization being the
same in all cases, a result which is to be attributed to the damping as already noted.
The absolute value of the galvanometer constant, together with a calibration of the
galvanometer scale, has been made in the following way : The battery current, measured by an
independent standardized galvanometer, was passed through the delicate galvanometer, shunted
by 84 cm. of heavy copper wire, 0.494 cm. in diameter, reading the deflections of the sensitive
instrument with various extra resistances interposed in the circuit; and the resistances of shunt
and battery were determined separately.
The battery resistance was measured by the "half deflection method" in which di being the
deflection through extra resistance R^ d % is a deflection, half as great, obtained with extra resist-
ance .R 2 . The battery resistance is r = R 2 (2 BI + G), where G is the resistance of the shunted
galvanometer, here practically zero. Three trials gave :
d 1 = 500 div., RI = 460 ohms, d- 2 = 250 div., R z = 204 ohms, r = 52 ohms.
<7 1 = 400 jR 1 = 584 " ^ = 200 " _R 2 = 25S " r = 68 "
^ = 300 ^ = 794 " d 2 = 150 ^ = 369 " r = 56
Average battery resistance = 59 ohms.
The resistance of the shunt was measured by short-circuiting it by a plug, when the very
low resistance of the heavy brass connections of the resistance box became the sole shunt,
reducing the galvanometer deflection almost to zero. The current from a single cell of gravity
battery, reduced by 1.100 ohms, was passed directly through the galvanometer thus shunted, the
galvanometer connections being opened and closed by a key. The valuation of the deflections
was made by repeating with shunt short-circuited, and either of the smaller (hundredth and
fiftieth ohm) coils in its place, using the formula for shunts:
C } 8
c~8+G
where Ci is the current through the galvanometer, C the total current, 8 the resistance of the
19
shunt, and G that of the galvanometer. In the present case, however, since 8 is very small
or or
relatively to 6?, the ratio ^ -^ is substantially equal to -^, which maybe used instead.
Putting in the plug also short-circuits the thermopile currents from junctions of unlike
metals, and changes of temperature cause these to vary, but by reversing the galvanometer
connections, their effects may be partly eliminated. With a high-resistance galvanometer this
trouble would cease.
Galvanometer connections, direct or reversed, are denoted by d and r in the following table.
Shunt, open or plugged (that is, short-circuited), is signified by o and p. The comparison deflec-
tions, in the last column but one, correspond to a hundredth-ohm coil, and to half the deflections
given by two different fiftieth-ohm coils.
TABLE 8.
Plugged.
Open.
Plugged.
Shunt.
Plugged.
Open.
Plugged.
Shunt.
0.01 ohm. Res. shunt.
3.
div.
3.0
2.7
4.1
ro
div.
15.0
18.2
20.6
rp
div. div.
3. 17. 9
7.0
6.0 (4.3)
dp
div.
+22.5
+20.0
+21.8
do
div.
+33.1
+35.5
+37.6
dp
div.
+20.4
+21.2
+18.8
div.
+ 35.4
20.8
div.
162.9
153.2
172.0
ohm.
13.6X0.01
163
=0.00083
19.3x0.01
3.3
17. 9 5.3 13. 6
+21.4
+35.4
+20.1
+ 13.6
162.7
dp
+11.7
+12.4
+13.5
do
+36.9
+33.0
+33.8
dp
+15.2
+18.0
+18.7
+ 34.6
W.9
rp
+ 2.9
+ 1.2
+ 1.6
ro
20.0
19.2
-22.0
rp
5.2
4.8
3.7
20.4
- (-1.4)
133.4
142.1
159.5
145
=0. 00133
+12.5
+34.6
+17.3
+ 19.6
+ 1.9
20. 4 4. 6
19.0
145.0
Heavy copper shunt reversed and solidly clamped.
dp
+11.0
+ 9.9
+11.5
do
+26.6
+31.5
+29.0
dp
+13.9
+15. 2
+15.5
+ 29.0
- 12.9
dp
+13.9
+15. 2
+15. 5
do
+34.0
+31.0
+31.9
dp
+21.0
+20.3
+21.8
+ 32.3
18.0
122.1
118.6
147.8
147.8
162.8
163.8
15.2x0.01
144
=0. 00109
16.3x0.01
+10.8
+29.0
+14.9 + 16.1 +14.9
+32.3
+21.0
+ 14.3
rp
3.2
2.0
2.5
ro
20.0
23.2
21.2
'? n
5.0
7.5
6.2
21. 5 12.
16.0
(4.4) 13.6
ro rp
31. 2 20. 9
33. 17. 2
31. 4, 19. 1
31.9
-(-16.5)
144
=0. 00113
2.6
21.5
6.2
17.1 13.9 31.9 19.1
15.4
143.8
Mean resistance of hea 1
fy shunt '. ...
0.00109
In the galvanometer tests, induction currents gave a stronger backward swing than happens
in the bolometric work where there is a continuous current only slightly varied by the resistance
changes due to radiation. Consequently deflections have been computed by a formula:
1
2
where e\ is the reading before connecting, d the extreme of the swing given by the current, and 6',
is obtained from three successive swings of the needle, after the current is broken, by the formula:
A single series follows in full (extra resistance, 270 ohms).
20
TABLE 9.
.,
d
P*j
*
<-,+*,
s
2
+2
+405
111 +35
_ 3
+4.9
+3. 5 +401. 5
403
117 +30
-5 +1.7
+0. 9 402. 1
+1 397
116
+30
5
+1 8
+1.4
395.6
389
114
+29
fr
+0.9
+0.5
388.5
+1 389
115
+26
7
-0.7
+0.2
388.8
388
113
+30
6 +1. 2
+0.6
387.4
+1
395
115
+31
3 +3. 4
+2.2
392.8
1
396
118
+27
9 1. 8
1.4
397.4
i
396
113
+33
2 +4. 8
+1.9
394.1
+2
396
111
+30
4 +2. 6
+2.3
393. 7
+0.5
+395. 4 114. 3
+30.0
5.0 +1.9
+1.2
+394. 2
The ratio of the current in the galvanometer to that in the shunt is taken as 1 : 18,800.
The mean results of five series are given.
TABLE 10.
Series.
Extra resistance
plus battery.
Current in Deflection,
shunt. 5
Current in
galvanometer.
Galvanometer
constant. ldiv.=
1
2
3
4
5
Ohms.
1,159
609
429
329
269
Ampere.
0. 00735
0.01399
0. 01986
0. 02590
0. 03167
Divisions.
114.7
211.6
298.5
394.2
484.2
Ampere.
3. 91X10- 7
7.44
10.56
13.78
16.85
Ampere.
3.40xlO- y
3.51
3.53
3.50
3.48
Mean galvanometer constant, 1 div. = 3. 48x10 ~ 9 ampere.
It will be seen that the galvanometer constant is the same in all parts of the scale, as nearly
as can be determined by this method. There have been some indications that the instrument is a
very little more sensitive for small deflections, less than 20 div.; but as the amount is hardly
appreciable, and seem's to vary with the slightest change in the hanging of the needle, no
correction has been applied.
Since the cylindrical magnets do not lie in the central plane of the coils, the induction damp-
ing is larger than usual, and departure from a logarithmic decrement was to be anticipated in the
vibrations. The means of the five series, similar to that given in full in Table 9, are:
TABLE 11.
I
d
n,
n 2 n 3
2
t+4
&
2
+0.3
+115. 1
31.2
+ 8.6 1.7
+0.5
+0.4
+114.7
+0.2
+211.7
60.3
+15. 5 4. 11 " +0.
+0.1
+211. 6
0.2
+298. 9
86.3
+23. 3 4. 9
+1.0
+0.4
+298. 5
+0.5
+395. 4
-114. 3
+30. 5.
+1.9
+1.2
+394. 2
+0.6
+484.
141. 6
+34. 6 9. 3
0.9
0.2
+484. 2
The next table contains the amplitudes (cii 0% a 3 ) of successive vibrations and the logarithms
of their ratios.
TABLE 12.
a,
a t
3
<
1 a,
2^
146.3
272.0
385.2
509.7
625.6
39.8
75. 8
109.6
144.3
176.2
10.3
19.6
28.2
35.0
43.9
0. 5651
0. 5550
0. 5560
0. 5460
0. 5503
0. 5766
0. 5713
0. 5678
0. 5816
0. 5769
Mean logarithmic decrements.
0. 5545
0.574!)
The air damping appears to be tolerably uniform, since there is no marked relation between
the logarithmic decrements and the amplitudes; but the influence of induction currents is seen in
the change Of the decrement in successive periods.
The needle is suspended by a single fiber of silk, 33 cm. long from the suspending piece to the
copper ring. The entire fiber is about 40 cm. long, is tied to the copper ring of the needle by a
loose square knot, and, at its other end, carries a weight equal to that of the needle. At the outset
the galvanometer is inverted, and the counterpoise hanging freely, the silk fiber is allowed to
stretch and untwist until it comes into a normal state; then the galvanometer is set up in its
usual position, the fiber passing over the edge of the suspending piece, but not being fastened
to it. The suspending piece is finally adjusted until the needle hangs centrally. As thus pre-
pared the silk fiber has very little tendency to twist, the image from the free but undisturbed
needle seldom wandering during the day more than the few divisions to be expected from the
diurnal variation of the magnetic declination.
The bolometric equilibrium can not be maintained perfectly in a room of changing temperature,
and some means of bringing the null point to any part of the scale at pleasure is desirable.
Variation of the field by weak magnets, although objectionable, has been used to some extent.
The change of field necessary in order to push the null point from one end of the scale to the other
was determined by measuring the deflection from a constant impulse.
TABLE 13.
Startiiig : Mean of 10 deflec-
point. tions.
Percentage
of deflection
at 100.
Division!.
Per cent.
+ 87. 61+0. 34
101.9
100
+85. 03+0. 38
100.0
200
+84. 99+0. 39
98.1
300
+81.27+0.51
96.1
400 i
+80. 83+0. 72
94.3
In order that the deflections may be Comparable within 2 per cent., the null point should not
be changed by more than 100 divisions during the observations. To avoid the necessity of more
than a slight change of field the electric current has been allowed to flow through the bolometer
for at least twenty-four hours before commencing observations, and the room has been kept at a
nearly constant temperature.
The cover glass of the galvanometer case has optically plane parallel surfaces, and the carefully
figured mirror gives a sharp image, permitting readings by estimation to a tenth of a division.
In some of the experiments I have made the exposure to radiation by pulling cords, at the
same time reading the galvanometer ; in others, it has been necessary to have an assistant shift
some part of the apparatus at the word of command.
SCREENS.
The bolometer chamber has been used with two different openings : First, a wide aperture,
limited by a series of graduated circular card-board diaphragms, the outermost 1.19 inches
(3.02 cm.) in diarieter, 3.92 inches (9.96 cm.) from the bolometer, giving an angular aperture of
17 16'. Second, a smaller aperture, the case being further protected by triple tin-plate screens,
with circular openings: the outermost 1.15 inches (2.92 cm.) in diameter, 12.3 inches (31.24 cm.) in
front of the bolometer (angle 5 21'): the middle and limiting aperture 1.02 inches (2.59 cm.) in
diameter, 11.3 inches (28.70 cm.) from the bolometer, giving an angular aperture of 5 10'.
The ratio of the squares of the angular apertures is 11.17 : 1, but the observed efficiencies
have the ratio 8.96 : 1, which is adopted. I can only conjecture that the difference is due to
the reflection of the bolometer's radiation by the polished tin plate, and the retention of a larger
proportion of the heat received from radiation when the aperture is partly closed by the metal
screen; but no experiments have been tried to test the hypothesis.
22
In order to transform the measures made in arbitrary units of a scale into absolute units of
radiant energy, and at the same time to furnish a check on the constancy of the measuring instru-
ments, the bolometer has been exposed from time to time to the radiation from blackened copper
screens containing water at different temperatures.
The unit of radiant energy employed is that which I have elsewhere called the radim,*
"representing a unit quantity of heat, namely, one gram- water-degree- centigrade heat-unit, lost
as radiation per square centimeter of surface per second of time, by a heated body, or transmitted
by the ether as an equivalent amount of radiant energy through a normal section of 1 sq. cm. in
one second of time."
The standard of radiation adopted is that of blackened copper at 100 C. to a surface of the
same material at C., filling the hemisphere, which, according to the measures of Dr. J. T.
Bottoinley may be taken as 0.0126 radiin. Measured radiations between any other temperature
limits have been reduced to the standard by multiplying by a factor obtained by dividing the
difference of radiations at the given limits, as read from the standard curve (derived from Table B,
p. 270, Astropliysical Journal, Vol. 8), by 0.0126. The deflections are further reduced to a standard
battery current of 0.033 ampere, corresponding to 100 div. of the battery galvanometer.
The radiating surface, seen through the full aperture of 17 16', occupied
(50 x tan 8 38') 2 X n = 181.06 sq. cm.,
the center of the radiating surface being placed 50 cm. from the bolometer, and its plane normal
to the line of sight. The mean angle with the line of sight of a circle in the radiating surface at
mean distance is
a tan - 1 ^ -?- = 6 7' .7,
2 x 50
where the radius of the bounding circle is
r = 50 x tan 8 38';
and the mean distance of the surface is
d = ^ 2 = 50.319 cm.
2 sin or
The bolometer of 0.19 sq. cm. receives of the total radiation, assuming equable emission at all
inclinations, the fraction
Jill? = 0.000 Oil 957
and the standard radiation received by the bolometer with full aperture is
E l = 0.000011957 x 181.06 x 0.0126.
= 0.000 027 278 radim.
The smaller aperture has been used with radiators but little removed. The radiation through
* The Probable Kange of Temperature on the Moon, Astrophysical Journal, vol. 8, p. 271, December, 1898.
23
this aperture, of 1.295 cm. radius, is virtually that of a surface of like area, 5.2685 sq. cm., and the
standard radiation received by the bolometer is
= 0.000 002 437 radim. *
The efficiency of the radiation coming through this smaller aperture, however, has been shown
to be 25 per cent, greater than that of an equal amount of radiant energy passing through the
large aperture (p. 21).
I proceed to give screen comparisons and the valuation of standard deflections.
March 12, 1892.
FIRST SERIES.
Battery galvanometer 100 div.
Hot screen 69.8 C., computed radiation 0.0154 radim.
Cold " 9.5 C., " " 0.0083 "
Radiation reduced from standard :
E=E 2 x~= 0.000 001 373 radim.
12o
d = 35.43 div. (mean of 10. small aperture) ; 1 div. = 0.000 000 0388 radim.
lar
563.4 div.
126
Standard deflection, on standard radiation, and with full aperture = 35.43 x 8.96 x -=
SECOND SERIES.
Battery galvanometer 100 div.
Hot screen 69.4 C., computed radiation 0.0153 radim.
Cold " 110.80., " " 0.0085 "
68
E = E 2 x -p>g = 0.000 001 315 radim.
S = 30.94 div. (mean of 10, small aperture); 1 div. = 0.000 000 0425 radim.
126
Standard deflection (full aperture) = 30.94 x 8.96 x gg- = 513.7 div.
*The quantities E { and E 2 are introduced purely as reduction factors, and do not represent exactly the quantities
of normal radiation received by the actual bolometer, although the latter may easily be derived from them.
The total radiation from each unit of radiating surface to a hemisphere is to the fraction of radiation emitted
per sq. cm. at angle (ii) with the normal, and received on an element of the hemisphere (Ss), in the p .oportion
2 it r x ^ ^ cos i sin i di : cos ii ds.
In the present case, cos ii may be taken as unity, Ss (the area of the bolometer) is 0.19 sq. cm., 5i = | degree, and
r 28.7 cm.
The numerical value of
2ier x ^^ cosisin i 5i= it r ^i 7r sin2i x
ooO
is 2587.7, and the bolometer receives 0.19 -H 2587.7 = - -- of the entire radiation.
13619
For any other radiator than lampblack, the relative radiation, p X (i), must be considered. The value of p
has been determined for air in the present research for nearly normal emission, but (i) remains unknown.
24
July 28, 1892.
Battery galvanometer 97 div.
Hot screen 76.0 C., computed radiation 0.0162 radim.
Cold 33.8 O., " " 0.0107 radim.
55
E = E, x jog = 0.000 001 073 radim.
- !? = 25.30 div. (mean of 10, small aperture) ; 1 div. = 0.000 000 0424 radim.
126
Standard deflection (full aperture) = 25.30 x 8.96 x -~- = 519.3 div.
March 10, 1893.
Battery galvanometer 98 div.
Hot screen 99.0 C., computed radiation 0.0200 radim.
Cold " 0.8 C., " " 0.0078 "
E - E, x 1 l2 ' = 0.000 026 412 radim.
MI x 126
6 = 515.9 x -Qg = 526.4 div. (mean of 10, full aperture); 1 div. = 0.000 000 0502 radim.
126
Standard deflection (full aperture) = 526.4 x ^ = 543.7 div.
March 3, 1894.
Battery galvanometer 101 div.
Hot screen 98.7 C., computed radiation 0.0200 radim.
Cold " 00.7 C., u " 0.0078
122
E = E v x ;* = 0.000 026 412 radim.
6 = ^jffi^ ~ = 482.6 div. (mean of 10, full aperture); 1 div. = 0.000 000 0547 radim.
126
Standard deflection (full aperture) = 482.6 x p^ = 498.4 div.
March 30, 1894.
Battery galvanometer 95 div.
Hot screen 99.l C., computed radiation 0.0200 radim.
Cold " 290.4 C., " " 0.0103
97
E = El x 126 = - 000 21 00 radim -
d = 364.2 X (jrj- = 383.4 (mean of 10, full aperture) ; 1 div. = 0.000 000 0548 radim.
126
Standard deflection (full aperture) = 383.4 x 97 = 498.0 div.
July 30, 1895.
Battery galvanometer 95 div.
FIRST SERIES.
Hot screen 98.3 C., computed radiation 0.0198 radim.
Cold " 23.7 C., " " 0.0097 "
E E v X = 0.000 021 866 radim.
6 = 456.1 x 93 = 480.1 (mean of 10, full aperture) ; 1 div. = 0.000 000 0456 radim.
16
Standard deflection (full aperture) = 480.1 x T = 598.9 div.
25
SECOND SERIES.
Hot screen 91 0., computed radiation 0.0187 radim.
Cold " 240 c., " " 0.0097 "
90
E =%! X jg6 = 0.000 019 484 radim.
8 = 401.7 x gl- = 422.8 (mean of 5, full aperture); 1 div. = 0.000 000 0461 radim.
126
Standard deflection (full aperture) = 422.8 x on = 591.9 div.
THIRD SERIES.
Hot screen 85 C., computed radiation 0.0177 radim.
Cold " 24 C., " " 0.0097 "
80
E = E l x pg = 0.000 017 319 radim.
d = 354.8 x g -- = 373.5 (mean of 5, full aperture); 1 div. = 0.000 000 0464 radim.
126
Standard deflection (full aperture) = 373.5 x ^Q- = 588.3 div.
FOURTH SERIES.
Hot screen 77 C., computed radiation 0.0164 radim.
Cold " 24 C., " 0.0097 <
E = El x 126 = 0<00 14 505 radilu -
6 = 300.6 x -gg- = 316.4 (mean of 5, full aperture) ; 1 div. = 0.000 000 0458 radim.
126
Standard deflection (full aperture) = 316.4 x -gy- = 595.0 div.
The last four series were made to test the validity of the mode of reduction for E, which is
sufficiently accurate for its purpose. The two series of March 12, and that of July 28, 1892. being
founded on rather small deflections taken with the small aperture, are less reliable than the others.
They give a mean value of 1 div. = 0.000 000 0412 radim, corresponding to 0.000 000 0412 x f =
0.000 000 0515 radim for the full aperture. The observation of March 10, 1893, with full aperture,
gave 1 div. = 0.000 000 0502 radim, and the galvanometer constant may be assumed uniform for
the first year (1892-93), when its value in amperes was measured. On March 3, and March 30,
1894, larger radiation was required to give a deflection of one division, namely, 1 div. =
0.000 000 0548 radim, or 74- per cent, greater than in 1892-93, the vibration of the needle having
meanwhile become 20 per cent, more rapid, or the squares of the times 36 per cent, smaller; and
finally, in July, 1895, the time of vibration being the same as in 1894, 1 div. = 0.000 000 0460 radim,
or 7 per cent, less than in 1892-93. The last change is perhaps attributable to simultaneous
changes in the magnetism, of the needle and in the magnetic field, but as the field was not
measured independently, no correction is available.
The variation of the radiator's surface is a possible source of error in these standardizings.
To guard against it, a uniform procedure has been followed. The screens are of copper, painted
dead black, with a very thin coat. Before using, this surface is lightly smoked with a fresh coat
of soot, uniformly distributed. From experience with such a surface, it does not seem probable
that variations of more than 2 or 3 per cent, are to be anticipated; but it is not asserted that this
standard fulfilled the ideal of an absolutely black body. After the measures of July 30, 1895, an
effort was made to carry the radiant emissivity of the hot screen somewhat nearer its maximum
value, by repeated smokings, while the screen was temporarily filled with cold water, until a coat
of soot i mm. thick had been deposited. The mean standard deflection of 593.5 was thereby raised
to 620.7, or by 4.6 per cent.
26
If the variations are attributed to errors, and all observations have equal weight, 1 div. =
0.000 000 0490 i 0.000 000 0010 radim, but in the author's opinion, it is best to accept the
variation as a fact and to take the valuations as given at the stated epochs, whence, for full
aperture, we have the following radiant values :
(1892-93) 1 div. = 0.000 000 0509 radim.
(1894) 0.000 000 0548 "
(1895) 0.000 000 0460
For the small aperture, the corresponding values are four-fifths of these
(1892-93) 1 div. = 0.000 000 0412 radim.
(1894) 0.000 000 0438 "
(1895) 0.000 000 0368 "
PSYCHBOMETER FACTOK.
The water- vapor in the air experimented upon has been measured by a stationary psychrom-
eter, checked occasionally by a dew-point apparatus. The usually adopted formula for a
ventilated or a sling psychrometer is :
/! =/ 2 _ 0.000 67 (t - t') H,
where f\ = the pressure of water- vapor at the dew-point, / 2 = the vapor pressure at the
temperature of the wet bulb, and H = the barometer reading, may be in either millimeters or
inches of mercury; but t and t', the dry and the wet-bulb readings, are in centigrade degrees.
The statement is made in books on the subject that the numerical factor by which the
difference (t t') is to be multiplied, may need to be doubled in a closed room; but since every
psychrometer must vary according to the kind of muslin with which the wet bulb is covered, and
according to the disposition of objects around it, the factor should be determined by experiment.
Two windows on opposite sides of the room were left open, producing a gentle circulation
of the air. Dew was formed on a polished tin-plate vessel in which water was cooled by ice, or
heated at pleasure. The cold water half filled the vessel, and the contrast between upper and
lower halves was noted.
(1)
C. C.
Dew formed at + 6.8 1 M g -
Dew evaporated at + 9.4 j 1V
(2)
C. C.
Dew formed at + 7.8 1 M g ,
Dew evaporated at + 8.9 | fl
Observed dew-point = + 8.3 C.=+46.9 F.
Corresponding psychrometer readings :
c F. c. F. C.
Dry bulb 77.1 ^ 25.0 i Difference 13 9 _ 7 7
Wet bulb 63.2 = 17.3 ( L
(2)
F. C. F. C.
Dry bulb 77.6 = 25.3 ) Difff . rpn( e 13 o _ 7 7
Wet bulb 63.7= 17.6 \ L
The windows were now closed.
(In ten minutes.)
(3)
27
(In thirty minutes.)
(In sixty minutes.)
(5)
c F. C. C F. C.
80.1 = 26.7
68.1 = 20.0
Open icindows.
By Hazen's Tables (Fahrenheit, p. 64) for the temperature 77 F. and dew-point 47, the
depression of the wet bulb (ventilated) is 17.25 F. The observed depression was 13.9 F., whence
(tf) must be multiplied by
factor = * = 1.24
For the temperature 77.5 F. (same dew-point), the depression by the table is 17.50 F., and
the observed depression 13.9 F.
Windows closed.
For the temperature 79 F. (same dew-point as before), by table, depression = 18.o F.,
observed, 12.4,
factor = iJ? = i- 49
1J.4
For the temperature 80 F. (same dew-point), by table, depression = 19.0 F., observed, 11.4,
factor = i 9 ^ = 1.6"
11.4
For the temperature 80 F. (same dew-point), the final observation gave depression 12.0,
factor = ^!? = 1.58
The first condition (two windows open) is seldom realized in bolometric work, and never unless
the outside air is nearly calm, which was not the case during the above experiments. In winter
the windows are usually closed during bolometric observations, this being necessary to prevent
air currents and sudden variations of temperature around the bolometer. The room in which
the experiments were made has a floor space of CO sq. m., and is connected with other rooms, all
heated by a hot-air furnace, and well ventilated. In warm summer weather a single window is
commonly open. These tilings being so, since the mean of the above determinations gives 1.45 for
the multiplier, 1.5 is adopted as the working factor by which (t t 1 } has been multiplied in finding
the dew-point by the unventilated psychrometer, and by Hazen's Tables. With this explanation,
further details will be omitted, and only the results of psychrometric measures will be stated.
Three successive pieces of apparatus have been used for measures of atmospheric radiation :
(a) A pair of open radiant cylinders.
(6) Hot air ascending from a furnace flue.
(c) A closed radiant cylinder with movable disk.
28
The horizontal air column in line with the bolometer is to be considered as composed of two
parts. The portion between the bolometer and the front of the radiating apparatus is of nearly
the same temperature as the bolometer, and acts chiefly by absorbing. The portion of air within
the apparatus both radiates and absorbs, but the differential effect is radiative, and for the sake
of distinction the first part may be called the absorbent, the second the radiant layer.
Psychrometer readings, as usually reduced, are stated in pressures of water- vapor on the
standard of the mercury gage (millimeters of mercury), or as a weight of wa'ter per unit volume
of air (grams per cubic meter) ; but in considering the absorbent or radiant effects it is more
convenient to express the amount of water-vapor as a depth of equivalent liquid water penetrated
by the line of sight within the limits of the radiative or absorbent column. For example, a
column of air 100 meters long and 1 square decimeter in section occupies 1 cubic meter, and if its
water- vapor be all condensed upon a normal section, a liquid layer 1 millimeter thick will be
produced for every 10 grams of vapor contained in the air column. If the volume of air has the
form of a cube 1 meter on an edge, the layer of condensed water being distributed over a normal
section of 1 square meter, will have a depth of 0.01 mm. for every 10 grams per cubic meter, the
depth of water being directly proportional to the length of the air column multiplied by the
absolute humidity. This mode of expression relates solely to the quantity of water present.
Nothing is predicated as to the quality of its absorption or radiation, which may vary widely
according to the physical state in which this definite quantity of water exists.
The chief atmospheric constituent affecting radiation being water-vapor, it is necessary to
consider the air depths (d), and the equivalent layers of liquid water (w) in d, for each gram of
water-vapor per cubic meter of air, involving the following constants in the successive pieces
of apparatus.
TABLE 14.
Absorbent layer.
Radiant layer.
Apparatus a
Apparatus b t
Apparatus bi
Apparatus c
tv =
d == 13. 2 inches = 33. 5 cm.
w = 0. 000 0335 cm.
rf= 10.0 inches = 25. 4 cm.
to 7.0 inches = 17. 8 cm.
0. 000 0254 cm.
0.0000178cm.
d ~16. 25 inches = 41. 2 cm.
to 11. 5 inches = 29. 2 cm.
0. 000 0412 cm.
0. 000 0292 cm.
d = 14. 8 inches = 37. 6 cm.
' = 0. 000 0376 cm.
={
36. 4 inches = 92. 5 cm.
0. 000 0925 cm.
16. inches = 40. 6 cm.
0. 000 0406 cm.
3. 5 inches = 8. 9 cm.
to 7. inches = 17. 8 cm.
f 0. 000 0089 cm.
\ 0. 000 0178 cm.
4. 25 to 60 inches = 10. 8 to 152. 4 cm.
Contents of cylinder usually dry or
nearly so.
DESCRIPTION OF METHOD (A) AND APPARATUS.
The ideal aimed at in the disposition of the apparatus was to obtain a concave surface of
polished silver at constant temperature, having the bolometer strips at its center of curvature,
and completely filling the circular openings in the multiple bolometer screens of polished metal.
Eadiations proceeding from the bolometer toward the concave mirror (distant about 125 cm.) would
then be directly returned, except as affected by absorption, while rays from any objects in front
of the mirror, but outside of the cone of rays from the bolometer to the mirror's edge, could not
possibly be reflected upon the bolometer.
The bolometer being at the bottom of the deep cylindrical cavity of its ebonite case,* pro-
tected from air currents by internal diaphragms, and further shielded by the multiple metallic
screens already mentioned, it was arranged to transpose the volume of air intervening between
the mirror and the outer bolometer screen, and to substitute volumes of hot or cold air so rapidly
* See Plate 2, accompanying Prof. S. P. Langley's article "On Hitherto Unrecognized Wave-lengths," in Am.
Journ. of Sci., vol. 132.
29
that the temperature of the bolometer should remain unaffected save by the feeble radiation of
the gas, the temperature of the concave mirror being expected to remain appreciably unchanged
in the brief interval of exposure, owing to the small absorption of radiation by silver and the
continual circulation of water within the metallic walls, as will be now described.
The mirror was made of silver-plated copper, so as to be both a good conductor and a poor
radiator, but owing to the thinness of the copper and its yielding quality it was found difficult to
preserve the spherical figure. The mirror formed the central portion of the front face of a rectan-
gular vessel containing water at the temperature of the room, and on testing its figure, certain
small portions, as viewed from the position of the bolometer, were found to reflect light from a
lamp flame placed outside, but close alongside the aperture of the bolometer screen. It was
evident, therefore, that some of these distorted surfaces might reflect enough radiation from the
interior blackened walls of the cases containing the hot and cold air to entirely vitiate the result.
It was recognized from the start that the radiating power of a gas is so greatly at a disad-
vantage, compared with the emissive power of a solid, that the least exposure of hot or cold metal
in front of the bolometer would give thermal indications, which might very easily be greater than
those to be expected from the short air column available for experiment. The failure to obtain a
perfect spherical reflector which should also be a good conductor, without going to greater expense
than was deemed advisable, led to a partial modification of the original plan in the coating of
the mirror with lampblack. The layer of soot being very thin, must retain (it was supposed)
substantially the temperature of its metallic backing, in spite of its being a good absorbent of
radiation,* while the greater part of the blackened spherical surface remains incapable of reflecting
outside rays to the bolometer, owing to its shape, except in a weak, diffusive way, and the specular
reflections from the small distorted areas are rendered ineffective owing to the feeble reflecting
power of lampblack and the obstruction of rays reflected from silver in traversing the discon-
tinuous particles of powdered carbon.
The first experiments were made to compare results with silver and with lampblack for a
background, in order to get a knowledge of the magnitude of the errors which are to be guarded
against, and of the legitimate radiations at our disposal.
The movable air chambers were cylindrical vessels of tin plate, 8 inches in diameter, and 36.4
inches long, provided with diaphragms of circular aperture, 6 inches apart, and graduated from
an opening of 2 inches at the end next to the bolometer, to one of 7 inches at the further extremity,
adjacent to and circumscribing the mirror face. The inner surfaces of the air chambers were
blackened, and apertures were provided at the middle, and 8 inches from each end, for the
insertion of thermometers, whenever the temperature was read. The bulbs were, of course, drawn
outside the limits of the radiating space during actual work. The air cylinders were contained in
tanks 3 feet long, and 1 foot square in transverse section, the cylinders projecting slightly at either
end, and being unjacketed at these ends, but being otherwise completely surrounded by the
contents of the tanks, which contained either hot or cold water, or a freezing mixture. The tanks
were mounted on a rolling carriage, moving between guides, and could be drawn to an accurately
adjusted stop on one side or the other, so as to bring the longitudinal axis of either air chamber
in line with the bolometer and the center of the mirror; and this could be accomplished by the
observer at the galvanometer by pulling a cord passing over pulleys to the movable carriage, thus
transposing the air vessels, while simultaneously observing and recording the galvanometer
readings.
The outermost aperture of the bolometer's multiple metallic screen, 1.15 inches in diameter,
at 12.3 inches from the instrument, was concentric with the 2-inch aperture of the near end of
the air chamber which was 13.2 inches from the bolometer, and since the angular aperture of the
opening in the screen, as seen from the bolometer, namely 5.35, was much smaller than those of
the air chamber, which were 8. 67 for the near aperture, and 8.07 for the further opening in front
of the mirrior, there was no danger that any portion of the walls of the air chamber could be
directly observed.
Since in shifting the air chambers to and fro, the larger or 7-iuch aperture remained always
*How far this supposition is invalidated will be sho^vn in the sequel.
30
nearly in juxtaposition with the silvered face of the fixed water tank, very little air could escape
at this end, and that which entered at the 2-iuch aperture was prevented from having free circula-
tion by the internal diaphragms. It was found that with an excess of 60 C., the excesses of either
of the internal thermometers of the air chamber above the temperature of the outside air seldom
differed from the mean by as much as 5 per cent. The temperature gradient of the central axis
of the air chamber has therefore usually been quite moderate.
The following temperature readings for a single day, March 15, 1892, are given in proof of
this statement :
TABLE 15.
Excess of hot cylinder
above outside air
temperature as in-
ferred from the mean
of the three ther-
Mean variation of
three internal
thermometers.
mometers.
e>0.
C. Per cent.
67.8
0. 6 = 0. 9
70.1
0.8 = 1.1
69.5
0. 9 = 1. 3
66.9
1.9 = 2.8
65.0
0. 4 = 0. 6
61.0
1.0 = 1.6
65.4
2. 1 = 3. 2
61.8
1.8 = 2.9
60.7
0.8 = 1.3
56.3
1.4 =2.5
There being no constant order in the relative excesses of the three thermometers, their mean
has been adopted as the average temperature of the air column.
CORRECTION FOR THE MAGNETIC EFFECT OF THE APPARATUS DURING MOTION IN METHOD (A).
The positions of stone piers, and other necessities of the case, compelled the placing of the
principal apparatus in a position where the shifting of its iron parts feebly, but appreciably,
affected the very sensitive galvanometer. Comparisons of the galvanometer readings in extreme
positions of the two air cylinders were therefore made, under otherwise identical conditions, to
obtain the magnetic effect upon the galvanometer, due to the movement of these considerable
masses of tinned iron at an average distance of 12 feet from the magnetic needle.
Experiment of July 29, 1892.
All parts of the apparatus were substantially at the temperature of the room. No conceivable
cause, therefore, existed for any temperature deflection. Moreover, variation of the thermal con-
ditions by making the blackened silver screen hot, but leaving the intermediate air cylinders cool
and equal in temperature, gave practically the same result, though obviously a less trustworthy
one, since it is difficult to maintain the temperature of the hot screen constant.
Exposures were made by alternating west and east cylinders that is, by bringing the central
axis of each cylinder in turn into the line of collimatioii of the bolometer. To eliminate galva-
nometer drift, each pair of readings with west cylinder in line was compared with the intermediate
reading with east cylinder in line.
Temperature of west cylinder (near thermometer),
Temperature of west cylinder (middle thermometer),
Temperature of east cylinder (rear thermometer),
Temperature of east cylinder (middle thermometer),
Temperature of blackened water-filled screen,
C
29.3
29.3
29.0
27.8
27.8
31
TABLE 16.
First series.
Second series.
West cylin-
der in line.
Mean
west.
East cylin-
der in line.
Deflection
east.
West cylin-
der in line.
Mean
west.
East cylin-
der in line.
Deflection
east.
div.
div.
101.2
99.0
97.3
99.3
102.8
+3.5
95.0
97.0
101.9
+4.9
98.0
97.7
102.0
+4.3
96.9
96.0
100.1
+4.1
98.2
98.1
101.0
+2.9
99.2
98.1
101.8
+3.7
96.1
97.2
101.0
+3.8
97. i 98. 1
101.5
+3.4
98.5
97.3
101.0
+3.7
96.6
96.8
102.0
+5.2
97.3
97.9
101.8
+3.9
97.9
97.3
101.3
+4.0
93.9
95.6
99.0
+3.4
96.4
. 97.2
100.7
+3.5
96.0
95.0
100.2
+5.2
95.9
96.2
100.9
+4.7
98.8
97.4
100.1
+2.7
94.2
95.1
98.5
+3.4
98.8
98.8
' 101.6
+2.8
93.7
94.0
98.0
+4.0
Mean,
+3.62
Mean,
+4.09
The probable errors of the two series being i 0.16 div. and 0.14 div., equal weights may
be given to them, and their common mean applied with opposite signs, according as the change
of position is from west to east, or the reverse, whence the mean magnetic deflection by presenta-
tion of east cylinder = + 3.86 div. ; by presentation of west cylinder = 3.86.
OBSERVATION OF AIR RADIATION BY METHOD (A).
The radiation measures with the nrst apparatus follow. The sensitiveness of the galvanom-
eter during these experiments remained unchanged. The astaticism, checked from day to day,
continued constant. The time of a half vibration of the needle, chronographically determined,
was 9.7 seconds.
A comparison of deflections with polished silver and blackened reflector showed that the
former were from two to three times the greater, proving, as had been anticipated, that the
reflections from the distorted surface of the silver were larger than the air radiation to be
measured. It is only necessary, then, to consider those measures in which, the bolometer being-
directed to the concave blackened surface, the alternate interposition of hot or cold columns
of air has given small but consistent positive deflections from the heated air. There remains
only the uncertainty whether, in spite of the backing of conducting copper and water, the outer
radiant layer of the lampblack may not change temperature by contact with the hot and cold air.
This point will be considered in connection with the results of other methods.
Each interposition of hot air has been made between a pair of cold ones whose mean is taken
for comparison, and the movements have been regularly timed in such a way as to allow the
galvanometer needle just time enough to complete its swing, 11 consecutive readings on the
cold air and 10 intermediate ones on the hot air, forming a series, as in the example at constant
temperature in Table 16.
32
Experiments of March 10, 1892.
West cylinder heated.
East cylinder surrounded by refrigerating mixture of snow and salt.
TABLE 17.
Deflections (hot).
Before first
T> .
\ f+* A
AT A 4
HT A
series.
series.
.oLlDer SeCOIHl
aeries.
Mi'.'iii iirst
series.
i\i PATI seconil
series.
First
Second
series.
series.
div. div.
Temperature of bolometer
15. OC.
14-. 4 C.
14. 5 C.
14. 7 C.
14. 5 C.
15.0
13.4
" " screen
20 C . C.
19 C . 6 C.
19. 2 C.
19 e .80.
19. 4 C.
17.3
11.2
" " room
12. 3 C:
12. 2 C.
12. 1 C.
12. 3 C.
12. 2 C.
15.2
15.8
Pressure of atmosphere
729. mm.
(AtO C.)
729.0mm.
729. mm.
12.9
15.4
Dew-point
5. 60.
5 C .6C.
5.6C.
13.1
14.4
Pressure of water vapor
<
6. 78 mm.
6. 78 mm.
12.9
15.9
Water per cubic meter
7. 03 grams.
7. 03 grains.
11.0
16.5
Temperature of hot air
57. 1 C.
54. 2 C.
48. 8 C.
55. 7 C.
51. 5 C.
17.1
15.6
" " cold "
12. 2 C.
11. 3 C.
9. 50.
11. 8 C.
10. 4 C.
11.2
15.4
" excess
69. 3 C.
65. 5 C.
58. 3 C.
67. 5 C.
61. 9 C.
13.4
13.1
Mean deflections
13.91
14.67
The probable error of the mean of the first series is i 0.51 div., and of the second, i 0.37 div.
The battery galvanometer stood at 99 div., and the deflections, reduced to the standard current
(100 div.) and corrected for the negative magnetic deflection of the west cylinder, become-
First series : (+ 13.91 + 3.86) 4- 0.99 = + 17.95 div.
Second series: (+ 14.67 + 3.86) -^- 0.99 = + 18.72 "
The mean temperature of the hot-air column was 39.() above that of the bolometer, arid the cold
air was 25.7 below the instrument. The mean atmospheric pressure was 729 mm. and the force
of water vapor 6.78 mm., equivalent to a layer of liquid water 0.000 236 cm. thick in the absorbent
column, 33.5 cm. long.
Experiments of March 15, 1892.
West cylinder heated.
East cylinder surrounded by cool water of nearly the same temperature as the bolometer.
Silvered reflector freshly blackened by smoking it over a smoky lamp flame.
TABLE 18.
Ale&n iii'ist
Deflections (hot).
Before nrst
series.
Between
series.
Alter second
series.
series.
M r;iii second
series.
First i Second
series.
series.
div.
div.
Temperature of bolometer
8. 7 C.
8.7C.
8.7C.
16.1
13.6
" screen
7.9C.
8. C.
8.OC.
8.OC.
15.0
12.7
" room
4. 4 C.
5.2C.
3. 1 C.
4.8C.
4.2C.
18.2
19.0
Pressure of atmosphere
738. 4 mm.
(AtOC.)
738. 4 mm.
738. 4 mm.
14.2
13.8
Dew-point
10. OC.
8-.9C.
7.8C.
14.2
7.7
Pressure of water vapor
2. 35 mm.
2. 55 mm.
15.7
12.9
Water per cubic meter
2. 57 grams.
2. 78 grams.
10.2
13.4
Temperature of hot air
73. 9 C.
72=. 1 C.
68. 1 C.
73. C.
70. 1 C.
10.2
12.9
" " cold "
+ 7. 9 C.
+ 7.5C.
+ 6.8C.
+ 7. 7 C.
+ 7.2C.
12.1
15.4
' ' excess
66. OC.
64. 6 C. 61. 3 C.
65. 3 C.
62. 9 C.
17.5
18.2
Mean deflections
14.34
13.96
33
The probable errors of the mean deflections are 0.61 div. and 0.60 div. Battery galva-
nometer = 102 div. Deflections reduced to standard and corrected :
First series : ( + 14.34 + 3.86) 4- 1.02 = + 17.84 div.
Second series : ( + 13.96 + 3.86) -=- 1.02 = + 17.47 "
The mean atmospheric pressure was 738.4 mm., and the mean force of water vapor 2.45 mm.,
equivalent to a liquid layer 0.000 090 cm. thick in the length of the absorbent column of air.
In the third and fourth series, the tank around the cold cylinder was filled with a mixture of
snow and salt, giving as wide a range of temperature as the structure of the apparatus would
permit.
TABLE 19.
Deflections (hot).
\Twn f nil r til
series.
series. series. series. series.
Third Fourth
series. series.
div.
div.
Temperature of bolometer
" " screen
8.7C.
8.OC.
9.3C.
8.OC.
8.9C.
8.OC.
9. 2 C.
8. C.
18.0
15.2
18.2
17.8
" " room
4.2C.
5.6C.
6. 3 C.
4 G . 9 C.
6.OC.
21.3
20.9
Pressure of atmosphere
Dew-point
(Approximatel 1
3 C .3C. 8. 1C.
f-)
1-. I C.
738 mm.
16.3
18.6
21.3
17.7
Pressure of water vapor
Water per cubic meter
Temperature of hot air
" " cold "
3. 59 mm,
3. 84 grams.
69. 6 C.
15-\ 2 C.
3.64 mm.
3. 90 grams.
67. 4 C.
15. Q C.
4. 22 mm.
4. 48 grams.
67. OC.
14-. 4 C.
3. 62 mm.
3. 87 grams.
68. 5 C.
15. 1C.
3. 93 mm.
4. 19 grams.
67. 2 C.
14. 7 C.
24.0
21.5
18.4
16.9
17.3
21.9
23.2
18.8
" excess
84. 8 C.
82. 4 C. 81. 4 C.
83. 6 C.
81. 9 C.
19.9
18.6
Mean deflections
19.01
19.57
The probable errors are i 0.60 div. for the third, and
the corrected deflections are
0.51 div. for the fourth series, and
Third series : (+ 19.01 + 3.86) -r- 1.02 = + 22.42 div.
Fourth series: ( + 19.57 + 3.86) + 1.02 = + 22.97
The mean air pressure was about 738 mm., and the mean force of vapor 3.78 mm., equivalent
to a liquid layer of water 0.000 135 cm. deep in a length of 33.5 cm.
Experiments of July 29, 1892.
Object: The measurement of radiation from warm air, containing 'considerable water vapor,
for comparison with results obtained in cold, dry weather. Also a determination of the absorption
of this radiation by glass.
East cylinder the bot one, the magnetic influence of moving masses being therefore the
reverse of that in previous measures. West cylinder surrounded by melting ice. Silvered
reflector, forming the background, freshly coated with soot.
The first and fourth series are comparable with previous measures, varying only in the higher
range of temperature and the larger quantity of water. In the second and third series, the
aperture of the bolometer case was covered by a pane of window glass 3.15 mm. thick, which
transmits about 76 per cent, of the total apparent solar radiation, and 14 per cent, of that from the
moon, and which is practically impervious to rays of greater wave-length than 4 microns, giving
us, in the absence of spectrobolometric measures, a preliminary approximation to the region of the
spectrum in which the radiation lies.
12812 Bull. G - 3
34
TABLE -20.
Before first ,
series.
After second
series.
Alter fourth
series.
Adopted for
1 and 2.
Adopted for
':* and 4.
