Some causes of variation in the polarization of sky light

TheJOURNAL OF THE

FRANKLIN

INSTITUTE

OF THE STATE OF PENNSYLVANIA

DEVOTED

2-U SCIENCE

VOL. CLXXI

AND

APRIL,

THE

MECHANIC

ARTS No. 4

19I I

SOME CAUSE’S OF VARIATION I:N THE POLARIZATION OF SKY LIGHT.* BY

HERBERT Professor

H.

of Meteorology,

KIMBALL, U. S. Weather

Bureau.

Introduction.-since the discovery of the polarization of sky light by Arago more than a century ago the phenomenon has been studied by many eminent investigators; but, while 5ts general features have been satisfactorily accounted for, certain variations that appear to be connected with atmospheric conditions still In the present paper the remain to ble examined and explained. general features of sky polarization wil be considered first, together with a brief reference to some of the theories that have been advanced to account for them. There will then follow a more detailed account o’f certain variations with location and with atmospheric conditions, which have been made the subject of extended obs’ervation by the writer. GENERAL FEATURES.--If we examine with a polariscope the light from a cloudless sky when the sun is on the horizon, we shall find that from 70 to 80 per cent. of the light from the zenith is plane polarized, and that the zenith is the point of maximum polarization, Furthermore, a maximum percentage of pblarized light is found in the plane at right angles to the direction of the incident solar rays, although the percentage decreases somewhat * Read before

the Philosophical

Society

[Nom.-The Franklin Institute is not responsible by contributors to the Journal.] Copyright, VOL.

CLXXI,

of Washington,

1911, by THE FRANKLIN, INSTITUTE.

No. 1024-25

Feb. 25, rgr1.

for the statements and opinions advanced

334

HEREERT

H.

KIMEALL.

with angular distance from the zenith. At the time of the equinoxes this plane cuts the horizon at the north and the south pints. Along the horizon, therefore, b’oth east and west from these points, the polarization diminishes. It also diminishes as we pas’s from the zenith towards the east or west; and reaches1 a minimum, in this case zero, at po,ints from 15' to 25' above the anti-solar point and the sun, -and which are called from their discoverers the neutral po’ints of Arago and Babinet, respectively. Generally speaking, the plane o,f polarization is the plane containing the sun, the point from which light is observed, and the eye of the observer. For the zenith this coincides with the vertical pIane o’f the incident solar rays; for a point on the horizon it is a horizontal plane; and for an intermediate point, a more or less inclined plane. In the vicinity ohf the neutral points the plane of polarization is more nearly horizontal than would be the case if the above rule applied, except that directly above them it is At all points directly below them it is ho5rizontal. vertical. As the sun increases’ its angular distance above the hoSrizon one continues to find the point of maximum polarization about go” from the sun and in its vertical. The maximum percentage of polarization is still fo’und in the plane at right angles to the incident so’lar rays ; and one co,ntinues to find points of zero polarization ab.ove the sun and the anti-solar point, although the distance o,f the former from the sun gradually diminishes, About the time that Arago’s neutral point disappears below the horizon Brewster’s neutral point makes its appearance above the horizon underneath the sSun. Other neutral points have also been observed at different times. The principa1 features of sky polarization are, therefore, a point of maximum polarization about 90” from the sun and in its vertical, a plane of maximum polarization at right angles to the incident solar rays, and points of neutral polarization at about rg” to 25 * above and below the sun, and about the same distance The plane of polarization is, in ablove the anti-solar point. general, the plane containing the sun, the point observed, and the eye of the observer; but this rule does not apply to the region immediately about the neutral points. It will also be useful to remember that the light vibrations occur in a plane which contains the point observed and the eye of the observer, and which is at right angles to the plane of polarization.