Temperature of bolometer
32-. OC.
32. OC.
32. C.
" " screen
29. 7 C.
29. 8 C.
30. OC.
29. 8 C.
29. 9 C.
" " room
32-. 6 C.
32-. OC.
32. 5 C.
32. 2 C.
Pressure of atmosphere
730.74mm.
(AtO C.)
731.76mm.
731.0 mm.
731.5 mm.
Dew-point
23. 9 C.
23. 3 C.
Pressure of water vapor
21. 63 mm.
21. 63 mm.
Water per cubic meter
21. 06 grams.
21. 06 grams.
Temperature of hot air
93. 2 C.
89 C . 1 C.
89-. 5 C.
91-. 2 C. 89~-.3C.
" " cold "
+6.5C.
+8 J .2C.
+8. 2 C.
+7 C .4C.
+10 C . 6 C.
" excess
86. 7 C. 80-. 9 C.
80-. 9 C.
76. 5 C.
78. 7 C.
DEFLECTIONS FROM HOT-AIR COLUMN.*
First series.
Second series.
Third series.
Fourth series.
d a'.
div.
div.
(lir.
21.1
10.1
3.8
26.9
18.5
3.4
2.8
27.8
25.0
7.4
4.5
22.5
23.6
5.9
5.3
20.6
24.8
4.1
6.4
24.4
26.3
9.1
4.7
21.9
29.0
4.3
6.0
22.5
24.0
4.5
6.2
21.7
24.0
4.5
6.4
24.6
29.3
2.6
7.0
24,4
Mean deflections
24.56
5.59
5.31
23.73
* Series 1 and 4 without glass, 2 and 3 through glass.
The probable errors of the means, in the order of the series, are i 0.65 div., 0.57 div.,
0.31 div., i 0.53 div. ; and the battery galvanometer reading being 96.5 div., the deflection ,
corrected for the positive magnetic deflection of the east cylinder, and reduced to the standard
current, are
First series : ( + 24.56 3.86) 0.965 = + 21.45 div.
Second series: (+ 5.59 3.86) - 0.965 = + 1.79 "
Thira series: (+ 5.31 3.86) 0.965 = + 1.50 "
Fourtu series : (+ 23.73 3.86) 0.965 = + 20.59 "
The glass used transmits
31 per cent, of radiation of wave-length, 1.9
18 " "
8 " "
3.1
4.3
Not over 2 - of the radiation from a surface of lampblack, at the temperatures with which we are
dealing, lies in this region of very limited glass transmission. Most of the fraction, indeed, will
be near the longest wave-length mentioned, and 0.1 is a fair index of its average transmission by
glass, so that, if we say that it is hardly possible for 2-5-0 of the rays from the lampblack back-
ground to escape absorption by glass, the statement is justifiable. If the deflection of about li
div. through glass is genuine, it must be of atmospheric origin. As the absorption of glass is
a discontinuous one, at any rate in this part of the spectrum, it is possible that the absorption
of a linear gaseous spectrum whose lines or bands do not coincide with those of glass, may be
much less than for a continuous spectrum like that of lampblack, and that 8 per cent, transmitted
in the present case may represent a fraction of gaseous radiation either of shorter wave-length
than 4 microns, or of greater wave-length than the region of lampblack emission, comparatively
unabsorbed.
In proof of the statement that the absorption of glass is discontiuous, it may be mentioned
35
that rays in a small part of the lampblack spectrum from a glass prism, in the region near 2^,
were found to be three times as transmissible by glass as in the same region from a rock-salt
prism, showing that certain rays which are present iu the rock-salt prismatic spectrum, have been
entirely cut oft' in the spectrum from the glass prism, and that those rays which remain pass
through glass with comparative freedom.
The mean atmospheric pressure in the experiments of July 29, was 731.3 mm., the vapor
pressure 21.63 mm., and the equivalent layer of liquid water in the absorbent air column was
0.000 706 cm., that in the radiant hot-air column being about twice as great, and five to seven
times as great as in the experiments of March 15. If the greater amount of water in the summer
air has increased its radiative power, the deflections in series 1 and 4, July 29, ought to exceed
those in series 3 and 4, March 15; indeed, without any change in radiant emissivity, some increase
of radiation was to be anticipated, because, although the temperature-excesses were smaller in
July, the range was on a part of the temperature scale farther from absolute zero, and where the
differential radiation, as shown in the figures for lampblack (Table 21), may be expected to be
greater. The summer deflections are actually a little smaller, indicating that the radiation
measured has been, to a considerable extent, that of the lampblack background, which has suf-
fered greater absorption by water in summer. The following tables exhibit these relations, the
last columns being stated in absolute radiant units. The radiating volume of air has the form of
a truncated cone whose angle is 5.35, the length of the frustum and depth of the radiating layer
being 92.5 cm., the diameter of its smallest section 3.1 cm., and that of its largest and most distant
section 11.8 cm., while the volume of the frustum is 4,510 cub. cm. The measured radiation
approaches the half of what might be expected from surfaces of lampblack at the given temperatures.
TABLE 21.
Date and series.
Temperatures.
Computed lamp-
black radiation to
a hemisphere.
Ratio to lamp-
black radiation
from 100 to C.
r
Computed lampblack
radiation through
small aperture.
EI X r
Cent.
t
Absol.
T
o
o
Radim.
Sadim.
March 10,1892 (1)
56
12
329
261
.0135J C070
. 0065] '
3r~
0. 000 001 355
(2)
52
10
325
263
. 0129 )
iooeer 0063
SH
0. 000 001 214
March 15, 1892 (1)
73
8
346
281
. 0158 1 A,
.0082f
1T6 = ' 603
0. 000 001 469
(2)
70
343
OJA
.0155) 0075
75 "-
0.000 001 450
7
280
. 0080 1
126
(3)
69
15
342
258
. 0153 ) AAQA
. 0063J" 0(J
90 711
12 _ 6
0.000 001 740
(4)
67
15
340
258
.0150) 0087
|l=. 690 0. 000 001 682
126
July 29,1892 (1)
91
7
364
280
.0186) mnfi
. 0080/' 01
=. 841 0. 000 002 050
(4)
89
11
362
284
.01841 ninn
. 0084J- UJ
126" ' 94
0.000 001 935
For the equivalent water depths in the first three columns of the next table, reductions of
water vapor in terms of mass (m), stated in grams per cubic meter, have first been made from the
indicated vapor pressures (p) and barometric pressures (B), reduced to the freezing point, using
the formula
^
p
0.000 8041
1 + 0.003 670*
where t is the centigrade temperature of the hot or cold air in the radiant air column. These
masses have then been multiplied by the factor (w) in Table 14. The liquid depths are given
in millionths of a centimeter.
36
TABLE 22.
,
Liquitl water in
Date and series.
Radiant layer.
Corrected
deflection.
Tempera-
tine
Measured radiation.
Absorbent
excess.
layer.
Hot.
Cold.
Divisions.
a
Radim.
March 10, 1892 (1) 567
200
236
17.95
67.5
0. 000 000 740
(2) 574
223
236
18.72
61.9
0. 000 OOC 771
March 15, 1892 (1)
186
230
93
17.84
65.3
0. 000 000 735
(2)
204
250
93
17.47
62.9
0.000 000 720
(3)
291
153
130
22.42
83.6
0. 000 000 924
(4)
317
158
140
22.97
81.9
0. 000 000 946
July 29, 1892 (1)
1473
754
706
21.45
76.5
0.000 000 884
" (4) 1480
916
706
20.59
78.7
0. 000 000 848
EXAMINATION OF PROFESSOR HUTCHINS' HYPOTHESIS " THAT RADIATION TAKES PLACE ONLY
WHEN THERE IS A FALL OF TEMPERATURE WITHIN THE LIMITS OF MOLECULAR ACTION."
In a research oil the Radiation of Atmospheric Air (Am. Journ. of Sci., vol. 43, p. 357-363,
May, 1892) Prof. C. 0. Hutchins endeavors to determine the effect of varying the thickness of a
radiating layer of air. "A flat sheet-iron pipe was made 100 cm. long, 10 cm. wide, and 2.5 cui.
thick." This pipe was supported in an inclined position and heated by Bunseu burners. " The
air exit was from a pair of jaws, one fixed, one movable, so that the thickness of the air column
at its escape could be regulated at pleasure. * * * The results were recorded as the amount
of galvanometer deflection per degree of t V. With openings less than 1 cm. no difference in
the amount of radiation can be detected. With larger openings a small increase is observed."
Opening, 0.5 1
Deflection per degree, 0. 193 0. 195 0. 245 0. 259
The conclusion drawn is " that radiation is very largely from the surface of contact between
the hot and cold air, which seems to indicate that a heated gas absorbs all or nearly all those
rays that it itself emits, and that radiation takes place only when there is a fall of temperature
within the limits of molecular actijn ;/ (p. 363, loc.cit.). The values given show that when the
air aperture was enlarged sixfold, radiation only increased in the ratio of 259 to 193, or by 34 per
cent. ; but it seems to me that the inferences are not warranted. The uprushing jet draws cool
air from the sides and mingles it with the hot air, and the effect of this admixture is proportionally
greater in a narrow jet, so that until the aperture is considerably greater than those used by
Professor Hutchins, the cooling by admixture very nearly neutralizes any gain from greater
depth in the line of sight. The viscosity of air prevents a:i indefinite extension of the mixing. A
jet of more than a certain depth at a given altitude above the nozzle will have its temperature
lowered by mixture only at the borders of the ascending air column, tfce central part of the cross
section of the heated air 'having a constant te nperature. Except for absorption of its own
radiation by the air any further increase of depth will then give radiant values greater in
approximate proportionality to the thickness of the layer. Professor Hutchins appears to have
been deceived by an eye observation, which he describes on page 359 (Joe. cit.). "By burning
touch paper at the bottom of the tube, the lamps beneath being lighted, the shape of the column
of air from the nozzle can be inspected at leisure by reason of the dense smoke that issues with it,
and by filling the throat of the nozzle it can be given such a shape that the column of heated air
will preserve uniform dimensions for a considerable distance from its exit." On the strength of this
observation of a uniformity of cross section in the ascending air column, a constant velocity and
identical composition of the jet "for a considerable distance from its exit" seems to have been
37
inferred; but this is incorrect, since, as I shall show, the thermal gradient of a cross section of
the air column is not only not a single valued quantity in a given instance, but the form of the
gradient varies with the aperture of the nozzle, and this implies variation of velocity and more or
less admixture of cool air.
DESCRIPTION OF METHOD B.
Method A having been discredited, or at least having come under suspicion, no attempt was
made to extend it to air columns of other dimensions; but, instead, the bolometer was pointed to
a cold screen entirely separated from the hot air which issued from an effluent chamber of wood
(fig. 3) placed over the hot-air flue from the furnace, whose register could be opened or closed by
pulling cords.
.in. ,-uv
* 7
/*
vn.
n
~f
< 7 m ^
/ x *^t'
- /O - ^,
A
~
LI fa ' \ i
^
;
/ ' * v \
16
The aperture through which the hot air issues has a length of 16 inches (40.6 cm.) and a
breadth of anything less than 7 inches (17.8 cm.), as determined by the position of a sliding panel.
By rotating the wooden casing through 90, either the longitudinal or the transverse axis of the
aperture can be made parallel to the line of sight, giving different depths of radiating air without
altering the section and general condition of the air stream. By means of the sliding panel both
the depth and sectional area of the air stream may be varied.
The hot air within the wooden effluent chamber does not entirely escape upon shutting the
register. The temperature within the aperture was 17.6 higher than that of the air in the line of
sight, 4 inches (10.2 cm.) above the aperture, when the register was closed; but with the register
open, the strong current of hot air maintained a uniform temperature in the vertical direction,
although there was a considerable thermal gradient in the horizontal direction along the trans-
verse axis.
Experiments of February 23, 1893.
The bolometer was placed 18 inches (45.7 cm.) from a vertical line through the center of the
aperture. When the aperture (16 by 6 inches) was end-on, the cone of rays included the diameter
of the air vein in the most distant section. The temperature of the air around the bolometer
strips, as determined by a thermometer bulb inside the bolometer case, was 10.8 0. at the begin-
ning, and 9.8 at the close. Successive readings of the temperature of the air of the room at
intervals of some minutes were 4.3, 4.5, 5.0, 4.3, 4.o. The temperatures on which the
deflections depend are those of the air in the line of sight. Three thermometers were placed in
the longitudinal axis of the aperture: (a] 3 inches from its farther end and 5 inches from the
center, (b) at the center, and (c) 3 inches from the nearer end. The temperature within the
38
aperture (register shut) was 24.0. The thermometers, elevated into the line of sight, uaa a mean
temperature of 6.4 which is that of the cold air.
In the hot air, the readings were
FIRST SERIES.
o
o
(a) 55. 8
(6) 56.2
(c) 56.
Excess,
49.4
49.8
49.6
57.0
59.2
50.5
SECOND SERIES.
Excess,
50.6
52.8
44.1
Mean excess, 49. 6
Mean excess, 49. 2
The thermal gradient of the transverse diameter of the air vein is represented, on the average,
by the following series :
49
46 46
30 30
15 15
Excesses.
The thermometers were here an inch apart.
The average temperatures of successive sections on either side of the longitudinal axis are :
47.5, 38.0, 22.5, 7.5; and as the line of sight, with side presentation, penetrates all of these
layers equally, the mean temperature of the radiant air in the second experiment is
(47.5 _|_ 38.0 + 22.5 + 7.5) -=- 4 = 28.9 C.
In determining the mean temperature for the end-on presentation of the first experiment, no
great refinement of computation is needed, and the section maybe roughly summarized by fourths,
as indicated in fig. 4.
__
_ ~- ~*
__----
"
7
61^
-. _____
-----.
^
-______
_
16 im&fies
% 4 (Plan)
In end-on presentation it is to be noted that, although the aperture has a width of 6 inches,
the heated air spreads to a width of about 8 inches at the level of the line of sigh t, and the bolometer
with its widest angular opening takes in the whole of this width at the distance of the farther end
of the aperture, as shown in the diagram.
The most distant quarter of the air vein may be divided into eight vertical layers, 1 inch
thick, and having the average temperatures just given. Cutting these layers by a horizontal
cylinder which includes the extreme width, the areas of the successive transverse sections, count-
ing from the axial ones, are:
(1) 1.571 1.076=0.495
(2) 1.0760.614 = 0.462
(3) 0.6140.227=0.387
(4) 0. 227
Sum =4 ?r= 1.571
To obtain the mean temperature of the entire section, these areas may be treated as weights,
giving as the temperature of the most distant fourth of the air vein
47.5 x .495 + 38.0 x .462 + 22.5 x .387 + 7.5 x .227
= 320.8 C.
1.571
Similarly, the next nearer quarter of the air vein may be considered as composed of six
vertical layers of the central hotter region cut by an including cylinder, the areas of successive
sections being
(1) 1.571 0.916 = 0.655
(2) 0.916 0.343 = 0.573
(3) 0.343
The mean temperature of the next to the most distant fourth is then
47.5 x .655 + 38.0 x .573 + 22.5 x .343
1.571
= 380.6 C.
The nearer half of the air vein may be assumed to consist of the four inner vertical layers
and the areas of their sections
(i)
(2)
1.571 0.614 = 0.957
0.614
The mean temperature of the first and second fourths of the air vein is :
fr + t t _ 47.5 x .957 + 38.0 x .614
2 1.571
= 430.8 C.
*
The final mean is, for first experiment
(32.8 + 38.6 + 43.8 + 43.8) -4- 4 = 39.7 C.
The observed galvanometer deflections were as follows:
TABLE 23.
First series (aperture end-on).
Second series (aperture sidewise).
div.
div.
11.8
4.0
9.9
1.7
12.2
3.1
6.9
2.9
6.3
0.0
11.8
3.8
14.5
2.3
12.2
1.5
9.2
4.2
8.0
5.3
Mean
= 10. 28 J- 0. 62
Mean = 2. 88^0. 34
Multiplying the mean temperatures by the depths of the radiating air layers, assuming these
40
to be proportional to the dimensions of the aperture in the direction of the line of sight, the com-
puted air radiations and their ratio are
(1) 16X39.7 = 635.2] 173.4
(2) 6x28.9 = 173.4/ "635.2 u -'
The observed ratio is
2.88 4- 10.28 = 0.280
the radiation for the greater depth being only a trifle less than its proportion according to the
product of depth and temperature.
The battery galvanometer read 96 div. Reduced to standard current and stated in absolute
units the radiations become
(Depth, 40.6 cm.) Eadiation = 10.71 div. = 0.000 000 545 radim.
( 15.2 cm.) = 3.00 div. = 0.000 000 153
For comparison with the results of the previous method, these deflections have to be reduced
to the smaller aperture by dividing by 8.96, giving
(Depth, 40.6 cm.) Eadiation = 1.20 div. = 0.000 000 049 radim.
( " 15.2 cm.) " = 0.33 div. = 0.000 000 014
With a depth of 92.5 cm. and an excess of 65, assuming proportionality of radiation to depth
and temperature combined, an assumption which now seems justifiable in this first approximation,
we might anticipate a radiation of
GO K QK
0.000 000 049 x jj^ X |0 = 0.000 000 181 radim.
The measured radiation by Method A (Table 22) being about four times as great as this, we
must conclude that something like three parts of the observed radiation in Method A were due to
an excessively thin layer of warm radiating lampblack, with a small amount diffusively reflected
by lampblack, and only one part to the hotter air.
The condition of the air in the experiments of this date was: Barometer, 724 mm.; dew-point,
5.3 C., corresponding to a vapor pressure of 3.09 mm., or to 3.34 grams of water per cubic
meter. By Table 14 this represents the following depths of liquid water in the end-on presenta-
tion &i and the sidewise presentation b- 2
cm.
fci, absorbent layer = 0.000 085
radiant " = 0.000 135 (cold)
" " = 0.000 118 (hot)
Z> 2 , absorbent layer = 0.000 127
radiant " = 0.000 051 (cold)
= 0.000 046 (hot)
Experiments of February 25, 1893.
The bolometer was placed 15 inches (38.1 cm.) from a vertical line through the center of the
aperture whose width was increased to 7 inches (17.8 cm.), giving a hot-air column a little over
9 inches wide at the level of the line of sight.
41
The longitudinal axis of the aperture in the end-on position lying east and west, thermometers
were placed at the level of the line of sight
(a) in the longitudinal axis of the air column 8 inches E. of center.
tfo\ u u u ct u u u Q a u a
f c \ a a u u u u u 3 u a u a
(d) " " " < ; " " " at the center.
(e) 2$ inches north of longitudinal, 1 inch east of transverse axis.
To test the effect of the hot air remaining in the effluent chamber after the register was closed,
the thermometers were read with the aperture alternately open and closed by a board cover.
Aperture open. Aperture closed.
o o
(6) 8.0 6.3
(c) 9.1 7.8
(d) 8.6 7.0
(e) 6.9 7.2
I have adopted for the temperature of the cold air (register closed, but aperture open)
The temperature of the bolometer case was 10.S, and the mean temperature of the air of the room
was 6.0.
The thermometer readings in the hot-air column in the first series were:
o
(a) 62.8^|
68 8 f 66.4 = mean of temperatures at east end of longitudinal axis.
(d) 71.0J
(e) 44.2
In the next series, thermometer (e) was transferred to a point in the longitudinal axis, 8 inches
west of center
East
(a) 45.(T
(6) 73.4
(c) 74.2 VMean of temperatures in longitudinal axis = 66.8.
Center (d) 74.8
West (e) 66.6
Thermometers (a) and (e) in this series, being near the point where the thermal gradient
becomes very steep, are liable to vary considerably for a slight displacement of the vertical axis
of the ascending air column.
The last two series of temperature readings have been taken with thermometers in the
transverse axis of the hot-air column in positions at even inches from the center
Third series. Fourth series.
o o
3 inches north of center 27.4 32.0
2 " " " " 63.0
1 inch " " " .... 70.2
Center 70.2 70.5
1 inch south of center 67.7 68.1
2 inches " " " 63.0
3 " " " " 47.8
4 " " " " 23.8
5 " " " " 13.4
42
These thermal sections show a spreading of the hot air, and its mixture with the surrounding
cold air for an inch or so outside the original dimensions of the stream at the aperture of the
effluent chamber. The heat, however, is nearly uniform for about 12 inches in the center of the
longitudinal axis. Fig. 5 exhibits these thermal gradients to the eye
Abscissae = distances from center of air stream.
Ordinates = temperature-excesses (C.).
1 and 2 = series along longitudinal axis.
3 and -4 = " " transverse "
10 8
ITl
The average thermal gradient of the transverse axis of the hot-air column may be represented
by the following series :
63
61 Clo
550 550
30 30
10 10
Excesses.
The average temperatures of successive sections on either side of the longitudinal axis are,
62, 58, 42.5, 20, 5; and the mean temperature of the radiant air, when the line of sight agrees
with the transverse axis of the air column, is
(62 + 58 + 42.5 + 20 + 5) 4- 5 = 37.5 C.
43
Fig. 6 shows the disposition of bolometer, aperture, and air stream in the end-on presentation.
In getting the meau temperature for this position, a small allowance has been made for the
lack of symmetry of the air column. Dividing the air stream into a nearer and a more distant half,
the mean temperature of the former may be taken as 61. The more distant half varying from a
__ __ 4. --
I
V
Jig. 6 (Plan)
mean of 61 at the nearest section to 40 at the most distant section, a rough approximation gives
its mean temperature, in the part cut off by the cone of rays, as 55, the final mean for the hot
air radiating to the bolometer being 58 C.
Two widths of aperture, 7 and 3% inches, were used with side presentation. In the end-on
position the breadth of the aperture was constantly 7 inches and the length 16 inches. The
observed galvanometer deflections follow:
TABLE 24.
First series, end
Second series,
Third series, end
Fourth series,
on (16 inches).
side (7 inches).
011 (16 inches).
side (3J inches).
(Uv.
div. div. div.
5.2
4.2
7.6
1.7
9.7
4.6
9.7
1.9
12.8
3.8
12.2
0.8
9.4
3.2
8.4
1.9
11.7
2.3
9.9
0.0
7.6
2.9
12.0
1.0
6.7
2.5
6.5
0.6
9.2
4. 6 13.
0.6
6.5
3. 8 4. 8
2.7
11.3
2. 7 10. 1
1.5
9.01^.56
3.46^.21
9. 42-J-. 59
0. 89^. 25
Observed radiation ratios.
Depth, 16
u
inches (40.6 cm.)
7 inches (17.8 cm.)
3.5 inches ( 8.9 cm.)
Deflection, 9.22
" 3.46
" 0.89
Eatio, 1.000
" 0.375
" 0.097
Assuming the radiant depths to be proportional to the dimensions of the aperture parallel
with the line of sight and the radiations to be proportional to these depths, computation makes
the air radiations and their ratios
(1) and (3)
(2)
16 x 58 = 928
7 x 37.5 = 262.5
3.5 x 37.5 = 131.3
Ratio = 1.000
" = 0.283
" = 0.142
44
The battery galvanometer standing at 99 div., the reduction to standard current and absolute
units gives
Depth 40.6 cm. Eadiatiou = 9.31 div. = 0.000 000 474 radim
" 17.8 cni. " = 3,49 div. = 0.000 000 178 "
" 8.9 cm. ' = 0.90 div. = 0.000 000 040 "
The deflections in the fourth series are too small to be trusted. As showu by the transverse
gradient, the ascending air has suffered a lateral displacement in the direction of the transverse
axis, presumably from a side draft; and since the end-on deflections are notably smaller than
on February 23, and relatively smaller than the corresponding side deflections which are not
influenced by the displacement, it is probable that the temperature allowance made in the preceding
computation is insufficient to compensate the actual variation at the time of radiation measurement.
It will, of course, be understood that the observations of temperature and radiation were not
synchronous, although made in immediate succession. Series 1 and 3 are therefore given half
weight in the final mean.
The condition of the air, February 25, was as follows: Barometer, 726 ram., dew-point, 1.9 C.,
corresponding to a vapor pressure of 3.98 mm., or to 4.24 grams of water per cubic meter. By
Table 14, the depths of liquid water in the various air layers are
Eadiant depth 40.6
* 17,
Absorbent layer = 0.000 075
Eadiant " = O.Ouo 172 (cold)
= 0.000 142 (hot)
= 0.000 124
= 0.000 075 (cold)
= 0.000 066 (hot)
Absorbent
Eadiant
u
TABLE 25.
.Radiation of hot air (for small aperture) reduced to a depth of 1 meter.
liadim.
Feb. 23 (1) 0. 000 000 049 . 406 = 0. 000 000 121, * = 40
(2) 0.000 000 014-^.152=0.000 000 092, * = 29
Feb. 25 (1, 3) 0.000 000 043 . 406 = 0. 000 000 106, * = 58
(2) 0. 000 000 016 . 178 = 0. 000 000 090. t = 38
Radiation of air at mean temperature-excess of 40 C. (Depth 1 meter.)
0. 000 000 121
0. 000 000 127
0. 000 000 073
0. 000 000 095
Mean = 0.000 000 104 radim.
DESCRIPTION OF APPARATUS AND METHOD C.
In order to experiment on the radiation of air at various pressures, and to be able also to
substitute other gases in the place of air, a closed vessel was needed. Of course this presupposes
some sort of window transparent to the gaseous radiation, but both the window pane and the walls
of the vessel visible through the window will contribute their own rays, and these must be capable
of being certainly distinguished from those of the gas. This was effected by making the window
pane of rock-salt and letting the opposite radiant wall be a movable one, formed of a blackened
copper disk attached to a steel rod sliding in a stuffing box at one end of a large iron cylinder.
By pushing the rod in and out, the length of the radiant air column could be changed without
varying the temperature and radiant power of the solid parts. The disk served the further
purpose of a stirrer, by the vigorous motion of which it was hoped that the temperature of the hot
45
air could be made appreciably uniform. This hope was only partially realized, as the sequel will
show; but, although it would be possible to devise a more efficient apparatus, the very errors of
this one have proved instructive, and the final results, after the discussion and elimination of these
errors, are believed to be trustworthy.
The radiation cylinder, as actually made, consists of an iron cylinder of 12 inches internal
diameter, 60 inches long, weighing 250 pounds, with flanges at the ends projecting outward to a
width of 2 inches. Heavy plates of cast iron are bolted to the flanges, the joints being luted with
red rubber. The front end-plate, facing the bolometer, carries lugs and a ring-piece, with clamping
screws by which a rubber-faced metal ring is held against a thick plate of rock-salt (thickness,
1.98 inches = 5.03 cm.; diameter, 3.80 inches = 9.65 cm.), holding it against a rubber ring sur-
rounding the 2-inch aperture in the center of the end-plate. A glass plate slides over the outside
of the salt, when not in use, to protect it from moisture. Preliminary experiments having proved
that rock-salt might be heated to 175 C. and presumably much higher without danger of crack-
ing, if it were shielded from currents of cold air and any sudden changes of temperature, but that
without this precaution the salt was almost sure to crack, the circumference of the cylindrical
block of salt was wrapped in about an inch of cotton wool. The large masses of metal (the end
plates weigh about 20 pounds apiece) prevent any sudden cooling of the solid parts. The rear
end-plate being pierced by a central aperture carries a stuffing box through which a half-inch
rod of polished steel passes, air-tight, with rubber packing, its position and that of its terminal
disk being read by divisions cut on the rod. The movable disk of blackened copper is 0.12 inch
thick and 11.85 inches in diameter, leaving an annular opening with an average width of 0.075
inch through which the air rushes when the disk plays to and fro. A thermometer in the front
part of the cylinder records the temperature of the air, and the disk is prevented from coming
nearer than 4.25 inches (10.8 cm.) to the front plate by a fixed stop. This defines the shortest
radiant air column which can be used, the longest being 60 inches (152.4 cm.).
The cylinder is heated from below by four large Bunsen burners, each having a protractor
stopcock, reading to degrees, for the ready regulation of gas flow. An outer cylinder of sheet iron
serves as a hot-air jacket to the inner one. Four openings below in the outer casing admit the
flames, and the same number above permit the escape of combustion products.
An air pipe at the side connects the inner cylinder with air-pumps and a mercury gage, and
a second air pipe leads to a small iron side-cylinder, or heater, provided with graduated stopcocks,
and joined to a series of drying flasks, generators of carbon dioxide, etc., according to the needs of
the experiment.
The apparatus is shown in plan on a scale of 1-12 in fig. 7.
7
iS
10 inches
The radiation cylinder has an approximate volume of 6,787 cubic inches = 111.3 liters, and
holds about 144 grams of air at 760 mm. pressure and C., containing, if unpurified, nearly 0.14
46
gram of carbon dioxide. The actual atmospheric pressure during the experiments was usually
from 730 to 735 mm.
The bolometer is carried by a massive stand which permits accurate adjustment, and holds
the instrument with a solidity which can not be improved. The mounting of the great cylinder
in the first experiment was not so firm, but it was afterwards stiffened by braces and gave no
further trouble. The entire apparatus stood on a stone pier.
The bolometer case was protected by the multiple tin-plate screens of small aperture, the
outer screen being 2.46 in. from the front of the lead ring which clamps the rock-salt to the
end-plate. In Jamin's " Cours de physique," 3 e ed., tome 3, 3 e fasc., p. 93, is an allusion to a
source of error neglected in the otherwise very careful work of Melloui. The polished rock-salt
plate reflects to the bolometer rays from a small annulus of the protecting screen, but the effect in
my observations is very minute ; first, because the polished tin plate does not absorb radiation
well and is not much heated ; second, because any rays which the screen may emit or reflect are
only feebly reflected by polished rock-salt; third, because the angular aperture of the measuring
instrument is small; and in general, since the gaseous radiation is measured by finding the
change due to motion of an internal disk, the effect in question is constant at a given temperature,
and without influence on the result.
GENERAL THEORY OF THE APPARATUS C.
When the disk in the heated apparatus is moved away from the bolometer, a deflection results
which is made up (1) partly of positive gaseous radiation, (2) partly of diminished disk radiation
due to greater gaseous absorption, (3) in part, of any change which takes place in rock-salt radia-
tion, which may be either positive or negative, (4) of any change in the disk radiation due to its
removal to a part of the cylinder having a different temperature. This also may be either
positive or negative, and is quite appreciable if the cylinder is not uniformly heated, for instance,
if one or more of the lamps are extinguished.
For the present purpose (2) need not be separated from (1). Absorption simply makes the
gaseous radiation appear smaller. Considering (1) and (3), the rock-salt, if the supply of heat
were equable, would tend to remain at a lower temperature, as a whole, than the gas within the
cylinder, because the outer surface of the salt is cooled by contact with the outside air, and its
entire substance radiates outwardly through a wide aperture. Nevertheless, since the thickness
of the rock-salt plate is great, while its conductivity and radiative power are small, a very
marked thermal gradient is produced within the salt, and in actual work its temperature is
always changing. The air gets its heat chiefly by contact with the hot iron ; the salt, on account
of its small absorption of the radiation passing through it, gets its heat mainly by the air
convection ; and thus the temperature-changes of the salt continually lag behind those of the air
and iron.* When the lamps are put out, the air and iron are at first hotter than the salt, but soon
they become cooler than it. The withdrawal of the disk exposes the rock-salt to radiation from
the walls of the cylinder, whose mean temperature may differ, and whose radiative power certainly
differs from that of the disk, and also to contact with the gas swept over the face of the plate.
If the gas is hotter than the plate, the salt is heated more rapidly than before by this increased
contact with the air during the withdrawal of the disk, but also when it is pushed back. This
part of the change is, therefore, eliminated in the same way that the effect of galvanometer drift
is removed by combining readings made before and after exposure. The part of the rock-salt
temperature-change due to variation of radiation during an observation is not thus eliminated,
but is too small to be measured.
The variations in the radiation of the copper disk (and to a smaller extent those of the rock-
salt) during an exposure by withdrawal of the disk, under certain extreme conditions, may equal
or exceed the effect attributable to the combined radiation and absorption of the inclosed hot gas.
Whether, therefore, there is any appreciable effect from the heated gas under the peculiar
conditions of these experiments with the radiation cylinder might be uncertain were it not for
the tests to be described.
*For further details in respect to rock-salt radiation, see the first part of my article oil "The Probable Eange
of Temperature on the Moon/' Astrophyaical Journal, vol. 8, p. 199, Nov., 1898.
47
We can not suppose that changes in the thermal condition of the solid parts of the apparatus
are ever entirely absent; but since the sign of these variations of temperature is reversed in passing
from heating to cooling conditions, it might be supposed that a mean between deflections obtained
with a heating cylinder and those from a cooling one would be due to gaseous radiation and
absorption, the effect of any possible changes in the copper disk canceling out, and those of the
rock-salt being eliminated by the mode of exposure, as already shown; but it will be seen subse-
quently that this interpretation of the results is not permissible, and that the effect of another
cause of discrepancy that of imperfect homogeneity of the gaseous radiating column must be
considered.
When the radiation cylinder is heating, the temperatures of the well-stirred air being taken
as abscissa, the observed radiations, plotted as ordinates, fall accurately upon a straight line,
radiation being proportional to excess. With a cooling cylinder the radiations are very much
smaller, and fall on a curved line. It would be very easy here, from an incomplete or an
imperfectly analyzed experiment, to draw erroneous conclusions.
The wrought iron cylinder (except where the flame plays directly upon it), by virtue of its
thermal conductivity, must be not very far from the mean temperature of the hot-air jacket (which
has been measured), but lagging behind somewhat both in heating and cooling. The temperature
of the air within the cylinder lags still more, because of its small conductivity. The cylindrical
surface of iron to be heated has an area of 2,263 square inches. The direct impact of the flame is
exerted upon not more than T F of this surface, and the play of a flame at 1,000 to 1,800 C. heats
this portion unduly, a considerable area of the floor of the radiation cylinder having, by conduction,
more than the average temperature. Columns of hot air rise within the cylinder along its central
axis during heating, over each of these hot places, and these columns, much hotter than the ineau
temperature of the air within the cylinder (which mean temperature is alone given by the ther-
mometer), produce the larger deflections during heating. The supposition that change of tem-
perature of the rock-salt has anything to do with the deflection has been, shown to be untenable,
and is most completely negatived when it is known that the total radiation of the salt is less than
that represented by the deflection in question, while the temperature of rock-salt, and thence its
radiation, changes very slowly. Variations of temperature in the copper disk in its two positions
may produce considerable deflections, but only under extreme conditions which are not those of
the actual experiment. Substitution of a blackened asbestos disk, a bad conductor of heat, in
place of the conductive copper, also makes little difference in the result with a cooling cylinder,
unless the temperature distribution is abnormal. The deflections obtained in the ordinary work-
ing can, therefore, only be due to the changing dimensions and temperatures of the hot-air columns
within the cylinder; and the fact that there is a larger radiation at a given mean temperature, as
indicated by the thermometer, when the temperature of the cylinder is increasing, together with
the observed relation between the rapidity of the heating and the amount of the radiative excess
over the measurement with a cooling cylinder, the deviation being greater the more rapid the
heating, testify that the radiation conies from a body subject to the internal changes and irregular
structure produced by convection ; and an effect which at first sight may seem anomalous becomes
a proof that the radiation observed is really that of the air, and is not due to any change in the
thermal condition of the solid parts of the apparatus during exposure. In passing from the condi-
tion of a heating cylinder to that of a cooling one, with but slight change of average temperature,
there is a continuous fall of radiation, that for the stationary point being less than for increasing
temperature, but more than for falling temperature.
When heated from below, the central region of an inclosed fluid is occupied by ascending
columns heated beyond the mean temperature of the mass, while during cooling the central
currents are cooler than the average. This central region in the present case is the only one
observed by means of the bolometer whose indications do not give the average radiation of all
the air in the cylinder, but that of the rapidly moving and thermally varying portion included
within the central cone of rays.
The composition of the axial radiating air column when heating may be analyzed, probably
with some approximation to the truth, as follows: Suppose that nine-tenths of the air in the
horizontal stretch of this axial line have a temperature of 90 and radiate with an intensity of
48
4 for each tenth, or 36 in all, while one-tenth is air just rising by convection and heated to 250
by contact with the hot iron. The radiative power of this tenth may be taken as 85, and the
total radiation is 121 ; whereas the radiation of a body of air at mean temperature
will be about 68 on the same scale, and the observed radiation is nearly double that appertaining
to the given mean temperature.
When the disk is "in" i. e., at its nearest approach to the rock-salt plate, while the tempera-
ture is increasing, the thermometer of the radiation cylinder is partially separated from the larger
part of the interior space and from the chief source of heat supply. The reading of the thermometer
is therefore lower, since the ends of the cylinder cool faster. But even with the disk out, the ther-
mometer reading is too low, as is shown by a rise of several degrees after a quick movement of the
disk to and fro several times when the heating cylinder has not been recently stirred. After
about ten minutes of cooling, however, with less frequent agitation, no change in the thermometer
reading occurs after stirring. The distribution of temperature is therefore more equable during
cooling. The thermometer, after vigorous stirring of the air, records its true temperature, as in
the use of the sling thermometer.
In order to get the thermometer out of the line of radiation, it had to be lifted a little above
the central axis of the cylinder. Hence, without mixture of the air layers, the reading should
have been too low in heating, too high in cooling. (See thermal diagrams.) The last error, however,
is inappreciable, and I think we may see why from the following considerations : When heating,
the metal at the bottom of the cylinder is quite hot; that at the top much cooler. The air is
heated by contact at the bottom, and being thus lighter and in unstable equilibrium, it rises
and carries heat to the middle space, mixing with cooler air until its ascension is stopped by the
top wall, and great diversity of temperature prevails. For example, internal air in immediate
contact with the iron top and bottom walls being at 50 and 250, respectively, an air temperature
of 90 should be found at some point in the upper half of the air space when the mean tem-
perature of the entire mass of air is 110, ascending thirds of the air being on the average 150,
100, 80. Stirring may then cause a rise of 20, as has actually occurred, and streaks of air as
hot as 200 may reach the central line, contributing more than their share to the total radiation
on account of their relatively greater radiative power.
The following centigrade temperatures of the hot-air jacket of the radiating cylinder were
observed (temperature rising; :
o
Jacket: At the top, near center 257
" " " " end 250
" " side " " 140
" "bottom" " 56
o
Upper half, 254 + 140 = 197
2
Lower half, 140+ 56 = 98 Mean =
2
Temperature of air within the radiation cylinder = 110.
A hypothetical vertical thermal section of the air in the cylinder is indicated in the diagram:
o
Top wall of cylinder
50
Internal air 90<
loolno
150J
Bottom wall
250
49
The cooling of the metal after the lamps are extinguished is chiefly from beneath by convec-
tion currents, which rush upward through the space between the radiation cylinder and the outer
jacket, while the air within the cylinder is cooled by contact with the metal at the top, whose
temperature differs less than before from the bottom temperature, and little change is suffered
by the air from contact with the cooler metal at the bottom on account of the feeble conductivity
of air and stagnation by greater density there. Thus the distribution of temperature in cooling-
may be this: Air in immediate contact with iron, 110 and 75 at top and bottom, respectively.
Air temperature by ascending thirds : 105, 110, 115. Mean, as before, 110.
The following temperatures of the hot-air jacket were observed after the preceding ones, but
with a cooling cylinder, all of the lamps but one (the second from the rock-salt) having been
extinguished :
Q
Jacket- At the top, near center 129
" " " " end 117
" " side " " 95
" "bottom" 56
o
Upper half, 123 + 95 = 109
2
Lower half, 95 + 56 = 75.5 Mean = 92
2
Internal temperature of radiation cylinder = 110.
A hypothetical internal vertical temperature distribution in close agreement with these
observations is shown in the diagram :
Top wall of cylinder 110
Internal air 112 - 5 {l}ojllO
105 1
Bottom wall 75
Here all layers of air have nearly the same temperature. The position of the internal ther-
mometer is of little consequence, and small change results from stirring.
Curves of radiation and temperature with a cooling cylinder pass so nearly through the points
of observation after prolonged stationary temperature that no great error will be committed by
assuming the cooliug observations to be correct after cooling has progressed for a little time.
That the larger radiations during rapid heating are abnormal, and indicate excessive heating
of the bottom of the cylinder and of the lowest layers of gas, is proved by the fact that under
these circumstances the apparent mean temperature of the gas, on putting out the lamps, does
not vary much during many successive stirrings, although the deflections diminish continually
until the customary reading corresponding to that temperature and uniform distribution of heat
is reached, after which the thermometer begins to fall rapidly and the radiation to diminish accord-
ing to the usual law.
Example: Cylinder containing carbon dioxide. After heating for several hours the lamps
were put out and readings taken during initial cooling. Battery galvanometer, 113 div., but here
all deflections have been reduced to standard current. Each deflection in this and the following
experiments, unless otherwise specified, is the mean of five concordant readings.
All temperature-excesses are reckoned from the temperature of the bolometer, there being no
other standard possible in the mode of exposure followed, and are given in centigrade degrees.
Pressure in closed cylinder varying from 744 mm. to 718 mm., mean 731 mm. (reduced to freezing
point). Temperature of room, 30.2; of bolometer, 35.2; dew-point, 13.9 C.
12812 Bull. G 4
50
TABLE 26.
Heating rate per minute.
Temperature.
Excess.
Radiation.
o
Divisions.
Series 1 : +0. 83
Lamps out
After 3 nun. 0. 13
" 7 " 0.73
" 12 " 1. 10
132.6
133. 2 Max.
133.0
131.4
125.5
97.4
98.0
97.8
96.2
90.3
+19. 2 (abnormal)
4-15.7 "
4-12.4 "
4- 8. 7 (normal)
Series 2 (after further heating) 127.4
Lamps out 136. 2 Max.
After 5 miu. cooling 0. 36 135. 3
" 10 " " 1.23 126.9
1
92.2
101.0
100.1
91.7
4-16.5 (abnormal)
4-14.5 "
+ 9.5 (normal)
The last and subsequent readings of each series are normal, the temperature, as indicated by
the internal thermometer, diminishing rapidly.
A similar result has been obtained in the use of an asbestos disk, but here other causes
assisted. To determine what change, if any, would take place if the radiative disk were noncon-
ducting, the copper had been covered with blackened asbestos on the side facing the rock-salt
window. With a heating cylinder the apparent air radiation was greater when the nonconducting
disk was used, and much greater when only the two central lamps were lighted and the ends of the
cylinder were at lower temperatures than under normal conditions, even although the duration of
the experiment was prolonged until a stationary mean temperature was reached. The surface
chilling of the disk in the forward position i. e., nearest to the rock-salt, increased the deflection,
and the effect persisted until the difference of temperature between the middle and the ends of the
cylinder ceased. The abnormal results at maximum temperature and during initial cooling, while
the apparent or recorded mean temperature is nearly stationary, are in this case due to the
combined effect of vertical and horizontal inequality of temperature.
Example: Cylinder filled with air at atmospheric pressure, thoroughly dried by phosphoric
anhydride, and purified from carbon dioxide. After heating continuously for 23 hours the recorded
mean stationary temperature was 68.9. The two middle lamps were then turned up for 1 minute,
until the temperature had risen to 71, when the lamps were extinguished.
TABLE 27.
Heating rate per minute.
Temperature. ; Excess.
Radiation.
IHviiions.
4-2.1
70.0
38.0
4-8.0 (abnormal)
Lamps out
71.0 max.
39.0
After 4 nun. cooling -j-0.
71.0
39.0
4-7. 5 "
" 8 " " 40.0
71.0
39.0
4-5. 8 "
" 12 " " 0.12
70. 8 38. 8
4-4. 6 "
" 16 " " 0.28
70.0
38.0
4-3. 9 "
20 " " 0.10
69.2
37.2
4-2.8 (normal)
Here, after prolonged but unequal heating, 20 minutes of cooling were required to give the
approximation to a normal value, recorded in the last line, the first reading being nearly three
times too large.
The preceding example was obtained after all parts of the cylinder had become well heated,
the inequalities of thermal distribution being comparatively small. The next experiments show
the extraordinary increments produced by the use of the asbestos disk with a rapidly heating
cylinder. The air within the cylinder was approximately dry, and purified from carbon dioxide.
Two middle burners were lighted, with cocks set at 30 div.
51
TABLE 28.
Heating rate
per minute.
Temperature.
Excess.
Radiation.
o
o
o
Divisions.
+1.2
62.4
25.
8
+ 8.4
4-1.4
72.5
35.
9
+16.2
+1.8
80.3
43.
7
+20.9
+2.1
90.0
53.
4
+24.6
+2.6
100.3
63.
7
+30.6
+2.0
108.9
72.
3
+35.5
The deflections are here four to six times as great as those with a cooling cylinder.
A repetition of the experiment gave the results in Table 29.
TABLE 29.
Heating rate
per minute.
Temperature.
Excess.
Radiation.
o c
B
Divisions.
+3.U 61.8
28.2
+ 13.4
+2. 4 70. 8
37.2
+17.3
+4.0 81.0
47.4
+25.0
+4. 2 90. 9
57.3
+26.1
+2. 8 100. 2
66.6
+32.6
+2.0
110. 2
76.6
+37.7
The observations may be represented by a straight line passing through the origin and a
deflection of 30 div. at excess 63, giving a mean deflection of 0.476 div. per degree of excess.
The ratios to the deflections of the cooling curve are, as before, about six to one at the middle of
the heating curve, where the rate of heating is greatest.
The asbestos in the forward position radiates to the cooler iron of the end-plate, and hence
becomes cooler. When withdrawn to the rear the blackened surface of the asbestos absorbs
radiation from the hot interior, and is also heated by contact with hotter gas; but, although the
copper back is now near a cooler end-plate, the uoucouductivity of asbestos prevents any influ-
ence from this cause. The positive differential effect is added to the true gaseous radiation. The
conductivity of copper, and the more equable distribution of temperature in the metal walls,
prevent any but a small temperature-change in the copper disk during the time of an observation
in the normal working of the heating cylinder, and the larger deflections with heating cylinder
are in this case due almost entirely to inequality of gaseous temperature, as is shown by the
closer agreement of the readings, after prolonged heating to a stationary temperature, with those
of the cooling curve; but the results with asbestos, under the same circumstances, are different.
When the lamps are put out, the distribution of temperature in the cooling iron, after a time,
becomes nearly uniform, the increase of 200 or 300 per cent, in the apparent gaseous radiation with
stationary mean temperature, due really to temporary chilling and heating of the surface of the
blackened asbestos, then ceases, and the values of air radiation, observed with a cooling cylinder,
are nearly the same with an asbestos disk as with copper. These measures may therefore be
included with those from which the final curves of air radiation are derived. The abnormal values
which have been purposely obtained by varying the method and conditions of working, are only
used to arrive at an understanding of the meaning of the ordinary results, and to derive some
indication as to their reliability. Many things which were puzzling at the time the experiments
were made are now clear to me, and I hope that they will be so to the reader who has the patience
to follow the details of a research beset with difficulties and intricacies.
The following experiment with the blackened copper disk exhibits the result of a still wider
departure from normal conditions, and bears witness to the necessity of some of the precautions
52
which were taken in the ordinary use of the apparatus. In heating the hot-air jacket around the
radiation cylinder, four large Bunsen burners are customarily employed, their positions being such
as to secure as uniform distribution of temperature as possible within the cylinder with the given
means. With only one lamp lighted, the effects are very different, according to the position of the
lamp. When the single lamp was at the end farthest from the rock-salt, there was a positive
deflection. The mean temperature of the inclosed air had been so regulated that it was falling,
a condition ordinarily attended by smaller galvanometer readings. On the other hand, when the
single lamp was at the rock-salt end, the deflection became negative with a heating cylinder, which
ordinarily gives increased readings.
The observation follows: Battery current, standard, or 100 div. Temperature of room, 26;
of bolometer, 31 ; dew-point, 11.7, corresponding to a pressure of aqueous vapor of 10.23 mm. or
10.28 grams per cubic meter, and to an equivalent liquid depth of 0.000 387 cm. in the absorbent
layer.
(a) Fourth lamp (farthest from the rock-salt) lighted. Burner cock set at 30 div. Temperature
of air in cylinder read immediately after vigorous stirring:
o
Temperature before experiment 102.2
" after " 97.8
mean = 100.0
Excess = 69.0
Cooling rate, 0.8S per minute; mean differential radiation (disk shifted from 0.35 to 5.0 feet)
- + 7.80 div.
(6) First lamp (nearest to rock-salt) lighted. Burner cock set at 35 div. The other lamp put out.
o
Temperature before experiment, 104. 6
Temperature after experiment, 108.
Mean, = 106. 3
Excess, = 75. 3
Heating rate, 0.68 per minute. Mean differential radiation (disk shifted as before)
= - 1.34 div.
Analyzing the component sources of radiation in these two experiments, and neglecting
absorption, it will be seen that in (a) the copper disk was getting hotter when "out," and was
cooling when "in," or at the end next to the rock-salt. Its thermal change had the same sign as
the hot-air radiation during exposure of the air column. The front walls of the cylinder were
cooler than the rear walls, and cooler than the copper disk, since the latter evidently suffered
not merely a halt in its thermal increment, when at the front, but a decided decrement of heat.
Changes in the temperature of the rock-salt contributed to the combined effect, although only to
a slight degree, since the radiating power of the rock-salt plate was but one-fourth that of blackened
copper at the same temperature, and its rate of change very slow. When the warm copper disk
was pulled out, the salt received radiation from the front walls of the iron cylinder, far from the
flame, and certainly cooler than the frequently heated copper, also less powerfully emissive.
At the same time, cooler descending internal convection currents played upon the salt, cooling it,
while the disk was getting hotter. The thermal change of the salt was, therefore, opposite to
that of the copper.
In experiment (6) the copper disk was heated at the front and was cooling while at the farther
end. Its change of radiation was therefore of the opposite sign to the always positive radiation
of the column of heated air (disk out), and since the rock-salt (disk out) was exposed to the
radiation of neighboring walls hotter than the disk, and also to the warmer internal convection
currents which then ascended at the front, the thermal change of the salt again had the opposite
sign to that of the disk.
53
If 6c = the variation of radiation dependent upon thermal change in the black copper in the time
of exposure,
<Ss = the corresponding variation depending upon thermal change in the rock-salt, modified by
its own absorption,
r = the mean radiation of the hot air, as affected by self-absorption and assumed to be con-
stant,
,r = the transmission of hot air radiation by salt,
y = the transmission of the radiation of black copper by hot air and salt,
z = the transmission of the composite radiant beam issuing from the rock-salt, exercised by
the air between the salt and the bolometer,
we may express the facts of these experiments thus :
(a) z (xr + y *c 6s] = + 7.80
(b) z(xr y*c+ <5s) = -1.34
The change of radiation of the rock-salt in a quiescent atmosphere has been found quite inap-
preciable during the time of exposure, and, although somewhat larger under strong convection
currents, it is still a very small quantity; but for illustration it may be included, taking 6s = -^
ydc. The equations give
Constant radiation of hot air xzr = + 3.23
Variation due to thermal change in copper yzSc = 4.6G
Variation due to thermal change in salt zds = 0.09
The total radiation of black copper, rock-salt, and air on this occasion was found to be 52.3
div., the excess being 74. This radiation is made up approximately of
Radiation of black copper, transmitted by salt T.9.3
Radiation of air, transmitted by salt 3.2
Radiation of rock-salt 9.8
. The rock-salt plate having absorbed one-fourth of the original radiation from the interior, the
initial deflections before absorption may have been :
Blackened copper 39.3 + 13.1 = 52.4
Air 3.2+ 1.1= 4.3
The indicated radiation for the blackened copper is not far from normal, but the air radiation
is only a little over one-third of that obtained by the usual method, no doubt because, with but
one lamp burning, only a part of the air is effective, the distribution of temperature being far from
uniform, as the variation in the temperature of the copper disk at opposite ends of the cylinder
also proves.
The influence of self-absorption of its own radiations by a gas brings into play another factor
which changes with the depth of the gaseous layer. By varying the play of the disk in exposure,
this feature may be partly determined, but its complete elucidation demands apparatus with a
great range of dimensions.
Paschen ("Ueber die Emission der Gase," Wied. Ann., Bd. 51, S. 30, 1894) finds that a 7-cm.
layer of carbon dioxide absorbs at the position of its chief band "like an infinitely thick layer,"
and that the absorption of aqueous vapor is by no means proportional to the depth, but increases
(at wave length 2.60 //) from GO per cent, to 80 per cent., when the depth of the vaporous layer
varies from 7 cni. to 33 cm. (loc. cit., p. 12). Hence, gaseous radiant emission is not proportional
to the depth, except for small depths, and it is conceivable that there may be, for a given depth,
some temperature of the gas at which there is such a compensation of emission by absorption
that increase of thickness will not affect the quantity disk radiation plus gaseous radiation plus
gaseous absorption. In fact, Paschen's fig. 8 (Taf. 1, Wiefl. Ann., Bd. 51) shows that the ratio of
gaseous emission to gaseous absorption for carbon dioxide changes with the temperature, and the
same figure permits a determination of one point on a curve of compensation of radiation by
absorption for this gas.
The first measurements made with apparatus C were to find the relation between air radiation
and depth, and to these we may now pass.
54
METHOD C. EXPERIMENTS IN 'WHICH THE DEPTH
BEEN VARIED.
AND PRESSURE OF THE AIR HAVE
Each of the two air-pumps diminished the pressure in the cylinder by about 100 mm. with
the first 20 strokes; but owing to the slow action of the valves, it was difficult to get the
final pressure below 50 mm., although the pumps worked well enough when the receiver to be
exhausted was small. In addition to this trouble, there has always been some leakage at low
pressures e. </., in one experiment where the air temperature did not exceed 100 C., the gage at
4 h 27 in read 04.G; at 5 h 32 the reading was 98.4 mm., the pressure having risen 3.8 mm. in 65,
or 0.0f>9 mm. per minute, and fresh leaks have frequently started from the strain of heating.
Consequently, in experiments with partial vacuum, it has been necessary to work rapidly, and in
spite of drying flasks, some aqueous vapor must enter through leakage. The final method which
overcame this difficulty was the introduction of a bowl of phosphoric anhydride within the
cylinder. After repeated exhaustions, allowing air to flow into the cylinder through a series of
flasks containing porous chloride of calcium, experiments were commenced January 25, 1893, with
air nearly dry, but still containing carbon dioxide in the usual small proportion. Without further
announcement, it may be understood that in all the readings which follow, the deflections have
been reduced to standard conditions of current and bridge. The change is usually very small,
but in the present case, with battery galvanometer 95 div., the arrangement of the bridge was
insensitive, and the multiplier is 2.0. Mean temperature of room, 20; of bolometer, 25; dew-
point, 12. 2. Pressure of aqueous vapor, 10.57 mm., or 10.71 grams per cubic meter. The
absorbent layer contained enough water to make a liquid depth of 0.000 403 cm. The disk was set
at even feet, but the initial reading with which comparison is to be made is that of the shortest
air column, 0.35 feet. The measurements were made at both ordinary and low pressures.
TABLE 30.
Position of disk, feet.
0.35.
1.
2.
3.
4.
5.
Temperature.
Excess.
Pressure.
Air depth {^
0.65
19.8
1.65
50.3
2.65
80.8
3.65
111.3
4.65
141.8
div.
dir.
div.
div.
dir.
Deflections
J o
1 o
4.8
6.0
15.0
15.8
23.2
24.0
35.4
32.6
33.6
32.0
170
185. 5
145-
160.5
95 mm .
723
Mean deflection
5.4
15.4
23.6
34.0
32.8
Change per foot
8.3
10.0
8.2
10. 4
1.2
The two series in this table, taken at pressures which vary in the ratio of 1 : 7.6, are almost
identical. The discussion of this at first sight rather startling fact is reserved for a subsequent
section. Except for the last foot the increase of radiation is proportional to the depth. In view
of what has been said as to the effect of unequal distribution of temperature it might be suspected
that the diminished deflection at the fifth foot comes from the chilling of the disk by proximity
with the cooler end-plate, but this is not the true explanation, as the next example demonstrates.
TABLE 31.
Cylinder filled with dry carbon dioxide.
Position, feet.
0.35
1. 2.
1
3.
4.
5.
Temperature.
Excess.
Pressure.
De P th {cm.
Mean deflection (div.)
000
0.65 1.65
19. 8 50. 3
3. 5 7. 6
2.65
80.8
10.4
3.65
111.3
10.5
4.65
141.8
10.2
142 C . 7
125. 8
7 66 mra.
Change per foot
5.4 4.1
2.8
0. 1
0.3
55
Two things are shown clearly by these concise tables, namely, that, allowing for the difference
of temperature, the apparent radiation of carbon dioxide is smaller than that of dry air at tempera-
tures not exceeding 200 0. and that the law of increase of radiation with the depth is entirely
different for these two substances. To make the last point quite certain, the experiment was
repeated with dry carbon dioxide, first at atmospheric pressure and then at low pressure. These
measures are given in full as an example of the mode of observation.
February 17, 1894.
Each complete observation consists of three successive series, of ten readings each, with
differential depths of carbon dioxide gas of 4.G5 feet, 1.G5 feet, and again 4.65 feet, the middle
series being contrasted with the mean of the extremes to eliminate the variation from change
of temperature. Each deflection is from three galvanometer readings, with disk in, out, and in
again, and is complete in itself.
Battery galvanometer, 100 div. Barometer, 734 mm,, which is the pressure of the gas in the
first three series. Temperature of the bolometer, assumed to be 5 hotter than the reading of
the dry-bulb thermometer placed beside the bolometer case. The temperature of the bolometer
is taken as the initial or comparison temperature.
At ll h 9 m , dry bulb = 63.8 F. = 17.7 C.
wet bulb = 55.l F. = 12.S C.
Difference, 8.7 + 4.4 (correction for uuveutilated psychrometer of 50 per cent.) = 13.l F.
Dew-point, 38 F. Kelative humidity, 0.38. Temperature of radiation cylinder = 121.0 C.
TABLE 32.
(Series 1.)
Position of disk.
In. Out. In.
Depth of gas (fet-t).
0.35 5.0 0.35
div.
105.1
113.0
104.1
104.6
+8.4
104.1
112.0
105.2
104.7
+7.3
106.1
113.3
103.4
104.8
+8.5
105.0
112.6
108.0
106.5
+6.1
100.0
109.5
103.0
101.5
+8.0
103.0
114.2
105.8
104.4
+9.8
106.1
114.2
105.8"
106.0
+8.2
103.0
112.1
102.5
102.8
+9.3
102.5
111.4
103.0
102.8
+8.6
103.0
112.2
104.0
103.5
+8.7
Differential radiation for depth (4.65ft.).
+8.29
At II 11 19 m , dry bulb = 65.0 F. = 18.3 C.
wet " = 560.0 F. = 13.3 C.
Difference = 9.0 + 4.5 (correction) = 13.5 F.
Dew-point, 38 F. Relative humidity, 0.37.
Temperature of radiation cylinder = 126.8 C.
Mean temperature of radiation cylinder (series 1) = 123.9 C.
" " " excess (series 1) = 100.9 C.
Mean dew-point, 38 F. = 3.3 C., or pressure of aqueous vapor = 5.78 mm., corresponding to
6.04 grams of water per cubic meter of air, and to an equivalent depth of liquid water of 0.000 227
cm. in the absorbent air layer. At II 1 ' 25 m , temperature of radiation cylinder = 133.0 C.
56
TABLE 33.
(Series 2.)
|
Position of disk. ,
In.
Out. In.
Depth of gas (feet).
0.35
2.0
0.35
die.
100.0
109.1
103.8
101.9
+7.2
99.2
107. 7
100.8
100.0
+7.7
100.8
109.6
103.8
102.3
+7.3
102.7
111.1
105.5
104.1
+7.0
105.5
114.0
107.0
106.3
+7.7
102.0
112.0
105.7
103 9
+8.1
105. 9
112.8
108.0
107.0
+5.8
97.8
105.0
98.2
98.0
+7.0
98.2
108.1
102.6
100.4
+7.7
102.6
111.0
101.9
102. 3
+8.7
Differential radiation for depth (1.65 ft.).
+7.42
At ll h 33 ra , dry bulb = 65^.9 F. ='18.8 C.
wet " = 570.0 F. = 130.9 C.
Difference = 8.9 + 4.5 (correction) = 13.4 F.
Dew-point, 40 F. Relative humidity, 0.38.
Temperature of radiation cylinder = 143.2 C.
Mean temperature of radiation cylinder (series 2) = 138.l C.
" " " excess " = 114.5 C.
Mean dew-point, 39 F. = 3.9 C., or pressure of aqueous vapor = 6.03 mm., corresponding to
6.23 grams per cubic nieter of air, and to an equivalent depth of liquid water of 0.000 234 cm.
in the absorbent air layer.
TABLE 34.
(Series 3.)
Position of disk.
In. Out. In.
Vf Ann
T) fl t'
Depth of gas (feet).
0.35
5.0
0.35
div.
105. 3
116.8
105. |
105.2
+11.6
105.0
120.0
106.8
105.9
+14.1
106.0
118.2
107.1
106. 6
+11.6
107.1
119.0
109.
108.1
+10.9
101.6
112.3
101.0
101.3
+11.0
101.0
112.0
101.8
101.4
+10.6
101.8
112.9
102.
101.9
+11.0
102.0
115.0
101. 8
101.9
+13.1
103.0
116.0
102.8
102.9
+ 13.1
102.8
115.0
103.7
103.3
+ 11.7
Differential radiation for depth (4.65 ft.).
+11.87
57
At ll h 43 m , dry bulb = 66.8 F. = 19.3 C.
wet " = 57.4 F. = 14.l C.
Difference = 9.4 + 4.7 (correction) = 14.l F.
Dew -point, 40 F. Eelative humidity, 0.37.
Temperature of radiation cylinder = 146.7 C.
Mean temperature of radiation cylinder (series 3) = 145.0 C.
" . excess " = 120.9 C.
Mean dew-point, 40 F. = 4.4 C., or pressure of aqueous vapor = 6.24 mm., corresponding 'to
6.50 grams per cubic meter of air, and to an equivalent depth of liquid water of 0.000 244 cm.
in the absorbent layer of air.
The cylinder was now partially exhausted for the low-pressure experiments.
At 12 h 6 m , dry bulb = 68.0 F. = 20.0 C.
wet " = 59.0 F. = 15.0 C.
Difference = 9.0 + 4.5 (correction) = 13.5 F.
Dew-point, 43 F. Eelative humidity, 0.40.
Temperature of radiation cylinder = 149.9 C.
Pressure in " " =85 mm.
TABLE 35.
(Series 4.)
Position of disk.
In. Out. In.
Depth of gas (feet).
0.35 5.0 0.35
div.
93.8
105.0
93.2
93.5
+11.5
93.2
105.1
90.7
92.0
+13.1
90.7
103.2
91.5
91.1
+12.1
91.5
103.5
92.2
91.9
+11.6
92.2
105.0
92.0
92.1
+12.9
92.0
102.0
91.2
91.6
+10.4
91.2
104.1
88.0
89.6
+14. 5
88.6
102.1
87.4
88.0
+14.1
87.4
101.1
86.8
87.1
+14.0
86.8
99. 4 86. 1
86.5
+12.9
Differential radiation for depth (4
65ft.).
+12. 71
At 12 h 12 m , dry bulb = 68.S F. = 20.4 C.
wet = 590.8 F. = 150.4 C.
Difference = 9.0 + 4.5 % (correction) = 13.5 F.
Dew-point, 45 F. Eelative humidity, 0.41.
Temperature of radiation cylinder = 154.0 C.
Mean temperature of radiation cylinder (series 4) = 152.0 C.
" " excess (series 4) = 126.8 C.
s
Mean dew-point, 44 F. = 6.7 C., or pressure of aqueous vapor = 7.31 mm., corresponding to
7.55 grams per cubic meter of air, and to an equivalent depth of liquid water of 0.000 284 cm.
in the absorbent layer of air.
Pressure of carbon dioxide, 85 lain.
58
TABLE 36.
(Series 5.)
Position of disk.
In.
Out. In.
Depth of gas (feet).
0.35
2.0
0.35
die.
99.0
109.6
100.2
99.6
+10.0
103.3
112.9
101.9
102.6
+10. 3
101 9
114.0
103.9
102. 9 +11. 1
97.2
108.4
97.0
97.1
+11.3
100.2
108.5
99.6
99.9
+ 8.6
100.0
111.4
101.8
100.9
+10.5
101.8
112.2
104.4
103.1
+ 9.1
99.0
109.8
100.2
99.6
+10.2
100.2
109.2
101.3
100.8
+ 8.4
100.5
111.1
103.2
101.9
+ 9.2
Differential radiation fordepth (1.65ft.).
+ 9.87
At 12 h 19'", dry bulb = 69.l F. = 20.6 C.
wet bulb = 58.6 F. = 14.8 C.
Difference = 10.5 + 5.3 (correction) = 15.8 F.
Dew point, 38 F. Relative humidity, 0.32.
Temperature of radiation cylinder = 163.S 0.
Mean temperature of radiation cylinder (series 5) = 158.9 C.
" " " excess (series 5) = 133.4 C.
Mean dew-point, 41.5 F. = 5.3 C., or pressure of aqueous vapor = 6.64 mm., corresponding to
6.90 grains per cubic meter of air, and to an equivalent depth of liquid water of 0.000 259 cm
in the absorbent layer of air.
Pressure of carbon dioxide =91 mm.
Mean pressure of car.bon dioxide (series 5) = 88 mm.
TABLE 37.
(Series 6.)
Position of disk.
In.
Out.
In.
Depth qf gas (feet) .
0.35
5.0
0.35
dir.
103.0
113.0
99.3
101.2
+11.8
99.3
112. 3
99.3
99.3
+13.0
99.3
111.0
97. 3 98. 3
+12.7
97.3
111.2
94.9
96.1
+15.1
94.9
108.2
95.0
95.0
+13.2
95.0
107.6
94.0
94.5
+13.1
94.0
110.0
94.1
94.1
+15.9
94.1
108.9
92.5
93.3
+15.6
92.5"
108.8
93.0
92.8
+16.0
93.0
107.2
92.0
92.5
+14.7
Differential radiation for depth (4.65 ft).
+14.11
59
At 12 h 26 m , dry bulb = 69.8 F. = 21.0 C.
wet bulb = 60.2 F. = 15. 7 C.
Difference = 9.6 + 4.8 (correction) = 14.4 F.
Dew-point, 43 F. Kelative humidity, 0.38.
Temperature of radiation cylinder = 164.S C.
Mean temperature of radiation cylinder (series 6) = 164.3 C.
" " excess (series 6) = 138.5 C.
Mean dew-point 40.o F. = 4. 7 C., or pressure of aqueous vapor = (3.37 mm., corresponding to
6.63 grams per cubic meter of air, and to an equivalent depth of liquid water of 0.000 249 cm.
in the absorbent layer of air.
Pressure of carbon dioxide = 96 mm.
Mean pressure of carbon dioxide (series 6) = 93.5 mm.
TABLE 38. Summary.
Series.
Air layer.
Carbon dioxide in radiation cylinder.
Pressure.
Water
cm. x 10
Tempera-
ture.
Excess.
Radiation.
Pressure. Ratio
64.65ft.
84.65 ~-S 1.65
51.>5 ft.
mm.
c
6
mm. div.
dii:
1 ! 734
227
123.9
100.9
734 8. 29
,
2
734
234
138.1
114.5
734
74a 10-08
7.42
3
734
244
145.0
120. 9
734 11.87
= 1.358
4
734
284
152.0
126.8
85 12. 71
5
734
259
158. 9
133.4
88
13.41
9.87
6
734
249
164.3
138.5
93.5 14.11
= 1.359
As in the case of air, there is scarcely any difference in the radiation which can be attributed
to change of pressure. The change of radiation with the depth is also unaffected by pressure.
When the depth is increased in the ratio ^-^ = 2.818, the differential deflection is only increased
10.2
in the ratio 1 : 1.359. Table 31 gives for the same depths the ratio of deflections ->-- = 1.342,
and the results of Table 31 for the 2d and oth feet are confirmed by the more elaborate measures
of Table 38.
Professor Paschen ("Emission erhitzer Gase. 7 ' Wied. Ann., Bd. 50, Taf. 9, fig. 9, 1893) gives
a series of spectral energy-curves for the principal maximum of carbon dioxide at temperatures
110, 158, 330, 622, 710, and 973 C., the radiation proceeding from a layer of the heated gas
about 3 mm. deep. At the lowest temperature, which is a little below the highest in my observa-
tions, the deflections are very small, and the spectral energy-curve is very flat, but is still shown
as a distinctly limited emission-band whose extreme wave-lengths do not differ by more than a
fraction of a micron. Measuring the areas of the first four curves of Paschen's figure, the relative
radiations are found to be
Temperature 110 158 330 622
Eadiatiou* 75 227 1,630 4,905
Drawing a curve through these values, and also (anticipating a little) one to represent my
final measures of the total apparent radiant emission, the depths of radiant gas being 3 mm. and
Measured in arbitrary units.
60
1,418 mm., the following approximate relative radiations for moderate temperature-excesses have
been read from the curves :
TABLE 30.
Depth. t=2(P
=40
<=60
#=80
=100 : =12(P
cm.
0.3 1
4
12
30
59
100
141.8 2
7
17
36
65
100
The rate of increase of radiation with that of temperature is greater for a 3-inm. layer than
for one of 1,418 mm., because the absorption in the mass of great depth partly neutralizes its own
radiation. This is proved by the preceding experiments, which have demonstrated that a 5-foot
layer of carbon dioxide radiates but little more than a 2-foot layer, and no more than a 3-foot layer.
The rate of increase of radiation with temperature for a 5-foot layer of air does not differ much
from the corresponding rate for carbon dioxide at these low temperatures, and the absolute radia-
tions also are not very different; Out, unlike carbon dioxide, the air radiates in proportion to the
depth. It may be that this is because the measured radiation of air in my final experiments has
been to a considerable extent that of its oxygen, nitrogen, or argon, and not merely that of the more
highly absorbent and at high temperatures more powerfully radiant carbon dioxide or water- vapor.
Since, at high temperatures and in thin layers, the radiative power of these strong absorbents is
immensely greater than that of air, it follows that the rate of radiant increase with the depth for
air at higher temperatures must be very much slower than for carbon dioxide, and that at partic-
ular depths and temperatures, which have been reached in the present research, the total radia-
tions of these substances are more nearly equal. It is not possible, however, that equable increase
of air radiation with depth can continue indefinitely, since the heat lost by layers of such dimen-
sions as we have in the atmosphere, and imparted by radiation from the atmosphere to the earth,
would have to be much greater, in that case, than it actually is.
The differential deflections in Tables 30 and 31 may best be compared by stating them as
percentages of the deflection with disk at 4 feet.
TABLE 40.
Position of
disk.
Depth of
gas.
Air at
185.5 and
723 mm.
C0 2 at Increase per foot.
19R3 H nrin
766 nun. Air .
C0 2 .
Feet.
0.35
1.0
2.0
3.0
4.0
5.0
cm.
19.8
50.3
80.8
111.3
141.8
18.4
48.5
73.6
100.0
98.2
o
33.3 28.3
72. f 30. 1
98. 7 25. 1
100. 26. 4
97 1
51.2
38.7
26.7
1.3
The slight decrease in the differential deflection at the fifth foot, as compared with that at
the third or fourth foot in the experiments with carbon dioxide, is possibly due to the chilling of
the radiating disk in the extreme end position, or to absorption of disk radiation by CO 2 , a point
which will be examined farther on; but the change in the air series at the fifth foot is presumably
to be attributed to a different cause. The observations of Table 30 were the first made with appa-
ratus C. Intermediate positions were reached by stopping the rod which carries the disk at
successive marks, but the end reading was secured by pulling out the disk until its clamp was felt
or heard to strike against the end-plate. The supports of the cylinder were not stiff enough to
resist the shock, and the entire mass of iron moved to and fro though a sufficient range to produce
a deflection of a few divisions on the galvanometer by magnetic influence. Suspecting such an
effect, which was, however, irregular, and one for which no correction can be applied, I had the
supports stiffened by braces, and the remedy proved effectual. The error only affects the readings
61
on the fifth foot in Table 30, and these have been rejected. Observations made after the insertion
of the braces, and with a cold cylinder, to see if any magnetic effect was exerted by the motion
of the steel rod, gave a deflection of 0.29 div. for the outward motion of 4.65 feet. As this is
included in possible errors of observation, no correction is applied for magnetic influence.
The relative increments of radiation, given in the last column of Table 40, demonstrate that a
layer of carbon dioxide, 3 feet deep, is sufficient to extinguish by its absorption practically all the
radiation of the peculiar quality emitted by this gas; and thus that no further increase in the
depth of the radiating layer is of avail for adding to the emission of the only rays which this
substance is capable of sending forth. If this is a general law, the brilliancy of a glowing gaseous
mass (a solar prominence, for instance) depends, after a certain depth has been exceeded, entirely
upon the temperature, but not on the dimensions of the layer; and the cooling of a gaseous mass
of great depth depends on the radiation of a comparatively shallow layer whose locus travels
inward. It might be inferred from the preceding experiments that layers of air and of carbon
dioxide, 1 foot deep, and at atmospheric pressure, radiate equally near the temperature of boiling
water to an iuclosure near the freezing point; but these results require the application of further
corrections before the final quantitative values can be stated.
RADIATION FROM MULTIPLE FLAMES.
In order to examine the effect of increasing depth on the radiation of a gas at high temper-
ature, a series of five Bunsen burners, with apertures 2.5 by 0.2 inches, giving flat flames, were
arranged so that the flames were presented broadside to the line of sight. Only so much of the
flame as could be seen through the narrow aperture of the multiple tin-plate screen was permitted
to radiate to the bolometer. The most distant flame was 2 feet from the bolometer; the nearest.
1A feet. Exposures were made by withdrawing a blackened copper screen containing cold water.
The shape of the flame is shown, full size, in fig. 8.
62
November 15, 1895.
Temperature of room, 14.8 C. Dew-point 7.8 C., corresponding to a pressure of aqueous
vapor of 7.88 mm., or 8.11 grains per cubic meter, and to an equivalent liquid depth of 0.000 371 cm.
in the distance to the nearest flame, and 0.000 494 cm. in the path to the most distant flame.
Battery galvanometer, 100 div.'
Shunt = 0.1451. Multiplier = 6.89. Temperature of cold screen, 10 to 18 C.
TABLE 41.
X umber of flames.
B
4
3
2
,/ most \
\ distant/
1 (nearest)
Depth of flaine.
3.0 cm.
2.4 cm.
1.8 cm.
1.2 cm.
O.Ccm.
0.6 cm.
244.5
217.5
175.5
128. 5
69
74
245
218
176
129
70.5
72
250.5
219
176
129.5
66.5
73
252
221. 5
174.5
128.5
69
73
Deflections
245.5
220.5
177
130
70
73.5
(Shunted galvanometer)
249
216
177
125
69.5
75.5
251.5
218
. 174.5
129.5
66.5
77.5
250.5
220
173
130.5
71
73
252.5
214
172.5
126
69
72
250
220.5
177
130
71.5
72.5
Mean (shunted)
249.1
218. 5
175.3
128.7
69.3
73.6
" (unshunted)
1723
1506
1208
887
478
507
Change per 0.6 cm.
217
298
321
395
4'
)3
The deflection on the most distant single flame is 94.2 per cent, of that on the nearest one, a
diminution which is probably due to the greater amount of water- vapor traversed by the rays from
the flame at the greatest distance, the radiant emission from the flame being largely that of very
hot steam, and one especially depleted of its peculiar rays by even a thin layer of its own
substance.
The addition of successive flames, each new one radiating through all the previous ones, gives
progressively diminishing increments of radiation, as shown in the last line of Table 41. The aver-
age depth of each flame was 6 mm., and the indication is that there will be very little increase of
radiation for addition of flame-depth beyond 20 cm. For carbon dioxide, the depth of the efficient
radiant layer is not over 90 cm, For air, the efficient depth must be many meters.
CONTINUATION OF MEASURES MADE WITH THE RADIATION CYLINDER.
The next four series of measures with the radiation cylinder have been made with a continu-
ously rising temperature. Hence, according to the general theory of the apparatus, the recorded
thermometer readings are lower than the true mean temperatures of the air within the cylinder,
by amounts which can perhaps be estimated later; but since all of these series have been taken
on a common plan, and the rapidity of heating has been nearly the same, the results are
comparable.
The curves of heating are given in fig. 9, abscissa? being intervals from the commencement of
heating and ordinates being recorded cylinder temperatures.
The rate of heating is a trifle slower for rarified air. Otherwise, the heating curves are
similar. The throw of the disk was to its full extent in every case, the radiant depth being
141.8 cm. Deflections were observed in groups of five every six minutes. Only the mean
readings are given here.
February 9, 1893.
Cylinder containing air at normal pressure, 737 mm., and nearly dry, but not purified from
carbon dioxide.
63
/fa* Cent.
/oo -win.
?ig. 9
Temperature of room, at 3 1 ' O m , ll.l C.; at 3 h 30 m , 12.2; at 4 h O m , 13.3; at 4 h 30, 14.4;
at 5 h O m , 15.5.
Mean dew-point, 4.4 C., corresponding- to a pressure of aqueous vapor of 6.24 mm. or 6.50
grams per cubic meter, and to an equivalent liquid depth of 0.000 244 cm. in the absorbent layer.
Lamps lighted at 3 h 20 m . Burner cocks set at 35 div.
The results are platted in fig. 10 ().
Abscissa 1 = temperature-excesses (uncorrected).
Ordiuates = deflections.
TABLE 42.
Cylinder temperature.
Bolometer
Observa-
tion No.
Time.
Mean tem-
perature.
tempera-
ture.
Excess.
Deflection.
Pressure.
Before.
After.
,
h. in.
o
o o
o
div.
mm.
1
3 8
9.3
9.3
16.4
7. 1
0. 5
TW
2
3 37
43.9
53.2
48.6
17.5
+31.1
+ 8'.50
1 Vl
3
3 43
53.2
63.3
58.3
17.7
40.6
+ 9.21
4
3 49
63.3
72.1
67.7
17.9
49.8
+11. 88
5
3 55
72.1
81.4
76.8
18.1
58.7
+11. 05
6
4 1
81.4
89.9
85.7
18.3
67.4
+12. 78
7
4 7
89.9
98.0
94.0
18.6
75.4
+12. 33
8
4 13
98.0
104.4
101.2
18.8
82.4
+14. 70
9
4 19
104.4
114.2
109.3
19.0
90.3
+15. 87
10
4 25
114.2
122. 1
118.2
19.2
99.0
+16. 06
11
4 31
122.1
130.
126.1
19. 4 106. 7
+19. 29
12
4 37
130.0
137.2
133.6
19. 7 113. 9
+21. 66
13
4 43
137.2
144.0
140.6
19. 9 120. 7
+22.64
14 4 49
144.0
150. 3 147. 2
1
20.1
127.1
+22. 48
64
February 10, 1893.
Cylinder containing partially dried air at low pressure.
Temperature of room, 13.8 to 14.S C.
Mean dew-point, 6.7 C., corresponding to a pressure of aqueous vapor of 7.31 mm., or 7.56
grams per cubic meter, and to an equivalent liquid depth of 0.000 284 cm. in the absorbent layer.
Lamps lighted at 4 h O m . Burner-cocks set at 35 div.
TABLE 43.
Observa-
tion No.
Time.
Cylinder temperature.
Mean
tempera-
ture.
Bolometer
temper-
ature.
Excess.
Deflection.
Pressure.
Before.
After.
h. in.
o
o
o
o
div.
mm.
1
3 51
13.6
13.7
13.7
18.8
5.1
+ 0.26
58.5
2
4 14
28.0
37.1
32.6
19.0
+13.6
+ 3.91
56.7
3
4 20
37.1
48.2
42.7
19.1
23.6
+ 6.73
60.0
4
4 26
48.2
58.2
53.2
19.2
34.0
+ 8.16
64.3
5
4 32 58. 2
67.6
62.9
19.2
43.7
+ 8.38
68.5
6
4 38 67.6
75.7
71.7
19.3
52.4
-f 11. 69
72.3
7
4 44
75.7
84.0
79.9
19.3
60.6
+11. 09
76.8
8
4 50 84.0
93.0
88.5
19.4
69.1
+12. 26
81.8
9
4 56 93.0
102.2
97.6
19.5
78.1
+14. 78
86.5
10
5 2 102. 2
109.7
106.0
19.5
86.5
+13. 99
91.5
11
5 8
109.7
118.1
113.9
19.6
94.3
+15. 60
96.5
12
5 14 118. 1
125.
121.6
19.6
102.0
+17. 22 101. 8
13
5 20 i 125.
131.6
128.3
19.7
108.6
+21. 43 106. 3
14
5 26
131.6
137.9
134.8
19.8
115.0
+22. 07 110. 8
15
5 32
137.9
144.2
141.1
19.8
121.3
+23. 39
116.8
The results are plotted in Fig. 10 (6). The cold cylinder leaked at the rate of 5 mm. in 15 min.
at the lower pressures. Computing the proportional leakage for three intervals in the above series,
and comparing the observed pressures, corrected for the expansion of air by heat, we have :
mm.
4 h 14 m to 4 h 44 m , change of pressure, 56.7 to 76.8
By thermal change, 56.7 X [1 + (60.613.6) X .00367] =66.5
Observed leakage,
Leakage, computed for 30 min. interval,
Residual,
10.3
10.0
+ 0.3
4 h 44"' to 5 h 8 m , change of pressure, 76.8 to 96.5
By thermal change, 76.8 X[l + (94.3 60.6) x .00367] = 86.3
Observed leakage, 10.2
Leakage, computed for 24 min. interval, 8.0
Residual, +2.2
5 h 8 m to 5 h 32'", change of pressure, 96.5 to 116.8
By thermal change, 96.5 X[l +(121. 3 94.3) X .00367]=106.0
Observed leakage,
Leakage, computed for 24 min. interval,
Residual,
10.8
8.0
+2.8
The excess of observed pressure over computed at the higher temperatures is probably
to be attributed to the real mean temperature being higher than that assumed from thermometer
readings in heating, as explained in the general theory of the apparatus; but it is possible that
the leaks may have increased in the course of the process of heating. Leaks in the luting had
been started by the previous day's heating and the joints had to be tightened at the beginning of
the observations of February 10. Another possible cause of the discrepancy is that some vapor
may have been evolved by the heat at the highest temperatures; but in this case some special
fluctuation of the readings of the galvanometer might be anticipated, and of this there is no sign.
65
February 24, 1894.
Cylinder filled with dry carboii dioxide at atmospheric pressure, 748 mm.
Temperature of room, 12.8 C. at 2 h 10"', to 15.l C. at 3 h 47.
Dew-point, 1.4 C., corresponding to a pressure of aqueous vapor of 5.05 mm., or 5.32 grams
per cubic meter, and 0.000 190 cm. of liquid water in the absorbent air layer.
Lamps lighted at 2 h 19 ra . Cocks 35 div.
TABLE 44.
Cylinder temperature.
Mean Bolometer
Observa-
tion No.
Time.
tempera- tempera-
ture, ture.
Excess.
Deflection. , Pressure.
Before.
After. .
h. m.
o
o
o o
o
div.
mm.
1
2 26
39.8
52.2
46. 18. 2
27.8
+ 3.20
748
2
2 32
52.2
63.0
57. 6 ! 18. 4
39.2
+ 4.78
3
2 38
63.0
75.3
69.2
18.5
50.7
+ 4.51
4
2 44
75.3
85.8
80.6
18.7
61.9
+ 7.63
5
2 50
85. 8 94. 8
90.3
18.8
71.5
+ 8.53
6
2 56
94. 8 104. 8
99.8
19.0
80.8
+10. 73
7
3 2
104.8
111.5
108.2
19.1
89.1
+ 8.10
8
3 8
111.5
122.8
117.2
19.3
97.9
+10. 80
9
3 14
122.8
130.8
126.8
19.4
107.4
+12. 92
10
3 20
130.8
136.8
133.8
19.6
114.2
+13. 49
11
3 26
136.8
144.1
140.5
19.7
120.8
+13. 45
12
3 32
144.1
150.6
147.4
19.9
127.5
+15. 80
The results are platted in fig. 10 (c).
June 27, 1894.
Cylinder containing dry carbon dioxide at atmospheric pressure, 730 mm. (at C.).
Temperature of room, 29.4 C., with a rise of one-half degree per hour.
Dew-point, 15.0 C., corresponding to a pressure of aqueous vapor of 12.67 mm., or 12.71
grams per cubic meter, and to an equivalent liquid depth of 0.000 478 cm. in the absorbent layer
of air.
Lamps lighted at 3 h 32 m . Burner cocks at 40 div.
TABLE 45.
Observa-
tion If 0.
Time.
Cylinder temperature.
Mean tem-
perature.
Bolometer
tempera-
Excess.
Deflection.
Pressure.
Before. After.
ture.
h. m.
o o
o
o
o
div. mm.
1
3 51
61.6
70.9
66.3
34.2
32.1
+ 5.59
730
2
3 57
70.9
81.2
76.1
34.2
41.9
+ 6.64
3
4 3
81.2
91.2
86.2
34.3
51.9
+ 6.34
4
4 9
91.2
101.2
96.2
34.3
61.9
+ 8.16
5
4 15
101.2
111.0
106.1
34.4
71.7
+ 9.50
6
4 21
111.0
119.6
115.3
34.4
80.9
+ 9.38
7
4 27
119.6
127.6 123.6
34.5
89.1
+10. 58
8
4 33
127.6
134.8 131.2
34.5
96.7
+10. 28
9
4 39
134.8 142.9 138.9
34.6
104.3
+ 9.72
10
4 45
142. 9 148 6 145. 8
34.6
111.2
+11. 73
11
4 51
148. 6 154. 2 151. 4
34.7
116. 7
+12. 69
:
12812 Bull. G-
66
The results are platted in fig. 10 (<?). Fig. 10 (a] gives for air a radiation of 24 div. at excess
130 C., or 0.185 div. per degree; and fig. 10 (b) gives 24 div. for 125 excess, or 0.192 div. per
degree, no appreciable change being produced by rarefaction. Fig. 10 (c) gives for carbon dioxide
a radiation of 14 div. for an excess of 120 C., or 0.117 div. per degree; and fig. 10 (d) gives 14 div.
24
22.
18
14
12.
10
L-
X
X
a
4
2
rf
G
&
10
g
o 9
50'
100
50'
100
10
for 118, or 0.119 div. per degree, both observations being at atmospheric pressure. Reducing
this deflection to the galvanometer constant of 1893, it becomes 0.1254 div., and the ratio of radia-
tions (141.8 cm. layer) is:
0.1885
Air : CO 2 . . . .
0.1254
= 1.50.
This ratio is, of course, only applicable to the limited range of depth and temperature from
which it has been obtained. The increase of water in the absorbent layer, in the ratio iqn = 2.52
has not affected the radiation of carbon dioxide. The bands of these substances, in the infra-red,
overlap to some extent, but if composed of fine lines, they need not interfere.
GASEOUS RADIATION WITH A COOLING CYLINDER- (LAMPS EXTINGUISHED).
The next experiments, conducted with a cooling cylinder, should give trustworthy values
according to the general theory of the apparatus.
67
June 28, 1894.
Cylinder filled with dry carbon dioxide.
Temperature of room, 30.4 C. ; of bolometer, 35.4.
Mean dew-point, 15.2 C., corresponding to a pressure of aqueous vapor of 12.84 mm., or 12.87
grams per cubic meter, and to a liquid depth of 0.000 484 cm. in the absorbent layer of air.
The measures were to be made near normal pressure, and at points marked with an asterisk,
a little carbon dioxide was allowed to flow into the cylinder to restore the pressure. Each deflec-
tion in the following table is the mean of five. The first reading in each series corresponds to the
maximum temperature and is abnormal:
TABLE 46.
Series 1.
Time.
Cylinder temperature.
Mean tem-
perature.
Excess.
Cooling
rate per | Deflection,
minute.
Pressure
at C.
Before. After.
h . m.
000
o
div.
mm.
2 8
744
2 11.5 133.2 132.8 133.0
97.6
0.13
+15. 68
2 15 132.8 129.9 131.4
96.0
0.73
+12. 44
2 17
731
2 21.3
126. 7 124. 3
125.5
90.1
1.10
+ 8.71
*2 23
718
2 29
751
2 32
117.0
112.4
114.7
79.3
0.81
+ 6.32
2 35
742
2 37
112.4
109.0
110.7
75.3
0.67
+ 4.65
2 39
737
2 47
105.1
103.8
104.5
69.1
0.48
+ 3.86
2 48
726
Series 2.
h. m.
o
o
o
div.
mm.
3 43
741
3 45.5
136.2
134.4
135.3
99.9
0.36
+14. 51
3 48
734
3 55
728
3 56.5
128.7
125.0
126.9
91.5
1.23
+ 9.52
3 58
715
3 59.5
125.0
119.9
122.5
87.1
1.70
+ 8.21
*4 1
706
4 14
741
4 16. 5 113.
109.4
111.2
75.8
0.72
+ 5.66
4 19
739
4 21 109.4
105.2
107.3
71.9
1.05
+ 4.55
4 23
733
4 25 105. 2
101. 7 103. 5
68.1
0.88
+ 4.09
4 27
729
The mean of the observed pressures in the first series is 736 mm.; in the second 730 mm.;
and the mean cooling rate is 0.80 per minute.
On this date a final series was taken with carbon dioxide as the radiant, to see if any effect
could be noted from varying the pressure while the temperature remained constant or was cooling
very slowly.
TABLE 47.
Temperature.
Excess.
Cooling per
minute.
Deflection.
Pressure.
o o
o
div.
mm.
134.8
99.4
0.53
+10.09
739
135. 99. 6
0.00
+11. 43
588
135.4
100.0
0.40
+11. 19
401
134.5
99.1
0.20
+12. 74
208
133.8
98.4
0.08
+12. 35
213
68
Here a slight increase of the deflection was observed when the pressure diminished.
The next experiments were made with air purified from both aqueous vapor and carbon
dioxide. The air entered the apparatus through a series of flasks and tubes. First came two
flasks (1 and 2) containing porous chloride of calcium; then (3) a long horizontal tube filled with
crushed and chemically pure hydrate of sodium, the stoppers being protected by asbestos. Next
(4) came a flask filled with a solution of sodium hydrate in glycerin, through which the air passed
in bubbles whose rate of flow could be regulated by the graduated stopcock. After this came (5)
another flask of porous chloride of calcium, and last (6 and 7) two flasks containing flocculent phos-
phoric anhydride. (1) and (2) protect the sodium hydrate from atmospheric moisture; (4) is relied
on to absorb the last traces of carbon dioxide. The water coming from the chemical reaction
2 NaOH + CO 2 = Ka 2 CO 3 + H 2 O,
is absorbed by (5), (6), and (7).