POLARIZATION EXPLANATION EFFECT

with

variation

of

particles

I +

it was

angles

to the incident

incidence

would

shown

beam

all the

plane.

would

the light showed

throughout

ing would of

much

scattered

light,

distinction effect partial

a part

instead

directions

the of

of

toward

point,

or the percentage

o and

of

IOO. 1888

SOret

distributed

of secondary

uni-

scatter-

probduced by a, beam of natural the a,ction of

and polarized

o,f the sun. angles

or

positive beam

per-

vibmrations in this in the primary polarized

polarization.

will

in The

be everywhere

polarization, go0

a beam

in a plane

The

to the vibrations

polarization from

to one

of the light

the sun, plus

the positive

and

angles

in this

the fraction

particles. were

polarized

total

at right

these points

the effect

prevailing,

negatively

an unpo-

the anti-solar

SCATTERING-In

contained

at right

place

it.

Between

t

bletween

diffusing

‘from

from

and this beam is said to’ be negatively

from

02 this

neutralize

vary

to the direction

beam are therefore

of

1fyi$i3

to the effect

directly

less intensity

pendicular

by

a hemisphere

be identical

coming

take

polarization

would

in a plane

be unpolarized.

SECONDARY

that if the small

formly light

would

OF

from

frolm

is to say at right would

of the sun and

be expressed

polarized

EFFECT

scattered

the

being

departure

as, at go”

polarized

That

of maximum

in com-

the light,

w;ith direction

incidence light

vibsrations

the light jwould

and the plane polarized

that

beam.

In the direction

respectively,

scatter

to’ this law the scattering of

be completely

light

1871

made turbid

are small

would

/3 is the angular

in the line

larized

diameters

the scattering

According

as intense

Furthermore,

of

the years

how a medium

of light

cos2p, where

the line of incidence. be twice

whose

the wave-length

by

335

SCATTERING.-Between

in the intensity

expressed

LIGHT.

POLARIZATION.

and others showed

by the presence parison

OF SKY

OF PRIMARY

and 1899 Rayleigh

SKY

OF

from

the sun, however,

thus the

to

giving sun.

only In

the light

the

would

still be unpolarized. But the diffusing formly

throughout

relatively

small

particles,

both

layers

particles,

segment of

gas

of and

than in the upper.

tribution,

Soret

instead

a hemisphere,

supposed

are

a sphere, of

As

foreign

of

being

and there

‘uni-

contained

in

are many

substances,

an approximation

a horizontal

distributed

actually

ring

in the

to.the

of diffusing

a

more lower

actual disparticles

336

HERBERT

H. KIMBALL.

to superpose its effect upon that of the hemisphere, In the light scattered by this ring horizontal pda.rization would predominate ; and in the direction of the sun and of the anti-solar point the superposition of this component upon the components due to primary scattering and the secondary scattering by the assumed hemisphere, would result in horizontally polarized light. As we proceeds towards the zenith, however, we so,on reach points where the vertically polarized light just neutralizes the horizontally polarized, giving us the so-called neutral points, DIFFUSION

BY LARGE PAmIcms.-Wiener

2 has shown

that

the presence of water drops would have little effect upon the polarization go” from the sun; that ice crystals would appreciabdy diminish the polarization in that direction; and that, within limits, the presence of any particles. whose diameters are large in comparison with the wave-length of light would greatly increase the sky iIlumina.tion and the proportion of natural light in the vicinity of the sun. REFLECTION FROM THE SURFACE OF TIEE EARTH.-My own obtservations, confirming those made by others, show that when snow covers the ground the percentage of sky polarization at the po’int of maximum may be diminished from 70 per cent. to 50 per cent., which corresponds to an increase in the ratio of the unpolarized to the polarized light of from 0~43 to 3:.oo. It is therefore evident that reflection from the surfa.ce of the earth increases the proportion of natural light. Reffection from large particles s.uspended in the atmosphere would also) produce this same effect. CAUSES OF VARIATION

IN SKY

PoLAPdZATIoN.-It

therefore

appears that an increase in the numbler of the diffusing particles, large or small, in the lower layers of the atmosphere, and, likewis.e, that increased reflection from the surface of the earth, must produce a Giminution in the polsitive polarization of sky light, and at the same time increase the distaace of the neutral points of Arago and Bsabinet from the anti-solar point and the sun, respectively. PERIODIC

VARIATIONS.

the percentage of For many years Jensen s has measured polarization at the zenith at different hours of the day. After correcting his readings for varying zenith distance of the sun, he finds that the minimum pollarization occurs at about the time

POLARIZATION OF SKY LIGHT.