Finally a bowl of phosphoric anhydride and, in the last experiment, pure sodium were
introduced directly into the radiation cylinder to absorb the small amount of impurity coming
from leakage.
The leakage being proportionally very much greater at low pressures, after a preliminary
exhaustion and filling, the pressure was kept about 50 mm. below the normal for a long time, the
outer air flowing slowly through the flasks and completing the purification by successive dilutions.
August 15, 1895.
Pressure, 731 mm. at C.
Temperature of room, 31.3 C.; of bolometer, 36.3.
Dew-point, 6.7 C. Pressure of aqueous vapor, 7.31 mm., or 7.56 grams per cubic meter,
equivalent to a liquid depth of 0.000 284 cm. in the absorbent layer. Disk of blackened asbestos.
Temperature in (1) co
" " (2)
" (3)
Deflections :
f from 100.
to 96. 4.
Excess 61.
9
" 91 ,
.5 " 89 .3
" 54 ,
,1
" 81
.0 " 79 .0
" 43
.7
(1)
div.
(2)
div.
(3)
div.
+13.8
13.9
'+7.2
8.4
+6.6
4.2
14.0
6.1
4.3
11.7
8.3
4.7
11.3
8. a
3.1
Mean deflections: +12.94. +7.66 +4.58
August 17, 1895.
Pressure, 728 mm.
Temperature of room, 29.9 C. ; of bolometer, 34.9.
Dew-point, 14.4. Pressure of aqueous vapor, 12.19 mm., or 12.26 grams per cubic meter,
equivalent to a liquid depth of 0.000 461 cm. in the absorbent layer. Disk of blackened asbestos.
Temperature in (1) cooling from 92. to 90. 9. Excess 56. 6.
" " (2) " " 79 .5 " 77 .2 " 43 .5
" " (3) " " 69 .4 " 68 .0 " 33 .8
" " (4) " " 60 .0 " 58 .8 " 24 .5
Deflections: (1) (2) (3) (4)
div. div. div. div.
5.5 3.7 3.0 2.7
7.2 4.0 3.2 2.9
6.6 5.8 2.0 3.1
7.8 3.8 1.3 2.2
8.0 4.1 1.0 2.5
Mean deflections : +7. 02 +4. 28 +2. 10 +2. 68
August 21, 1895.
Pressure, 735 mm.
Temperature of room, 25 C. ; of bolometer, 30.
Dew-point, 4.7 C. Pressure of aqueous vapor, 6.37 mm., or 6.63 grams per cubic meter, equiv-
alent to a liquid depth of 0.000 249 cm. in the absorbent layer.
69
Temperature in (1) cooling from 105. 9 to 105. 0. Excess 75. 5
' " (2) " " 100 .0 " 96 .7 " 68 .4
Deflections:
(3)
(4)
89 .5 "
80 .2 '
86 .6
,77 .2
" 58 .1
" 48 .7
(1)
div.
(2)
div.
(3)
div.
(4)
div.
6.0
7.6
2.6
1.6
7.4
5. 5
3.0
1.1
9.5
6.4
2.0
2.8
8.9
5.7
2.1
0.7
9.3
5.6
4.6
0.8
Mean deflections : +8. 22 +6. 16 +2. 86 +1. 40
August 22, 18V 5.
Pressure, 738 mm.
Temperature of room, 27 C. ; of bolometer, 32.
Dew-point, 7.8 C. Pressure of aqueous vapor, 7.88 mm., or 8.11 grams per cubic meter, equiv-
alent to a liquid depth of 0.000 305 cm. in the absorbing layer.
Deflections :
i(l) constant at
71. 0.
Excess 39.
(2) "
(i
71 .0
" 39 .0
(3) cooling
from 71.
to 70 .5
" 38.8
(4)
" 70 .
5 " 69 .4
" 38 .0
(5)
" 69 .
4 " 69 .0
" 37 .2
(1)
(2)
(3)
(4)
(5)
div.
div.
div.
div.
div.
11.6
6.8
5.3
3.0
2.3
8.0
5.4
4.8
5.6
3.9
7.0
6.6
4.2
3.4
2.0
5.0
6.1
5.6
4.4
3.4
5.9
4.1
3.3
3.3
2.4
Mean deflections: '+7.50 +5.80 +4.64 +3.94 +2.80
The radiation cylinder on this occasion had been heated for a long time by the two central
burners. only. The horizontal inequality of temperature produced by the uneven heating persisted
until the end of this series. The last reading is nearly normal.
Finally the radiation cylinder was kept at a nearly constant temperature not far from
100 C. for a week, the air being in contact with metallic sodium. The following readings
were taken during the interval:
September 13, 1895.
Pressure, 733 mm.
Temperature of room, 26 C.; of bolometer, 31.
Dew-point, 12.2 C. Water-vapor pressure, 10.57 mm., or 10.71 grams per cubic meter.
Equivalent liquid depth in absorbing layer, 0.000 403 cm.
Temperature, 100.0 C. (steady). Excess, 69.0.
Deflections: 7.3, 6.3, 8.0, 7.8, 8.2; mean, + 7.52 div.
September 14, 1895.
Pressure, 737 mm.
Temperature of room, 23.5 C.; of bolometer, 28.5.
Dew-point, 9.4 C. Pressure of aqueous vapor, 8.78 mm., or 8.98 grams per cubic meter.
Equivalent liquid depth in the absorbent layer, 0.000 338 cm.
Temperature, 97.8 C. (steady). Excess, 69.3.
Deflections: 7.0, 8.4, 7.7, 7.0, 4.5; mean, + 6.92 div.
September 19, 1895.
Pressure, 733 mm.
Temperature of room, 28.8 C. ; of bolometer, 33.8.
Dew-point, 17. 8 C. Pressure of aqueous vapor, 15.14 mm., or 15.04 grams per cubic meter.
Equivalent liquid depth in the absorbent layer, 0.000 566 cm.
Temperature, 96.2 C. (steady). Excess, 62^.4.
Deflections: 8.9, 7.1, 7.2, 9.1, 6.8; mean, +7.82 div.
70
FINAL CURVES OF APPARENT RADIATION BY METHOD C.
Eejecting the first members of each series, because they are vitiated by inequalities of
temperature, the remaining deflections with carbon dioxide on June 28, 1894 (Table 46), form a
16**
/4
12
10
8
6
4
2
/B
16
/2
10
8
6
4
2
Ttadiat
.of
7?
Aipipa pent
141.8
Oil
Jlppa
1W.S
Dry
Cm.
7)
cm.
Jli
ii*.
tf
i/oxlde
\\
of
+
' 4
<|P=4o/
= 739
tooC.
2 8 mm.
10 20 30 40 SO 60 70
<to too* G.
single consistent series, representing the maximum apparent radiation from this gas, so far as
radiation depends upon depth, which deserves exceptional weight (fig. 11). Passing a mean curve
71
through these points and those of Table 47, and multiplying the ordinates by the ratio 1.5,
already obtained for air radiation from a layer 141.8 cm. deep, as compared with the radiation of
a like layer of carbon dioxide, and reducing to like instrumental conditions, a curve is obtained (fig.
12) which represents, as well as any which I can devise, the considerable range in air values which
have been obtained between August 15 and September 19, 1895. The curve falls between the
observations of August 17 and August 21, passes between the records of radiation at stationary
temperature of September 13 and 14, although considerably below the stationary point of Sep-
tember 19, and is sufficiently below the obviously abnormal curve of August 22 to be free from
the suspicion of being affected by any remaining inequality of temperature. The readings of
August 21 are a little too small, the rock-salt plate having a deposit of dust on its surface. The
observations of August 15 have not progressed far enough to be entirely uninfluenced by
inequality of temperature. Even the deflections at stationary temperature may be a little too
large on this account, and the curve should pass below them rather than through them. In
plotting these variant air values lines have been drawn through the mean positions, showing the
extreme range in the deflections (fig. 12).
The observations of carbon dioxide radiation were made in 1894, those of air in 1895. Conse-
quently the ordinates for the curve in fig. 12, obtained by multiplying those of fig. 11 by 1.5,
have been further multiplied by the ratio of the galvanometer constants in those years, which, by
I OO
p. 20, is -. ^ = 1.19, giving with the condition of instruments in 1895 these values for air radiation:
<3b8
Excess: 10 20 30 40 50 60 70 80 90 100
Deflection: 0.38 0.86 1.54 2.50 3.78 5.4G 7.60 10.59 14.52 19.64
Reduced with the galvanometer constant of 1894, the following table is obtained, giving the
adopted apparent radiations of a 141.8 cm. layer for every tenth degree of temperature excess from
to 100, as read from the smooth curves, the values being expressed finally in absolute units, or
radims x (10)~ 9
TABLE 48.
Temperature
excess.
10.
20=.
30.
40.
50.
60.
70.
80.
90.
100.
CO,
Air
</i>.
0.21
0.32
</ir.
0.48
0.72
<Uv.
0.86
1.29
div.
1.40
2.10
div.
2.12
3.18
div.
3.06
4.59
div.
4.26
6.39
div.
5.93
8.90
div.
8.13
12.20
div.
11.00
16.50
CO 2 *
Air
9
14
21
32
38
57
61
92
93
139
134
201
187
280
260
390
356
534
482
723
* Radiation in ninth-radims.
The measured gaseous radiations are somewhat too small, because the gaseous absorption of
disk radiation has been greater with the disk out, thus diminishing the deflection, and because
the rock-salt and the absorbent layer of air have kept back a part of the radiation of the hot gas.
I>y Method B (ante, p. 44), the radiation of 1 meter of moist air is about 0. 000 000 104 radim
at 40 excess.
By Method C, the radiation of dry air, reduced to the same depth, is 0. 000 000 065 radim at
40 excess.
Both radiations have been diminished by absorption. In particular, the result by Method C
requires an increase of about one third on account of the absorption by the rock-salt plate. The
hot moist air might be expected to radiate more powerfully than dry air at the same temperature,
and the remaining difference is probably attributable to this qualitative distinction.
Although the affinity of rock-salt for moisture made the result of the experiment somewhat
problematical, I decided to try to measure the radiation of water-vapor by Method G, allowing
steam to run into the hot and partially exhausted cylinder. I had supposed at the time of making
this experiment that the gradual introduction of steam into a hot partially exhausted vessel would
not be attended by liquid condensation. The result proved that the flow of steam was too rapid,
72
and that the cylinder should have been full of air at the start, the air-puinps being used merely
to keep the pressure from rising much above normal. Hirn, in 1862, had found that the sudden
diminution of pressure in steam at 152 C. and 5 atmospheres pressure, gave a cloudy condensa-
tion, but this result was unknown to me until I read it in Preston's Theory of Heat, published
about the time of my observations. I regret that the simple expedient of allowing air to remain
in the cylinder while the steam was entering did not occur to me until after the apparatus was
dismounted.
EXPERIMENT ON THE RADIATION OF STEAM.
Temperature of room, 33 C. ; of bolometer, 38.
Dew-point, 3.l C. ; pressure of aqueous vapor 5.70 mm., or 5.96 grams per cubic meter. Equiv-
alent liquid in the absorbent layer = 0. 000 224 cm. After exhaustion to 79 mm. the mean tem-
perature of the radiation cylinder was 132, cooling at the rate of 1.5 per minute, and the mean
deflection from air, at 99 excess, was + 13.02 div. The heater, containing boiling water, was
then connected until the pressure reached 731 mm., the temperature meantime rising to 142, or
to an excess of 104. A mean deflection of + 5.20 div. was then obtained, followed by another of
+ 4.84 div., excess 101. Within 15 minutes after these readings, the pumps having been worked,
the pressure had diminished to 126 mm., temperature 135, excess 97. The mean deflection had
increased to -f 25.62 div., the temperature being nearly stationary.
Undoubtedly, the watery condensation at first precipitated a film of moisture, or dew, on the
rock-salt, which diminished the deflection by its irregular scattering of the rays; but when the
pressure was removed, this film evaporated, and even through the now corroded rock-salt plate,
which transmitted scarcely more than two-thirds of the radiation, this deflection of 25.6 div. was
measured. I infer that with a clear plate, something like 38 div., or about 70 per cent, of the
radiation of lampblack at a like excess, might be obtained from a layer of steam, at 126 mm.
pressure, 142 cm. deep. Under these circumstances, and within the range of my observations,
water-vapor (with no allowance for absorption by the vapor in the air of the room), radiates about
three times as powerfully as air. In small amount, however, water-vapor radiates much more
than the simple proportion of the quantities would indicate.
EXPLANATION OF RESULTS AT LOW PRESSURES.
I have alluded (ante, p. 54) to the small difference between deflections at ordinary and at low
pressures as being at first sight surprising; but the explanation is simple enough. According to
Duloug and Petit (Ann. de Chimie et depliys. (2), tome 7, p. 337, 1817), convection in air at 720 mm.
pressure removes from a hot body 2.548 times as much heat as at 90 mm. pressure; but since the
mass of unit volume is eight times as great at the higher pressure, the air heated by convection
o
at the lower pressure, (1) if equal volumes are set in motion, must get t> =3.139 times as hot;
or else, (2) if the air gets no hotter, 3.139 times as large a volume of low-pressure air must move
in the convection current in the same interval of time.
Under identical thermal conditions, the radiation cylinder being heated by four large Bunsen
burners, with stop-cocks set at 35 div., air, first at 737 mm. and second at 83 mm. pressure, was
heated to the same extent (80. C.) in one hour, with little difference in the radiation from the
heated air column. The final temperature of the entire body of mixed air may be nearly the same
in either case, but the radiation through the limited aperture should be greater in the first condi-
tion, because radiation increases more rapidly than temperature, and the smaller volume of
superheated low-pressure air should have the greater radiant efficiency. The true rate of increase
of gaseous radiation with rise of temperature, as will be eventually shown, is such that if the
temperature is three times as great, the radiation is increased in something like the ratio of eight
to one. Hence if the volume of rarefied air has one-eighth the mass, and is three times as hot as
the same volume of high-pressure air, the radiation per unit of mass (condition 1) will be eight
times as great for the air of smaller density, or identical per unit of volume for either high or low
pressure. The actual rate of heating depends on that of the iron cylinder, and not on the thermal
capacity of the air, whose mass is relatively insignificant. The result of the measurements of
73
gaseous radiation implies that the volume of air set in motion in the unit of time by convection is
independent of the pressure, but that the temperature of this volume is such that the radiant
effect of unit mass increases in inverse proportion to the mass of unit volume. The argument
also implies that, at the same temperature, the radiant effect is proportional to the mass of the
radiating gas, and is independent of the volume which this mass may occupy, always with the
provision that the mass is a small one, or not great enough for the self-absorbent action of
the gas on its own radiations to produce any essential modification of the radiant power.
Since the heating of the bottom of the iron cylinder by the flames was far from uniform, it is
evideut, as has been demonstrated already in other ways, that the measured radiation does not
proceed uniformly from the entire mass of air in range with the bolometer, but from local
columns of hot air rising over the hotter spots in the iron and passing into the field of the
bolometer-aperture at a volumetric rate, as appears from the present argument, which is the same
in the rarefied as in the denser air. It has been shown that the disposition, or thermal condition,
of the components of the radiating mass at the same mean temperature, and thence the combined
radiation of the whole, is different according as the cylinder is heating or cooling, and that the
true air radiation probably lies near the values obtained with negative thermal rates. It is also
found that the emission of gaseous radiation increases at a more rapid rate than the temperature,
so that if ordinates represent radiation and abscissas temperatures, the curve should be concave
upward. Nevertheless, with rapid heating the observations are well represented by a straight
line, evidently because the diminishing rate of heating at the higher temperatures gives less
powerful convection. Small but excessively heated volumes, giving the larger part of the
radiation, then become less predominant, as equilibrium approaches, and the diminution of the
convection-correction cuts off the more rapid rise of the energy-curve which would otherwise
occur at higher temperature.
It is possible that the apparent radiation of carbon dioxide, at constant temperature, increases
at low pressures (as indicated in Table 47, p. 67) by not more than 30 per cent, of the value at
normal pressures ; but the variation is not beyond the limits of error of the observations on which
it rests.
According to Duloug and Petit (loc. cit.), the cooling power of air, as far as it depends on
pressure, is represented by the ratio ^ n<45 -^-jV' 4 '"', and that of carbon dioxide by the ratio
ps\- _^2)i - 517 . Hence the influence of change of pressure upon convection is greater for carbon
dioxide than for air, but this is open to various interpretations. A part of the removal of heat
by gaseous contact is due to mass convection, and part to the penetrative power of the flying
molecules, as G. Johustoue Stouey has demonstrated (On the Penetration of Heat across Layers
of Gas, Phil. Mag. (5), vol. 4, p. 424, Dec., 1877); but in either mode the effect finally depends
partly on the capacity of the gas for heat, and this, for equal volumes, is greater for carbon
3307
dioxide than for air in the ratio = 1.393; while in part the magnitude of the effect is con-
o i o
487
nected with molecular velocity, which is greater for air in the ratio ^ = 1.227. The combined
O*/ i
effect can only be found by experiment. At normal pressure the cooling by carbon dioxide is
0.965 of that by contact with air, but at low pressures the relation is reversed.
METHOD D. RELATIVE RADIATION OF AIR AND STEAM, AND OF CLEAR AND SMOKY AIR.
In this method the cylinder was provided with a pressure gage, recording in pounds per
square inch to a pressure of 15 pounds above the normal. The cylinder then served as a reservoir
for either compressed air or steam. On opening a stopcock the air, or steam, issued from a hot
brass tube, one-half inch in diameter, as a hot jet between the bolometer and a blackened screen
containing water at the temperature of the room. The bolometer was protected from air currents
by a rock-salt plate. In the first experiments partially dried air was used. Three dishes contain-
ing flocculeut phosphoric anhydride, were placed on the floor of the compression cylinder, and air,
compressed by a pump, was forced into the heated cylinder, but was not allowed to stand long
enough to become thoroughly dried.
The objections to the method are that the amount of the radiating gas can not be accurately
74
measured, aud that its temperature, after leaving the nozzle, is lowered by mixture with cold
surrounding air. For these reasons the deflections have only a relative value. The temperature
of the room, owing to the escape of considerable volumes of hot air or steam, rose rather rapidly,
but was kept within bounds by opening windows.
September 28, 1895.
Temperature of room varying from 16.7 C. to 22.0.
Mean dew point, 8.3 C. Pressure of water vapor, 8.15mm., or 8.37 grams per cubic meter.
Temperature of air blast on issuing, (1) 140, (2) 221.
Mean deflections, (1) 1.94 div., (2) 3.45 div.
September 30, 1895.
Mean temperature of room, 15.6 C.
Mean dew-point, 6.l C. Pressure of aqueous vapor, 7.02 mm., or 7.27 grams per cubic meter.
After several charges of steam had been allowed to escape in order to remove the air from
the cylinder, readings were begun. The deflections increased as the steam became purer. The
following successive readings were taken : + 4.6, + 5.8, + 7.0, + 8.1, + 9.8, + 9.8, 4- 10.3, -f 11.0,
+9.5, + 11.0, + 11.6, + 11.0. The temperature having fallen slightly during the last readings,
the cylinder was left to heat a little longer, and the final measures were made.
Temperature of steam blast on issuing, 202 C.
Mean deflection, + 12.39 div.
Corresponding air deflection, + 3.07 div.
Steam radiation four times as great as that of air. The undried air between the bolometer
aud the jet has probably absorbed more of the aqueous radiation than of that from the air, so that
the ratio is, if anything, too small.
The superheated steam, on issuing, formed mist, and a part of the radiation comes from finely
divided liquid; but the next experiment does not indicate that these condensed particles can have
any great effect on the result.
In order to test the possibility of appreciable radiation from fine particles suspended in air,
two wide-mouthed bottles were prepared with dipping inlet and free outlet tubes, the first one-
fourth filled with strong ammonia water, the second containing about as much hydrochloric acid.
Air from a foot bellows was blown through the coupled flasks, and a dense column of chloride of
ammonium smoke arose immediately in front of the hot blast nozzle. As soon as the hot-air blast
was turned on, this cloudy column was sheared off and mingled with the hot air. About one-
fourth as much air issued from the smoke jet as from the hot blast, but the latter can not have
been cooled thereby much more than in the ordinary suction and mingling of the surrounding air.
The particles being excessively fine, and comparable in their dimensions with the shorter waves
of light, as shown by the blueness of the smoke where it was thinner, the microscopic crystals
must have taken the temperature of the air in which they were immersed almost instantly. The
cloud appeared fully as dense as the mist from the condensed steam in the previous experiment.
October 3, 1895.
Temperature of room, 17.7 0. to 18.8.
Mean dew-point, 4.4 C. Pressure of aqueous vapor, 6.24 mm., or 6.50 grams per cubic meter.
Temperature of hot-air blast, 200 C.
The range of pressure was a little lower than in the experiments of September 28, and the
deflections are therefore a little smaller, but all are comparable with each other.
75
TABLE 49.
First series.
Second series.
Third series.
Air 3lear.
Air clonrtv
with XHjCl.
Air clear.
div.
div.
div.
+1.6
+2.0
+2.4
2.7
1.8
2.0
1.7
2.6
1.2
2.3
1.3
0.7
2.4
1.3
4.0
0.7
2.8
2.1
3.9
2.0
2.8
2.0
1. 1
1.2
1.5
2.5
1.4
1.5
1.5
1.2
1.2
2.1
2.3
Means -j-1. 95
+1.91
+1.75
There is no appreciable difference between the radiation of clear and of smoky air in small
masses, but it would not be safe to generalize, from this experiment, in regard to radiation from
large masses of smoky air.
COMPARISON OF SOME OF THE PRECEDING RESULTS WITH THOSE OF TYNDALL.
The experiment suggested by Professor Abbe in its simplest form (Prefatory note, pp. 1-2)
has been partly realized in Method D, with the exception of the unessential addition of a
background at the temperature of melting ice, and it has also been performed by Tyndall
(Contributions to Molecular Physics in the Domain of Radiant Heat, p. 42 et seq., American edition
of 1873.) As a method of heating an air jet, Professor Tyndall's placing of a hot copper ball within
a ring nozzle may have been efficient, but neither the temperature nor the mass of the air can be
accurately measured in this way. The results are therefore only qualitative. The deflection from
hot air being 0, that from carbon dioxide is given as 18 (p. 43 loc. cit.)', but this does not fully
express the facts. It is true that when air was turned on through the nozzle the deflection
did not increase, but hot air was already passing before the thermopile by simple convection.
We read further:
The radiation from air, it will be remembered, was neutralized by the large Leslie's cube, and hence attached
to it merely denotes that the propulsion of air from the gas holder through the Argand burner (or annular nozzle)
did not augment the eft'ect.
The 18 from carbon dioxide is therefore a differential effect, and requires the original deflec-
tion, without compensating cube, for its interpretation, but this is -nowhere stated.
The jet of heated gas in Tyndall's experiment was of relatively small thickness. With a
deeper layer the relative position of the two gases in question, as radiants, may be more nearly
equal, since, as I have shown, air radiation from layers increasing up to several feet in thickness,
varies nearly as the depth, while the radiation of carbon dioxide soon reaches a maximum.
Variations in the ratio of radiation with increasing depth are noteworthy in other gases, as
in Tyndall's Contributions (p. 97), where a layer of olefiant gas (C 2 H 4 ) having a depth of eleven
units, radiated 1.62; and one of air of the same depth, containing one-sixtieth of ether-vapor
(C2H 5 ) 2 O, radiated 5.82, the radiation from unit-depth of each gas being taken as unity.
The figures quoted above for radiation of air and carbon dioxide are of an indeterminate
ratio, but the absorption of 33 inches of carbon dioxide for radiation from a copper plate, "raised
to a temperature of about 270 C." (loc. cit., p. 72), is stated (loc. cit., p. 80) to be ninety times that of
air. Even if the radiations of large masses of air and carbon dioxide are equal at some specified
temperature, those of thin layers or jets must nevertheless be very unlike, the radiation from the
thin jet of air being much smaller than that from a carbon dioxide jet. Other temperatures may
yield different radiation-ratios for the two gases, while absorption varies at a still different rate.
Consequently, no safe inference as to radiation-ratios can be drawn from those for absorption.
76
This is shown by the following observations by Pascheu for the principal band in the spectrum of
carbon dioxide at 4.25/1 ( Wied. Ann., Bd. 51, S. 20, 1894):
TABLE 50.
Temperature of
7 cm. layer of CO 2 .
Intensity of
radiant emission.
Absorption by
hot + cold CO 2 .
C.
mm. div.
Per cent.
17
89
183
17.5
77.5
290
60
68.6
377
118.7
36.7
480
261
19
The absorption is that produced within the limits of the band on the spectral energy-curve of
blackened platinum at 400 to 500 C. The small remaining absorption band at the highest tem-
perature has a wave-length 0.17/< shorter than the corresponding emission band, and is due to cold
carbon dioxide in the air of the room, the radiation of the hot gas very nearly neutralizing the
absorption by the hot gas at 480.
On page 95 of the Contributions, Tyudall gives the ratio of apparent radiations from carbon
dioxide and air, dynamically heated by compression, as 3 : 1, and on page 186 deflections are given
whose ratio is 2:1. But these figures are not considered entirely trustworthy, since the radiation
measured is supposed to be, to an uncertain extent, that of the end plate and walls of the contain-
ing tube, heated by contact with the hot compressed gases; and any differences in the observed
radiation are to be attributed partly to the varying readiness with which heat is transferred by
conduction and convection from the gas to the solid, and partly to differences in the amounts of
heat produced by compression and transferred in this manner. Professor Tyndall, in pointing out
some of the defects of the arrangement, says :
A brass tube 3 feet long and very slightly tarnished within was iised for dynamic radiation. Dry air on
entering the tube produced a deflection of 12. The tube was then polished within and the experiment repeated;
the action of dry air was instantly reduced to 7 C .5. The rock-salt plate at the end of the tubs was then removed
and a lining of black paper 2 feet long was introduced. The tube was again closed, and the experiment of allowing
dry air to enter it repeated. The deflections observed in three successive experiments were 80, 81, 80 [correspond-
ing to a force nearly 70 times as great as the first]. * * A coating of lampblack within the tube produced the
same effect as the [black] paper lining; common writing paper was almost equally effective. (Loc. cit.,p. 187.)
Now, the paper, being a poor conductor, must acquire on its inner and radiative surface, by
direct contact with the dynamically heated gas, a higher temperature than the brass, in which
any gain of surface temperature is quickly distributed to deeper layers of metal; but the thin
coating of lampblack, backed by conducting metal, is in an intermediate position as a conductor,
and might be expected to take on its radiating surface a temperature at any rate lower than that
of the paper; yet both blackened paper and blackened brass are said to have behaved alike.
Tyndall's explanation that the deflection of 7.5 is mainly due to radiation from brass to which
heat from the compressed air has been transferred, can hardly be maintained without modification,
since blackened brass is not 70 times as good a radiator as bright brass, and no inconsiderable
part of the 7.5 may have been true air radiation. I shall return to this point subsequently
(p. 110) with fresh material for a more searching test of its truth.
The long tube in Tyndall's research was made of polished metal, and the thermopile was pro-
vided with its conical polished reflector, in order to secure the advantage of larger galvanometer
deflections, through multiple reflections at large angles of incidence on the inner walls of the tube
in those experiments where an independent source of radiation was situated at or beyond the
farther end of the tube. When such a tube is used for the dynamic heating of a gas, a large part
of the heat produced by gaseous compression is unquestionably transferred to the walls of the
tube; but since the mass of the gas and its thermal equivalent are small, while those of the tube
are at least several hundred times greater, the tube can not become much heated unless the process
is repeated a great many times. The large deflections from lampblack and paper are possibly
77
produced by a special condensation and development of heat in the pores of these substances.
The argument on page 186 of the Contributions, which makes a "residual deflection of 6" (after
absorption by an extra 13 inches of quiescent carbon dioxide) represent the radiation of polished
brass, does not appear to be conclusive, and, in fact, is put forth rather as a surmise.
Admitting the deflections to be of genuine gaseous origin, Tyudall's observations would make
a 3-foot layer of carbon dioxide radiate two or three times as much as air. In my experiments
the air apparently radiated twice as strongly as the carbon dioxide. In view of the very powerful
radiation from water-vapor, and of the difficulty with which this substance is completely elimi-
nated, it may be urged that my samples of air were not dry; but since greater precautions were
taken in drying the air than in drying the carbon dioxide, the latter being merely passed through
several flasks of porous calcium chloride, while the air, in some of my experiments, had stood for
a week in contact with phosphoric anhydride, I do not think that the larger radiation, where air
was used, can have proceeded from aqueous vapor in my samples. Only one of my air series gave
deflections as small as for carbon dioxide, and this I have had to discredit, owing to a deterioration
of the rock-salt plate.
Thus far we meet only uncertainty and discrepancy, but if the reader will have patience all
of this shall eventually be cleared away.
It is desirable to have a more careful analysis of TyndalFs experiment than is given in the
original memoir. Where the most distant part of the tube was set off as a radiant chamber by a
rock-salt partition the direct radiation of its contained gas or walls was received under a smaller
angular aperture and with proportionally smaller effect than where the partition was nearer to
the thermopile; but the concentration of the beam reflected from the polished cylindrical walls of
the tube was nearly the same in either case. The diameter of the tube is not stated. I will
assume it to have been 2.4 inches, as in another case, and the distance of the thermopile from the
nearer end of the tube to have been inches, and thus compute the angular areas of the sections
on these assumptions. The lengths and deflections in the following table are taken from Tyndall's
Table XXXV for carbon dioxide, and the radiant energies are deduced from the deflections by
the calibration of the galvanometer. (Contributions, p. 57.)
di is the distance in inches to the nearest section.
d. 2 = " " " " " " farthest "
l = d t f?i =the length of the radiating column.
a t = the angular area of the nearest section.
a z = " " " " ' farthest "
TABLE 51.
l
2
3 4
5
6
d t
52.6
40.0
19.1
6.0
6.0
6.0
d>
55.4
55.4
55.4
19.1
40.0
52.6
I
2.8
15.4
36.3
13.1
34.0
46.6
a\
7
12
32
511
511
511
2
6
6
6
52
12
7
(a,+fl. ; )-2
6.5
9
29
281.5
261.5
259
Deflection
1
3.7
16.8
17.5
23.3
33.6
Radiation
1
3.7
17.2
18.0
25.7
48.6
Between (4; and (5) there is an increase of 20.9 inches in the length of the radiating column,
and the radiation is greater by 7.7 units; but with a further addition of 12.6 inches to the leugth in
(6), the radiation gains 22.9 units, or three times as much as for the larger increment of length in
(5). Table XXXIY, for carbon monoxide, gives a very different relation for the same distances,
the increment of radiation in (5) being 10.4 units, and in (G) 6.0 units, numbers which are nearly
proportional to the gain in length. I have no hesitation in saying that the deflection from CO 2 in
(6) is a mistake. The 33.6 is possibly a misprint for 23.6, since, as I have shown, there is no
increase in the radiation of carbon dioxide beyond the third foot.
The deflection in (1) Table 51 is too small for use; but with a trifling addition to the radia-
78
tioiis in (4) and (5), reducing them to the lengths of (2) and '(3), we may make the following
comparison :
TABLE 52.
^tin^ column 1 " Kadiation c 2-
Ratio.
Mean angular
area.
Ratio.
Inches.
36
15
17-26
4-19
1:1.53
1:4.75
29-261
9-282
1:9
1:31
Ratio of ratios,
1:3.10
1:3.44
The changes seem to be mainly due to differences in the angular area, but this influences
principally the radiation which comes directly to the thermopile, and the total radiation from the
gas is made up approximately as follows:
Length. Reflected radiation. Direct radiation. Total.
15 inches } < 2 > ' 5 = 4 '
<(4) 3.5 +(0.5x31) =19.0
36 inches p) " = 17 '
<(5) 15.9 + (1.1x9) -^25.8
These radiations appear to be genuine, but there is no conclusive evidence that the radiation
of polished brass has contributed to them appreciably. The observations on air are not given in
detail, and we only know from page 186 that whereas the 3 foot layer of CO 2 gave a deflection of
16.8, dry air gave 8 or 9.
The temperatures of the gases are not so easily found. In general, the temperature of a gas
being the sum of the kinetic energies of its molecules, divided by their number, may be very differ-
ently constituted according as the limits of variation of molecular velocity are wide or narrow.
Eadiation and absorption within the gas need also to be considered. In the present case the radi-
ation has been measured in the midst of a complex series of operations, and we do not know even
approximately what proportion of the heab of compression has been ceded to the metal. Professor
Tyndall has attempted a thermometric measurement of the temperature of the dynamically heated
gas, which may be given for whatever it is worth. He ; 'had the tube perforated and delicate
thermometers screwed into it air-tight. On filling the tube the thermometric columns rose, on
exhausting it they sank, the range between the maximum and minimum amounting in the case of
air to 5 F." (loc. cit., p. 45). If the proportion of heat transferred to the walls is the same in the
two gases, we must conclude that at excesses of a few degrees carbon dioxide radiates more than
air; but the observation is open to the interpretation that the proportion of heat given to the
walls is not the same for either gas, and the precise ratio has still to be determined. Some varia-
tions in the ratio of gaseous radiations at different temperatures need not surprise us, since the
radiations are made up of bands of very different wave-lengths with various rates of increase by
change of temperature. Even solid bodies may have spectral energy-curves of quite different
shape, as I have shown in a comparison of the spectra of the Welsbach light and of the illumi-
nating gas flame of an Argand burner. ("Further considerations in regard to laws of radiation."
Astrophysical Journal, vol. 4, p. 45, June 1806). The relative radiations of particular wave-lengths
for these lights vary nearly as 1 to 4 in different parts of the spectrum, the spectral energy-curves
crossing and recrossing, and much wider ranges occur in gases where each baud has a law of its
own. Before arriving at a more definite conclusion a further study of the relation between
gaseous radiation and absorption must be made.
MODIFICATION OP ATMOSPHERIC RADIATION BY THE ABSORPTION OP CONSTITUENT
GASES AND VAPORS.
Having made a preliminary clearing of some of the sources of error incidental to the appara-
tus, the method of observation, and the properties of matter, we are now prepared to take up a
very important subject the modification of radiation from gases or solids by gaseous absorption.
79
Gaseous radiation and absorption are so intricately interwoven that one can not be explained
without also considering the other. Observations of gaseous absorption exist in great abundance,
but those on gaseous radiation are comparatively few. It is largely in consequence of this one-
sided distribution of evidence that so many questions in this department remain open, and that
others which have really been settled for a long time do not obtain recognition or are reopened on
insufficient grounds.
The chief absorbent of the Earth's atmosphere is water-vapor, but its action is complicated by
the relation between vapor and mist. Even considerable changes in atmospheric aqueous vapor
in warm weather, if unattended by misty condensation, produce only slight variation in the direct
rays of the midday sun, not, however, because water- vapor does not exercise a great absorption,
even on solar rays, but because so much moisture is always present in warm weather that nearly all
of the rays absorbable by aqueous vapor have been eliminated, and the remaining radiation is
comparatively transmissible. Haze, however, of whatever description, whether formed of mineral
particles, smoke, or finely divided liquid or solid water, acts at all seasons, and independently of
the amount of the vapor of water dissolved in the air. Mist and haze have little effect on the
emission of radiations of long wave length from air by virtue of its own temperature, or on the
transmission of long ether- waves by the atmosphere, but they have great influence in stopping and
scattering those short ether- waves which are especially prominent in sunlight.
Ferrel says (Recent Advances in Meteorology, p. 56, fl 43, 1886) < the difference in the intensity
of the solar rays at the earth's surface at sea level, when the atmosphere is very clear and when it
is somewhat hazy, is small, and therefore the whole diminution of intensity in passing through is
due mostly to the pure atmosphere;" but this is not correct. The direct rays of the sun are much
impeded by haze, but are nevertheless nearly as effectual in warming the earth's surface indirectly,
because a large part of the rays scattered by the haze still reaches the earth as sky radiation,
which bears an increasingly large proportion to the direct solar rays as haze grows denser. In a
general way, this influence of the scattering of light by fine particles is recognized by Ferrel on
page 59 of the same work, but its application to the point noted on page 56 escaped his attention.
Other inconsistencies occur in the same connection. Thus, on page 59, we read : " It is thought
that pure dry air absorbs very little of the sun's [radiant] heat in its passage through to the earth.
If so, the loss of intensity must be caused mostly, in this case at least, by the irregular reflections in
all directions." But at the end of the same paragraph it is said that these reflections " depend very
much in some way upon the vapor contained in [the clear atmosphere] where it exists. But as this
is found mostly in the lower strata near the earth's surface, and only in a small measure in the
middle and upper strata of the atmosphere, its effect is small in comparison with that of the whole
depth of a dry atmosphere." The only idea which I can derive from the passages which I have
italicized is that pure, dry air influences the sun's radiation very little, and mainly by irregular
reflection, while water vapor is even less effective. The last inference is further emphasized in
paragraph 44, page 56: "According to the experiments of Dr. Tyudall on the diathermancy of a
small portion of air contained in a tube, with regard to heat radiations from terrestrial sources
the diathermancy of clear air depends almost entirely upon the aqueous, invisible vapor in it, sev-
enty times as much heat, according to the result of the experiments, being absorbed by it as by the
dry air through which the rays pass. This result, however, differs very much from that which had
been obtained by Magnus in experiments on the same subject, and this gave rise to considerable
discussion between these physicists, Magnus maintaining that the absorption of heat in Tyndall's
experiments was by a film of condensed vapor on the inside of the tube through which the rays
passed. And this seems really to have been the case, according to experiments which have since
been made to verify the results." Nevertheless the opinion is repeatedly expressed elsewhere (as
on page 57 loc. cit.) "that aqueous vapor in some way diminishes the diathermancy of the atmos-
phere to terrestrial heat radiation." The only inference which I can draw is that the entire subject
was in a state of hopeless confusion in the mind of one who has elsewhere exhibited extraordinary
keenness of intellectual perception. The authority of so great a master as Ferrel perhaps has
something to do with the fact that the subject still remains obscure. Most of the errors have
been repeatedly refuted, but the refutations fail to attract attention.
80
The fallacy of Magnus, wno asserte^ that he got an aosorptiou of 14.75 per cent, from dry air,*
where Tyndall found practically none, has been abundantly exposed. Tyndall showed that the
glass plates which Magnus used to close his glass vacuum tube must have been heated by
absorption of the radiation which passed through them, acting thus as secondary sources of radia-
tion, and that, being chilled by convection, their thermal effect was diminished on admission of
dry air. Tyndall used end plates of the feeble absorbent, rock-salt, whose thermal change was
relatively small, and this prevented the error in question in his measures. With the glass plates
used by Magnus the absorption of so potent a substance as aqueous vapor, being greatly masked
or reduced by the nontransmissiou of radiation by glass in that region where aqueous absorption
is chiefly exercised, was further completely overwhelmed by convection, and remained undetected
from these causes, combined with lack of sensitiveness in the measuring apparatus.
On the other hand, Tyndall does not completely meet the criticism that a portion of the
absorption attributed by him to aqueous vapor may have been due to a very thin film of liquid
water condensed on the metallic reflecting surface of his tube, but contents himself with showing
that substantially the same relative absorptions were obtained when blackened tubes were used,
and finally with tubes so wide that the radiant beam concentrated by a rock-salt lens did not
touch the walls, so that condensation could not have had any material influence on the result.
(Contributions, etc., p. 394.) Magnus, in instituting his criticism, overdid the matter, claiming
that all of the absorption, measured by Tyudall and attributed by him to aqueous vapor, was due
to the liquid film. Lecher and Pernter (Sitzb. der A: Akad. der Wissensch. zu Wien, July, 1880;
Phil. May., (5) Vol. 11, p. 1, Jan., 1881) in repeating the charge have overlooked the experiment
with the rock-salt lens. The claims so far made rest upon mere assertion, but the following
considerations, based on internal evidence drawn from the experiments as published, indicate that
further elucidation is desirable.
It is to be remembered that in his earlier measures, owing to the iusensitiveness of his heat-
measuring apparatus, Tyndall used a wide-angled conical reflector to concentrate the rays upon
his thermopile, and transmitted the radiant beam through polished tubes in order that radiation,
proceeding from the source under a wide angle, might be fully utilized by multiple reflections. Of
course the mean path. of the rays was somewhat longer than the tube.
Professor Tyndall makes the following statement:
The absorption is exerted wlien only a small fraction of an atmosphere is introduced into the tube, and it is
proportional to the quantity of air present. This is shown by the following table, which gives the absorption, by
humid air, at tensions varying from 5 to 30 inches of mercury :
HUMID AIR.
Absorption.
U.6DS1OU.
Observed.
Calculated.
Inches.
5
16
16
10
32
32
15
49
48
20
64
64
25
82
80
30
98
96
"The numerical value depends entirely upon the disposition of the apparatus, and has no connection with the
absorption of air. Thus, Dr. Franz, by using a 3-foot tube lined with black paper, which cut off internal reflection
and diminished the heating of the glass end plates, had obtained an apparent absorption of 3.54 per cent, for dry air,
and Magnus, with a nearly similar tube 1 meter long, got 2.46 per cent., concerning which Tyndall says : " Professor
Magnus himself finds that the quantity of [radiant] heat transmitted through his unblackeued tube is 26 times that
which passes through his blackened one where the oblique radiation is cut off. In the case therefore of the naked
tube, the flux of [radiant] heat sent down by the heated glass plate adjacent to the lamp, to its fellow at the other
end, and likewise the [radiant] heat sent directly from the lamp to the same plate are greatly superior to what they
are in the case of the blackened tube. The plate adjacent to the pile becomes therefore more highly heated, and as
its chilling is approximately proportionate to the difference of temperature between it and the cold air, the with-
drawal of heat will be greatest when the tube is unblackened within. * It is, I submit, not a case of
absorption, but of direct chilling by the cold air." (Contributions to Molec. Plnjs., pp. 419-420.)
81
The third column of this table IB calculated on the assumption that the absorption is proportional to the quantity of
vapor in the tube, and the agreement of the calculated and observed results show this to be the case, within the
limits of the experiment. It can not be supposed that effects so regular as these, and agreeing so completely with
those obtained with small quantities of other vapors, and even with small quantities of the permanent gases,
can be due to the condensation of the vapor on the interior surface. When, moreover, 5 inches of air were in the
tube, less than one-sixth of the vapor necessary to saturate the space was present. The dryest day would make no
approach to this dryness. Condensation under these circumstances is impossible, and more especially a condensa-
tion which should destroy, by its action upon the inner reflector quantities of [radiant] heat so accurately pro-
portional to the quantities of matter present. (Heat Considered as a Mode of Motion, Am. Ed., pp. 405-406, 1869.)
In this quotation the air is said to have been humid, and yet, when reduced to a pressure of
one-sixth of an atmosphere, to have contained "less than one-sixth of the vapor necessary to
saturate the space." But if the air was anywhere near saturation at the ordinary pressure,
it must have been supersaturated when reduced to a pressure of 5 inches, a fact which was per-
fectly well known to Tyndall, since he has described it on page 46 of the same work. I can only
reconcile these statements by supposing that either Tyndall inadvertently overlooked the increase
of relative humidity in air at reduced pressure, when writing this passage, or else that the descrip-
tion of the air as "humid" is very misleading; and I submit that the case is not quite so axio-
matic as its author maintained, and that precipitation of liquid water on the inner walls of the
tube at low pressures, if we take the first horn of the dilemma, may have diminished the reflecting
power of the polished walls, while the lessening of the vapor contents at the same time would
render the air more transmissive, giving a certain degree of compensation which is not incompat-
ible with an increment of vaporous absorption by no means proportional to the air pressure.
On page 404 (Heat as a Mode of Motion) we read :
The air of the laboratory was dried and purified until its absorption fell below unity ; this purified air was
then led through a U-tube filled with fragments of perfectly clean glass moistened with distilled water. Its neu-
trality, when dry, showed that all prejudicial substances had been removed from it and in passing through the
U-tube it could take up nothing but the pure vapor of water. The vapor thus carried into the experimental tube
produced an action ninety times greater than that of the air which carried it.
Tyndall has pointed out (Contributions, p. 387) that merely letting dry air bubble through cold
water is not a perfect means of moistening it, but passage through U-tubes filled with wet glass
is an effectual method of producing saturated air. The moistening described on page 404, Heat as
a Mode of Motion, is not explicitly stated to apply to the conditions of the experiments with
"humid" air on page 405; but in the Contributions (p. 411) it is stated the amount of aqueous
vapor capable of being taken up by air at a temperature of 15 C., produced an absorbtion forty
times that of air; and again (p. 412), we read : "It is with this common outer air, and not with air
artificially saturated with moisture that I find the absorption of aqueous vapor to be fifty or sixty
times that of the air in which it is diffused." Numerical values depend upon absolute quantities
of vapor and these upon temperatures and concomitant details which are provokingly infrequent
in TyndalPs memoirs, but from these supplementary statements one would infer that the humid
air which gave an absorption of 98 in the table already quoted, must have been very nearly
saturated, and that the measures at low pressures are open to criticism. Since, however, the
experiments of Aitken show that air which is free from dust may be supersaturated without
precipitation, I do not mean to assert that the precipitation did necessarily occur.