337

of maximum temper;ature, w$ich is also the time of maximum convection. Rubenson 4 found the polarization at the polint of maximum to be less in summer than in winter, a fact that may also be partly attributed to convection. Busch 5 has found the distances of the neutral points of Arago and Babinet fro,m the anti-solar po’int and the sun, respectiyely, to vary greatly from year to year,-in the case of the latter from a,n average of 15.4’. in ISgo to an average of 30.8” in 1903. Reference may also be made to my own observations,6 which show that the po’larization at the point of maximum in the year 1903 averaged IO per cent. less than the- average for the years 1903 to’ 1910, inclusive. The year 1903 follo,wed violent volcanic Although eruptions in the West Indies and Central America. this was not a year of maximum sun spots, Jensen p points out an apparent connection between the years with a maximum elf sun spots and the years when the neutral points are at a maximum distance from the sun and the anti-solar point. ’ NON-PERIODIC VARIATIONS. EFFECT OF WATER VAPOR.--Some observations by Crova and Houdaille 8 in 1888 indicate a connection between atmospheric transmission of solar radiation and sky polarization. During the past five years I have made a great many olbservations that clearly show such a connection. They also1 show1 a relation between sky polarization and local conditions, such as character of the soil, convection, etc. In order that these various relations may be more easily understood, the cbservations are summarized in Table I, where P, indicates the percentage of polarization of sky light at the point of maximum, E the vapor pressure, and Q2 the intensity of solar radiation on a surface normal to the sun’s rays a,nd at mean solar distance, expressed in gram-calories per minute per square centimetre. p2, e and Q, were all three measured when the sun was 60’ from the zenith. The significance of &‘2 is given below. The Washingtoa observations cover the period from Decemat other stations, includber, 1905, toi May, 1910. Observations on the position of the neutral points, ,ing some at Madison, Wis., and which are given in Table III, were obtained in connection with field work during the summer and fall of 19x0. All the data were obtained when the sky was practically cloudless.

HERBERT

338 TABLE

I.-SUMMARY

H. KIMBALL.

OF SOLAR RADIATION AND SKY POLARIZATION WITH TIME SUN 60' FROM'THE ZENITH.

OBSERVATIONS

WASHINGTON,

D.C. PZ

No. of half-day

series of observations

.......................

IO.

..

..

-

IO.

9. 1.7. 4. 7.

....................... ....................... ........................ ....................... ........................

Averages

GROUP 2

.

.................... ~. ~__ GROUP

68.2 66.2 62.4 57.8 sr.9

I.238 1.183 I.057

......

6x.3

I.2IO

...... ...... ...... ...... ......

67.7 65.8 63.1 57.4 53"2

3

I...

I3 ..........................

.

.

5 .......................... , ..........................

. ... Averages ...................

Sept.

rp. A.M 1.3.

. . . . . . . . . .

SANTA .

FB, NEW

.. 1 . . . .: .. ..

. .

....................

P.M ....................

I%, A.M., .................. 8.P.M

....................

0.884

..

....................

MEX.

_

61.0

6.50

1.282

70.8

66.8

8.48 7.87 8.81 8.48 8.48

1.360 1.39Q 1.343 1.334 I.319

68.8

8.42

I.349

j.16

I .420

I

I .360 X.440 1,452

66.5.

4.17 3.40 e-49 4.95 2.61 3.99

I.359

I.344 I.417 I.420 I.388 I.337 I.341

68.9

3.83

I

,406

I.387

7.04

T

.228

I.239 I.314 I .299 1.35Q x.283 I.317

EL; 67.8

I..