Abandoning tubes, Tyndall tried the method of displacing the free air between a cube of
boiling water and the thermopile, alternately by air dried by fresh chloride of calcium and by air
moistened by passing through a cylinder filled with fragments of quartz moistened with distilled
water (Heat as a Mode of Motion, p. 407), obtaining a differential deflection of about 15, corre-
sponding (by p. 403, loc. cit.)-to an aqueous absorption of about 2 percent. (Temperature not
mentioned.)
Hoorweg (Pogg. Ann., Bd. 155, S. 385-402, 1875) repeated this experiment. No difference as
great as 0.2" per cent, could be found at first between the absorption of dry and moist air, as
exercised upon radiation from a Leslie's tube. The transverse dimensions of the air blast are
not explicitely stated, but probably the air issued from a narrow jet. He then repeated the
experiment with a moistener 50 cm. long and 9 cm. broad, obtaining for the absorption of moist
air 1.7 per cent, (temperature 9 C.); and finally with a moistener 100 cm. long and 9 cm. broad,
the source being a black copper plate heated by a Bunsen burner, he obtained, with an air
12812 Bull. G 6
82
temperature of 7.5 C., an absorption of 2 per cent, by moist air, which might perhaps be doubled
by substituting a source at 100 C.
I fail to see the cogency of some of the remarks in this paper. The final conclusion in regard
to aqueous absorption is stated by this author as follows :
From this I believe that 100 meters of ordinary air are still not by a long way in condition to produce the
results which Tyndall already obtained from 10 feet, namely that 10 per cent, of the entering rays would be
absorbed.
In regard to this statement, I can only say that its truth or falsity depends upon what is to
be understood by "ordinary air." The temperature and humidity of what would commonly
be considered as ordinary air vary so widely with the locality and the season, that without
numerical definition of water contents such an assertion is too loose to be of any value. Tyndall's
statement,* criticized in this passage, is drawn up in the same undefined way and is equally
devoid of meaning, unless interpreted by other passages.
Dr. H. Buff (Pogg. Ann., Bd. 158, S. 177-213,1876) used an apparatus patterned after that
of Magnus (Pogg. Ann., Bd. 112, S. 531; Phil Mag. (4), vol. 22, p. 85, 1S61), but with a few altera-
tions which Dr. Buff considered improvements. In fact, results were obtained which differed from
those of Magnus, and indicated the source of some of his errors which had already been explained
by Tyndall. Dr. Buff, however, appeared to think that he had overcome these errors, whereas it
is evident that the method as conducted by both Magnus and Buff is unsound.
Instead of the glass-walled vessel to hold hot water which was used by Magnus, Buff had a
vessel of sheet brass, polished on the bottom, and radiating downward upon a thermopile. Double
side walls, stuffed with cotton wool, prevented rapid cooling. The metal vessel rested air-tight on
a, glass cylinder 20 cm. high and 7.5 cm. wide, which, in turn, was made air-tight on the plate of
an air-pump. The thermopile of iron and germau-silver wire, beaten out to a breadth of 12.5 mm.
and soldered, was 23 mm. below the heating surface. In the first experiments the air was dried
by passing it slowly through a 40-cin. tube of fused chloride of calcium. It is evident that the
heating effect observed was a complex of convection, conduction, and radiation from a variety of
sources. The maximum deflection, which was attained after a lapse of fourteen to twenty-two
minutes, was due mainly to slow heating of the glass cylinder by conduction, and to the convec-
tion and radiation started by the resulting disposition of heated walls. The effect continued for
thirty minutes, although the temperature of the hot water meanwhile had fallen continuously.
Dr. Buff having obtained, as he imagined, a transmission of 47.7 per cent, from 4.5 cm. of dry
air, next increased his layer of air to 10 cm. The results were not such as tp meet his expecta-
tions. "The absorptive power of air, instead of proportionately increasing, as I had supposed,"
he says, "seemed to decrease from the 50 per cent, previously observed to 20 and even 15 per
cent." Yet notwithstanding this most improbable result, his confidence in the accuracy of his
method and its interpretation (which differed in no important respect from that of Magnus)
remained unshaken, while Tyndall's was branded as "unreliable," and these measures of Magnus
and Buff have been repeatedly quoted as authoritative, in spite of their complete overthrow by
Tyndall.
Blackening the bottom of Buff's brass vessel containing the hot water increased the deflec-
tions "but feebly, though the radiating power of the source of heat must have been G or 7 times
greater than previously ;" a result which proves that only a minute part of the observed effect can
have been due to the radiation of the blackened brass, and which consequently demonstrates that
the large variations observed were at any rate not due to absorption of radiation by the inclosed
gases.
Only one other point in this paper requires mention, namely, the assertion that a plate of
rock-salt, 0.3 cm. thick, absorbs 40 per cent, of the radiation from a vessel of hot water, and that
* "Eegarding the earth as a source of heat no doubt at least 10 per cent, of its [radiant] heat is intercepted
within 10 feet of the surface." (Heat as a Mode of Motion, p. 404.) It is to be borne in mind that this refers espe-
cially to radiation from a surface which is commonly moist and that such radiation through nearly saturated surface
layers of air may be especially obstructed by aqueous vapor. (See Contributions, p. 395, and this bulletin, p. 90
to 106.1
83
the therinoclirose of rock-salt and dry air are similar,* Buff maintaining that Tyndall found no
absorption by air because bis rock-salt plates bad already sifted out the rays for \vhich air is
opaque. Pi-ofessor Tyndall, in bis reply (Proc. Royal Soc. London, vol. 30, p. 10, Dec., 1879),
points out that be bad already (see Heat as a Node of Motion, p. 399) tried the experiment of
bringing the naked face of his thermopile "within one-twentieth of an inch of [the] terminal plate
of rock-salt. There was not the slightest alteration of the previously obtained result. Dry air, as
before, behaved like a vacuum." The course of the radiation was here through a succession of
vacuum, salt, vacuum (or dry air at pleasure), salt, and one twentieth inch of normal air to the
pile. There was little probability that so thin a layer of air as one-twentieth inch could sift out
and totally remove any appreciable amount of a special class of rays; and Melloni's measurement,
which made the transmission of a plate of rock-salt, 0.26 cm. thick, as great as 92.3 per cent, of the
total radiation, almost all of the loss being due, not to absorption, but to nonselective surface
reflection, might well have been deemed sufficient to prove the fallacy of Buff's suggestion that a
few cm. of air or a small fraction of a cm. of rock-salt can totally remove a large percentage of
the radiation; but to put the matter beyond all possible doubt, Tyndall constructed a new appa-
ratus (loc. cit., fig 1, p. 16) placing the thermopile in a chamber filled with hydrogen, protecting
against hydrogen convection currents and radiation from side walls by diaphragms, and intro-
ducing a central variable chamber containing dry air, in which the thickness of the air layer could
be varied from zero, when the inclosing rock-salt plates were in contact, to 3 inches, "which
exceeds by more than 50 per cent, the thickness of the layer to which Professor Buff ascribes ail
absorption of 50 or 60 per cent." "Repeated experiments with this apparatus proved the absorp-
tion of the layer of dry air in the chamber to be nil."
The supposition of an identical absorption by rock-salt and air was then tested by comparing
the transmission of a thick plate of rock-salt in vacuum with its transmission in air. There was no
sensible difference. There is consequently no similarity in the therrnocbrose of air and rock-salt.
Finally, Tyndall shows that Buff's method, although defective "even when every care is
bestowed upon it," may be improved. "A glass cylinder, 12 inches long and 2f inches in diameter,
is mounted on the plate of an air-pump. On it is placed a tin vessel with a brass bottom, intended
to contain the water which warms the bottom or source of heat. A thermopile is mounted on the
air-pump plate on which the cylinder stands, one of its faces being presented to the bottom of the
tin vessel. The conical reflector is abandoned, a piece of tubing, blackened within, aud intended
to cut off the radiation from the sides of the vessel, being pushed over the pile. Instead of bring-
ing brass and glass into direct contact, as in the apparatus of Professor Buff, a washer of non-
conducting india rubber, an inch and an eighth in thickness, separates the one from the other.
There is no chilling by cold water, and the distance of the pile from the source renders it difficult
for heat to pass by convection from the one to the other." With this apparatus, instead of finding
olefiant gas more diatherinaut than air, as Buff had done, Tyudall obtained an absorption of 33
per cent, from a depth of 11 inches of olefiaut gas, while air and hydrogen did not differ appreci-
ably from a vacuum in their readiness of transmission. The results agree with Tyndall's earlier
measures obtained by other methods.
It might be supposed that such a complete exposure of the fallacy of Magnus' method, both
in its original form and as modified by Professor Buff, would forever settle the questions at issue;
and that Buff's further statement that be, like Magnus, found no difference between the absorp-
tion of dry aud moist air would be taken for what it is worth, namely, nothing at all; but such
statements as those quoted from Ferrel, made six years after this crushing rejoinder, show that
old errors die bard.
Prof. W. M. Davis, in his Elementary Meteorology (p. 145, Boston, 1894), says:
The action of water vapor on insolation and terrestrial radiation has been much discussed. Some have regarded
it as diathermanous to insolation, but relatively opaque to terrestrial radiation, and have therefore attributed to it
a controlling influence in determining the temperature of the atmosphere. More careful experiments have, however,
shown that water in the truly vaporous state is as diathermanous as pure dry air to terrestrial radiation; and that
it is only water in the liquid state that exerts a strong control over radiation from the earth. This appears to be
confirmed by observations on the diurnal range of temperature under varying conditions of humidity. If the
* It will be shown subsequently (p. 114) that there is an analogy between the radiant powers of rock-salt and
dry air, but not identity.
84
temperature of the air is well above saturation, the range is relatively strong; if near saturation, the range is
diminished, even though no visible clouding of the sky occurs; if a thin hazy cloud is formed, the range is greatly
reduced.
The experiments which have been interpreted in favor of the diathermancy of water-vapor
have been refuted long ago, and Professor Davis, since the publication of his book, has given
evidence that he no longer adheres to the erroneous doctrine there enunciated. (See his "Absorp-
tion of Terrestrial Kadiation by the Atmosphere," Science, N. S. Vol. 2, p. 485, Oct. 11, 1895.)
The diminution of the daily range of temperature with a clear sky, as saturation approaches, is to
be attributed partly to a change in the quality of aqueous absorption, but also to the increase of
water- vapor and its ascent to exceptional heights in the atmosphere in considerable quantity,
whereby the escape of surface radiation is impeded by the strong aqueous absorption of the infra-
red rays, especially for those between 5/< and 8/<, not far from the point where the maximum energy
in the radiation from bodies at ordinary temperatures resides. The presence of large masses of
water-vapor in the upper air may not always be indicated by high relative humidity at the sur-
face, any more than by clouds, but it is evidenced by the strengthening of the rain-band, as seen
in the spectroscope, as well as by the diminution of the diurnal range of temperature; and after
heavy rainfall has depleted the upper air of moisture, the direct rays of the sun are intensified,
and to a still greater degree the loss of heat by radiation from the earth's surface, so that the
change of temperature between day and night reaches its greatest value, and at the same time
the rain-band fades out, showing that it is the withdrawal of the invisible veil of water-vapor
which has increased both radiation and daily range. The statement on page 32 of Professor
Davis' book that "water vapor is, like clear air, a poor absorber of nearly all kinds of waves,"
and the doubt which is cast upon the theory that the atmosphere is a trap which allows solar rays
to enter more freely than surface rays are permitted to escape, are both overthrown by the expert-
mental demonstration of the efficacy of aqueous vapor as an absorbent of infra-red rays.
Prof. Thomas Preston in his Theory of Heat (p. 485, London, 1894) says in introducing the
experiments of Lecher and Pernter (published in 1880) : "But these new investigations, instead of
settling the question in dispute between Tyudall and Magnus as to the comparative absorptions
of dry and morst air, place the whole matter in a state of greater uncertainty. For whereas Tyn-
dall found an exceedingly low absorption for dry and a high absorption for moist air, while Mag-
nus found the same absorption for both, and that tolerably high, the results of the experiments of
Lecher and Pernter show practically no absorption for either; or, in other words, both dry and
moist air act as a vacuum toward radiant heat." These and numerous other less explicit state-
ments in current scientific literature show that even down to the present day the question of the
action of aqueous vapor upon telluric radiation is still regarded by many as an open one.
I proceed to the discussion of the last-named observations, which contain some puzzling but
not inexplicable features. Lecher and Pernter (Sitzb. tier A;. AJcad der Wiss. zu Wien, July, 1880;
Phil. Mag. (5), vol. 11, p. 1, Jan., 1881) by substituting a thin horizontal plate of lampblacked
copper brought suddenly to 100 C. by a jet of steam, in place of the arched dome of glass heated
by hot water in the original apparatus of Magnus, succeeded in shortening the time of exposure
and diminishing the convection until they were able to confirm Tyndall's observation of the sen-
sibly perfect transmission of radiation by dry air. But with a layer of 31 cm. of air they could
detect no difference between the absorption of moist air and dry. Magnus' galvanometer and
thermopile were too insensitive to measure this difference, even if his arrangement had been free
from its other defects ; but Lecher and Pernter's instruments apparently had the requisite delicacy,
and we must seek elsewhere for the cause of their failure.
The face of the thermopile was covered with lampblack, which is very hygroscopic, "and like-
wise the bottom of the radiating vessel. Whenever this was heated in moist air and in a closed
vessel, moisture was driven off from the coating of the radiator and probably deposited to a suffi-
cient extent upon the blackened thermopile to largely compensate by the development of latent
heat for the slight diminution of radiation by only a few inches of moist air, while the radiation of
the hot vapor (diminished by aqueous absorption) was added to that of hot metal. The short time
of exposure (90 sec.) diminished the influence of convection currents, but favored the inclusion of
a transitory phenomenon, like the evaporation of hygroscopically imbibed moisture.
The importance which has been attributed' to the observation makes it desirable to analyze it
85
somewhat critically. Comparing measurements of the absorption of various gases and vapors by
Lecher and Pernter with those made on the same substances by Tyndall, it will be seen that the
differences between their results for the absorption exercised on the radiation from a blackened
metal plate at 100 C. are too large to be neglected, and in the case of vapors the discrepancies
are excessive, as the following table shows :
TABLE 53.
Lecher and Pernter.
Tyndall.
Length.
Pressure. Absorption.
t.
Length.
Pressure.
Absorption.
t.
(t)
|
CHI.
mm.
cm.
mm.
Chloroform, CHC1 3
Ether, (C 2 H 6 )jO
31
31
70
13
0.0050
0. 0504
'" -
126
126
13
13
* 0. 216
* 0.541
Source
( inno
Benzole, C ri H 6
31
42
0.0619
g = 126
13
* 0. 345
Ethylene, C>H 4
Carbon monoxide, CO
31
31
751
744
0. 4826
0. 0660
s'ol ' 5
762
762
1 0. 328
1 0. 068
[Source
1 270
0.551
0.076
Carbon dioxide, CO 2
31
748
0. 0810
g 5 762
1 0. 076
0.094
* Heat as a jlode of Motion, p. 441. (Conditions described p. 431.)
t Contributions to molecular Physics, p. 170.
* Temperature of source 100 C. Masses of gas equivalent to those in the experiments of Lecher and Pernter.
To account for their discrepancies Professors Lecher and Pernter refer to observations of Beg-
nault (Mem. de VAcad. JV., t. 26). "Regnault has observed that the tension of vapors is less in
vacuum than in a space filled with air, and he explains this as the result of condensation on the
walls. This causes a diminution of the vapor tension, so that while in a vacuum compensation is
instantly made by the liquid, in a space filled with air this requires time, and the full vapor
tension is never reached."* How, in the cases cited Tyndall employed an exhausted tube, into
which his vapors were allowed to expand from a sample tube connected with a vapor flask, the
vaporization being made "without the slightest ebullition" (Contributions to Molec. Phys., p. 179),
but since there were no special precautions to keep all parts of the vapor chambers at the same tem-
perature, it is conceivable that, on the opening of the vapor flask into the sample tube, a portion of
vapor condensed on the walls of the latter, and subsequently, when the lower valve was closed
and the upper opened, this condensed liquid evaporated into the absorption tube. Thus there
may have been a larger quantity of vapor present in the absorption tube than might have been
expected from the temperature of evaporation. In this way we may explain the fact, commented
on by Lecher and Peruter, that the pressure in the vapor flask, computed from Tyndall's data,
* This statement hardly expresses the facts of the original observations which are contained in Me"moires de
1'J.cadernie des Sciences de I'Institut Imperial de France, t. 26, p. 700, Paris, 1862. Regnault found that the density
of aqueous vapor, relatively to that of air, increases as the saturation point is approached.
Relative hu-
midity.
Relative den-
sity of aque-
ous vapor.
Relative hu-
midity.
Relative den-
sity of aque-
ous vapor.
Per cent.
Per cent.
100
0. 64693
87.0
0. 62499
96.4
0. 63849
73.3
0. 62140
96.4
0. 62786
30.2
0. 62078
Regnault himself says (p. 701) : " The experiments which have been made at temperatures very near those of
saturation give densities larger [than the theoretic density], and the difference is so much the greater as we
approach nearer saturation. I conclude from this that the density of the vapor of water, in the vacuum and under
feeble pressures, may be calculated after the law of Mariotte and according to the theoretic density, provided the
fraction of saturation does not surpass 0.8, but that this density increases notably toward the state of saturation.
This last circumstance may be due to two causes : either the vapor of water experiences, really, an abnormal con-
densation on approaching the state of saturation, or else a part of the water remains condensed upon the glass
walls and only takes the gaseous state when the interior vapor is far from saturation."
Lecher and Pernter ignore Regnault's first explanation that aqueous vapor becomes abnormally condensed on
approaching the point of saturation, but it will be shown subsequently that this condensation is a fact.
86
approaches the boiling point of the volatile liquid in several instances, whereas the experiments
were actually conducted at a much lower temperature. But, admitting the truth of this part of
the criticism and the uncertainty of the vapor densities computed from the relative volumes of
sample and absorption tubes, the argument does not apply to experiments (such as those quoted
in Table 53) in which the vapor pressures, measured by a manometer, fell far short of those for
saturation at the presumed temperature. Tyndall is, unfortunately, very seldom explicit in
describing his conditions of experiment, but it may be inferred from some of his statements that
the temperature of his apparatus was in general that of the apartment, and not far from 15 C.,
at which temperature, and under complete absence of air, it is improbable that there can have
been any appreciable liquid films condensed from the vapors in question. Moreover, the point
can be subjected to a much more severe test.
Tyndall, in his Contributions (p. 171), gives a series of measurements in which not the vapor
pressure, but the thickness of a layer of air saturated with ether- vapor, was varied. Here, if the
absorption had been due to a film of liquid ether condensed on the rock-salt plates, the mere vari-
ation in the distance between these plates could have had no effect upon the transmitted radiation.
In the next table Tyndall's results are given in comparison with a series by Lecher and Pernter, in
which, however, it is the pressure of the ether- vapor which has been varied. Whether it is per-
missible to make comparison under these circumstances will be considered presently. The
temperature in Lecher and Pernter's experiment was 7.4 C., which fixes the pressure attainable
at the upper limit at a figure probably lower than Tyndall's; but since Tyndall's greatest depth of
air and saturated ether- vapor was only one-sixth of that used by Lecher and Pernter, the latter
ought still to have had the greater absorption; nevertheless, according to their determination, the
absorption was actually less. In Table 51, Zis the length of the absorbent column, p is the pres-
sure of the ether- vapor, t is the fraction of radiation from a lampblack surface transmitted by the
ethyl ether, x is the exponential coefficient of transmission in the formula,
t = e~ mx
where e is the Naperian base, and m is the mass of absorbent vapor in a column of unit section.
Without further data no absolute comparison is possible, but since m is proportional to 7p, and I
in the one case is constant and equal to 31 cm., p being constant in the other case, and probably
about 35 cm., or nearly the same, p and I may be taken respectively in place of m in a preliminary
computation of a multiple, nx, differing only slightly from x.
TABLE 54. Ether-vapor.
Tyndall.
Lecher and Pernter.
I
P IP
t
nx for 1 cm. I
I
f
lp
t
nxtorlna.p
em.
cm.
cm.
cm.
0.127
35 ?
4.45
0.979
0. 1672
31
1.28
39.68
0. 9496
0. 0404
0.254
35 ?
8:89
0.954
0. 1854
31 4. 12
127. 72
0. 8737
0. 0328
0.508
35?
17.78
0.913
0. 1792
31
7.86
243. 66
0. 7794
0. 0317
1. 016
35 ?
35. 56
0.857
0. 1519
31
12.52
388.12
0. 6924
0. 0294
2.032
35 ?
71.12
0.790
0. 1160
31
23.33
723. 23
0. 5859
0. 0229
3.810
35 ?
133. 35
0. 654
0. 1115
5.080
35 ?
177. 80
0.649
0. 0851
For equal masses of ether- vapor the absorption and the exponential coefficient are consider-
ably larger in Tyndall's series than in that of Lecher and Peruter; but in both the value of x
increases as the absorbent mass diminishes,* and in nearly the same ratio, Tyudall's rate being
slightly the greater. Thus, Tyndall's measures show that with a variation of the mass in the
ratio, 1:20.00, there is a change in x in the ratio, 1:0.4590, while Lecher and Pernter, for a mass
change in the ratio, 1:18.23, have a variation of x in the ratio 1:0.5673. From the result of this
test, I think it can not be denied that the absorption by a vapor measured by Tyndall is genuine.
Lecher and Pernter have also been measuring an effect which depends on the amount of vapor
* Lecher and Pernter say: " x always becomes smaller as the thickness of the layer becomes smaller/'' which is
obviously erroneous.
87
present, and where their results deviate from those of Tyndall it is owing to the defects of their
method. It seems to me that the capacity of lampblack for condensing vapors to the liquid state,
and absorbing them in its pores, is partly* responsible for the apparent inactivity of aqueous
vapor in Lecher and Pernter's experiments by the compensation already explained; and it is note-
worthy that their deviations from Tyudall are greatest in the case of the more condensible vapors,
while for the permanent gases there is approximate agreement, especially if the comparison be
made between the absorption of equal masses t exercised on radiation from the same source.
This has been done in the last column of Table 53 for the three permanent gases by interpolating
values, for a pressure of 7.~> inches of mercury, from Tyndall's Contributions to Molecular Physics,
Table XX, p. 37, for COj, and Table I, p. 22, for C 2 H 4 , assuming that the total radiation is repre-
sented by the mean of the values on pages 18 and 19, or 334 units.f The figures for CO are
obtained in the same way from Table XIX, p. 30. The pressure selected is such as to give an
absorbent mass nearly identical with that of Lecher and Pernter. The result indicates that,
where the physical state remains unchanged, it is permissible to compare the effects of equivalent
masses even under diverse conditions of pressure or, in other words, it is the number of molecules
encountered in passing through a given gas which determines the absorption of radiation.
From certain discrepancies in the relative positions of absorbent vapors in Tyndall's lists
Lecher and Peruter deduce a variation of some 30 per cent, between the results from black and
from polished tubes, and conclude that the unconformities which Tyndall attributed to impurities
in his substances are really due to the variable proportion in which the transmission through a
film of liquid adhering to the walls and the direct transmission through vapor enter into the
results, according as a reflecting or a nonreflecting tube is employed. The criticism, however, is
hardly conclusive, especially since they found their remarks on some of Tyndall's earlier measures
in which the probable error of observation was large.
Finally, while themselves recognizing that transmission must be expressed by an exponential
formula,
t = e - mx
in which, unless the radiation be homogeneous, x varies as a complex function of m (the absorbent
mass), any constant exponential coefficient being inapplicable to cases of absorption where par-
ticular rays are constantly dropping out, because totally extinguished, the authors fail to apply
their knowledge where it is peculiarly needed, namely, in treating Yiolle's comparison of solar
radiation at the top and bottom of Mount Blanc. They rightly conclude that the absorption of
16 per cent, exercised on the solar rays by a layer equivalent to 2,428 meters of air at normal
pressure, and having a pressure of water- vapor of 5.3 mm. at the bottom, must have been largely
due to the aqueous absorption; but, applying an erroneous formula, they then deduce a mean
* It is evident that if the explanation given here is correct the numerical result must also depend in part upon
the dimensions of the apparatus.
t Tyndall (Heat as a Mode of Motion, p. 433-435) has given an argument which proves that equivalent absorb-
ing masses must be used, if the relative absorptions of dift'erent liquids and vapors are to be compared.
tFrom the explanation of the calibration of the galvanometer (pp. 17-19), and from the values juxtaposed in
Tyndall's Tables I, III, and elsewhere, it is evident that the quantities labeled " absorption per 100 " are not per-
centages, but absorptions stated in terms of forces, corresponding to galvanometer deflections, as read from a curve
of calibration.
$ The values for the interpolation curve, in the case of carbon dioxide (4-foot layer, temperature of source 10(P
C., Joe. clt., p. 15), follow :
Pressure Absorption
(obs.).
Absorption
(inter-
polated).
Pressure.
Absorption
(obs.).
Absorption
(inter-
polated).
Inches. Per c<tnt.
Per cent.
Inches.
Per cent.
Per cent.
0.5
1.50
1.8
3.0
6.53
5.8
1.0
2.25
3.0
3.5
7.34
6.3
1.5 3.14
3.8 i
5.0
7.49
7.8
2.0
4.19
4.5 !
10.0
10.78
11.3
2.5
5.33
15.0
14.37
13.9
88
absorption of 0.007 per cent, by 1 meter of air of the given humidity and for sunshine, and compare
this with Tyndall's absorption of radiation from a low-temperature source by a fresh layer of moist
air, leaving the inference that this measurement several hundred times greater than that com-
puted on their assumption must necessarily be wrong. This reasoning is quite inadmissible.
In sunshine the rays absorbable by water form but a small part of the total radiation, while in
the low- temperature sources employed by Tyndall they constitute the larger part. Besides this,
the principal part of the absorption is exercised by the first few meters of moist air or their
equivalent. It is perfectly safe to say that eveu at the summit of Mount Blanc an amount of
aqueous vapor had already been traversed many times exceeding that in Tyndall's meter or there-
abouts of moist air, and that a large part of the rays for which aqueous vapor is especially
opaque and whose absorption was measured by Tyudall had already been sifted out. The reasoning
by which Professors Lecher and Pernter support their failure to detect any absorption from moist
air is, therefore, not justified.
Tyndall's last contribution to this subject is a paper on "The action of free molecules on
radiant heat and its conversion thereby into sound" (Phil. Mag. (5), vol. 13, pp. 435-462, and 480-
526, May and June, 1882). It contains a variety of incidental results which have a bearing on
questions which have arisen in connection with the present research. The beginning of the paper
gives an excellent historical summary of the Tyndall-Magnus controversy. On pages 455-456 we
read concerning Magnus' experimental determination of the radiation from heated gases passed
through a hot tube 15 mm. in diameter, bent up at the end, so that the vertical current ascended
400 mm. in front of the pile:
"When dry air was sent through this tube the deflection produced was three divisions of a scale; when air
which had passed through water at a temperature of 15 C. was sent through the tube the deflection rose to 5 div. ;
when the water was warmed to 60 or 80 F. the deflection was 20 div. ; and when the water boiled the deflection
was 100 div. In this last experiment, however, a mist appeared, so that, as urged at the time, the radiation could
not be said to have been purely from vapor. In the other case no mist was visible, but it was nevertheless concluded
that the 20-div. deflection was due to the formation of mist at the boundary of the ascending current.
Tyndall concludes that the first deflection came
Not from dry air, but from the adjacent aqueous vapor which had been warmed by the dry air.
That the deflection in the second experiment was small is not surprising. The radiation which could reach the
pile from a jet of air only 15 mm. in diameter, and containing such moisture as could be taken up at 15 C., must
have been extremely small under any circumstances. But in the present case eveu this small radiation was
diminished by the passage of the [radiant] heat through 400 mm. of undried air. I should demur [says Tyndall]
to the explanation of the third experiment and question the warrant to imagine a mist which could not be seen.
Even the fourth experiment where mist was visible, yielded, I doubt not, a mixed result, part of the effect, and probably
the smallest part, being due to the mist, and part of it to the vapor.
On pages 483-484 Tyndall refers to his own experiments on the transmission of a parallel
beam of radiation from a rock-salt lens, described in his Contributions (p. 394), and says that the
tube was rough brass, tarnished, and that the heating of the tube from air dynamically heated by
compression, and from the partial condensation of vapor on the walls of the tube when the air
was moist, produced a small radiation from its inner surface which disturbed the result. Hence
in his new apparatus the interior of the tube was silvered and polished.
The absorptions measured by Tyudall are greater when the source is a slowly vibrating or
low-temperature one, except in the case of absorption by carbon dioxide ; but if the apparatus
could be made sensitive enough to work with a very low-temperature source of radiation whose
spectral maximum should be at a longer wave-length than the region of especial absorption, the
result found for carbon dioxide would, no doubt, be the general one.
The radiation from a hydrogen flame proceeds principally from highly heated vapor of
water and its absorption by 38 inches (96.5 cm.) of air at 60 F., saturated with moisture and con-
taining an amount of water-vapor equivalent to a liquid layer 0.001 271 cm. deep, was found to be
10.7 per cent., while dry air produced no measurable absorption.
The thin liquid films produced by condensation of vapors on rock-salt plates when the con-
centrated vapors were allowed to flow over a plate placed in the path of the radiant beam were
found to have no effect on transmission, unless, as in breathing on a plate, the film amounted to a
89
visible wetting ; but if the plate was put iu contact with the pile the liberation of latent heat in
the act of condensing from vapor to liquid produced powerful deflections.
The assumption that absorption depends upon the mass of the absorbent material traversed
by the rays, and therefore is constant if the density of a vapor varies inversely as its depth, has
appeared probable. To test the assumption further, Tyudall had two tubes whose lengths were
as 3.5 to 1 and measured the percentage absorptions of ether- vapor, (C 2 H 5 ) 2 O, at inverse pressures.
TABLE 55.
Radiant source.
Inches. Inches.
Zi=38.0 _pi-L
/:=10. 8 2> 2 =3.5
Ip
38
Per cent.
a=30. 3
30.0
A dull lime light
Brighter liiue light
Brightest lime light .
38.0
10.8
2.0
7.0
Ip
76
38.8
38.5
38.0
10.8
1.0
3.5
Ip
38
22.3
22.5
38.0
10.8
2.0
7.0
If
76
29.5
30.0
38.0
10.8
1.0
3.5
Ip
38
18.4
18.8
38.0
10.8
2.0 Ip
7.0 76
25.7
25.6
The assumption of constant absorption of radiation from a source of constant temperature by
an absorbent of constant mass is verified in this case, the physical state remaining unchanged.
The question whether the absorption of a given mass of material will remain constant when its
state changes from the liquid to the vaporous condition demands separate treatment. Tyndall's
answer for ethyl ether is contained in the following paired values :
Radiant source.
Lime light with mirror
Absorption.
Per cent.
/Ether vapor 32. 4
rock-salt lens
Incandescent platinum with rock-salt lens -I
The same 011 another occasion
liquid 32. 9
vapor 33. 3
liquid 33. 3
vapor 66. 7
liquid 67. 2
vapor 71.
liquid 70.
In like manner hydride of amyl (source of radiation not stated) gave equal absorptions of 51
per cent, in the two states. It is, of course, impossible to assert from these few observations that
alike identity of liquid and vaporous absorption will hold good for other substances, although
Tyndall's opinion was to the contrary,* and I shall show later that it does not hold true for water.
The experiments which give the title to the paper and introduce a novel method follow. By
interrupting a convergent beam concentrated on a small bulb containing a vapor, employing for
this purpose a toothed wheel revolved with such rapidity as to give the number of pulsations
which evoked the resonance of the bulb, Tyndall found that the heat, instantaneously absorbed
and radiated by the vapor, produced alternate expansion and contraction, giving a musical note
whose intensity was proportioned to the combined absorbent and radiative power, as well as to
the difficulty with which the substance volatilizes. The expansion could also be made evident
upon a manometer. When radiation from a lime light was concentrated by a mirror upon a cylin-
*In regard to the equality of liquid and vaporous absorption Tyndall says (p. 500) : "A general law of molecular
pnysics is, I apprehend, here illustrated."
90
drical vessel 4 inches long and 3 inches wide, with rock-salt end plates, the following water
pressures were obtained on the manometer, according to the contents of the vessel:
Chloroform, CH 3 C1 350 j Carbon monoxide,;CO 116
Aldehyde, C : H.,O 325 Oxygen, O, 5
Olefiant gas, CiH 4 315
Ethyl ether, (C 2 H 5 ):O 300
Nitrous oxide, N,O 198
Marsh gas, CH., 161
Carbon dioxide, CO 2 144
Hydrogen, 11? 5
Nitrogen, N 2 5
Dry air 5
Humid air, at 50 C .130
Although a few of the more absorbent of these substances, such as nitrous oxide and marsh
gas, may exist as barely perceptible traces in the Earth's atmosphere, and carbon dioxide in larger
proportion, the interest of this series to the meteorologist of course centers in the absorption of
moist air relatively to that of dry air. The numbers, however, do not coincide with the relative
absorbent values, being modified by the radiant powers of the substances, but as it is precisely
this combination of radiative and absorbent qualities which determines the thermal state of the
atmosphere, these relations are significant. In alluding to their meteorological bearing Professor
Tyndall remarks (p. 516) :
The radiant power of air being practically -nil, it retains for a considerable time the warmth imparted to it
during the day, while when it is dry the rays from the surface of the earth pass unimpeded through it. Hence the
relative refrigeration of the surface [at night and in dry weather].
The radiant power of dry air is underrated by Tyndall here and elsewhere,* but the general
accuracy of his analysis of the atmospheric thermal mechanism remains unimpaired.
If the exact equivalence in absorption by equal masses of a substance in the liquid and in the
vaporous states had been as firmly established as Tyndall imagined, his measures of the absorption
of liquid water (Heat as a Mode of Motion, p. 430) could be utilized in connection with the atmos-
pheric problem. The observations, which were made on radiation from a plautinum spiral raised
to a bright red heat by an electric current, follow:
TABLE 56.
Thickness of liquid
water.
Absorp-
tion.
Inches.
cm.
Per cent.
0.02
0.05
80.7
0.04
0.10
86.1
0.07
0. 18
88.8
0.14
0. 36
91.0
0.27
0.69
91.0
For comparison of absorption by water in the vaporous condition, the following values of the
absorption by an air column, nearly 100 meters long, with varying humidity, have been taken from
a treatise on the Moon's radiation, which includes some subsidiary researches on atmospheric
absorption ("The Temperature of the Moon, from researches made at the Allegheny Observatory,"
by S. P. Langley, assisted by F. W. Very. National Acad. of Sci., vol. 4, part 2, 3d Memoir, p. 186,
Washington, 1889). In the last column I have deducted 2.5 per cent, from the original numbers for
the absorption of carbon dioxide.
* The small expansions of dry air and its chief constituents, nitrogen and oxygen, are attributed by Tyndall to
a warming of the apparatus and to expansion of the gas by heat communicated to it by convection, rather than to
heating by direct absorption of radiation by the gas; but, as in the case of dynamic heating, no sufficient reason is
given for rejecting these smallest readings.
91
TABLE 57.
Relative
humidity.
Per cent.
53
60
61.5
82
Equivalent
depth of
liquid
water.
Absorp-
tion.
em.
Per cent.
0.096
12.1
. 0. 151
19.3
0.166
21.8
0.205
30.4
Plotting tlie observations with depths of precipitable water for abscissa? and absorptions for
ordinates, it will be seen that the curve (fig. 13) departs slightly from a straight line, and more as
7
30
28
26
24
22
20
1*
16
12
X
-a
KK
y
X
X
/
fib
.53
10
8
6
aos
0.15
0.20 c-m.
. 13
the relative humidity increases, at least for relative humidities above 60 per cent. I infer that for
an equivalent depth of 0.2 em. of liquid water, for which an absorption of 28.8 per cent, is indicated,
92
a reduction of 3.6 per cent, should be made to allow for au iucremeut of absorption dependent upon
greater relative humidity, the remaining absorption of 25.2 per cent, being due to normal water-
vapor, plus an unknown but evidently very small correction for the effect of dry air.
For the equivalent depth of 0.18 cm. the absorption of water- vapor is 22.6 per cent., which may
be compared with Tyudall's third observation (Table 56), whence it appears that for this amount
of water the liquid absorption is four times the vaporous; but the rate of absorptive increase
with growing depth is very different for the two states, and for an equivalent depth of one-half
millimeter we have vaporous aqueous absorption, G.2 per cent. ; liquid aqueous absorption, 80.7
per cent., the liquid absorption being thirteen times greater than the vaporous.
No allowance is made here for any change produced by differences in the radiant source; but
I shall now develop a method by which we may be independent of the temperature of the source.
By combining spectral energy-curves and curves of absorption for homogeneous rays, we may
deduce the total absorption for any case which can be given.
The following measurements of the distribution of energy in the spectrum of a blackened
radiator filled with boiling water, and at a distance of 110 meters, are taken from page 186 of the
memoir on the temperature of the Moon, already cited. The barometer stood at 739 mm., and the
mean dew-point was + 12.7 C., corresponding to 0.122 cm. of precipitable water. The deviations
are those of a rock-salt prism whose angle (p. 132 loc. cit.) was ''always very near 60." The trans-
formation factor, for reducing the galvanometer deflections to those of a normal spectrum,
are taken from my paper "Further considerations in regard to laws of radiation" (Astrophysical
Journ., vol. 4, p. 43, June, 1896), and the wave-lengths are from Eubens' dispersion curve adopted
in the same paper.
TABLE 58. Spectral energy-curves through water-vapor (radiant source, 99 C.).
Minimum
deviation
(rock-salt.)
Wave-
length.
Prismatic
deflection.
Transforma-
tion factor.
Xormal
deflection.
o
U
OQ 1
Oi/4
3.10
31.3
.305
9.5
39
4.26
40.0
.364
14.6
38|
5.22
48.8
.432
21.1
38*
6.03
28.4
.491
13.9
38i
6.76
30.2
.549
16.6
38
7.41
42.6
.599
25.5
37f
8.01
52.0
.647
33.6
37|
8.59
55.7
.691
38.5
37i
9.11
62.0
.733
45.4
37
9.60
50.0
.772
38.6
36i-
10.45
48.0
.839
40.3
36'
11.2
42.0
.898
37.7
35|
11.85
33.2
. 949 31. 5
35
12.4
27.2
. 991 27.
Eadiations of shorter wave-length than about 2/t are inappreciable in the spectrum of a
body at the boiling point compared with one at the freezing point of water, and I have omitted
such, assuming them to have been due either to reflected solar rays or to errors of observation.
As the aperture for admitting radiation from the distant radiator, whose area was over 1 sq. m.,
also permitted wind to blow upon the measuring instruments, some irregularities are due to this
cause ; but the great depression between 5/i and 9//, in fig. 14, where the normal ordinates in the
last column of Table 58 are plotted, occupies the position of the great absorption-baud of aqueous
vapor and must be attributed to it.
Table 59 contains a spectral energy-curve observed with a fluorite prism by Paschen through
33 cm. of aqueous vapor at 100 0., corresponding to a layer of 0.0194 cm. of precipitable water.
(Wied. Ann., Bd. 51, Taf. 1, fig. 3, heft 1, 1894.)
93
TABLE 59. Absorption by steam.
Minimum
deviation
(fluorite).
"Wave-
length.
Radiation
nuabsorbed.
Radiation
after
absorption.
Transmis-
sion.
Absorption.
O '
ft
Per cent.
Per cent.
28 46.5
5
99 74
74.7
25.3
28 16
5.5
76
16
21.1
78.9
i'T 41. r,
6
56 .
5
9.0
91.0
27 5.5
6.5
41
3
7.3
92.7
26 25. 5
. 7
30.5
6
19.7
80.3
25 40
7.5
21
15
71.4
28.6
24 52
8
14.5
13.5
93.1
6.9
24 1
8.5
7.5
7.5
100
The measured radiations are not given in this paper, and the values, corresponding to ether-
waves differing in length by half a micron, have been read from the curves. The source of radia-
tion was a hot sheet-iron cylinder over an Argaud burner. The absorbent vapor was contained
in a cylindrical metal tube 4 or 5 cm. in diameter, closed by end plates of thinnest copper, in
which were open slits "of such dimensions that no rays reflected from the inner walls of the tube
could reach the bolometer, but only such radiation as had passed directly through the gas layer
in the tube. In this way all disturbance by ' adhesion of vapor,' etc., was excluded. A slender
20
10
\
01 234-56 7 S 9 10 11 12 13
15 16 17 ft /9 20 21 M
Great water-vapor absorption-band. (Equivalent liquid = 0.122 cm.}. Energy-curve of normal
spectrum, reduced from rock-salt prismatic spectrum.
metal tube was screwed into the middle of the tube. This served to convey the gas under inves-
tigation in a slow but steady stream through the tube. In this way there was interposed a
flowing layer of gas, of dimensions not exactly known, but very constant." (Loc. clt., p. 4.) These
measures are not available to as great wave-lengths as those made with a rock-salt prism, because
94
the absorption of fluorite nearly obliterates the radiation in the extreme infra-red spectrum where
water- vapor begins to recover trausmissive power.
Completing the missing portion of the energy-curve in fig. 14, as in the upper broken line, by
the aid of spectral measures on a near radiator at the same temperature in dry weather, and
adjusting the areas so as to give the same absorption (15.3 per cent.) which the curve in fig. 13
indicates for a depth of 0.122 cm. of precipitable water, the following radiant energies and
percentages of absorption are obtained:
TABLE 60. Absorption by aqueous vapor.
Wavi-
Kmliatinn Kwliatioii Pei . cent!is ,,
Absorption.
length.
on absorbed.
absorption.
traiKsimtreu.
0.1220 cm.*
0.0194 cm.t
0.0041 cm. J
M
Per cent.
Per cent.
Per cent.
5 26.0
21.3
81.9
18.1
25.3
5
5.5 31.2
19.0
60.9
39.1
78.9
40
6 36.4
14.0 i 38.5
61.5
91.0
68
6.5
41.6
14. 33. 7
66.3
92.7
70
7
45.6
20.0
43.9
56.1
80.3
47
7.5
48.0
26.8
55.8
44.2
28.6
20
8
48.5
32.2
66.4
33.6
7.9
14
8.5
47.6
39. 2 82. 4
17.6
5(f)
* Absorption by water vapor in 110 meters of air at ordinary summer temperature, equivalent to 0.1220 cm. of liquid water,
t Absorption by 33 cm. of steam at 100 C., equivalent to 0.0194 cm. of liquid water. (Paschen, Wied. Ann., as above, Table 59.)
t Absorption by 7 cm. of steam at 100 C., equivalent to 0.0041 cm. of liquid water. (Paschen, Wied. Ann., Bd. 52, Taf. II, fig. 1, curve
1 c, in which, ordinates are percentages of absorption.)
For comparison two series of absorption values for steam, deduced from curves given by
Professor Paschen, are included in the last two columns of Table GO. These are not obtained
by direct measurement, but from a comparison of the curve of observation after absorption with a
restoration by estimation of the curve before absorption. In regard to the restoration, obtained
by drawing a continuous curve tangent to the shoulders on either side of the band, Paschen says
(Wied. Ann., Bd. 51, S. 11) that it "has thus too low rather than too high ordinates," and in
consequence the indicated absorption is too small. This especially affects the estimates of
absorption of the longer waves from 7.5 // to 9 //, where, the energy being very small in the fluorite
spectrum, a comparatively slight change in the curve will produce a large alteration in the
estimated absorption. The effect of this error is less noticeable with a source of radiation at a
high temperature, such as was used by Paschen, but applied to observations on a low-temperature
source, these small absorption values from 7.5 ;.i to 9 // will give a restored curve of uuabsorbed
radiation having a depression at the maximum, which is inadmissible. The larger values of
absorption are therefore to be preferred at the borders of the band, at least on the side of greater
wave-length.
A further comparison of these results shows that a short column of concentrated, or satu-
rated vapor absorbs more powerfully than an equal amount largely diluted with air, and further
from the point of saturation. The absorption of a layer of saturated steam, 7 cm. deep (Table 00,
Series 3) containing 0.0041 cm. of precipitable water, undiluted, exercises as great an absorption
as 0.1220 cm. of precipitable water distributed as uusaturated vapor through 11,000 cm. of air.
The quantity of vapor is here 30 times as great, the dilution 1,571 times as great in case 1 (Table
CO) as in case 3. I have shown, however, that in the free air, where the dilutions are not widely
different, the absorption is nearly proportional to the vapor contents, at least up to a depth of
100 meters.
A more extensive comparison may be made. I have found that a layer of water, 40 cm. thick,
is almost absolutely impervious to solar infra-red radiation beyond wave-length 1.0 p. No such
absorption occurs with the most humid air as the sun approaches the horizon, although the abso-
lute amount of water in a vaporous form, interposed in the path of the rays, must often be even
greater than that contained in a liquid layer 40 cm. thick. Hence from the result of this test,
made for us in nature on a grand scale, we have conclusive evidence that the selective absorption
of vaporous water is not identical with that of liquid water, but that the former is comparatively
95
permeable to infra-red radiations. Nevertheless, the general form of the absorption curve in the
infra-red spectrum, as to its coarsest details, or broad groups of absorption-bands, and their rela-
tive intensities is very similar in the two cases.