9, A.M .................... Averages.

4.47 6.66 6.07 8.32 9.69

43.0

_._-I_--A.M..

I.314 = -259

61.4

GROUP 4 a.......................................

20,

-..

_

...........

Sept.

jo.8

_.

...... ...... ...... . . ...... ......

8. ......................... ,..............~

Calories

Per cent.

GROUP I

QIZ

e

FLAGSTAFF,

ARIZ.

Dates Sept.25,A.M _......

... . ... .. ....... 27,A.M . . .._.................. 28, A.M . . . . . . . . . . .11.. . . . . . , ....... ....... 30, P.M., I.... . . , . ....... 26,A.M ,_._.__..__..__,._..... 28,P.M. .._._. . . . . . . . . . . ....... 26, P.M. . . . . . . . . . . .......

Averages

..

.......

r.

..

.......

.

70.6 70.

: I

69.8 69.3 68.1 68.1

I.397

I.417

.4*&!

PHOENIX, ARIZr. Oct. 5, A.M.. 3,A.M... 5, P.M... 3, P.M... ,,A.M... 7, P.M..

6,

.

.

P.M... 8, A.M..

.

6;A.M..

.

..... ..... ..... ..... ..... . . . ... ..... .....

Averages................,,.............

, .

.

. .. . 1

. . ....

. *. . .._. .. ... . . .. ..... ... ..... .....

63.2 62.8 62.7 62.0 60.7 59.6 59.4

I.291

:E:: 60.9

-

::;5: 8.81 5.16 4.17 5.79 4.37 8.18

I.319 I.292 I .337 I .240 I.274 I .239

6.72

I.276

I.268

I.238

1.256 * 1.263 1.284 __~

POLARIZATION OF SKY LIGHT.

339

The data for Washington have been arranged in four groups in such a way that the averages folr groups 2 and 3 give nearly equal values8 for PZ, but values of e differing by 4.26 mm. The corresponding difference in the values of (Js is 0.044, indicating that an increase of I mm. in the value of e diminishes the value of a2 by 0.010. This is very closely in accord with the empirical equation of Abbot and Fo’wle,g namely, F = 5.1 + 0.12 Eowl, where F indicates the depetion of solar radiation intensity due to, water vapor bsand absorption in the solar spectrum expressed as a percentage of the value of the solar constant. expressed in J% = 2.3 e is the vapor content of the atmosphere millimetres of depth of water, and m is the secant of the sun’s zenith distance. When ML= 2, a change of I mm. in e will produce a change o’f about 0.55 in F, which is equivalent to a change in the intensity of solar radiation of about 0.011 calories, or practically the same as, found from the data in Table I. We may therefore employ the equation Qr2= QZ-o.o.rr(e’-e) to adjust the values of QZ obtained with various values of e to values Q’2, correspo,nding to any desired uniform value of e = e’. In Table I they have been adjusted to a value of e’= 6.0 mm. The resulting values of a’, show very clearly that a relation exists between e’, and P,, but do not indicate a direct relation between the latter and e. Similarly, the averages for Santa Fe, N. Mex., and Flagstaff, Ariz., if we omit the data for Santa Fe on September 20, give nearly equal values for P,, but values of e differing by 4.59, and values of a2 differing by 0.057, indicating a diminution of 0.012 in (Jz for an increase of I.0 mm. in e. Santa Fe is about 7000 feet and Flagstaff about 6goo feet above sea, level. At this elevation the investigations of,Abbot and Fowle l* indicate that an increase of 1.0 mm. in e shosuld cause a diminution of only after employing this latter value to o.oog in (Jz. However, obtain (J’2 corresponding to e’= 6.0 mm., the data indicates that with a transparency of the atmosphere at these two stations such that their average values of a’2 differ by only about one per Here cent., the averages of sky polarization are in accord. again the etiect of e upon the value of PZ is not apparent. After adjusting the values or Q2 obtained at Phoenix, Ariz., to values of a’, corresponding to e’ = 6.0 mm., we may bring VOL. CLXXI, No. 1024-2.6