Passing to the absorption- spectrum of liquid water, I have measured the ordiuates in the
spectral energy-curves for a fluorite prism which Pascheu has given ( Wied Ann., Bd. 52, 1894,
Taf. II, fig. 2, curves 1 to 4), in which a blackened platinum strip at 450 C.* was the radiant
source. These readings have been divided by the ordinates with empty cell to obtain the corre-
sponding percentage transmissions which are given in the next table.
TABLE 61. Absorption by liquid water.
Wave-length.
2fi 2.5/x
3*
3.5 M
4 n-i 4. 5 ju. 5 ju. 5. 5 /LI 6/A 6.5/x
7. 7.5 M 8^ 8.5^
Min. deviation . .
30 47' 30 34'
30 18'
29 59'
29 38' 29 14' ! 28 47' 2816' 2742' 276'
26 26'
25 40'
24 52'
24!'
WATER.
cm.
0.0000 374 507
007
556
443
339 262 194
133
101
86
63
38
18
a
v
-S
0. 0015 350
373
58
397
318
244 193 146
45
64
60 42
28
16
2
0. 0030
340
330
6
317
298 135 135 92
5
15
18 14
9
6
H
0. 0080
305
135
2
137
147 21 33 23
2
a
.0015
93.6 73.6
9.6
71.4
71.8
72. 73. 7 75. 3
33.8
63.4
69.8 66.7
73.7
88.9
If
.0030
90. 9 65. 1
1.0
57.0
67.3
39.8 51.5 47.4
3.8
14.9 20.9
22.2
23.7
33.3
H ' S
.0080
81.6
26.6
0.3
24.6
33.2
6.2 12.6 11.9
1.5
.
&
.0015
6.4
26.4
90.4
28.6
28.2
28.0 26.3 24.7 66.2
36.6
30.2
33.3
26.3
11.1
'5 ^
. 0030 9. 1
34.9
99.0
43.0
32.7
60.2 48.5 52.6 96.2
85.1
79.1
77.8
76.3
66.7
^
^
. 0080 18. 4
73.4
99.7
75.4
66.8
93.8 87.4 88.1 98.5
The transmissions in this table, for the longer wave-lengths, have been multiplied by the
ordinates of an uuabsorbed normal spectral energy-curve at 100 0. to obtain the figures in the
last three lines of Table 62, and the curves in fig. 15.
TABLE 62. Spectral energy-curves through liquid water (radiant source 100 C.).
Wave-length.
5p
5.5/a
B M
6.5/ii
7/u
7.5ft. Sfj.
8.5 M
WATER.
cm.
(1) 0. 0000
26.0
31.2
36.4
41.6
45.6
48.0
48.5
47.6
(2) 0.0015
19.2
23.5
12.3
26.4
31.8
32.0 35.7
42.3
(3) 0.0030
13.4
14.8
1.4
6.2
9.5
10. 7 11. 5
15.2
(4) 0. 0080
3.3
3.7
0.5
[0.5]
[2.2]
[2.8]
[1.0]
[2.0]
Measures made with a fluorite prism are not available for wave-lengths longer than 9 ju where
the absorption of fluorite becomes large, but after this point aqueous absorption is comparatively
insignificant until the region of the spectrum beyond 13 // is reached. Solar and lunar radiations
longer than 9 // penetrate our atmosphere freely, even in moist summer weather, and Tyndall's
observations (quoted in Table 56) show that 9 per cent, of the rays from platinum at a bright-red
heat resist the absorption of liquid water. This remnant is distributed at irregular intervals
through the spectrum. As the region beyond 12.5 //.comprises but a small fraction of the total
energy from such a source, I shall assume, merely for the present purpose, that aqueous absorp-
tion ends at 12.5 //, and as it is probable that certain feeble atmospheric absorption bands of
*Subsequeut measures by Paschen have indicated that the uuabsorbed maximum in this curve has been dis-
placed toward the shorter wave-lengths, owing to the imperfect absorption of the loug waves by the bolometer,
and that the maximum should be at 4 //.
96
greater wave-length than 9 /* are due to water-vapor, the curves are drawn undulating in the
dotted portions supplied to complete the areas. The spectral region between 9 // and 12 jj. is very
readily transmitted by water- vapor, but the limits of liquid absorption are wider. Aqueous
0/2345
7 8 9 10 11 12 13 14 15 16 il 18 f9 20 21 JU
ffig. 15
Energy-curves of normal spectrum after absorption by liquid water.
absorption increases again gradually beyond 12 //, and is perhaps the cause of the practical
ending of the spectrum near 20 /;.
Measuring the areas of the curves in fig. 15, and comparing 2, 3, and 4 successively with the
unabsorbed energy-curve (1), the following transmissions of total radiation from a source at
100 C. are obtained :
TABLE (53.
Depth of liquid
Area of spectral
Transmission of
Absorption of
water.
energy curve.
total radiation.
total radiation.
cm.
Per cent.
Per cent.
(1) 0.0000
1.420
100.0
(2) 0.0015
1.016
71.5
28.5
(3) 0.0030
0.630
44.4
55.6
(4) 0.0080
0.341
24.0
76.0
If the aqueous absorption is exercised on radiation from a red-hot source, wave-lengths from
2ju to 5/i must be included, which is done in Table 04, the transmissions being obtained from
Table 61, and combined with radiant values from a normal spectral energy-curve, taken from the
reduction for a source estimated at 815 C., given in rny paper, u Further considerations concerning
laws of radiation" (Astropliysical Joitrn., vol. 4, p. 43), in which, however, the temperature has
probably been placed too high, since the position of the unabsorbed maximum more nearly agrees
with that of the ideal black body at 450 C. (see footnote, p. 95 5 compare also my note in Astroph.
Journ., vol. 10, p. 208, Oct., 1899) ; but the discrepancy may arise in part from the use in the
present case of a radiant which is not an ideal black body.
97
TABLE 04. /Spectral energy -curves through liquid water (radiant source 815 C. ?).
Wave-length. In 2.5ft. 3|u
3.5. 4,
8ju.
9,
lOju
15, ; 20,
WA.TKB.
em.
(1) 0.0000
40
67 160 187 193
190 isi'
154 117 84
60
42
16
o
(2) 0.0015
37.4
49. 3 15. 4
133.5 138.6
136.8 134.1
52.1 81.7 61.9
(3) 0. 0030
36.4
43.6 1.6
106.6 129.9
75.6
93.7
5. 9 24. 5 19. 9
(4) 0.0080
32.6
17.8 0.5
46. 64. 3
11.8
22.9
2.3
These values are plotted in fig. 16. Three principal regions of large absorption are shown.
The first, extending from 2.2/i to 3.7^u, with the minimum near 3//, occupies the position of Lang-
ley's X and associated bands (xi Xi) i n ^ ne solar spectrum. The second depression from 4.2// to
5.2/< (minimum at 4.7/0 encroaches on the great carbon dioxide baud, but does not seem to be as
^oo
150
\
\
\
oLZ
/ 2 3 4 5 6 7 8
to ft 12 f3 14 i5 16 11
l. 16
f<J 20 2i
Energy-curve* of normal spectrum after absorption by liquid water.
strongly developed in the vaporous absorption of water: neither does it appear in the absorption
of 0.0015 cm. of liquid water, although quite well marked in the curve for 0.0030 cm. The third
region is that of the great aqueous absorption band from 5.2 jn to 7.0/< with a subordinate extension
to 9//, its deepest depression being at 6. 1//. The vaporous absorption differs in showing two
minima, at 5.86/< and 6.51/<. A succession of smaller bands follows, the absorption of the liquid
diminishing from S^u to 12/. In this region aqueous vapor has very free transmission, and the
same is true of a liquid layer 0.0015 cm. thick.
12812 Bull. G - 7
98
Comparing areas in fig. 16 the following transmissions of total radiation from a source
estimated at 815 C. are found :
TABLE 65.
. Deptli of liquid
water.
Area of spectral
energy curve.
Transmission of
total radiation.
Absorption of
total radiation.
cm.
Per cent. Per cent.
(1) 0.0000
2.576
100
(2) 0. 0015
2.175
84.4
15.6
(3) 0.0030
1.487
57.7
42.3
(4) 0. 0080
1.015
39.4
60.6
Within the given limits of temperature (100 and 815 C.) the transmission for every thickness
is greatest for the radiation from the hotter source, a result which is as old as the measurements of
Melloni, but which is here presented no longer as an empirical fact, but as a piece of knowledge
which may be rationally conceived and which can be applied deductively to a variety of special
cases.
We are now in a position to assert confidently that so long as the physical state remains
unchanged and the total aqueous absorption does not exceed 50 per cent, the increment of aqueous
cm
absorption is nearly proportional to the depth of the absorbing layer, but beyond this point the
rate of increase in the absorption falls off very rapidly until finally further addition to the layer
produces almost no effect.
Next, by comparing the curves in figs. 13 and 17, it can be stated that the absorption of total
99
radiation by water-vapor iu bigb dilution in the free air falls far below its absorption when
condensed to the liquid state, but in a ratio which varies with the depth of the absorbent mass,
as the following table shows:
TABLE 66. Aqueous absorption of total radiation (radiating body at 100).
Depth of pre- Absorption Absorption
cipitable by liquid bv vapor
Ratio
liquid absorp"
water. water.
in 100 m. air.
vapor absorp".
cm.
Per cent.
.001
19.5
0.125
156
.002
38.0
0.250
152
.003
55.5
0.375
148
.004
63. 3
0.500 1 127
.005
67.9
0. 625 109
.006
71.2
0.750
95
.007
73.8
0.875
84
.008
76.0
1.000
76
.009
78.0
1.125
69
.010
79.8
1.250
64
From this comparison it appears that with a radiating source at the boiling point of water,
10 microns of liquid water absorb 156 times as powerfully as the same amount of water dis-
tributed in the vaporous state through about 100 meters of air. We have seen that even an
approach of the aqueous vapor to its condensation point increases its absorptive power (Table 57
and fig. 13). Paschen's result, already described (ante, p. 94), shows that saturated aqueous
vapor at 100 C. exercises an intermediate absorption between that of the liquid and the invisible
nonsaturated vapor of the atmosphere, 40 microns of liquid water absorbing 63 per cent, of radia-
tion from a source at 100 C. (by Table 66), while the same quantity of water in the form of steam
takes out about 15 per cent., and distributed as atmospheric vapor only one-half of 1 per cent, (by
fig. 13 and Table 66).
The identity of absorption in the liquid and vaporous states which Tyndall found for ethyl
ether and amyl hydride, presumably obtains only for those substances which do not change their
molecular constitution in passing from one state to the other. The influence of molecular form
upon absorption was, indeed, recognized by Tyudall, who says ( Contributions to Molecular Phys.,
p. 98):
No coincidence between the vibrations of a radiating body and those of oxygen, hydrogen, or air could make any
one of these substances a good absorber. They are physically incapacitated from communicating^ motion, and hence
in an equal degree from accepting motion. The form of the atom [molecule?!, therefore, or some other attribute
than its period of oscillation [let us say, rather, some attribute on which that period depends], must enter into the
question of absorption.
See also pages 102-105 (loc. cit.), where ozone is shown to absorb immensely more than oxygen.
The atoms are here the same. It is the molecular form alone which has changed.
It is probable that some of the most important selective radiations of these elementary gases
are of short wave-length and are not emitted until high temperatures are reached. We know that
the linear absorption of cold oxygen in the visible spectrum is very feeble, requiring a long
column of gas to show the A, B, and a groups of lines in the spectrum of a lime-light; but there
is a region of great absorption in the extreme ultra-violet. Von Schumann finds that a layer of
air linni. thick cuts off all rays beyond 0.175//; and Liveing and Dewar (Proc. E. Soc. London, vol.
46, p. 222, 1889) have found that the absorption of 18 meters of oxygen in the ultra-violet is of the
nature of a broad diffuse band, whose limits extend to greater wave lengths on the less
refrangible side as the pressure increases. At a pressure of 97 atmospheres, when the mass of
oxygen in their tube was "rather greater than is contained in a vertical column of equal section
of the Earth's atmosphere," the rays were completely absorbed to a wave-length of 0.2797//. At
50 atmospheres the total absorption had its limit at 0.2696^; and at 23 atmospheres the limit of
extinction had receded to 0.2599//.
Two kinds of bands appear in the absorption-spectrum of oxygen, in regard to which
100
Professors Liveing and Dewar make some suggestions which are of interest in the present con-
nection :
The absorptions of the class to which A and B belong must be those \\hich are most easily assumed by the
diatomic molecules (O 2 ) of ordinary oxygen. As for the other class of absorption, the diffuse bands, since
they appear to have intensities proportional to the square of the density of the gas, they must depend on a change
produced by compression. This may either be the formation of more complex molecules, as for example O^, corre-
sponding to the deviation from Boyle's law exhibited by oxygen gas, or it may be the constraint to which the
molecules are subject during their encounters with one another. Increase of temperature would affect the former,
tending to diminish the number of complex molecules formed at a given pressure, but would have no effect on the
latter, for though the number of encounters of the molecules in a length of time would be greater the higher the
temperature, yet so long as the volume was unaltered the ratio of the duration of an encounter to that of free
motion would be sensibly unaltered. So far as any change due to temperature has been observed, it is that a rise
of temperature slightly weakens the diffuse absorptions (loc. cit. pp. 227, 228).
Consequently these observations favor the hypothesis that compression produces a limited
number of complex and highly absorbent oxygen molecules which, even though few in number,
are able to impress a peculiar character upon the spectrum.
Profs. W. Ramsay and J. Shields ("The molecular complexity of liquids," Trans. Journ. Chem.
Soc. London, vol. 63, p. 1089, 1893), from their experiments on the surface tension of liquids as
a function of the relative number of molecules per square centimeter of surface and the tempera-
ture, conclude that several molecules of water-vapor unite to form a complex molecule of liquid
water; but ethyl oxide has the same molecule in the liquid as in the vaporous state. Regarding
oxygen as tetravalent, the liquid molecules of water may be closed chains, e. g.:
H H
C-U-,
H O O H
H O O H
(H 2 0) 4 = I |
At 60 C. the composition of the liquid molecule of water is (H 2 O)^, while at the temperature
of maximum density most of the complex molecules are represented by the second formula.
The gradual formation of closed chains as the aqueous vapor approaches saturation,* must
take place most readily if the molecules of vapor are not widely separated by diluting air.
Meteorologists have often commented on the peculiarities of nearly saturated air, and some have
conjectured that gaseous water exercises no appreciable absorption, and that the absorbent
effects attributed to it are really due to a mist of liquid water, relative humidity being more
important than vapor tension as an index of absorptive power. We have seen that gaseous
water does produce a very potent influence of its own, but it seems to me to be demonstrated by
what precedes that there is a remarkable increase in absorption by water at the critical point of
incipient condensation, and as this point is somewhat closely approached. The suffocating sensa-
tions experienced in a very hot muggy atmosphere are attributable to the partial cessation of
evaporation from skin and lungs, but the thermometric effects, such as the diminution of the
daily range of temperature under a clear sky, which becomes very noticeable when the relative
humidity is high, can be due only to strong absorption of the long-waved terrestrial radiations,
and it is interesting to note that the difference between the absorption of liquid and vaporous
water lies chiefly in the greater absorption of longer waves by the former. Professor Pascheu
says ( W ied. Ann., Bd. 51, S. 22, 1894) :
Liquid water has a very deep absorption-band which reaches from [fluorite minimum deviation] 29 55'
[3.58//J to 30 40' [2.29/<], and has its maximum at 30 23', 2.92u [subsequently corrected to 2.84/<], while the corre-
sponding band of the water- vapor at 100 extends from 30 18' [3.00/<] to 30 40' [2.29//J, and has its maximum at
30 31', 2.66/i [subsequently corrected to 2.58//]. That of the liquid water begins consequently at the same place
as the gaseous on the side of the short waves, but ends at longer waves. A maximum also appears in [the absorp-
tion of] liquid water at 27 40' [6.02//] ; for water-vapor at 100 its position is 27 53' [5.85/*]. * If we
remember that the emission-maximum of the oxyhydrogen name lies at 30 26' [2.75/u], we can indeed say that
* Compare Regnault's observations cited, ante, p. 85.
101
liquid water absorbs the vibrations that the gaseous emits or absorbs. The liquid absorbs, however, in addition,
such as belong to neighboring longer waves, and these indeed so much stronger that the absorption-maximum lies
3' farther toward the long waves than the emission-maximum of the oxyhydrogen flame.
The spectral energy-curve of the oxyhydrogen flame, given by Pascheu ( Wied. Ann., Bd. 51,
Taf. 1, tig. 6, 1894), shows, in addition to the emission-baud just mentioned, which corresponds
with the absorption-band of the solar spectrum called A' by Langiey, also the correlatives of the
solar bands fl and W. The band A" is partly due, and the baud Y wholly due, to the absorption-
bands of carbon dioxide, discovered by Knut Angstrom. I quote Paschen's description of his
identifications :
Since Langley's bands W, fl, X, Y, etc., coincide within the errors of measurement with the absorption-bands
determined by me, we may refer the given bands of the solar spectrum with great probability to the CO 2 and H : O
contained in our atmosphere. The wave-lengths of Langley's bands are: W at 1.4//, corresponding to the emission-
band of H:O at 1.4/w ; 1 at 1.83//, corresponding to an emission-band of H ; O at 1.83// ; J=2.64yU, corresponding to
H ; O = 2.66/u ; Langley's band widens at low sun toward the longer waves. The new band arising at 2.94// coincides
with the absorption-maximum of liquid water which I find lying at 2.92/<. r=4.6// corresponds to the COa baud
at 4.63//. From 5u to ll/ Laugley's solar spectrum is divided. Here lie the strong water-vapor absorptions (maxima
at 7. 1// and 8.1/<). (Loc. cit., p. 18.)
The last two wave-lengths were subsequently corrected after more accurate comparison of
deviations from a fluorite prism and wave-lengths as given by a grating, becoming 5.86yw and
6.51//. The limits of the great water baud are also more nearly S^u and 8//, the correction affect
ing chiefly the wave-lengths above 5 microns. In this passage Dr. Pascheu has misunderstood
Laugley's use of the word " maximum," which refers to an elevation in the energy-curve of tlie
solar spectrum and not to the point of greatest absorption in a cold band. Langiey (Am. J. Sci.
(3), vol. 30, p. 403, 1888) distinctly says that 2.94/< is a subordinate maximum of the solar spectral
energy-curve, and again he says (p. 404): "From 4.0/< to4.5// we have another region of almost
complete absorption, followed by a maximum at 4.6//." It appears probable that some of these
numerical values will require further slight adjustment. Langley's original value for the center
of Y, namely, 4.25;/, has since been confirmed by Paschen, who gives from his measures with a
grating 4.245;< ( Wied. Ann., Bd. 52, S. 222).
The region of the solar spectrum from wave-length 2.3// to 3.3/< is especially variable.
Subordinate absorption-bauds on the less refrangible side of A become apparently transposed in
relative importance as the altitude of the sun above the horizon or the vapor-contents of the
atmosphere change.
Observations made during the winter indicate that the baud at 2.64,/u is, with a high sun, largely filled up,
especially on the less refrangible side. At noon a subordinate maximum has been found within the low sun limits
of this band at 2.94/u, and a second one at 2.80/< frequently accompanies it, producing subordinate minima at 2.89
and 3.02/<. As the absorption increases with a sinking sun, these subordinate maxima disappear to a very great
extent, that at 2.80. being the first to vanish, as well as the quickest to grow, so that at noon, on a cold day, it not
only surpasses the maximum at 2.94, but even begins to approach that at 3.20/*, while, when the sun's altitude is
less than W~, the nearly uniform part of the band extends from 2.45/< to 3.15/i without a break. (Langiey, Memoirs
of the National Academy of Science, vol. 4, 2d Mem., p. 167, 1887. )
The varying form of the spectral euergy-curve is doubtless due to the complex linear composi
tiou of the bands, individual lines, or groups of lines, having very different rates of growth as the
absorbent depth varies; and to a corresponding variation in the emission of the several lines
composing a group, coupled perhaps with the effect of self-absorption of its own radiations by the
outer layers of a gas or vapor, is to be attributed the change in the measured positions of infra-red
bands, noted by Langiey and abundantly confirmed by Pascheu. Of the two principal centers of
the great absorption-baud of water vapor, the longer at 0.5 1/t appears to expand to still greater
wave-lengths and the shorter at 5.86 i to still shorter wave-lengths, or in either case away from
the common center, as the mass of the absorbent increases; and Paschen shows that the same
movement occurs in the maximum points of the emission-bauds of water- vapor as the temperature
rises. The following- table is quoted from his paper ( Wied. Ann., Bd. 52, S. 215, 1894), with wave
lengths approximately corrected by his latest measures of fluorite dispersion ( Wied. J.nra.,Bd. 53,
S. 822).
102
TABLE 67. Emission-spectrum of irater-vapor.
Temperature.
Position of the highest point in
Maximum I.
Maximum II.
Deviation.
Wave-length.
Deviation.
Wave-length.
Oxyhydrogen flame
Bunseu flame, 1,470
1,000
o /
26 58
27
ft
6.60
6.57
o /
28 29
28 25.5
28 23
5.28
5.34
5.38
600, approximately,
100
27 2.7
27 5. 5
6.54 28 11
6.50 27 51.3
5.58
5.87
17 (vapor)
17 (liquid)
27 6.5
6.48 27 48
27 40
5.92
6.02
The relative strength of the maxima of the strongest emission-bauds in the spectral energy-
curve of water-vapor at different temperatures follows closely the relation between the corre-
sponding intensities at the same wave-lengths and temperatures in the spectrum of a black body;
and the absolute intensities are not far behind. This indicates that at these points the radiant
power of a comparatively small mass of vapor is nearly perfect; but this can not be said of the
borders of the bands, and we need not expect that any completely consistent rule sho.uld be fol-
lowed in their variation. The bolometer covers several alternations of radiant or absorbent
spectral lines and their intervals, giving us the sum of the series. If the lines broaden and the
intervals fill up until the lines coalesce completely, the limits of perfect radiation or absorption
widen, and if the band is one-sided, its center changes its position in the spectrum. So long as
there is no disintegration of atomic groupings increased heat may bring out new lines and give
greater complexity to the spectrum, changing the aspect of a group. Since the centers of several
aqueous bands shift to longer waves as the temperature rises, their structure probably resembles
that of the A and B groups of oxygen, in beginning with strong lines on the side of the short
waves and gradually fading out in a long series of feebler and more widely separated lines on the
side of the long waves. The shifting of the center of Maximum II (Table G7) is in the opposite
direction, and is also more rapid than that of I. In II the relatively greater increase of radiations
of short wave length with rising temperature may assist, as suggested by Paschen, but only by
aiding a process depending on structural detail of the band, which here fades out in the same
direction as the shifting of the maximum ordinate in the spectral energy-curve of a black body.
In I a similar greater increase of short than of long waves can not entirely overcome the struc-
tural shifting to the side of the long waves; and the same is true of the band A", while fl and V,
situated in a part of the spectrum where the rate of increase of intensity with temperature varies
rapidly with the wave-length at flame temperatures, have the structural shifting toward long
waves slightly overbalanced by the more general formal change, as is shown in the next table, also
taken from Paschen's work ( Wied. Ann., Bd. 52, S. 226), the wave-lengths corrected as before.
TABLE 68. Emission-spectrum of water-vapor.
Temperature :
c
/
u
Oxyhydrogen flame
Deviation 30
26.0
A = 2.75
Bunsen flame
30
25.
5
2.77
Over 1,000 -X
30
26.
2.75
500
30
29
2.65
100
30
30.
8
2.59
Oxyhydrogen flame
f 30
52.
1.78
Bnnsen flame fl<
30
51.
5
1.81
Over 1,000
30
51.
1.84
Oxyhydrogen flame
[ 31
3
1.34
Bnnsen flume W<
31
2
1.38
Over 1,000
31
2
1.38
103
For the wave-lengths of the last three bands we need not depend on transformations from
dispersion measures, since these maxima can be identified in the grating- spectrum of the Bunseii
flame. Paschen's curve ( Wied. Ann., Bd. 50, Taf. IX, fig. 8) gives the following values:
i Group W extends from l.33jn to 1.50//.
' I Subordinate maxima, 1.35// and 1.42#; mean, 1.385//.
( Group O, extends from 1.75yu to 2.10//.
' } Subordinate maxima, l.SO//, 1.86//, and 1.97^; mean, 1.877//.
( Group A"/ extends from 2.42yu to 3.02//.
' 1 Subordinate maxima, 2.51//, 2.70//, and 2.83 /u; mean, 2.680//.
In the absorption-bands of the solar spectrum, the deepest depression of D, extends from
1.81/< to 1.87 /u according to Langley ("Researches on solar heat," Prof. Papers of the Sig. Sen\, No.
15, p. 228, Washington, 1884), and the extension of the group on the side of the long waves is
much feebler than in the emission-baud of the Buuseii flame. The subordinate maximum of A at
2.83/i in the flame spectrum appears to agree with the minor band in the solar spectrum, called xi
by Laugley, the wave-length of which was originally given as 2.89^ (ante, p. 101). That at 2.70//
agrees in position with one of the bauds of CO 2 .
Captain Abney and Lieutenant-Colonel Festing have photographed a continuous spectrum
through several inches of water, getting the absorption-spectrum to a wave-length of l/< ("Atmos-
pheric absorption in the infra-red of the solar spectrum," Proc. R. Soc. London, vol. 35, p. 80, 1883).
Three inches of liquid water give the following bauds: (1) begins with a strong, sharp edge at
0.735/< and extends to 0.765yU, fading out thence on the side of the long waves, very gradually.
Great A is included in its diffuse margin. (2) in like manner begins with a strong, sharp edge at
0.833;/, between Brewster's A" and Y, and fades out gradully toward the long waves, the principal
part of the baud extending from 0.833/t to 0.875//. The strong pair of lines, A, in the solar
spectrum, due to calcium, wave-lengths 0.854/t and 0.866/Y, is included in the diffuse margin. (3) is
a very strong band between wave-lengths 0.942// and 0.986//, occupying nearly the same position
as the bands in the solar spectrum, called p a t by Abney. It is bordered by hazy extensions
and broadens to 0.88yu, when the depth of water is increased to 1 foot. These three bands are not
composed of fine lines, but are diffuse, and they appear in photographs of the solar spectrum,
superposed on groups of lines, and becoming very strong when the relative humidity approaches
saturation. The authors say :
Besides these linear absorptions, photographs taken on days of different atmospheric conditions show banded
absorptions superposed over them. : ' On a fairly dry day the banded absorption is small, taking place princi-
pally between A9420 and A9800; a trace of absorption is also visible between A 8330 and A9420. On a cold day, with a
northeasterly wind blowing [this being for England the dry quarter], and also at a high altitude on a dry day,
these absorptions nearly, if not quite, disappear. When the air is nearly saturated with moisture, * * *
except with very prolonged exposure, no trace of a spectrum below A8330 can be photographed. (Loc. cit., pp. 80-81.)
Comparing these observations with those of Liveing and Dewar on the two kinds of oxygen
bands, linear and diffuse, and with the facts adduced here which show that there is a very large
increase in the absorptive power of aqueous vapor when nearly saturated, it seems probable that
the diffuse bands of liquid water and of a saturated vapor are due to the complex aqueous
molecules discovered by Ramsay and Shields, while the groups of fine lines in nearly the same
positions in the spectrum belong to simpler molecules which no longer exist in the liquid state,
but are present in variable proportion in the vapor, according to the temperature and the degree
of saturation.
Abney and Festing in another paper ("The influence of water in the atmosphere on the solar
spectrum," etc., Proc. R. Soc. London, vol. 35, p. 328, 1883) give spectral energy-curves for the crater
of the positive carbon of an arc-light after absorption by various thicknesses of liquid water,
obtaining evidence that nearly all of the great cold bands in the solar spectrum to 3/< are due to
water. The liquid absorption bands are, however, much more intense than the vaporous ones,
and coalesce to form extensive regions of complete absorption. In addition to these curves, rough
photographs of the solar spectrum to a wave-length of 2.2/n were taken on cold dry days, which
confirm the presence of all of these water-bands and give their positions more accurately than
the heat measures made in the spectrum with a linear thermopile whose aperture was one-fiftieth
of the length from the D line to the end of the infra-red spectrum from a glass prism. In the
104
following table these thermal measures (loc. cit., p. 332) are exhibited as percentage-transmissions
iii the last three columns :
TABLE 69. Transmission of spectrum by liquid i.cater.
Radiation
through
empty glass
celL
Deflection through
Transmission l>y
J inch
water.
1J inches
water.
24 inches
water.
inch
water.
1J inches
water.
24 inches
water.
Per cent.
Per cent.
Per cent.
At .D-line in yellow
7.5
7.3
6.8
3.2
97
91
43
Maximum in orange-yellow
8.7
8.7
8.5
4.0
100
98
46
Orange band
10.0
9.2
8.8
3.7
92
88
37
Maximum in red
16.7
16.7
16.0
10.7
100
96
64
Red baud (near A)
19.3
18.5
17.0
2.3
96
88
12
Maximum near 1"
22.8
22.8
20.6
1.4
100
90.
6
Baud between A" and Y
24.6
23.0
21.0
0.3
93
85
1
Maximum (Herschel's a)
25.4
24.7
22.0
0.0
97
87
Band (Abney's p 6 r)
27.7
21.5
5.3
78
19
Maximum (HerscheFs /?)
30.0
26.3
10.0
88
33
Band (Abney's #)
[26. 7]
18. 5
0.5
69
2
Maximum (Herschel's y)
[24.9]
19.0
7.0
76
28
Band (Abuey's W)
18.5
* 0.7
0.0
4
Maximum (Herscnel'sS)
11.6 -
3.0
26
Band (Langley's fi)
[5.4]
0.0
Maximum (Herschel's )
[2.9J
1.5
52
Band (Langley's X)
0.0
The extreme infra-red region of the spectrum, beyond the great water-band, has recently
been explored by Prof. H. Eubens and E. Aschkinass ( Wied.Ann., Bd. 64, S. 584, 1898 ; translated
in the Astrophys. Journ., vol. 8, p. 176). The radiation from the mantle of a zirconium burner
passing through a cast-iron tube 75 cm. long, "heated above 100 by four Buusen burners beneath
it," and fed with a permanent stream of aqueous vapor, was formed into a spectrum by a prism of
sylvite, which at a wave-length of 18// still transmitted " some 70 per cent., and at 20// some 30
per cent., of the incident radiation." The general results are thus stated by the authors (Astropliys-.
Journ., vol. 8, p. 190) :
Water-vapor shows only faint absorption in the spectral region between A = 9/i and A = ll/u, as compared with
shorter and longer waved parts of the infra-red. From this follows the minimum [emission] observed in the emis-
sion [curve of hot water-vapor] at A = 10.7//. Beyond 11/i the absorption begins to increase and becomes almost
total at A=20,u, whereby the maximum observed in the emission [from hot water-vapor] at A = 13.1/i is explained.
[The transferring of the maximum from 20/i in absorption to 13/i in emission is about what might be expected from
the rate of increase of the radiation of a black body with shortening wave-lengths, combined with the larger trans-
mission of the shorter waves by sylvite in this part of the spectrum.] In the region between 11/z and IS/n, water-
vapor possesses six conspicuous maxima of absorption, which have according to our observations the wave-lengths
A = 11.6/4, 12.4/1, ISAju, U.Sju, lo.lju, and 17.5,u.
The intensities of absorption of these six bands are 10, 20, 28, 43, 63, and 88 per cent., respec-
tively; while at 20,w, as stated, the absorption is nearly 100 per cent. Beyond this point, at wave-
lengths 24.4 w, aqueous vapor exerts only a very slight absorption (Eubens and Nichols, Pliys. Rev.,
vol. 4, p. 322, 1897; also Wied. Ann., Bd. 60, S. 418, 1897). Since air was not excluded from the
apparatus, it is possible that the total absorption at 20 jn may have some other origin (see p. 113).
It will be evident that the interrelations of aqueous absorption and radiation in terrestrial
meteorology must be complex. The radiations of clouds, the sea, and to a considerable extent
those of moist earth and vegetation do not difl'er much from the radiant emission of a solid black
body whose spectral energy-curve has its maximum, at terrestrial temperatures, in the immediate
vicinity of the chief aqueous absoiption-bands. The depletion of radiation is especially great if
the coincidence of maximum radiation and principal absorption is exact ; but the position of the
maximum of aqueous absorption in the spectrum varies with the amount of water and with its
physical state. The position of the maximum of the unabsorbed energy-curve also varies with
the temperature of the radiating body and of the surface to which it radiates. Thus there is room
for a great variety of combinations.
The apparent absorption of a layer of heated vapor is a differential one, being the resultant
105
of a series of operations made up of the sum of the original radiation of the body behind the
vapor, minus the absorption exerted upon this radiation by the vapor, plus the emission of the
vapor's own radiation, diminished by the absorption of the radiation from deeper vaporous layers
by the vapor subsequently traversed. Since the vaporous emission varies with the temperature,
the apparent absorption of the hot vapor likewise varies, except at temperatures too low for
appreciable emission. This is very well shown in the series of absorption and emission curves
for carbon dioxide at temperatures from 180 to 480, given by Paschen (Wied. Ann., Bd. 51,
Taf. 1, fig. 8, 1894). At the highest temperature the apparent absorption is almost nothing, the
radiant emission by the hot gas having counteracted its absorption. I have already noted
(ante, p. 53) that this observation may be used in constructing a curve of temperature and
depth at which absorption exactly compensates radiation. Another point on such a curve is
given by the present measures (ante, p. 54), which show that for a temperature of 126 C. the
effective radiating depth of carbon dioxide is only a little over 3 feet, let us say 100 cm.
Pascheu's measurement gives the temperature of 480 C., corresponding to a depth of 7 cm.
ABSORPTION OF RADIATION BY CARBON DIOXIDE.
Prof. Kuut Angstrom ( Wied. Ann., Bd. 39, S. 300, 1890; see also the preceding article, begin-
ning p. 267), quoting observations by Lecher which show that the solar rays, after sifting by an
air-mass of three atmospheres, are almost entirely deprived of those ether- waves which are sus-
ceptible of absorption by a moderate depth (1.05 meters) of carbon dioxide, concludes that, since
the mean quantity of this gas in the atmosphere is less than 0.02 j>er cent., corresponding to a
vertical depth of less than 1.5 meters of CO 2 , and in three atmospheres to less than 4.5 meters, the
transmission by one meter of carbon dioxide, within the limits of the CO 2 absorption-bands, is
between 20 and 30 per cent., because the transmission of these particular rays, after a preliminary
sifting through 0.5 meters of CO 2 , has been found to follow the simple exponential law :
i = Ix /'",
where I is the initial intensity of the limited radiation, t the transmission by unit-mass, m the
actual mass of carbon dioxide (measured as the depth in meters of CO 2 traversed by the rays), and
i the resultant intensity after absorption, by which law this degree of trail smissibility secures the
extinction of these rays. The strength of the chief carbon dioxide band in the solar spectrum
also appears to agree with what might be anticipated from the known absorbent mass of this gas
in the Earth's atmosphere, and the assumption that carbon dioxide gas has a simple molecule
under every degree of dilution and that its absorption depends entirely upon the mass of gas
traversed, is warranted.
One other assumption, however, is less commendable. While such small transmissions as 20
to 30 per cent, are the rule in limited regions, or bauds, in the infra red, it is not permissible to
apply them, as Angstrom has done, to the entire infra-red of the solar spectrum, thereby raising
the estimated solar constant to four small calories.* It must be understood that the absorption of
20 to 30 per cent, is the mean absorption of a series of bands which include special rays totally
absorbed, as well as intermediate ones which go free.
Angstrom's result indicates that about 4.5 meters of carbon dioxide is sufficient to almost
completely cut off the radiations absorbable by this gas, and taken in conjunction with Keeler's
observation (Am. J. Sci. (3), vol. 28, p. 196, Sept., 1884) that 3.4 meters of carbon dioxide absorb
35.8 per cent, of the radiation from a Bunsen burner name, the two ought to give approximately
the relative values of CO 2 and H 2 O radiations from this flame whose spectrum is purely one of
bands. We should anticipate from these facts that not over 40 per cent, of Bunsen flame radia-
tion is due to carbon dioxide, the rest coming mainly from water- vapor. This differs somewhat
from the relative areas of the sums of the respective maxima in Pascheu's curve of energy in the
spectrum of the Bunseu flame, but as the composition of ordinary illuminating gas is variable,
"The application of the method by which Angstrom obtains this value leads to the absurd result that over
60 per cent, of the original solar radiation is contained in the spectral region occupied by the bands of carbon
dioxide. The limits of these bauds have now been ascertained, and it is certain that they do not cover a length of
the solar spectrum possessing more than a small fraction of this proportion of total radiant energy.
106
some range in the aqueous component of flame-radiation must be expected from this cause; and,
besides this, the temperature of the flame is not a constant quantity, while the relative radiations
of the different components do not vary with the temperature according to the same law. Never-
theless, I believe that the chief cause of the discrepancy is the considerable absorption by the
fluorite of Paschen's prism of those emission-bands of aqueous vapor which are of greater wave-
length than those carbon dioxide bands which furnish the larger part of the emission at high tem-
peratures. Separating the CO. and H 2 O bands in Paschen's curve ( Wiefl. Ann., Taf. IX, fig. 6),
I found the relative areas were :
CO 2 :H 2 O = 115:1<)7
Making allowance for fluorite absorption increases the proportion of aqueous radiation, and
reverses the ratio. Hence less than half the radiation of the hot gases of the Bunsen flame is due
to carbon dioxide.
The growth of the band-emission, as temperature rises, agrees so nearly with the rate of
increase of the total radiation of carbon dioxide that another reason is added to Paschen's argu-
ment in favor of the absolute discontinuity of its spectrum. Zollner and Wu'llner having reached
the conclusion that a gaseous layer of infinitely great depth would send out a continuous spec-
trum from the broadening of the lines, a conclusion which presupposes that emission and absorp-
tion are never zero for any wave-length, Paschen tested the hypothesis by observing the absorption
of 33 cm. of carbon dioxide at the maximum in the spectrum of an incandescent lamp (1 = 1.4/.;),
a point quite outside the special regions of absorption for this gas. Xo difference greater than
one part in four thousand could be found between the absorption of air and CO 2 at this point.
"It is improbable that such absorptions, if they were present, should be the same; it is more
likely that both are zero. However, in consequence of the moisture of the air, a small and
equal absorption may have been present every time." ( \Vied. Ann., Bd. 51, S. 33.)
"The fact that CO 2 exerts an absorption which at any other spectral positions than those of
its absorption-bands is zero within the limits of errors of observation stands in connection with
another fact that the breadth of the absorption-bauds in question does not grow with increasing
depth of the layer." The breadth of the principal CO, absorption-band, at A = 4.25//, remained
unchanged when the thickness of the cold gas-layer was increased from 0.3 cm. to 33.0 cm., the
absorption of the maximum meanwhile increasing from 55 to 90 per cent. "For line spectra it
follows * * * that with increasing thickness of the gas-layer in emission the lines only become
brighter, but, in general, can not spread themselves over the entire spectrum." (Loc. tit., p. 34).
This does not prevent the greatest variety as to strength and rates of growth in such spectral lines
as those of water- vapor, but the carbon dioxide spectrum is much simpler. Besides the two bands
discovered by Knut Angstrom
(1) at 2.3/< to 3.0/*, maximum 2.7/<, and
(2) at 3.9/i to 4.7/v, maximum 4.25//,
Rubens and Aschkinass have discovered a third strong band in the extreme infra-red. With a
thickness of a little more than 20 cm. of CO 2 , "the whole region of absorption is limited to the
interval from 12.5yu to 16;<, with the maximum at 14.7/f. Aside from this region not the slightest
absorption could be detected between 8yu and 20//, even when the box was completely filled
with carbon dioxide," giving a depth of 65 cm. (Astrophys. Journ., vol. 8, p. 191, 1898.)
The absorption at different points in baud (3) (loc. tit., p. 189, fig. 9) is as follows:
[Source, zirconium burner Absorption by 20 cm. -(- of COj.]
Wave
length.
Absorp-
tion.
Wave-
length.
Absorp-
tion.
Wave-
length.
Absorp-
tion.
/'
Per cent.
/'
Per cent.
/'
Per cent.
12.5
1
14.0
28
15.0
70
13.0
4
14.5
67
15.5
30
13.5
10
14.7
75
16.0
2
The absorption at the center of band (2), according to Paschen (Wied. Ann., Bd. 51, S. 9),
amounted to 30 per cent, from the small trace of carbon dioxide in the air of the room. This was
107
increased to 89 per cent, by the addition of a 7 cm. layer of the gas, but after this absorption was
reached, further increase of the layer up to 33 cm. made little difference. At baud (1) (loc. cit.,
p. 10), an initial absorption of 10 to 20 per cent, by the air of the room was increased to about 30
per cent, by the 7 cm. layer, and to 43 per cent, by a layer of CO 2 33 cm. thick.
Owing to the very local distribution of the bands of carbon dioxide, the total amount of its
absorption varies greatly with the temperature of the radiant source on whose emanations the
absortion of the gas is exercised. Assuming that the absorption by a thickness of 1 inch of CO 2
at 30 inches pressure is identical with that of 48 inches of CO 2 at 0.625 inches pressure, we have
from Tyndall's measures (Contributions to Molec. Phys. 7 pp. 37 and 170):
Temperature of source of radiation 100 C. ; 1 inch of CO 2 * absorbs 2.2 per cent.
a a tt a 2 it a a 3^4. ..
" " " 270 C.; 1 " " " 6.3 "
(t tt it tt > It it
.6
Hence the absorption of radiation from the source at higher temperature is two to three times
as great as for the radiation from the low-temperature source. The reason for this is seen on com-
paring the spectral energy-curves of the sources. The chief baud of carbon dioxide (A. = 4.25/<)
falls near the maximum ordinate in the curve for 270, but affects a relatively insignificant region
of the spectrum of a body at 100 C. On the other hand, the chief absorption by water-vapor
agrees more nearly in wave-length with the maximum of the source of lower temperature,
whose radiation, in consequence, is relatively more depleted in passing through moist air than
that of a hotter body.
From the figures just given we may infer that the amount of carbon dioxide in 100 meters of
air at normal pressure absorbs about 2.5 per cent, of the radiation from a source at 100 C.
APPLICATION OF THE FOREGOING STUDY OF GASEOUS ABSORPTION TO THE RESULTS
OF LABORATORY EXPERIMENTS.
We are now ready to correct the measured values of apparent gaseous radiation, obtained in
Method C, by allowance for the modifications introduced by gaseous absorption.
By Table 48, p. 71, the apparent radiation of 141.8 cm. of carbon dioxide was:
At excess 50 C. r = 93 x (10)- 9 radim
" " 80 C. 260 " "
" " 100 c. 482
According to the data in the chapter on screens, the corresponding measured radiations of a screen
of sooted copper (the initial temperature being 35 C.) were:
At excess 50 C. (358 absol. T.) r = 1335 x (10) ~ 9 radim
" " 80 C. (388 absol. T.) 2321 " "
" 100 C. (408 absol. T.) 3095 "
From the curve (fig. 18), representing the absorption by carbon dioxide of radiation from sooted
copper at 100 C., founded on the observations of Tyndall, already cited, it may be inferred that
a 5-foot layer of CO. intercepts 18.4 per cent, of the rays. The corresponding absorptions for the
sources at lower temperatures will be about 0.8 and 1.5 per cent, smaller, or 17.6 and 16.9 per cent.,
respectively. Hence the disk-radiation, in the extreme positions, was diminished as follows:
Depth. Temperature-excess. Disk-radiation absorbed by
60 in. 50 C. 1335 x 10~ 9 x 0.169 = 225.6
CO:
xio- 9
and by rock-salt.
169 x IO- 9
60
in.
80
C.
2321 x
10- 9 x
0.176
= 408.5
X
io- 9
306 x
io- 9
60
in.
100
C.
3095 x
10~ 9 X
0.184
= 569.5
X
io- 9
427 x
10 - 9
Compare ante, footnote on p. 87.
108
At the smallest distance (4^ inches) the disk-radiation must have been diminished thus:
Depth. Temperature-excess.
4J in. 50 C.
4J in. 80 C.
4 in. 100 C.
Disk-radiation absorbed by CO-2
1335 x 10~ 9 x 0.055 = 73.4 x 10~ 9
2321 x!0~ s x 0.055 = 127.7 x I0~ s
3095 x 10- 9 x 0.055 = 170.2 x 10- 9
and by rock-salt.
55 x 10~ 9
96 x 10~ 9
128 x 19~ 9
All of these radiations have suffered an absorption of about 25 per cent, by the rock-salt
plate, * as given in the last columns for comparison with the measured radiations also absorbed to
20
18
16
14
10
8
6
4
2
J\adiaticm In/
tQ
20
30
40
50
60
18
approximately the same extent. The observed apparent radiations of the gas must be increased
by the differences of these numbers and further increased by the absorption of rock-salt.