H. KIMBALL.

HERBERT

340

together in Table II the average values for Flagstaff, Santa Fe, and Phoenix, and the averages fo,r the best observations at Washington, which latter have b,een obtained from the data for group I, the first ten series elf group 2, and the.first eight series o’f group 3. From this table it is evident that with a given transparency of the atmosphere after allowance has been made for band absorption by aqueous vapor, the percentage of polarization of sky light with the sun 60” from the zenith is greatest at Washington and least at Phoenix. In Table III are given observed distances of the neutral points elf Arago and Babinet from the anti-solar po’int and the sun, respectively, and the highest polarization that has been observed with the sun on the horizon. At Washington no observations have been made on the position of Babinet’s. neutral point, and at TABLE

II.-AVERAGES WITH

OF SOLAR THE SUN

RADIATION

AND

SKY

POLARIZATION

6~9’ FROM THE ZENITH.

Station

Phoenix........................ Washington. . . ..

... ... ..

Madison no measurements were made of the polarization a,t the The data indicate that with the sun on the point of maximum. ho,rizon the positively polarized light, which results principally from the primary scattering by small particles, is relatively the weakest at Washington and Madison, and strongest at Flagstaff and Santa Fe. Comparing the data of Tables II and III, it is seen that the difference in sky polarization with the sun on the horizon and at 30” above is least at Washington and greatest at Phoenix. If we study the local conditions that exert a modifying influence upon sky polarization, it must be no,ted that Washington and Madison are in regions of dense vegetation both with -respect Phoenix, Ariz., is to the forested areas and the open country. in a treeless valley; the soil is light in color and extremely fine in texture, and at times the dust arising from it covers the surface like a fog. About Santa F6 the country is generally covered with

POLARIZATION OF SKY LIGHT.

341

a scattered growth of stunted trees, while Flagstaff is in the midst of a forested area, although the grolwth is much less dense than is the case in the Eastern States. These two latter stations are near the fooct of valleys, at the heads of which are mountains over IZ,OOO feet high. There is strong air drainage down these valleys at night, and in consequence the atmolsphere at sunrise is remarkably clear. Soon after sunrise the valleys become hot, and there is a reversal of wind direction, which brings in more or less dust from the plains below. At Santa FC the pyrheliometer readings at this time sometimes showed a falling off in radiation intensity of as much as 8 per cent. even before the wind at the surface had changed its direction. This was accompanied by decreased polarization of sky light at the point of TABLE

III.-SKY XI

Station

POLARIZATION OBSERVATIONS WYITHTHE SUN ON THE HORIZON.

Distance ofArago’s neutral point from the anti-solar point

Distance of ~~~~1 net’s neutral point

Max

Max

0

Washington, D. C Madison, WIS.. . . Phoenix. Ariz.. . . Flagstaff, Aria.. . . Santa-F&, N. M..

21.2

21.7

X9.5 .

21.6 18.5

Min. Mean. ______~ 0 0 16.4 18.0 18.2 16.1 16.1

19.1 rg.6 18.8 17.9 IT.2

from the sun

Min. ~0 0 .... . . . .

18.8 19.1 18.8 16.2

Mean. 0 ....

I 7.6

18.0

16.2 14.4

17.7

14.7

Maximum

/ Period covered by the observations

P;;o!? zenith ____-I

IPer cent. _74.9

Jan. J$Y

g-May zs-Aw.

19, zgro 4.1910

8,1g10 Sept. 2gSept. 30, rgm Sept. T-Sept. ao, 1910

16.0 IS.5

s-act.