Temperature-excess. Radiation of CO 2 through rock-salt, affected by COj absorption but corrected for salt.
50 C. \ 93 + (169 55)} x (10)- 9 - 0.75 = 207 x 10- 9 4- .75 = 276 x 10" 9
80 c. {260 + (306 - 96) | x (10)~ 9 0.75 = 470 x 10- 9 -> .75 = 627 x 10- 9
1000 C. |482 + (427 - 128) } x (10)~ 9 - 0.75 = 781 x 10~ 9 4- .75 = 1041 x 10~ 9
Finally these values must be further corrected for absorption by 4^ inches of carbon dioxide.
Only approximate estimates are available for this quantity. From TyudalFs Contributions,
page 185, Table XXX V, two minimum values of the absorption may be obtained A layer of CO 2
34 inches deep absorbed : ^r = 0.662, and one 13.1 inches deep absorbed -.-g-'g = 0.607 of the radia-
tion from a more distant layer of the same gas. A smooth curve through these points and the
* See my determination of this quantity. Astronln/fi. Journ., vol. 8, p. 211, Nov., 1898.
109
zero point, as in fig. 19, gives an absorption of -10 per cent, for a depth of 4^ inches. Since a
portion of the radiation caine from the walls of a metal tube and was more transmissible than the
gaseous radiation, and since the gaseous radiation does not increase much after the third foot, the
true absorption of its own rays by CO 2 is certainly greater than that given, but I am unable to fix
60
40
30
20
10
im of
J\ aviation
Co
fl
10
15
20
25
30
35
a more definite value for the absorption by the smallest depth. Accordingly, the true radiations
which the bolometer might have recorded, if it could have received the unobstructed emission of
rays from a free layer of carbon dioxide 141.8 cm. deep, are:
(50) 276 x 10- 9
(80) 627 x 10-
(100) 1041 x 10- 9
.6 = 460 x 10- radim.
.6 = 1045 x 10- 9 radim.
.0 = 1735 x 10- 9 radim.
Absorption by dry air being, according to Tyndall, one-ninetieth that of carbon dioxide, the
corresponding disk-corrections for air are, respectively, 1, 2, and 3 x 10~ 9 , and with further allow-
ance for absorption by rock-salt the corrected air radiations are:
(50) (139 + 1) x 10- 9
(80) (390 + 2) x 10- 9
(100) (723 + 3) x 10- 9
0.75 = 187 x 10- 9 radim.
0.75 = 523 x 10-" radim.
0.75 = 968 x 10- 9 radim.
The radiation of carbon dioxide is thus found to exceed that of air in every case. The absorption
of rock-salt for air radiation may differ from the absorption found for ordinary low-temperature
sources of radiation, but not greatly, as the close agreement of results obtained by Method B
without absorbent plates proves. (Ante, p. 71.)
110
Tyiitlall's comparisons of radiations from gases dynamically heated (quoted ante, p. 76) were
made with 3-foot layers. As I have already explained, the radiation of carbon dioxide is almost
exactly the same for a 3-foot layer as for one of 5 feet; but the air radiation with the shorter
depth is reduced proportionally. Hence at 50 excess the radiation of 3 feet of air should be
J X 188 x 10- 9 = 112 x 10-' radim,
5
or about one-fourth of the corresponding radiation from carbon dioxide. Thus the discrepancy
between my measures and those of Tyndall no longer exists after the application of the final
corrections, or, rather, at first sight, is turned to the opposite side.
Theory gives 30.5 C. as the temperature-excess produced by the dynamic heating of air at
normal pressure flowing into an exhausted receiver, and 23 C. is the corresponding temperature
from the dynamic heating of carbon dioxide. The observations of the radiation of CO 2 with a
cooling cylinder, however, do not extend as low as this, and nothing will be gained by substituting
results at the theoretical temperature in the preceding computation.
We may now test a conjecture put forth by Tyndall, that a residual deflection remaining after
absorption of the radiation of a dynamically heated gas by a cold layer of the same gas is due to
radiation from the walls of the tube to which heat has been transferred by contact. "To these
latter" [rays], he says, "the gas in the second chamber would be much more permeable than to
the former, and to these latter, I believe, the residual deflection of 6, or thereabouts, is mainly
due. That this number turns up so often, although the radiations from the various gases differ so
considerably, is in harmony with the supposition just made. In the case of carbonic oxide, for
example, the deflection is reduced from 13.7 to 6.3, while in the case of nitrous oxide it is
reduced from 19.5 to 6.2; in the case of olefiant gas it is reduced from 59 to 10.4, while in
other experiments (not here recorded) the deflection by olefiant gas was reduced from 44 to 6."
(Contributions, p. 186.) With the quadruple ratio (4.11 : 1), which 1 now give for the radiations of
carbon dioxide and air, and calling the unknown tube radiation x, the apparent radiations
measured by Tyndall from 36.3 inches of CO 2 (deflection = 16,8), and from air (deflection = 8 to
9) give
(4.11 x 8.5) - 16.8
-53T-
justifying Tyndall's supposition, and incidentally supporting the accuracy of both his and my
measures. After wandering through such a maze of corrections as the foregoing an independent
check does not come amiss.
The true radiations from the dynamically heated gases in Tyndall's work were
OO 2 , 11.0; air, 2.7;
but the large deflections, obtained when blackened tubes were used, were probably due, as I have
suggested (ante, p. 76-77), to heat developed by condensation of gases in the pores of lampblack.
The experiment on the radiation of steam (ante, p. 72) may now be reduced. The density
of steam at 135 C. (excess 97), and at normal pressure, being -TV.,, the liquid equivalent of 142 cm.,
at 126 mm. pressure, is
1 126
142 x 533 X 760 = 0.040 381 cm.,
which by fig. 13 (ante, p. 91) will absorb 5.1 per cent, of radiation from lampblack at 100. The
disk having an excess of 97, the correction for absorption of disk-radiation by vapor and salt may
be taken as
2942 x 10~ 9 x 0.051 x 0.75 = 113 xlO' 9 radim,
and the apparent radiation of steam, reduced with the instrumental constant at the epoch, is
38 x 43.8 x 10- 9 '= 1664 x 10~ 9 radim.
The absorbent layer contained 0.000 224 cm. of equivalent liquid water whose absorption exercised
on the special aqueous rays is by no means negligible, as shown by Tyndall's observations on the
Ill
aqueous absorption of rays from the hydrogen flame (cited ante, p. 88), from which ail absorption
of about 1.0 per cent, may be inferred in the present case, and the measurement of radiation from
a 5-foot layer of low-pressure steam, as finally corrected, is :
{113 + 1664 + (0.019 x 1664)| x 1Q- 9
-n-r-r - = 2412 x 10~ 9 radim.
u. < o
Reduced to radiant emission to a complete hemisphere, this becomes 0.01247 radim, which is about
81 per cent, of the constant for lampblack at the given temperature.
Before stating the total gaseous radiation a more accurate reduction of the observations at
different depths than was possible before shall be given.
From the curve (fig. 18) the values of CO 2 absorption of disk-radiation, corresponding to even
feet, are taken and used to correct the percentages in Table 40. By page 108, the correction to
299
CO. radiation for absorption of disk-radiation (both being absorbed by rock-salt) is rg^ = 62 per
cent. This will appear in the final column of the next table, the other numbers in this column
being derived from it.
TABLE 70.
Depth of
C0 2
CO 2 absorption
of disk-radiation. ~ a '
6 i
Correction
c = b X 62
per cent.
12.9
Inches.
Per cent.
Per cent.
Per cent. Per cent.
4i
ai= 5. 5
12
a-f= 9. 6
4.1
31.8
+19.7
24
a :i =13. 9
8.4
65.1
+40.4
36
a 4 =16. 4
10.9
84.5
-|-52. 4
48
a 5 =17. 8
12.3
95.3
+59.1
60
Ort=18. 4
12.9
100.0
+62.0
Applying the corrections in the last column to the observed radiations we have :
TABLE 71.
Depth.
0.35 foot.
1 foot.
2 feet.
3 feet.
4 feet.
5 feet.
Per cent.
Per cent.
Per cent.
Per cent.
Per cent.
Per cent.
CO 2 radiation
33.3
72.0
98.7
100.0
97.1
Correction (c)
+19.7
+40.4
+52.4
+59.1
+62
Sum
53.0
112.4
151.1
159.1
159.1
Corrected CO 2 ra-
diation express-
ed as a percent-
33.3
70.6
95.0
100.0
100.0
age of the high-
est value.
The air values in Table 40 will not be changed appreciably by a correction for the absorption
of disk-radiation by air. Accordingly, the percentage of radiation from different depths of the
two gases may now be finally stated.
TABLE 72.
CO 2 Air.
C0 2
Air.
Feet.
Centimeters.
100 100
125 100 125
4
100 80 100 100 100
3
99 60 75 91.5 75
2
80 40
50
70.5
50
1
48 20
25
40.5
25
i
2.5
6
2.5
112
Values obtained with the factor E 2 (p. 23), and representing the actual radiation falling upon
the bolometer as measured in absolute units, are reduced to hemispherical emission by multiplying
by the factor :
2 n X (28.7)'
0.19x5.2685 ~
An approximate conception of the relations between the total radiation passing through the
unit of surface in the unit of time, the temperature, and the depth from which radiation proceeds,
may be obtained for carbon dioxide and air by combining the variations from change of temperature
with those for change of depth, which is done in the following table (73) completing the experi-
mental part of this research.
TABLE 73.
Depth. 125 cm.
100 cm.
75 cm.
50 cm.
25 cm.
2. 5 cm.
Air.
CO 2 .
Air. CO 2 .
Air.
CO,.
Air.
CO.,. Air.
C0 2 .
Air.
CO 2 .
o
100
.00442
.00897
. 00353 . 00897
. 00265
. 00821
.00176 .00632 .00088
. 003,3
.00009
. 00054
90
. 00325
.00697
. 00260 . 00697
. 00195
. 00638
. 00130
. 00491 . 00065
.00282
.00007
.00042
80
. 00238
. 00540
.00190 .00540
. 00143
. 00494
. 00095
.00381 : .00048
. 00219
. 00005
. 00032
70
.00173
. 00417
. 00138 . 00417
. 00104
. 00382
. 00069 . 00294
. 00035
. 00169
. 00004
.00025
60
. 00123 . 00319
. OOC99 . 00319
. 00074
. 00292 . 00049 . 00225
. 00025
. 00129
.00002
.00019
50
.00086
.00238
. 00068 . 00238
. 00051
. 00218 . 00034
. 00168
. 00017
. 00096
. 00002
.00014
40
.00056
.00169
. 00045 . 00169
.00034
. 00155
. 00023
.00119
.00011
. 0006S
. 00001
. 00010
30 . 00035
.00111
.00028 .00111
. 00021
. 00102 . 00014
.00078
. 00007
. 00045
. 00001
.00007
20 .00019
.00064
. 00016 . 00064
. 00012
. 00059 . 00008
.00045
. 00004
. 00026
. 00000
. 00004
10 .00008
.00027
. 00006 . 00027
. 00005
.00025 .00003 .00019 .00002
.00011
.00000
.00002
These values in fractions of a radim are plotted in Fig. 20.
At 100 C. excess of temperature, and at a somewhat greater excess above the freezing point,
air 1 cm. deep radiates 0.000 036 radim, or 0.000 000 36 radim per degree. With an excess of
only 1 C. the radiation may be estimated as 'about 0.000 000 06 radim. These quantities are
considerably smaller than the 0.000 001 14 radim found by Professor Hutchins (Am. J. Sci. (3)
vol.43, p. 362, 1892), who, however, did not dry his air. Moreover, as has been shown, Professor,
Hutchius underestimated the depth of the radiant layer of gas, which makes his measurement
of radiation per unit of depth too large. On the other hand, my values exceed that deduced by
Maurer from meteorological considerations, namely, 0.000 000 Oil 6 radim. The difference here is
very likely due to absorption by air of its own radiation, where large masses are involved, as in
the atmosphere.
The region of the spectrum in which the radiation of air lies, may possibly be inferred from the
following facts: A region of powerful oxygen absorption exists in the ultraviolet, to which, in all
probability, a strong baud of emission corresponds ; but it is not likely that any emission, produced
by simple heating, can be felt in this part of the spectrum at low temperatures. The linear
oxygen absorption groups A,/>, and a in the red, and a series of faint diffuse bauds, of which
the strongest corresponds with Brewster's telluric band 6 (A = 0.565// to 0.585yu) in the yellow,
together with any others of a like order which await identification in the infra-red, are too
insignificant to have emission counterparts which will account for any appreciable fraction of the
low-temperature radiation of this gas. Nitrogen and argon are, so far as we now know, of still
less importance, since no telluric bands have as yet been traced to their presence in the
atmosphere.
Two facts remain to be considered. Hutchins found that a plate of quartz, 0.5 cm. thick,
reduced the deflection from hot air from 151 div. to zero; and it has been noted (ante p. 34) that
0.315 cm. of glass appeared to transmit 8 per cent, of air-radiation. Besides the region of quartz-
absorption at 0.103/^, H. Kubeus and E. F. Nichols (Phys. Rev., vol. 5, p. 105, Aug., 1897) have found
bauds of metallic reflection and total absorption for this substance at 8.50 //, 9.02yw, and 20.75//.
The first two of these bands, with the neighboring region from 8/1 to 9.5^ through which trans-
mission by a layer of quartz, so thin as 18 u, does not exceed 10 per cent. (Nichols, Phys. Rev., vol.
4, p. 307, 189?), can not cover the atmospheric bauds which we are seeking, since in this part of
113
the spectrum solar rays pass through the atmosphere easily, and the principal emission of radiation
from hot aqueous vapor, between 5yu and 8 7, also lies outside of this region. Hence it is perhaps
permissible to infer that the low-temperature emission of air, which is so completely absorbed
by quartz, has a wave-length not far from 20.75A/, and that air also absorbs strongly in this
region; but, if so, the ratio of air- radiation to the radiation of carbon dioxide ought to diminish
as the temperature rises, at least until those very high temperatures are attained which favor the
emission of the ultra-violet band of oxygen, and there is no evidence of this. I am not disposed
OOQ
50 60 10 80
S^ig. 20
r
30 100 HO ttO c-m.
to insist upon my observation of a feeble transmission of radiation from air by glass, because
it rests upon a very small deflection, but, if genuine, it indicates a discontinuity and essential
difference in the absorptions by glass and quartz at this extreme wave-length.
GENERAL APPLICATION OF THE PRECEDING STUDIES OF ABSORPTION AND RADIATION
TO THE PROBLEMS OF ATMOSPHERIC RADIATION.
We have seen that a highly absorbent gas, and one which is also an equally powerful radiant
in thin layers, may have little more radiative power than a bad radiator when the depths are
greater, the positions of the two being finally reversed at still greater depths, as indicated by the
extended curves of fig. 20, and that, in fact, there is not as much difference as might be imagined
12812 Bull. G - 8
114
between the radiation of the different constituents of the atmosphere at ordinary temperatures
and when in large masses. The facility with which a highly radiative vapor parts with its heat
is largely annulled by self-absorption of its own radiations in deep layers, and since in gases heat
is transferred from molecule to molecule with the greatest ease, it is probably a fact that small
masses of mixed gases or vapors, such as are used in laboratory experiments, radiate chiefly by
their most highly radiative molecules, the others transferring their heat to these kinetically;* but
in such great masses as are concerned in atmospheric thermal and radiant processes, it is the
feebly radiative molecules which act as radiators, except in a comparatively thin outer layer.
While laboratory experiments are necessary for a correct understanding of the processes
which go on in the simplest cases of gaseous radiation and absorption, actual quantitative values
which may be of use in large-scale meteorological computations will probably still have to be
derived by meteorological methods.
There seems to be some analogy between the radiant powers of dry air and rock-salt. Both,
if the suggestion on page 113 be accepted, emit ether- waves ot very great length. Both are highly
transmissive in that part of the spectrum where fall the emissions from bodies at ordinary tempera-
tures. In small masses they are very bad radiators, but their relative radiant efficiency increases
with the depth of the radiant layer.
The powerfully radiant vapors, such as ammonia, like the metals among solids, radiate from
a very feeble depth. In the spectral region of their principal emission, after exceeding this depth,
no further increase is to be expected, even though the radiant layer be increased to infinity; and
as the radiations of these vapors are limited to definite spectral regions, the total emission must
finally exhibit an equally definite relation to that of a black body, depending upon the position
and extent of those parts of the spectrum within which the vapor is a perfect radiator. In like
manner, a gas which is very feebly absorbent or radiant in thin layers, has some depth of maximum
efficiency at which its peculiar bands attain the greatest possible development. If these bands,
while feeble, are wider, or occupy more extensive regions of the spectrum than those of the strongly
radiant vapor, and are of such wave-lengths as to be emitted with equal readiness at the given
temperature, the gas in a layer of great depth may surpass a like depth of vapor as a radiator,
although, when in thin layers, the vaporous radiation immensely exceeds the gaseous. Again, if
the emission bands of the gas are more numerous, and occupy very extensive regions of the
spectrum, while those which can be emitted by the vapor at the same temperature are of small
extent, a layer of the gas less than the depth of maximum efficiency (except, perhaps, at some
temperature which especially favors the vapor's emission) may radiate better than the vapor, the
feebleness of the gaseous emission-bands being compensated by their great number or wide range
through the spectrum. The rate of increase of radiation with temperature-elevation will depend
also upon the region of the spectrum to which the emission is confined, long waves increasing in
strength more slowly than short waves.
The discrepancies between the results of different observers of gaseous radiation, working
under various conditions of depth, temperature, etc., after the elimination of errors involved in
methods of observation, are capable of being reconciled, and seem to demand varieties of spectral
structure, such as those which have been mentioned, for their explanation. To apply the argu-
ment to the components of the atmosphere: Carbon dioxide, so far as is now known, has only
three emission-bands in the infra-red. Within narrow spectral limits, the radiation of this gas is
very powerful, requiring only about a meter-layer to give maximum efficiency. The almost equally
slow increase of air-radiation with rise of temperature is perhaps due to the long wave-lengths of
its bauds; but the very gradual growth of its radiation as the depth enlarges is best explained by
the supposition of an extensive spectral region filled with numerous feeble emission-bauds which
grow in strength very slowly as the depth increases, but which, nevertheless, in their sum total,
eventually surpass the radiation of the few strong bauds of carbon dioxide. Whether oxygen,
nitrogen, or argon are concerned in this primarily feeble einis&ioii can not be stated. In a different
category from either of the other atmospheric constituents, is water-vapor. Its spectrum, consists
of many bauds composed of very numerous fine lines. Some of these bands are strong, reaching
maximum development with a slight depth, while others grow slowly. The extent of spectrum
* See Tyudall's experiments in "varnishing" air molecules with those of more powerfully radiant vapors.
115
filled with these groups is very great, and thus the radiation is large with a small thickness of
vapor, and yet continues to increase through a wide range of depths. The importance of aqueous
vapor as a radiator is therefore great ; nevertheless, in layers of atmospheric dimensions, there may
not be as much difference in the relative efficiency of atmospheric constituents as might at first
appear. Throughout the greater part of this vast aerial envelope the gaseous molecules can not
radiate, except so far as the stronger radiators emit to the weaker, and these to the outer world.
The different sorts are quite independent of each other, but those of a kind are hemmed in by
other molecules of the same absorbent properties which cry "no thoroughfare" to ether- waves
which have their own vibratory period. Thus it is that, in the upper air, temperature remains
almost constant through day and night, and only changes as the vertical circulation of storms, and
the general movement of the entire atmosphere from equator to poles and back, replaces the air
at any given level and terrestrial position by other air which has acquired its temperature else-
where under freer conditions. Only at the borders of its domain is any constituent of the air
entirely free to change its temperature by its own radiation.
An important relation results from the facts embodied in the theory of a maximum radiant
depth in a gas, when combined with the further knowledge that this depth is reached at different
distances for particular wave-lengths, and is quickly attained for those rays which lie near the
maximum of an emission-band. It seems permissible to say already that so far as gaseous radia-
tion depends upon simple heating of the gas, the ordinates of the maxima in bands of different
wave-length (the depth being sufficient to give maximum; radiant efficiency for these special rays)
are related to each other in the same way as are the ordinates in the spectral energy-curve of a
black solid body. As the temperature rises, the heights of the emission-bands of short wave-
length increase more rapidly than those corresponding to the longer waves, and with the limita-
tion noted as to manner of excitation, bands at the shortest wave-lengths only become sensible at
those high temperatures at which similar radiations first appear in the spectrum of a black solid.
Not only is this relative agreement maintained, but the absolute energies in the spectrum at a
gaseous band-center and at the same point in the spectrum of lampblack for the same tempera-
ture are almost identical, any slight inferiority of the gaseous radiation being probably attributa-
ble to the linear constitution of the band and the absence of the condition of maximum efficient
depth for some of the rays of the complex bundle. This point has been established for aqueous
vapor and carbon dioxide by the observations of Pascheu on the emission of heated gases. After
noticing facts brought forward by Pringsheim, among others that thin wires are. only heated to
about 150 C. by certain flames, such as that of carbon bisulphide, " which, notwithstanding, send
out an abundant and absolutely blue light," and commenting that, in spite of the low temperature
of the wires, "the luminous molecules may, nevertheless, have a very high temperature" a con-
clusion which has also been reached by Smithells on theoretical grounds Paschen demonstrates
experimentally that, whatever part chemical action may have in originating high temperatures,
the vapor of water and carbon dioxide whose discontinuous emissions make up the chief part of
the spectrum from a Bunsen-burner flame, radiate solely by virtue of their heat, however imparted.
The emission-bands discovered by Julius in flame-spectra were reproduced by Paschen by simply
heating the gases without any combustion whatever. The emission-bands of carbon dioxide were
" still certainly perceptible" with the gas at 73 C., at which temperature there can be no question
of dissociation or of chemical action ; and the emission from aqueous vapor was followed to 280 C.
The maximum of CO 2 radiation at wave-length 4.3 /<, exhibited the following intensities at the
given temperatures: At 842 C., 5G6 div.; at 707 C., 357 div.; at 450 C., 114 div.; at 306 C., 37
div.j at 204.5 C., 11.1 div.; at 165 C., 6.6 div.; at 114 C., 3.0 div.; and the highest maximum of
water-vapor at wave-length 2.7 j.i gave": At 900 C., 146 div. ; at 638 C., 25.4 div. ; at 496 C., 5.6
div. ; at 400 C., 2.1 div. ; at 284 C., 0.6 div. ( Wied. Ann., Bd. 50, S. 428, 429, 1893.)
Here radiation has increased with temperature at a more rapid rate for water than for carbon
dioxide, or in accordance with the usual law for continuous spectra where the shorter waves have
a more rapid rate of increase of energy than the longer ; but the relation between the intensities
of maxima in different parts of the spectrum is not given by these experiments, since the maxima
compared do not belong to the same substance, nor can it be a definite one even for a single
radiator unless the depths exceed maximum efficiency for every one of the bands.
116
In the spectrum of steam, 7 cm. deep, at 500 C., the heights of the long- waved maxima are
nearly equal to the corresponding ordinates in the spectral energy-curve of lampblack at the same
temperature. At wave-length 5.6;.-, "where the water- vapor spectrum has the intensity 87 mm.,
lampblack at 500, under like conditions, gives a galvanometer deflection of about 110 mm." At
6.O// "these intensities are for water G6, for lampblack about 80," but at 2.7 j.i "on the other hand,
for water 139, for lampblack 320 mm.," showing that the depth of 7 cm. is insufficient to fully
develop the radiation of the last-named band. ( Wied. Ann., Bd. 51, S. 3G, 1894.) The height of the
emission- maximum at 2.7 /.i was increased from 20 mm. to 139 mm. when the depth was increased
from 3 mm. to 70 mm. (Loc. cit., p. 35.)
The changes in the spectral energy-curve of radiant aqueous vapor produced by variations of
temperature are still more marked than those from varying depth. Thus while the aqueous
absorption is most intense in the long-waved bands, and while these bands are also most promi-
nent in the emission at low temperatures, the band at 2.7/t has a height twenty times as great as
the former in the spectrum of the oxyhydrogen flame. Hence different bands in the spectrum of
the same substance follow different laws of increment, both as to temperature and as to depth.
Carbon dioxide at wave-leugth 4.3;-, in even so small a depth as 7 cm., behaves very much like
a black body, both as regards the absolute intensity of its radiation and its variation with the
temperature. Paschen's curve for the latter quantity (Wied. Arn., Bd. 51, Taf. 1, fig. 9) falls but
little below the corresponding curve for lampblack, indicating that 7 cm. is very near the maximum
efficient depth for certain rays from this gas.
It is not to be expected that a vapor which is quite colorless and transparent for luminous
rays should give a continuous visible spectrum even when highly heated; but the same gas in
another part of the spectrum may have its vibrations damped through a wide range of wave-length,
provided the depth or density of the radiant layer be sufficient. The wide bands thus produced
resemble those limited spectral regions within which certain phosphorescent solids and liquids
radiate exclusively, but without giving definite line-spectra.
Strongly colored gases which absorb visible rays emit continuously in the same visible region
of the spectrum. Mr. J. Evershed's experiments on the radiation of heated gases (Phil. Mag. (5),
vol. 39, p. 465, 1895) prove "that besides iodine, the vapors of bromine, chlorine, sulphur, selenium",
and arsenic can all be made more or less incandescent by heating to the temperature at which
glass combustion-tube softens, and the light emitted by each of these glowing vapors appears to
give a perfectly continuous spectrum, while the corresponding absorption-spectra are selective.
Thus there is no such close relation between emission and absorption as is implied by Kirchoff's
law of radiating bodies. There seems, however, to be a general relation between the total absorbing
and radiating power for the visible rays."
The production of those distinct and widely separated vibrations which give line-spectra,
demands considerable freedom of motion, such as exists in the partial vacuum of a Geissler's tube,
in the high dilution of minute traces of metallic salts distributed through the mass of a Buusen
flame, or in the very thin surface layers at the inner and outer surfaces of such a flame, where
chemical action is going on. Spectral differences are also found at different flame-levels, testifying
to a succession of chemical interchanges which undoubtedly favor the production of line-spectra.
Thus, cupric chloride in the Bunsen flame gives successive sheaths of yellow, red, blue, and green
flame, due to metallic copper, cuprous chloride, and cuprous oxide, as Professor Sinithells has
shown by means of his cone-separator for studying the flame of the Bunsen burner. (Phil. Mag. (5),
vol. 39, p. 122, 1895.) Very brilliant spectra of the copper salts may be obtained by means of a
copper wire which has stood for some time in hydrochloric acid, and has become deeply corroded.
There is also in this case a partial separation of the flame-effects as successive layers of the corroded
film burn off.
The mechanism by which the discontinuous radiations of the electric glow in rarefied gases
and of flames are produced has been the subject of much speculation. Werner Siemens, in 1882,
wrote :
If we assume that the gas-molecules are surrounded by a sheath of ether, an alteration of these sheaths of
ether must take place whon two or more such molecules combine chemically. The resultant movement of the ether-
particles must be compensated by vibrations which may form the starting point of the outflow of waves of light
117
and radiant heat. In quite a similar way we can picture the light-effects which appear when an electric current is
passed through gases. ( Wied. Ann. Bd. 18, S. 315.)
Since the current conducted by gas appears to be always accompanied by chemical action, the glow might be
explained as in llarnes through the oscillating environment of the etherial sheaths of the gaseous molecules by
which the passage of the electricity will be facilitated. (Loc. cit., p. 316.)
Others have imagined the gaseous molecule to consist of a congeries of atoms whose configura-
tion being changed by electrification, or during the act of chemical combination, for example,
certain of the atoms being temporarily separated from their groups, or ionized, there results a
series of atomic oscillations about a mean position, until the energy of the disturbance is dissi-
pated as radiant energy of similar periods. As thus stated, this hypothesis offers no suggestion
of the mode by which energy is transferred from the atoms to the ether. But if the gaseous mole-
cule is composed of linked atomic vortices of ether, or of associated concentric vortices, in which
are critical or limiting surfaces, conditioned by changes of form or velocity of etherial movement,
the rearrangement of these groups determined by chemical interchange, or their disturbance from
positions of equilibrium by electrification, may engender waves in the critical surfaces whose
periods depend upon the dimensions and surface- velocities of these loci. The passage of systems
of waves over such closed surfaces may give foci of interference, and it is possible that the con-
nection and order observed in the frequencies of the numerous sorts of vibrations which the atoms
of one element can execute simultaneously, or at least in such rapid recurrent succession that the
series can not be distinguished from a simultaneous one, are to be thus interpreted.
The hypothesis of Arrhenius which assumes ionization of a gas wherever line-spectra are
produced, demands a certain amount of ionic dissociation even at comparatively low temperatures,
and this has perhaps not been demonstrated except under peculiar conditions of electrification;
but whether, for example, we conclude as Liveing and Dewar did (Proc. Roy. Soc. London, vol.
30, p. 152, 1880; see also vol. 34, p. 418, 1882, where somewhat conflicting testimony is given), that
the bands in the spectrum of the blue base of a Buiisen flame are due to carbon and hydrogen in
the act of uniting or separating, in the formation or destruction of acetylene, the chemical union
of these two substances being considered essential to the exhibition of this spectrum, or whether,
with Lockyer and others, the spectrum in question be attributed to carbon vapor alone, I think
we must agree with Arrhenius that it is an atomic rather than a molecular motion which produces
the line-spectrum, and, in general, it is molecular motion which gives extensive diffuse bauds,
such as those of the absorption-spectra of liquids, and the absorption and emission spectra of
some gases.
Is it necessary, however, that atoms should be completely free in order that their vibrations
may give line-spectra? A distinction between the spectra of free and of partially constrained
atoms may be granted, but it seems permissible to assume that some of the most persistent vibra-
tions may be emitted by atoms in the midst of their aggregations which constitute the molecules.
Prof. A. A. Michelson ("On the broadening of spectral lines," Astroph. Journ., vol. 2, p. 251, Nov.,
1895) finds that rarefied hydrogen (pressure about 1 mm.) gives out its characteristic spectrum
under the action of an electric discharge at a remarkably low temperature. The width of a line
having been proved to increase as the temperature rises in the ratio of the square roots of the
absolute temperatures, the width of the red hydrogen line in an uuheated tube was found to
correspond to a temperature not more than 50 C. above the surroundings, or 320 absolute. The
emission of visible radiations at such a low temperature implies that the rays are not produced
by simple heating (molecular motion or rectilinear motion of free ions), but that the passage of the
electric spark by ionic motions increases the motions (either rotations or oscillations) within the
molecules, modifying the internal atomic motions without changing the rectilinear velocities of the
atomic aggregates to any great extent. On the contrary, since hydrogen and other simple gases
may be heated to very high temperatures without causing them to emit visible radiations, it is
evident that the shocks produced by external collisions, due to rectilinear motions, are not as
efficacious in setting up internal atomic vibrations as are the torsions experieiK ed during the
passage of a spark. The aurora is a case in point. In the middle latitudes it occurs usually at
heights exceeding 40 miles, where the air is intensely cold, and is an instance of visible atmos-
pheric radiation produced, not by direct thermal means, but electrically.
118
ATMOSPHERIC DUST.
The experiments with dust-laden air have indicated that the addition of a small amount of
solid matter, diffused through a large volume of air, does not change the radiating power of the
latter perceptibly. The same conclusion may be drawn from the use of smoke to prevent frost, for
if the finely divided carbon increased the radiating power of the air, the protection would be less
effectual. The principal result which can be traced to the presence of floating dust is its modifica-
tion of atmospheric transmission by the reflection and scattering of rays during their passage
through the turbid medium.
Tyndall imitated the blue color of the sky, and even the peculiar polarization of its light
which is a maximum 90 from the sun, and which exhibits neutral points where the plane of
polarization changes by precipitating a mist of attenuated solid or liquid particles, of scarcely
more than molecular dimensions, from mixed rarefied vapors capable of reacting chemically under
the influence of light. By choosing substances, " one at least of whose products of decomposition
under light shall have a boiling point so high that as soon as the substance is formed it shall be
precipitated,' 1 '' solid or liquid particles of great fineness are produced without having time to cohere
into coarser agglomerates. " By graduating the quantity of the vapor this precipitation may be
rendered of any degree of fineness, forming particles distinguishable by the naked eye, or particles
which are far beyond the reach of our highest microscopic powers." (Contributions to Molecular
Physics, p. 431, from Proc. Roy. Soc. London, No. 108, 1869.)
As the particles become coarser they cease to reflect selectively, at least in the visible spec-
trum, but return light of every refrangibility in nearly equal proportion. In this way a cirro-
stratus cloud spreads white light all over the sky, overpowering the blue light. In like manner a
fog, dense enough to obscure the rays of the sun, may diffuse enough of sunlight to produce quite
a bright general illumination; but in this case the reflection is not absolutely devoid of selective
properties. To the palm of the hand held up, the position of the un.seen sun is revealed through
the sensation of warmth produced by solar rays of great wave length which are capable of pene-
trating the mist. The obscure rays may also be recorded by the actinoineter, and analyzed by the
spectroboloineter, which shows that a mist, capable of keeping out all of the visible rays in the
direct beam, may still transmit infra-red waves beyond 2/< rather freely.
Lord Eayleigh (Phil. Mag. (5), vol. 47, p. 375, 1899) finds that diffraction from the molecules of
the air, which are of small dimensions relatively to the waves of light, is competent to account for
a large part of the selective scattering of short waves in sky light, and for the actual transmission
of the visible part of the spectrum. If .r is the distance through which light must pass in air at
atmospheric pressure before its intensity is reduced in the ratio of the basis of natural logarithms
to unity,
*= 32 ,f ( ;%
where n is the number of molecules in the unit of volume, or 19 x (10) 18 per cubic centimeter
according to Maxwell, /< is the refractive index as modified by the spherical molecules, j.i 1 = .0003,
and A is the wave-length of light. Taking Bouguer's estimate of the transmission of star-light by
an entire atmosphere, namely 0.8, we find, since the maximum sensitiveness of the eye for light as
faint as that of the stars is about at wave-length
A = 5 x (10) - 5 cm.,
x = 40 kilometers.
The homogeneous atmosphere being 8.3 kilometers thick, the observed transmission by 40 kilo-
meters is :
r\ 40 -
0.8 ) M = 0.34
which does not differ much from the assumed transmission, = 0.37.
' e
If Bouguer's eye was most sensitive to yellow rays at A = C x (10) 5 cm., x = 83 kilometers,
and the corresponding observed transmission, (0.8) ln = 0.11, is less than a third of that computed by
119
the hypothesis of molecular diffraction, leaving a considerable part of the blue light of the sky to
be supplied from other sources. There can be no doubt, however, that the exponent of A should be
larger than 4 at the blue end of the spectrum, and smaller than 4 in the infra-red, as Lord Eayleigh
suggests (loc. cit., p. 383). The formula, as it stands, gives for A = 0.293yi< a transmission by one
atmosphere of 0.17, and for A = 1.0/t a transmission of 0.99; but the former is known to be zero,
and the latter, as far as it depends on selective scattering, is probably more nearly equal to
0.91) 0.17 = 0.82. The sudden termination of the solar spectrum at 0.293;/ may be produced by
a local absorption-baud of oxygen, but selective scattering gives nearly the same limit.
Coruu (Comptes rendus, t. 88 and 89) finds that the limit of atmospheric transmission in the
ultra-violet with a clear sky, depends on the barometric pressure, thus on the oxygen and nitrogen
contents, rather than on aqueous vapor or other variable constituent of the air. If it were not
for this fact it might be supposed that the molecules of water-vapor, or the products of condensa-
tion resulting from the continual diffusion of a very rare aqueous vapor into the upper atmosphere,
might be the sole cause of sky-color, since, as Tyndall remarks (Heat as a Mode of Motion, p. 414),
"the color of the firmamental blue, and of distant hills, deepens with the amount of aqueous vapor
in the air," and in part this may be an additional cause of coloration, although it appears to be of
no importance in determining the limit of the spectrum. The association of the deepest blue sky
with the descending air of the tropical calms may be explained by the purification which the air
has undergone. The coarser dust having been washed out in the abundant precipitation of the
equatorial rains, the genuine color of the sky resulting from molecular diffraction is no longer
obscured by the more general scattering of light by the larger and unassorted particles.
The beautifully colored coronas and patches of color seen upon incipient cirrus near the sun
are due to diffraction from ice or water particles of a coarser order than the molecular, and
graduate into cases of simple and indiscriminate reflection from still coarser particles, an effect
which becomes very great at large angles of incidence, and produces the strong glow around
the sun, never absent except in a sky of exceptional purity, such as can only be found at great
altitudes.
Whymper in his Travels Amongst the Great Andes of the Equator, page 324, thus describes the
effect of clouds of volcanic dust from Cotopaxi:
When they commenced to intervene between the sun and ourselves the effects which were produced were
truly amazing. We saw a green sun, and smears of color something like verdigris green high up in the sky, which
changed to equally extreme blood-reds, or to coarse brick-reds, and then passed in an instant to the color of tarnished
copper, or shining brass. No words can convey the faintest idea of the impressive appearance of these strange
colors in the sky seen one moment and gone the next resembling nothing to which they can properly be compared,
and surpassing in vivid intensity the wildest effects of the most gorgeous sunsets.
I think there can be no doubt that these vivid colors were entirely due to diffraction, owing
their brilliancy to the uniformity in the size of the particles producing them. The description
reminds one of the colors of soap bubbles in sunshine. Cirrus clouds are apt to be composed
of ice crystals in the act of forming from vapor. The particles are constantly growing in an
irregular way, and numerous diffraction rings produced by means of swarms of particles of as
many different diameters, are superimposed, so that the blended colors are not pure, and there is
much white light.
In general, a part of the diminution of solar rays in passing through the air is due to selective
scattering by air-molecules, to which diffraction by ice-crystals of minute size, and reflection from
dust of every sort may be added in a hazy atmosphere; but these causes have very little influence
upon the true atmospheric radiation which consists chiefly of long waves but little affected by dust.
SUMMARY.
The exposition of a few leading principles is needed to give entrance and guidance in a general
survey of the subject. Atmospheric radiation is so extensively modified by atmospheric absorption
of rays that the subject of the atmosphere's transmissive power must be included.
The atmosphere by its molecular constitution produces a selective scattering of the rays which
pass through it, which is greatest for the short waves. Ether-waves of greater length than 2^u
are but little affected by selective scattering, but throughout the visible spectrum there is an
120
increasing depletion of the direct radiant beam, progressing a little more rapidly than the inverse
fourth power of the wave-length. The rays taken out of the direct beam in this way do not alter
the temperature of the air, and a large part of them reach the Earth's surface. The same is the
case with the light diffracted by minute ice-crystals, or more indiscriminately reflected by coarser
dust-particles.
An entirely different process is involved in the production of local line and band absorption.
Special rays are absorbed by the atoms and molecules of the various atmospheric constituents.
Here the energy which exists in the ether as radiation is transformed into the energy of molecular
or atomic movement, and remains in the atmosphere as an increase either of its sensible tempera-
ture or of its latent heat. The ultra-violet rays appear also to produce chemical change in some
of the atmospheric substances, accompanied by electrification. The composition of the atmosphere
is being continually changed by emanations from the Earth and its inhabitants, and the atmospheric
thermal energy is increased in this way, and especially by the latent heat of vaporization of water.
Heat is also developed dynamically whenever there are descending movements in the air. High
winds in dry and dust-laden air generate large amounts of frictional electricity, and a part of this
thermal and electrical energy imparted to the air from many sources, is eventually given out again
in the form of radiation.
The actual spectral energy-curve of a depleted sunbeam is a complex of an exceedingly varie-
gated original radiant energy, as further modified by telluric absorption, every one of whose lines
and bands has a separate origin and law of variation. In like manner the radiation emitted by
the air is made up of a great variety of individual lines and bands, each having a law of its own,
depending on the pressure, depth, temperature, and physical state of the productive constituent.
In a measure the emission by the air resembles its absorption, but is confined to the longer waves
when thermally produced at relatively low temperatures. Unknown regions in which the oxygen,
nitrogen, argon, and krypton of the atmosphere radiate at low temperatures, remain to be explored.
The chief radiations which can now be definitely placed in the spectrum are those of aqueous
vapor and carbon dioxide. Owing to the feebleness of these radiant bands at low temperatures,
the positions and relative intensities of the more refrangible ones are best studied in the absorption-
curve of the solar spectrum.
The following table (75) of positions and intensities of infra-red bands in the solar spectrum
has been compiled from two plates (a) A to cj 2 , (&) (*>i to deviation 38 45' accompanying an
article on the "Infra-red solar spectrum of a 60 rock-salt prism," published in the Annual Report
of the Smithsonian Institution for 1897, Appendix Y, pp. 66-68. The standard temperature of the
prism is stated to be 20 C. "The positions of about 225 absorption lines and bands are deter-
mined * * * between deviations of 40 25' and 38 45', corresponding to wave-lengths 0.76 u
and 5.20 //, respectively." These curves are the culmination of Langley's long labors in the solar
spectrum. No band is included in the present list which is not also shown on the three bolographs
exhibited by Professor Langley at the Oxford meeting of the British Association (Astropliysical
Journal, vol. 1, p. 162, pi. 9, Feb., 1895). The numbers assigned here to the intensity of absorption
at the centers of the individual bands have been obtained by comparing the bolographic ordinates
with those of a smooth curve passed by estimation through the unabsorbed maxima. A list of
these maxima and their intensities in the prismatic spectrum follows:
TABLE 74.
Minimum de-
viation.
40
40
39
39
39
39
39
24.5
9.0
56.4
47.0
38.0
28.5
12.0
Intensity of
radiation.
11
24
38
54
63
31
18
[14]
[28]
[45]
[64]
[77]
[H2]
[36]
121
The numbers in brackets are the values obtained by correcting for atmospheric absorption.
The adopted curve has been made symmetrical on the side of greater wave-length to allow for the
undoubtedly very large absorption of the entire spectrum as the great bands of water- vapor and.
carbon dioxide are approached, since in this region the intervening points of comparatively unab-
sorbed energy begin to be encroached upon by the bands. The corrected values have been
assigned after taking account of the-extensive stretch of almost total absorption between 5 // and
8//, and the probable form of the original spectral energy-curve before the radiation entered the
Earth's atmosphere has been inferred by supplying these missing regions. The limits adopted for
the breadths of the bands and groups of bauds are somewhat arbitrary, owing to the very gradual
way in which the slopes of the energy-curve begin :
TABLE 75.
Designation of band. ^HSTot
Wave-length.
Transmission. Absorption.
AVave-lengths assigned
by other observers.
Source and
remarks.
C I
/*
Per cent. j Per cent.
Great A
40 24.0
0.76
1-^-14. 2= 7. i 93 Abney. Telluric.
A,
40 23.6
0.77
214. 5=13. 8 86
Photography. Dif- \ Oxygen.
fraction grating.
Brewster's Yi
40 16. 7 to
0.82
10^20. 6=48. 5 52
. 816-. 821
lucludes so-
15. 5
lar Na. 818.
" Y
40 15. 3
0.825
8-21. 3=37. 6
62 . 823
J 3
40 15. to
0.83
922. 4=40. 2 50 . 825-. 832
13.5
" Ji 40 12.2
" X 40 11.7
0.855
0.86
16-24. 6=65.
1525. 2=59. 5
35 .854
40 .866
j Solar Ca.
40 10. 5
0.875
2026. 4=75. 8 24
40 7. 7 to
. 895- . 91
18-30. 0=60. 40 . 895-. 903
6.6
Telluric,
Abney's n
40 6. 6 to
. 91 - . 915
1830. 9=58. 3 42 . 905-. 911
probably
6.0
aqueous.
40 6. to
.915- .92
1831. 8=56. 6
43
. 912-. 918
5.2
Rbo-tau group 40 4. 6 to
0. 925 to
Breadth,
39 59.5
0.985
U.060/*.
Abnev's p 40 4. 6 to
.925- .935
633. 4=18.
82
. 930-. 939
3.5
" 6 40 3.5 to
1. 3
.935- .965
835. 7=22. 4
78
. 943-. 950
Telluric,
" r 40 1. 3 to
.965- .985
2338. 4=59 9
40
probably
39 59. 5
aqueous.
39 58. 7
1.00
32-^41. 4=77. 3
23
i 39 54.8
1.06
3748.3=76.6 23
Great phi group 39 53. 7 to
1.085 to
Breadth,
39 47.0
1.24
0.155.
Abney's # 39 53. 7 to
1.085 to
952. 7=17. 1 83
Telluric wa-
51.6
1.125
ter vapor.
39 51. 6 to
1. 125-1. 13
1155. 0=20.
80
51.1
39 51.1 to
1.13 -1.16
13-56. 9=22. 8
77
Includes so-
49.8
lar Na 1.132.
39 49. 3
1.17
3959. 4=65. 7
34 !
39 48.5
1.19
4360. 9=t70. 6
29 Grating and spec- i
trobolometer.
\i
39 46. 5 to
1. IT. -1. 28
45-66. 0=68. 2
32 Paschen.
45.2
Great psi group 39 45. to
1. 28 to
Bunseu flame, 1.33//
Breadth,
39 38. 2
1.52
to 1.50//.
0.240//.
39 43.7
1.32
2970. 9=40. 9
59
Abney's W
39 43. to
1. 34 -1. 40
473. 4= 5. 4
95
41.0
39 40.8
1.405
8-75. 0=10. 7
89
Telluric
39 39.9
1.44
1676. 1=21.
79
water va-
39 37.5
1.54
5876. 8=75. 5
25
por.
39 36.8
1.57
5876. 4=75. 9
24
39 36.1
1.59
58-75.9=76.4
24
Great omega group 39 34. 8 to
1. 65 to
Bunsenflame.l.75/< Breadth,
39 28. 5
2.03
to 2.10^. 0.370w.
Langley's 1 39 33. to
1. 75 -1. 87
166.4= 1.5
99
30.8
" co, 39 30. 3 to
29.6
1. 91 -1. 97
9-65. 0=13. 8
86
Telluric
water va-
" GO.- 39 29. 6 to
1.97 -2.03
21-63. 0=33. 3
67
por.
28. 5
122
TABLE 75 Continued.
Designation of baud.
Minimum rock-
salt deviation.
Wave-length.
Transmission.
Absorption.
Wave-lengths assigned
by other observers.
Source and
remarks.
o /
n
Per cent.
Per cent.
Great chi group
39 28. to
2. 08 to
Bunsen flame,2.42/i
Breadth,
39 11. 5
3.48
to 3.02/u.
1.400//.
Langley's JT
39 23. 7 to
2. 36 -9. 86
1_49. 0= 2.
98
H(~\ i f~1f\
* \J "+ V-< V/->
17.9
Xi
39 17.2
2.92
3-43. 5= 6. 9
93
39 16. 4
2.99
3-42. 5= 7. 1
93
39 15. 9
3.02
941. 7=21. 6
78
X-2
39 15.0
3.10
:!-40. 3=- 7. 4
93
39 14. 3
3.15
539 3=12. 7
87
39 13. 8
3.20
438. 6=10. 4
90
39 13. 2
3.24
7-37. 8=18. 5
82
39 12.6
3.29
12-36. 8=32. 6
67
Telluric
39 11. 3 to
3.41 -3.46
1434. 5=40. 6
59
water va-
10.7
por.
39 10. 7 to
3. 46 -3. 53
14-33. 3=42.
58
9.6
39 9.1
3.58
11-31. 8=34. 6
65
39 7. to
3. 73 -3. 80
9-29. 0=31.
69
6.3
39 6. 3 to
3. 80 -3. 87
928. 2=31. 9
68
5. 5
Great upsilon
/ 39 5.5 to
1 38 55.0
3. 87 to
4.60
Grating and spec-
trobolometer,
Breadth,
0.730//, tel-
group
f 39 2. to
4. 12 to
l-f-21. 4= 4. 7
95
Paschen. Bunsen
luric carbon
2^
| 38 56.5
4.43
flame,4.15//-4.39//.
dioxide.
The great bands of which the radiation of the atmosphere at slight excess of temperature
mainly consists, lie in the infra-red spectrum beyond the limit of this table. Fig. 21 is a provisional
spectral energy-curve of the radiation of moist air for the temperature + 50C. The positions of the
bands rest upon the observations of Paschen, Eubens, and Aschkinass, and relate to the emission
A
\
01 2 3 4 5 6 7 8 9 10 \\ (2 13 14 \5 \k (7 18 (9 20 2f 22 23 U
ffig. 2 i
Approximate spectral energy-curve of air radiation.
from aqueous vapor and carbon dioxide, with the exception of the radiant energy of extreme
wave-length, which I have provisionally assigned to one or more of the permanent gases, nitrogen,
oxygen, etc., on the strength of Hutchins' observation of the absorption of air radiation by quartz.*
L Seep. 112.
123
The form of the curve will vary according to the temperature arid composition of the air. The
relative heights of the maxima are assumed to vary inversely as the absorption, but some devia-
tion from this rule must be anticipated. Similar curves for depths of air giving maximum radiant
efficiency at the principal bands may be constructed for other temperatures by first drawing the
appropriate energy-curve for a black body, and then inserting and graduating the heights of the
radiation-bauds, so that the highest may be included by the curve.
It has been explained that a considerable part of the radiation of short wave length diffused
by the dust and finer particles of the atmosphere, reaches the surface of the earth.* Not so,
however, that portion of solar radiant energy which has suffered the special absorption which
causes the cold bands of the infra red spectrum. This energy remains in the air as an increase
of temperature, and is subsequently lost again as atmospheric radiation ; but since the greater
density and humidity of the surface air obstructs downward radiation, and since, further, in any
radiant interchange which can proceed through the deeper and denser layers the excess of expendi-
ture is in the hotter air, which is usually beneath, it follows that atmospheric radiation, with rare
exceptions, proceeds mainly outward.
Suppose that one- fifth of the entering radiation remains behind in a layer of air 20 kilometers
deep. Then during one hour in the middle of the day, the solar constant being 0.03 radim,
X 0.05 x 3600 = 36 small calories will be imparted by the sun to each column of 1 sq. cm. section
and 2,000,000 cm. high. The upper layers have the opportunity of attacking an unsifted sunbeam
and of taking out those rays at the baud-centers which are totally absorbed by very small quanti-
ties of matter. Hence in spite of the rarefaction of the air and of its chief absorbent at high
altitudes, the absorption per unit of absorbent material being very much greater at the start, the
actual distribution of absorption at different altitudes may be tolerably uniform. If the heat
developed in the extinction of solar rays is distributed uniformly through the entire 20 kilometers,
each kilometer receives 1.8 small calories in a vertical column of 1 sq. cm. section during one hour
in the middle of the day, and the consequent elevation of temperature is 0.7 C. at. an altitude of
20,000 meters, but only 0.07 C. at a. height of 1,000 meters. The upper part of the first layer,
because it receives the undepleted rays, will continue to absorb with the same intensity during
the hours of sunshine, and the entire layer on account of the obliquity of the rays and longer paths
with a low sun will absorb more powerfully as the sun's altitude diminishes, and at the equinoxes
might have its temperature raised at least 8.4 in one-half day if none of the heat were lost; but
as the losses certainly exceed the gains, the diurnal range is not likely to be more than one-half
of this amount.
The deeper layers of air receive solar radiation which has been depleted of its more absorb-
able rays, and as the sun nears the horizon a relatively larger part of the energy remains in the
upper air, whence the lowest layers may not be heated in one-half day more than four or five
times as much as in one hour at midday, and the diurnal range of temperature due to absorption
of solar rays probably does not exceed two or three tenths of a degree in the 2 or 3 kilometers of air
above the surface. Very much larger ranges occur in the first 1,000 meters from the ground, but
they are due to ascent of air heated by contact with the soil and cease at an altitude of about
1,000 meters, where the lower cumulus clouds mark the upper limit of this convection. (See
"Exploration of the arr by means of kites" at the Blue Hill Meteorological Observatory, Ann.
Harvard Coll. Astron. Obs., vol. 42, part 1, p. 103, 1897.) Only in case the previous sifting had
deprived the sunbeam of all of its absorbable rays, or provided the thermal energy were lost by
reradiation as fast as it is received, could there be a complete absence of thermal effect.
The advancing part of an anticyclone receives air directly depleted of moisture in the pre-
ceding area of precipitation. The dry air is a bad radiator, and the full increment of temperature
by compression in the descending air is preserved. Hence the adiabatic rate of cooling in unsat-
urated air with increase of altitude is maintained or exceeded in the front part of the anticyclone,
as Clayton has observed (loc. cit., p. 118). But in the western part of the anticyclone and the
advancing region of a following cyclone the greater easterly velocity of the upper air carries along
'See the previous chapter on atmospheric dust, p. 118.
124
an overhanging mass of warm, moist air which diminishes or reverses the upward fall of tempera-
ture. The alternation of hot and cold waves in winter brings a considerable range of temperature
in the lower air which must not be confounded with that produced by the direct absorption of
solar radiation.
The depth of 20 kilometers has been taken as denning somewhat approximately the part of
the atmosphere within which water-vapor can exist in appreciable quantities or what may be
called the aqueous atmosphere.
It is evident, after what has been said in regard to the small depth from which atmospheric
radiation can pass freely, that radiant emission from so great a depth of air as 20 kilometers, or
even from a small fraction of a kilometer, can only take place by the slow process of one portion
of air radiating to a neighboring one which is at a slightly lower temperature, and this in turn to
other volumes not far away, the process being repeated over and over again until the upper
regions of freer transmission are reached.
The curve of transmission of radiation by the terrestrial atmosphere, given in fig. 22, is
intended to represent only the most important features. It relates to a vertical transmission
through a clear air of only moderate humidity, and includes (1) the general fact of selective
sniftering of short waves, (2) the progressive strengthening of baud absorption in the infra-red,
100 %
so
70
60
SO
40
30
<0
01
WJ A
2 3 4 5 6_ 7 8
ca co.
10 1M2 13 U 15 f6 17 i8 i9 20 ^\ JUL
of radiation by the Earth" 1 s atmosphere,
due mainly to water-vapor, including bands at O.Ooj/, 1.1;*, 1.4//, 1.9jw, 2.5ju, and 4.7/Y, until (3) the
great bands of this substance between 5yu and 8/<, marked in the figure (strongest absorption
at 5.9/^, 6.5//, and 7.5^), are reached, (4) the greater but decreasing transmission beyond 9/* with
absorption-bands at 0.0/y, lO.O^u, 11.6/y, 12.4^, 13.4//, 14.3;/, 15.7^u, 17.5//, and perhaps at 20/v, still
attributable to aqueous vapor, with the exception (5) of a wide band extending from 12.5yu to 16yu
with a maximum of absorption at 14.7^, denoted by A in the figure, which with the band at 4.3/<
and the smaller one at 2.7^, is produced by carbon dioxide, and finally (0) a region of almost total
absorption beyond 20w, here provisionally attributed to the permanent gases of the atmosphere.
125
The absorption by carbon dioxide, by water-vapor, and possibly also by the permanent gases,
practically obliterates the solar spectrum beyond 13;/, since the unabsorbed radiation is here very
feeble.
Some of th ' consequences of atmospheric absorption may be briefly pointed out. The
absorbent action of carbon dioxide and the permanent gases is almost invariable; but the absorp-
tion bands of aqueous vapor are much stronger in summer than in winter, and the selective
scattering of short waves also increases in summer. One result of this variation is that the direct
rays of the midday sun, received upon a normal surface, are more powerful in winter than in
summer, in spite of the greater distance traversed by the sunbeam through the air in winter.
Dr. Emil Bessels* noted that the rays of the arctic sun in early spring, although making a very
small angle with the horizon and penetrating a great depth of air, affected the actiuouieter much
more intensely than later in the season after the sun had risen higher, but when the air had become
rnoist.t
The direct effect of the sun's rays upon a normal surface is less in the tropics than in temperate
regions, and less at sea level than upon a mountain top, owing to the difference in the aqueous
component of the air; and the ability of the solar radiation to maintain a high temperature in the
torrid zone or at sea level is due to the accumulation of the thermal energy imparted to the Earth's
surface by reason of the retention of the escaping radiation from that surface by a moist and
highly absorbent atmosphere rather than to the direct power of the sunbeam. The position of the
great water band (E in fig. L"2) covers a region of the infra red spectrum in which terrestrial
radiation is near its maximum, and the emission from the soil is still strong at the great A band;
but the sun's rays are most powerful in the visible spectrum where aqueous absorption is small
and the bands of carbon dioxide completely lacking. Thus the penetrative power of the incoming
is greater than that of the outgoing rays, and this relative difference, which increases with the
amount of moisture in the air, produces an accumulation of thermal energy at the Earth's surface,
which would generate a very high temperature were it not that the sign of the function is reversed
after sundown. The cumulative effect of continuous sunshine gives a mild summer to the arctic
regions with a sun of lower altitude than that which brings vigorous winter weather in lower
s Scientific Results of the r. . Arctic Expedition. Steamer Polaris. Vol. I, Washington, 1876. $ Solar
Radiation, pp. 80-82.
tin Lieutenant Ray's Report of the International Polar Expedition to Point Barroiv, Alaska (Washington, 1885),
differences of black and bright bulb thermometers are given for this station between February 1 and August 27,
1883. During the mouth of March differences above 45 F. were measured on twelve days, during April on fourteen
days, during the first half of May on seven days ; but after this the differences did not again reach 45. In June a
difference greater than 40 was only attained on three days, and during July and August the excess of the black bulb
did not once reach 40 ; . This sequence of low readings is no doubt partly due to the greater cloudiness of the
summer months, for the black-bulb thermometer requires time to reach a maximum reading which often fails to be
recorded during the brief intervals between clouds. Nevertheless, the highest reading of all, 82. 3 F., being made
on the 8th of May, which has its parallel in the frequent maximum reading at 9 or 10 a. m. in a diurnal curve of
intensity, confirms the result of Dr. Bessels, and with many other similar facts, proves that altitude of the sun
above the horizon is not the only important factor conducing to intense solar radiation.
The reader may al.so consult the Report on the Proceedings of the V. S. Expedition to Lady Franklin Bay, by
Adolphus W. Greely, vol. 2, p. 377. Chart No. 17 (Washington, 1888). The curve of solar radiation attains its
maximum in May, and ir is noted that "the effect of increasing humidity or aqueous vapor in intercepting the solar
[radiant] heat is shown in a most marked manner.''
These observations of solar radiation were made with conjugate bright and black bulb thermometers in
vacuum chambers of glass, an instrument which, as we now have it, is not capable of giving accurate quantitative
values. The chamber is supposed to be a vacuum, but there is usually no means of verifying the supposition.
Minute quantities of certain vapors; coudensible at low temperatures but evaporated in hot sunshine, may alter
the indications widely. If it is desired to get rid of all convection and penetration of gaseous molecules within the
envelope, a 'very perfect vacuum must be obtained, and variations either in the degree of exhaustion or in the
material of the transmitting walls will produce serious discrepancies in instruments exposed side by side. Glass
also does not transmit the longer radiations readily, and the amount rejected will vary with the thickness and
quality of the glass, with the nature of the surrounding surfaces, and especially with the previous depletion in
passing through the atmosphere, which is the very thing we are seeking. A part of the heat registered comes from
short- waved sky reflection, and this is relatively greater with a low sun; nevertheless the existence of an absolute
low-sun maximum radiation can not be thus explained, and since the chief defect of the instrument is that it shuts
out much of the radiation of long wave-length and obscures its variation, it is quite possible that a perfect acti-
nometer would show as great or greater seasonal fluctuations.
126
latitudes, continuity of accumulation more than compensating the advantage of greater trans mis
sion in winter.
The beat entrapped through, the differential transmission of solar and terrestial radiation by
aqueous vapor, and carbon dioxide is mainly stored in the lower layers of the atmosphere, and
because the absorption by air heavily loaded with moisture is nearly complete for its own radia-
tion, this stored-up energy continues for a long time as a controlling balance wheel in the mechan-
ism of the weather. As long as the mantle of water vapor remains unbroken, thermal fluctuations
are kept within narrow limits. Storms may make inroads upon the continuity of this aqueous
atmospheric envelope, but evaporation of moisture restores the rents. Rolled up in great bosses
covering hundreds of thousands of square miles of territory, the thickened mantle of vapor brings
hot waves. Displaced by downward movements bringing the dry air of the upper atmosphere to
the surface, corresponding cold waves result. The gradual accumulation of moisture in higher
and higher atmospheric layers during the summer, clothes the temperate regions with so deep a
protective covering of moist air, that summer conditions are prolonged in the autumn to a time
which is astronomically the correlative of late winter. The absence of this deep protective layer,
whose formation can only be effected gradually, permits late frosts in spring, long after the sun
has resumed his ascendency. In the middle of a sunshiny day, by the evaporation of moisture
from the earth's surface and its ascent in convection currents, the vapor of water is carried up to
high levels; but during the night most of this accession of moisture is diffused into colder or drier
regions of the upper air, where it is either condensed and no longer exists in the air as vapor, or
is so diluted and reduced in relative humidity as to be of slight absorptive value when the sun
next rises. The increase of moisture in the upper air at midday is the cause of the flat-topped
diurnal actinornetric curves which are observed on all but the coldest and driest days. As the sun
mounts above the horizon, the intensity of his rays augments, giving an actiuometric curve, which,
on an exceptionally dry day, is approximately a parabola, symmetrical about the midday ordinate;
but, in general, the apex of the curve is truncated, and after about 9 a. in. the curve becomes flat-
topped with minor fluctuations indicating the activity of the convective process, and the passage
of invisible clouds of vapor across the line of sight. At the same time the curve of relative
humidity of the surface air becomes deeply depressed, while at high levels the tension of aqueous
vapor increases in the middle of the day, indicating the rapid removal of aqueous vapor from the
lower to the upper air. The earth has its lowest temperature and the air, if clear, its greatest
transmission in the early morning hours when, as a whole, the atmosphere, according to observa-
tions at high levels, has its smallest content of aqueous vapor, a condition which is evidently cor-
related with the maximum actinometric effect observed by Bessels in the arctic spring months.
It appears certain that on our Earth surface temperatures lower than 73 C., or 200 absolute,
can not occur, possibly because of the almost total absorption by the atmosphere of all radiations
beyond 13//. Paschen's law of the wave-length of the maximum in the normal spectral energy-
curve of a black body gives at this temperature :
Thus the position of the no.rmal maximum in the energy-curve for the lowest arctic temperature
very nearly coincides with the great absorption -band of carbon dioxide ( J, fig. 22), discovered by
Eubens and Aschkiuass; and at lower temperatures the maximum would be found at still greater
wave-lengths on which the permanent gases of the atmosphere may possibly exercise a complete
absorption. In the midst of much conflicting testimony as to the region of the spectrum in which
the absorption of pure air resides, this suggestion is at least worthy of consideration.
By the same law a sunlit surface of rock at 340 absolute temperature, if radiating like a
black body, must have its spectral maximum at 8.5/<; and taking the mean temperature of the
earth as -4- 15 C., its spectral maximum would reside on the average at 10//. Some deviation
from the law is to be expected and does occur in the spectra of solids, which do not conform to
the ideal of blackness. Since it appears to be a general law that the radiation of a body is
especially large in that spectral region where its absorption is exercised, it is possible that the
radiation of the ocean at a mean surface temperature of -f- 15 C. will be found to have the maxi-
127
mum in its spectral energy-curve displaced to a wave-length shorter than 10//, and approaching
the great band (Z) where the absorption of atmospheric moisture is greatest, and that this is
another cause, in addition to the large specific heat and mobility of water, conducing to the
slowness of oceanic temperature changes; but more important as a retainer of oceanic heat is the
extension of the band -. to greater wave-lengths in the absorption of the layer of air nearly
saturated with moisture, which always hangs over the water.
The absorption of terrestrial radiation by atmospheric moisture lies somewhere between such
curves as those of figs. 14 and 15. Aqueous absorption is very greatly increased as the air
approaches saturation, because the molecules of water-vapor then become complex and have an
absorptive power approaching that of liquid water.* The absorption of the atmosphere and the
surface temperature which can be maintained by its aid, increase both with the absolute and with
the relative humidity.
Not only is the absolute temperature of the soil dependent upon atmospheric moisture, acting
in conjunction with the heat supplied by the sun's rays, but also the diurnal range of surface
temperature. " Where the laud is moist the changes of temperature are less than where it is dry
or arid," but it is the condition of the air and not that of the soil which makes the radiation
possible or impossible. The following illustration under nearly the same insolation must suffice
as an example.
After several weeks of rain in May, the daily range for the first week of pleasant weather in
June was 9. 5 C. At the beginning of August, after two months of drought, the range had
increased to 12. 1 0., and the highest range of the week in June (10. 4 C.) was less than the
lowest (10. 6 C.) of the week in the time of greatest drought.
TABLE 76.
*
Date.
Kange.
Sky.
Date.
Range. Sky.
C.
o C.
June 3
8.8
Clear Cirrus.
July 31
11.0 Clear, smoky Cirrus p. m.
4
10.4
Alto-cumulus showers.
Aug. 1
11.9 " " cloudv evening.
5
9.2
Cloudy Rain.
2
11. 2 Cloudv, 0.01 inch of rain.
6
8.8
Cloudy a. m. ; clear p. m.
3
12. 8 Cumuli.
7
10.4
Cirrus Cumuli p. m.
4
14. 5 Clear, then cumuli.
8
9.5
Clear Hazy.
5
10. 6 Clear.
9
9.1
(t n
/>
12. 4 Clear Smoky.
Mean.
9.5
Mean.
12.1
On Pike's Peak the range is greater in winter than on the plains, but less in summer. Here
also the mountain climate is relatively drier than that of the plains in winter than in summer.
In free air the diurnal range is small, but in this case because the radiation which has escaped
the previous action of the chief absorbent of radiation, water- vapor, is deficient in absorbable
rays, and small toll is taken by the air. On a mountain, and still more on a plateau, the increased
power of the sun's rays heats the rocks, and thence the surface air, more than at lower altitudes,
and unless the wind is so strong as to remove the surface air before ifr is much heated, replenish-
ing it with cool air from the free atmosphere around the mountain top, the range may be greater
on the mountain than on a low-lying plain, because of the more powerful insolation.
The spectrum of the radiation of the atmosphere consists entirely of lines and bands; and
since the atmospheric absorption acts within the same limited regions of the spectrum, atmospheric
radiation is largely annulled by an absorption which is identical in quality, or as to the kinds of
rays affected, with the thing on which it is exerted, and can differ only in regard to the rapidity
with which extinction or emission vary with the depth, or by a redistribution of energy, according
to which the radiation in process of transmission may be absorbed by one constituent of the
atmosphere but emitted again by a different one, or passed on by a series of alternate radiations
and absorptions. In any case the depth from which atmospheric radiation can directly proceed is
See p. 100, et seq.
128
limited, and the amount of the emission is relatively greater for a small depth. Hence laboratory
experiments which deal with small layers of air, give radiant values which are too large to be
applied without discrimination in meteorological problems.
Owing to the feebleness of the radiation-bands in the spectrum from air at such moderate
temperatures as prevail in the atmosphere, and owing further to the limitation of the emission to
the outer layers of large masses of air, small effect is to be anticipated from the radiation of
elevated bodies of warm air to a cooler underlying surface. Clayton's kite experiments on Blue
Hill have demonstrated the existence of high warm layers of clear air above cold layers and a cold
surface, when the surface winds are from a cold quarter, and wheu the surface temperature has
been changed very little by the substitution of warm for cold air at the upper level. Radiation
effects are immediate, and it is possible that under these circumstances a slight elevation of
temperature from the radiation of the warm air may be discriminated in advance of the slower
rise of temperature produced by the commingling of air currents and the bodily transfer of super-
ficial air from warmer regions by cyclonic movement. The most advantageous occasion for testing
such a possibility is immediately after a severe cold wave in winter, for then the absorbent power
of the lower air for the hypothetical radiation from the warm upper layer will be least. The return
of an elevated body of relatively warm air after a severe cold wave is usually heralded by an
increase of cirro-stratus cloud, and this alone may make surface temperature greater by the action
of the aqueous vapor whose presence is made known by the cloud, the vapor imprisoning more of
the sun's rays in the daytime, and impeding the escape of terrestrial radiation at night.
I will give two examples of recovery from cold waves, observed at Providence, R. I., taking
the data from the records of the City Engineer's Office and of the Ladd Observatory.
Cold wave of January 6 to 10, 1896. The minimum of 8 F. on the morning of the 6th was
followed by a gradual recovery, lasting four days. Bach day saw a recovery of about 7. The
air on the Gth was very dry (relative humidity 22 per cent.). The barometer, which had risen to
30.37 inches on the evening of the Gth, fell very slowly to 29.81 inches on the morning of the 10th.
In this case there was no pronounced cyclone, but 3 inches of snow fell from 2 p. m. on the 7th to
2 a. m. on the 8th, and 11 inches from 3 p. m. on the 9th to 7 p. m on the 10th. The clouds began
to gather on the morning of the 7th. The wind continued north during the four days, except for
a short time on the 9th.
Cold icave of February 16 to 19, 1896. There was a fall of 2.5 inches of snow, ceasing at 3 p.m.
on the 16th. The thermometer, which at a. m. on the 16th was 42 F., fell steadily to 8 F.
on the morning of the 17th. The highest temperature on the 17th was -f 7 F. at 5 p. m. after a
day of unclouded sunshine. The barometer, after 7 a. m on the 17th, was steady at 30.30 inches.
Relative humidity rose slowly during the night of the 17th to 18th from 40 per cent, to 55 per cent. ;
lowest temperature, F. at midnight. Sky clear until the morning of the 18th, when there was
a trace of snow (clouds 0.9); temperature + 2.5 at 6 a.m., February 18th, and barometer falling
(30.20 inches). Relative humidity and temperature then increased rapidly, until at 1 1 p. m. snow
began to fall, continuing until 9 p. in. on the 19th, when the barometer had descended to 29.27
inches. The wind continued north until noon of the 19th, when it changed to the southeast.
Here a part of the rise of 10.5 in tht; first twenty-four hours after the minimum must be attributed
to the influence of sunshine. More rapid recoveries than this are almost invariably accompanied
by a change of wind to the south, or by a sudden accession of moisture, implying the importation
of warm air from a milder neighborhood.
The solar radiation of 0.05 radim often produces a rise of temperature of 15 C. between sun-
rise and midday (no account being taken of atmospheric absorption). A rise of temperature at
the rate of 1.5 C. in six hours after a cold waye may frequently be observed, indicating a radiation
of 0.005 radim, if due to a warm upper layer of air, assuming that the lower layers are dry enough
to permit the passage of this radiation with no more obstruction than that which affects the sun's
rays. An upper layer of warm and moist air, 10 C. above surface temperature and 1 meter
thick, will radiate 0.0002 radim, but the radiation must be twenty-five times as great if the
recovery of heat after a cold wave is to be attributed to direct atmospheric emission. Some effect
could no doubt be produced by an indirect process involving layers of considerable depth, but
there is no warrant for the supposition that the warm upper currents in the cases cited have an
129
excess of 10 above surface temperature. The existence of warmer air a few meters above the soil
which is unduly chilled by nocturnal radiation at the calm center of an anticyclone is not in ques-
tion here, for this air, although it is so near, being dry, does not radiate enough to prevent the
surface refrigeration.
It seems probable that after the descent of dry air at the center of an anticyclone has ceased
and unimpeded surface radiation to space has produced the minimum surface temperature of a
cold wave, the gradual recovery of heat and moisture by the lower atmosphere is effected princi-
pally by the absorption of the sun's rays, by evaporation from the surface, and by the mingling
of air from warmer regions, and that any contribution which atmospheric radiation from upper
warm layers may give to this recovery of heat is not likely to produce a rise of temperature of
more than 1 C. per day.
The power of warm air to radiate must depend largely on its isolation. An upper body of
warm moist air, if fi eely suspended in the midst of dry air, immediately becomes a good radiator,
not only by virtue of its high temperature, but because of its containing an especially emissive
substance. The radiation, however, owing to the peculiar absorption of its own rays by the moist
air, can only proceed through a small surface layer, which soon becomes saturated by the cooling.
The great increase of absorption which has been shown to occur at the condensation point of
water prevents further cooling by radiation, except in an excessively thin surface shell of cloud,
and it is doubtful if any large proportion of rainfall is produced through cooling of moist air by
radiation, even in those towering cumulo-nimbi which ascend into dry regions where the radiant
effect is greater. While cumulus clouds may be thimble-shaped shells, the typical rain-cloud
generates its rain, not by any skin-squeezing process, but by expansive cooling which affects the
entire volume of air. ,
Air radiation must usually proceed more easily upward than downward, because the higher
layers are apt to be drier and more transmissive than the lower. Cooling by radiation, although
of small moment in the lower air, must be added to cooling by expansion as a cause for the cold
of the high atmosphere; and the diminution of absorption of its own radiation by- air at great
altitudes on account of lessening aqueous vapor, so far compensates for decrease of radiant power
at very low temperatures that cooling by air radiation may be effective to the outer limit of the
atmosphere, and may prevent the retention of such molecular velocities as would permit the
escape of air molecules, except in the very unusual case of the ejection of intensely hot vapor to
great heights by volcanic eruptions. The former prevalence of vigorous vulcanism on the Moon
has perhaps had more to do with the loss of the Moon's atmosphere than the smallness of its
attraction, at least the fact that one or more of Jupiter's satellites exhibit phenomena which are
presumably atmospheric, warns us not to place too great faith in the theory that a small planet
must necessarily have a relatively small atmosphere. Another cause which has peculiarly favored
the loss of the Moon's atmosphere by the escape of individual molecules of high velocity has been
the slowness of its axial rotation, which permits an accumulation of heat during the long day until
surface temperatures considerably above that of boiling water are attained. (See the author's
"Probable range of temperature on the Moon," Astroph. Journ., vol. 8, Nos. 4 and 5, Nov. and
Dec., 1898).
The results of the present research prove that within moderate depths of only a few meters
the radiation of dry air, purified from carbon dioxide, increases quite uniformly with the depth;
that the radiation of a 1-meter layer of purified air at 50 C. and near atmospheric pressure
(735 mm.), as compared with one at C., is 0.00068 radim, representing a transformation and
transfer of thermal energy of 0.00068 small calories every second through each square centimeter
of limiting surface; that the radiation of a like depth of carbon dioxide at the same temperature
is three and one-half times that of air, or 0.00238 radiin, which is very nearly a maximum for this
temperature, further increase of the radiant depth being unattended by a corresponding addition
of radiant energy, showing that equilibrium between radiation and emission has been almost
reached at this depth; that the radiation from a layer of steam 5 feet deep at one-sixth of atmos-
pheric pressure is two and one-half times that from a like body of dry air at temperatures near the
boiling point of water, and eight-tenths of the radiant emission from the black solid body; while
for smaller depths the radiant power of water-vapor is relatively greater, a steam jet of small
12812 Bull. G 9
130
dimensions radiating over four times as strongly as one of air, a ratio which would doubtless have
been considerably greater if the air had been perfectly dry.
There appears to be no reason to doubt that the radiation of a moderate depth of homogeneous
air at a given temperature depends on the product of the depth by the density, and remains the
same when depth and density vary inversely; but the absorption of a given mass of aqueous vapor
has been found to be smaller when distributed through a large volume of air than when concen-
trated.* The phenomena are conditioned by molecular relations. Beciprocal variation of depth
and density does not change the number of molecules which are engaged in the radiant transaction
in a homogeneous medium; but dilution by another substance involves a partition of energy
among molecules whose radiant and absorbent properties are dissimilar.
As an absorbent of terrestrial radiation aqueous vapor is very much more efficient than any
other atmospheric ingredient; but as radiators when in large masses, the substances which
compose the atmosphere do not differ as widely as might be supposed, and the position of chief
radiant may be assumed in turn by either aqueous vapor, carbon dioxide, or the permanent gases,
according as the depths and temperatures of the emissive and absorbent layers change.! The
depth of gas which gives maximum radiation at short range is an insignificant quantity compared
with atmospheric dimensions, and radiation from either the atmosphere of the Earth or the solar
chromosphere is a superficial phenomenon, even when the masses of heated gas measure thousands
of miles in thickness. The fineness of the chromospheric lines in the solar spectrum, although
the shifts of the Fraunhofer lines indicate pressures of many atmospheres at the base of the
chromosphere, is a sufficient demonstration that only the outer layers radiate. If the emission
proceeded also from the depths of the chromospheric mass, the lines of hydrogen and some other
elements would be greatly widened ; and if the Earth's atmosphere radiated unimpeded throughout
its depth, its thermal changes and its radiant effects would be enormous. Instead of this, we
find the atmosphere playing the part of a conservator of thermal energy, and must gratefully
admire the beneficent arrangement which permits the Earth to be clothed with verdure and
abundant life.
* See p. 94.
t This statement can not be absolutely verified, because tlie dimensions of my apparatus were insufficient to
give the maximum radiation for pure air, but it is strongly indicated by the curves and on theoretical grounds.
ANALYTICAL TABLE OF CONTENTS.
Page.
Letter of transmittal . . . - - 3
Prefatory note , ....- -- - 5
MEASURING INSTRUMENTS. THE BOLOMETER.. 6
Computation of currents by simple theory of Wheatstone's bridge ,. 7
Reid's theory of the bolometer 8
Relative efficiency of the same bolometer with different areas exposed 10
Influence of a temperature-gradient in the bolometer strips 10-11
Tests of efficiency of bolometers 12
Disturbances produced by convection 13
Radiation and convection rates in thermometers and bolometers 14-15
Rate of heating of thin black platinum by radiation 16
THE GALVANOMETER - - - 16
Mode of astaticizing .. . . . 17
Specific magnetism of hollow magnets used in galvanometer needle 18
Determination of resistance of battery by half-deflection method 18
Measurement of galvanometer shunt .. .-- 19
Measurement of galvanometer constant 20
Logarithmic decrements for galvanometer needle 20
Suspension of needle . . 1 -. 21
Variation of magnetic field ..,,. 21
SCREENS (USED IN STANDARDIZING INSTRUMENTS) 21
Computation of reduction factors for instrumental readings obtained with different apertures 22-23
Screen comparisons and valuation of standard deflections. .- 23-25
Adopted values of instrumental readings in absolute units of radiation 26
PSYCHROMETER FACTOR . - -- 26
Air depths and equivalent layers of absorbent water in different pieces of apparatus 28
DESCRIPTION OF METHOD A AND APPARATUS . - 28
Dimensions of movable air chambers and apertures ... .. -- .. 29
Correction for the magnetic effect of the apparatus during motion in Method A 30
Observations of air radiation by Method A 31-34
Apparent small transmission of air radiation by glass. ...: 34
Discontinuity of the absorption by glass in the infra-red spectrum . 35
Computed radiation of lampblack at the given temperatures. 35
Observed radiations (subsequently shown to be only in part atmospheric) 36
Examination of Professor Hutchins' hypothesis " that radiation takes place only when there is a fall of
temperature u-ithin the limits of molecular action " 36
DESCRIPTION OF METHOD B 37
Method of determining thermal gradient and mean temperature of ascending air vein with first
arrangement of apparatus . 38-39
Measured air radiation with first arrangement. 40
Measurements of thermal gradients of air vein in second arrangement of apparatus 41-42
Observed values of air radiation with second arrangement .... 43-44
Observed values (Method B) reduced to a depth of 1 meter and temperature 40 C 44
DESCRIPTION OF APPARATUS AND METHOD C . - 44
Dimensions and plan of radiation cylinder 45
General theory of the Apparatus C ... . . 46
Evidence of discontinuity of thermal distribution in the radiating gaseous mass when heated from
below, requiring the rejection of certain measures, but proving the gaseous origin of the radiation. 47
Distribution of temperature (heating cylinder) 48
Distribution of temperature (cooling cylinder) 49
Abnormal radiant values (heating cylinder) . .. . . 50-51
Change of sign of apparent air radiation when temperature inequalities are extreme 52
Analysis of the last experiment 53
131
132
Page.
METHOD C. EXPERIMENTS ix WHICH THE DEPTH AND PRESSURE OF THE AIR ARE VARIED 54
First measures with air and with carbon dioxide .._ . 54
More elaborate observations on CO; 55-59
Determination of the variation of apparent radiation of CO> with change of depth 59
Comparison of rates of increase of radiation with temperature for a 3-inm. layer of COj (deduced
from Paschen's curves), and for a layer of 1418 mm. determined by the present observations. .. . 59-60
Comparison of the apparent radiations of air and of CO- at different depths expressed as percent-
ages, showing nearly uniform change in air, but rapid diminution of radiant increments with
increase of depth in CO- 60
Limitation of the effective radiant depth in carbon dioxide. . 61
Radiation from multiple flames . . 61
Evidence of self -absorption of flame radiation by successive flames, and of further absorption by
the aqueous vapor of the room . . . 62
Measurements of air radiation and of COi radiation made during cumulative heating of gaseous masses . 62
Measurements of gaseous radiation made during gradual cooling of the gasemis masses and with com-
paratively uniform temperature gradients - 66
Apparent gaseous radiation by Method C , -.- 70
Experiment on the radiation of steam 72
Explanation of results at loiv pressure , . 72
METHOD D. RELATIVE RADIATION OF AIR AND STEAM AND OF CLEAR AND SMOKY AIR 73
COMPARISON OF SOME OF THE PRECEDING RESULTS WITH THOSE OF TYNDALL . __ 75
Radiation of gases dynamical! y heated by compression - 76
Radiation from different depths of CO^ ... - 77
MODIFICATION OF ATMOSPHERIC RADIATION BY THE ABSORPTION OF CONSTITUENT GASES AND VAPORS. . 78
ABSORPTION OF RADIATION BY AQUEOUS VAPOR AND GENERAL CONSIDERATIONS CONCERNING ABSORP-
TION BY VAPORS AND GASES - . 78
Quotations from Ferrel's ' ' Recent Advances in Meteorology " 79
Magnus' criticism of Tyndall's work and its refutation 80
Discrepancies in Tyndall's results, not hitherto noticed. 81
Hoorweg's measures of aqueous absorption - 81
Buff's modification of Magnus' method - 82
Tyndall's refutation of Buff's criticism - -- 83
Quotation from Davis' "Elementary Meteorology".. 83
Quotation from Preston's " Theory of Heat " 84
Observations by Lecher and Pernter, and by Tyndall, compared 85
Regnault's observation of a variation in the density of aqueous vapor 85
Comparison of observations by Tyndall and by Lecher and Pernter on the transmission of radiation
by ether- vapor. ... - -- 86
Criticism of the estimate of aqueous absorption drawn by Lecher and Pernter from Violle's
measurements of solar radiation at top and bottom of Mount Blanc 87
Tyndall's final paper in 1882, containing:
(a) Further criticism of later observations by Magnus on the radiation of aqueous vapor 88
( 6) Measurement of aqueous absorption of radiation from a hydrogen flame 88
(c) Proof that absorption of radiation by ether- vapor is constant if the product of depth by
pressure remains the same .. . . . 89
(d) Observation of equality of vaporous and liquid absorptions of radiation from various sources
in the cases of ethyl ether and arnyl hydride, and incorrect general conclusion drawn by
Tyndall from these facts - - - 89
(e) Observations of variations of pressure in gases produced by radiation and depending on
combined radiative and absorptive powers of the gas 90
Absorption of radiation from a red-hot spiral by liquid water (Tyndall) . 90
Absorption of radiation from lampblack near 100 C. by the aqueous vapor of the atmosphere
(Langley and Very) .... --
Preliminary conclusion, drawn from a comparison of these observations, that aqueous absorption
of radiation varies with the relative humidity of the air and with the physical state of the water. 92
Spectral energy-curve of lampblack near 100 C. absorbed by water- vapor in the atmosphere . . 92
Spectral energy-curve of hot sheet-iron absorbed by steam (Paschen) _ 93
Evidence that concentrated water-vapor absorbs radiation more powerfully than an equal amount
of vapor largely diluted by air _ - - - 94
Spectral energy-curves of black platinum at 450 C. absorbed by various depths of liquid water
(measured from Paschen 's figures ) 9~>
Examples of a new mode of derivation of the transmission of total radiation from any source:
a. Temperature of source 100 C ..... - 95-96
b. Temperature of source 81 "r C. (?) - 97-98
133
MODIFICATION OF ATMOSPHERIC RADIATION, ETC. Continued. Page.
ABSORPTION OF RADIATION BY AQUEOUS VAPOR, ETC. Continued.
Curves of absorption of total radiation by liquid water 98
Determination of ratio of aqueous liquid and vaporous absorptions of total radiation 99
Observation by Liveing and Dewar of two sorts of oxygen absorption-bands (linear and diffuse),
corresponding in all probability to molecules of different complexity 99
Observation by Ramsay and Shields of various degrees of complexity in the molecules of liquid
water 100
Suggestion that the remarkable increase of absorption of radiation by aqueous vapor as saturation
is approached, and the corresponding increase of vapor density observed by Regnault, may be
due to the formation of a limited number of complex molecules in the vapor _ . . 100
Paschen's observations of the spectral positions of absorption-bands due to liquid water. 100
Paschen's identification (in 1894) of aqueous and carbon dioxide absorption-bands (between l/< and
8//), as observed by him, with the telluric absorption-bands of the solar spectrum measured as to
intensity and position by Langley - 101
Shifting of position of maximum in bands of radiant emission from heated water-vapor with chang-
ing temperature (Paschen) ,.. - - - 102
First photographs of diffuse infra-red absorption-bands of liquid water by Abney and Festing in
1883, and discovery of two kinds of aqueous bands (linear and diffuse) due to atmospheric moist-
ure, the diffuse increasing with the relative humidity, and probably attributable to the complex
molecules discovered 10 years later by Ramsay and Shields 103
First quantitative measures of spectral energy-curves of the positive carbon of an arc-light after
absorption by liquid water, made with a linear thermopile by Abney and Festing in 1883, and
here stated as percentage transmissions at points of spectral maximum and minimum energy,
proving that nearly all of the infra-red cold bands of the solar spectrum to 3// are due to water, 103-104
Discovery of six infra-red absorption-bands between 11/u and 18//, due to water-vapor, by Rubens
and Aschkinass, in 1898 ... 104
ABSORPTION OF RADIATION BY CARBON DIOXIDE 105
Knut Angstrom's estimate of the absorption of solar rays 105
Keeler's measurement of absorption of Bunsen flame radiation , 105
Relative radiation of HiO and COj in the Bunsen flame 106
Absolute discontinuity of the spectrum of CO- (Paschen) 106
CO 2 bands discovered by Knut Angstrom . . . . , 106
CO 2 band at 14.7/* discovered by Rubens and Aschkinass 106
Absorption by CO 2 of radiation from sources of different temperatures (Tyndall) 107
APPLICATION OF THE FOREGOING STUDY OF GASEOUS ABSORPTION TO THE RESULTS OF LABORATORY
EXPERIMENTS ... - 107
Curve of absorption of lampblack radiation by CO 2 , derived from Tyndall 's measures 108
Approximate curve of self-absorption of CO 2 radiation, derived from Tyndall's measures 109
Corrected radiations of CO 2 and of air obtained in this research by Method C 109
Verification of Tyndall's surmise as to the origin of a residual deflection 110
Corrected value of steam radiation (Method C) ... Ill
Corrected percentage radiations from different depths of CO 2 and air.. Ill
Concluded absolute values of radiation from pure air and from carbon dioxide at temperatures below
100 C. and with depths varying between 2i and 125 cm 112
Comparison with previous results of Maurer and of Hutchins for air _ 112
Question of the probable spectral region in which the radiation of pure air resides 112-113
GENERAL APPLICATION OF THE PRECEDING STUDIES OF ABSORPTION AND RADIATION TO THE PROBLEMS
OF ATMOSPHERIC RADIATION 113
Probable existence of different types of gaseous radiation, corresponding to varieties of spectral struc-
ture 114
Rates of increase of emission-bands from CO 2 and H 2 O with rising temperature, derived from the spec-
tral energy-curves published by Paschen 115
Approximate coincidence of this rate and also of the absolute intensity at the maximum of the chief
COi band with the corresponding quantities for lampblack (Paschen ) ... 116
Evershed's observation of continuous visible emission-spectra from highly colored gases which give
linear absorption-spectra 116
Conditions favoring the production of radiations giving line-spectra 116
Hypotheses concerning the mechanism of radiant emission 116-117
ATMOSPHERIC DUST 118
Tyndall's imitation of sky phenomena by means of fine particles 118
Rayleigh's molecular diffraction theory of sky color. 118-119
Cornu's observation of an ultra-violet limit of the solar spectrum dependent on barometric pressure .. 119
Whymper's observation of brilliant sky colors from volcanic dust .. 119
134
Page.
SUMMARY 119
Various origins and complexity of atmospheric radiant emission 120
Wave-lengths and intensities of infra-red cold bands in the solar spectrum (to 4.15/0, mainly due to
telluric atmospheric absorption, derived from Langley's holographs 121-122
Approximate spectral energy-curve of air radiation inferred from a combination of the spectral energy-
curve for a black solid with measurements of positions and absorptions at band-centers 122
Estimate of solar radiant energy absorbed by the Earth's atmosphere at different levels 123
Clayton's observations of diurnal temperature-range at different levels in the lower atmosphere 123
Chief telluric absorption- bands between and 2Qju , and their intensities 124
Seasonal, regional, and altitudinal effects of atmospheric absorption upon the power of solar radiation 125
Differential transmission of solar and terrestrial radiation by aqueous vapor and carbon dioxide, and
the seasonal and diurnal thermal effects depending on variation of atmospheric moisture 126
Wave-lengths of maxima in terrestrial spectral energy-curves by Paschen's law 126
Dependence of terrestrial surface temperature-range upon relative humidity and this upon molecular
complexity of water-vapor 127
Loss of heat from the atmosphere by radiation dependent upon transfer through successive sets of
molecules 127
Test of possibility of radiation to the Earth's surface from upper warm layers of airs by the phenomena
of recovery from cold waves. 128
Immediate atmospheric radiation confined to shallow layers 129
Cooling by radiation in uper air (in addition to cooling of ascending currents by expansion) effectually
lowers the temperature and prevents kinetic escape of air molecules 129
The fineness of the solar chromospheric spectral lines a demonstration that only the outer chromospheric
layers of a given substance radiate 130
Confinement of immediate gaseous radiation to small depths limits the loss of heat by large masses of
heated gas and increases the protective power of the Earth's atmosphere against sudden loss of heat. 130
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