-

maximum, and w s usually folk 17Ned by th e formation of cumulus clouds, At Flagstaff the effect of the reversal in wind direction on the pyrheliometer readings and on the polarization was less marked, and there was less tendency to form clouds; but both solar radiation intensity and sky pojlarization showed a slight falling oFf in the afternoon, which was undoubtedly due to the increased scattering of light in the lower atmosphere on account of the dust intro’duced by convectio8n. At Phoenix the radiation wa,s more -intense during the afternoon than during the morning hours, without a corresponding This. may have been due to the increase in sky polarization. effect of smoke from the city, which diminished noticeably in density as the day advanced, perhaps on account of a decided diurnal variation in wind direction. In this way the atmospheric transmission in the direction of the sun might be increased,

HERBERT H. KXMBALL.

342

without noticeably affecting either the secondary scattering or the reflection from lorwer surfaces in a direction 90” from the sun. The distance of Babinet’s point from the sun was, slightly greater at sunset than at sunrise at both Pho’enix and Flagstaff. The increased dustiness of the atmosphere due to convection appears, therefore, to have slightly decreased the sky polarization during the afternoon as compared with the forenoon hours at the three’ stations above named. It is not believed that the great diurna1 variation in sky polarization observed at Phoenix as compared with that at Flagstaff and Santa Fe, and especially as compared with that at Washinaon, can be attributed to convection, since we do not find a corresponding diminution in atmospheric transmi.ssibility. TABT,E IV.-SKY POLARIZATION WITHDIFFERENTREFLECTINGSURFACES. Sky polarization Station

Date Noon

___~ _~_ Santa FB,N. Mex.. . . . Sept. 8, ~gro Santa F&, N. Mex . . . . . Sept. II, rgro Phoenix, Ariz . . . _. . . . Oct. Washington, D. C . . . . . Dec. 2:’ :gii I: ~gmg Washington, D. C.. . . . Dec.

Sun on horizon

I Per cent. pe’ ,8”“ I Yt* 77.6 56.2 ~ . . . . !

59.1

j

71.0

< I

50.6

;

Remarks

i , / i

Clear sky. Sky $++covered with cumulus -1clouds_ at noon.

73.0

t Uear

74.1

1Clear sky.

66.6

sky.

: Clear sky.

Snow on ground. No snow.

Perhaps analogous conditions ‘exist at Santa Fe when clouds commence to form, and at Washington when the ground is covered with snow. Polarization data for these several conditions are given in Table IV. There was little difference in solar radiation intensities at At Washington the Santa Fe on September 8 and I I, 1910. radiation was more intense on December 23, Igo& than on December I, 1909. It seems rational to attribute the low percentage of sky polarization at noon at Phoenix to causes similar to those that produced like effects at Santa FC and Washington, namely, reflection of In the case of Santa F4 light to the sky from lomw-lying surfaces. these were the surfaces of cumulus clouds; at Washington the light was reflected upwards from a snow surface, and at Phoenix from the light c&red surface ,of the ground and the dust layer just above it.

OF

POLARIZATION

SKY

343

LIGHT.

In comparing sky polarization &servations at different stations it is therefore necessary to take into account the relative intensities of reflection from the surface. It now remains to account for the apparent relation between Q’, and P, indicated b.y the data for Washington in Tabae I, and of wihich we find little trace in the data for other stations, In other wo’rds, when the solar except possibly at Santa Fe. radiation intensity decreases from 1.302 to 0.902, why does the sky polarization diminish from 70.8 to 43&o, as shown in the averages of groups I and 4 in Table I? From my, original records it is found that of the ten series of observations included in group I, seven occurred in November, TABLE Date

Oct.

TO,

V.-DAYS

Fz

1907,P.M.

June 8, 1908, P.M.. May x, rgo8$ A.M.. June 27s 39087A.M.. Apr. 29, xgo8, P.M..

I

j2.9 j2.2

WITH

8.18 12.68

51.4

Apr. 17, rgo6, P.M. Apr. 25, rgo7r A.M.

.$I .o 43.4

4.44 6.76

May 18, 1906,

42.5

8.50

APL Apr.

17, rgo6, A.M.. 17, Igo8, A.M..

P.M..

52.0

:::,9

Q2

e

3.63 x3.61 4.75 4.57 3.81

52.1

Low

Q’S

o-992

I.016

I

I

.a16

VALUES Wind, direction

.08g

OF P,

AND

Q’,.

Remarks

Rain on Oct. II.

I.049

I .036 0.994

I .087 1..066 .I .c35 I.020 0.97Q

I .017 0.931

I .ooo NW. 0.939 ~ S.

Followed period bE.heavy Lunar halo, I A.M., 18th; 18th. Followed period of heavy Lu;6yh halo, P.M., 25th,

Cl.838

0.866 ~ NW.

Exces&ely

I.113

0.982

rain. Rain, rain. RImI,

hot.

-

1906, in the southeastern quadrant o’f decided high barometric areas, and the remaining three occurred in September, November, and Decemb’er, 1909. The two1 series in grolup 4 and the eight series in groups 2 and 3 having the lowest values. of P, and Q’2 were all obtained in the months of April, May, and ‘june, except one, which was obtained in October. Data relative to these ten series is given in Table V, from which it is seen that lunar halos were observed on the nights follolwing two of them, and that seven were followed .by rain before midnight of the succeeding day. On none of these days was there marked dustiness or smokiness in the loiwer layers ,of the atmosphere, and there was almost a complete absence oE clouds, although on some days it was noted that the sky had a streaked appearance. It therefore appears that w/e here have to do with optical haze, or reflection from non-homogeneous layers or currents of air. According to

344

HERBERT

H.

KIMBALL.

Hann,ll its occurrence under certain conditions is indicative of the approach elf fine weather, while under certain other conditions it is evidently the forerunner of nucleation and rain. CONCLUSIONS.

From the data here presented it appears that while the polarization of sky light is greatly modified by reflection from the s’urface of the earth it is intimately connected with meteorological processes and conditions. Decreased polarizatioln may be produced by mechanical haze, due to the presence of large particles of any description in the atmosphere, or by optical haze, due to a lack of homogeneity in the atmospheric layers. While this latter condition is not of itself a sufficient criterion on which to’ base a weather forecast, in co,nnection with other data it should be of assistance in determining the extent to which upper air coaditions are disturbed. It is a question, however, whether pyrheliometric readings would not be more useful for this purpose, since these latter are only affected bly the conditions along the path of the incident sol& rays. BIBLIOGRAPHY. 1 Arch.

sci. phys. nat. Gen?ve, 3 ser., tome 20, 1888, pp. gt-471. Dr. Christian: Die Helligkeit des klaren Himmels und die Beleuchtung durch Sonne, Himmel und Riickstrahlung. Abh. die Kaiser]. Leap.Carol. Deutschen Akad. der Naturforscher., Band 73, Nr. I, Halle, rgoo; Band 91, Nr. 2, Halle, 1909. aJensen, Dr. Chr.: BeitrHge zur Photometrie des Himmels. Schr. Nat. Ver. Schlesw.-Hoist., Kiel, Bd. II, Heft. 2, pp. 281-346. de la lumi&re atm0spheriqu.e. Nova acta. Sot. ’ Rubenson, R. : Polarisation sci., Upsala, 3 ser., 1864-5, pp. 1-145. Felix M. : Meteorologische ‘See Pernter, J. M., and Exner, Optik. 4. Abschnitt, p. 614, Wien, 1910. ’ Solar radiation, atmospheric absorption, and sky polarization, at Washington, D. C. Bulletin of the Mount Weather Observatory, vol. iii, part 2. ‘Die gegenwirtigen Probleme und Aufgaben welche mit den Studium der Abdruck aus den A&r. atmosphirischen Polarisation verkniipft sind. Nachr., Nr. 4283, Ed. 179, Nov., rgo8. ’ Crova, A., & Houdaille : Observations faites au sommet dn Mont Vcntoux sur l’intensite calorifique de la radiation solaire. C.-r. Acad., Sci., Paris. tome 108, 1889, pp. 35-39. ‘Annals of the Astrophysical Observatory of the Smithsonian Institution, vol. ii, p+ 130.

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