MAY, 1901. MONTHLY WEATHER REVIEW. 209
bins to the Atlantic coast, severe thunderstorms are not un
common. On the Great Lakes the severer storms of Ma?
advance from the middle-eastern slope of the Rocky Moun
tains. These storms average about two a month, and thei
approach is indicated by rapidly falling barometer and ea8
to southeast winds. After the passage of the center of t
storm the wind shifts to northwest with rising barometer.
I n May the regions in which agricultural products are sub
ject to damage by frost are usually confined to the extremc
upper Missouri, and Red River of the North valleys, and thc
Rocky Mountain and Plateau regions from central Nev
Xexico and the Texas panhandle northward.
-.--
SOME UAUSES OF THE VARIABILITY OF EARTHSHINE
By H. H. KIMBALL.
(Read before the AsLronomlcal and Physloal society of Toronto, June. 1901 I
When we observe the new moon shortly after sunset we are
generally able to distinguish the outline of the whole moon
and the dark part is usually of a delicate green tint, or cop-
per color. At the hour of sunset the sun is shining upon
the half of the world that is west of UE, while the eastern
half is shrouded in darkness and night. Between UE and thc
sun in the west is the moon, whose western half is illiiinined
by the 8~11, but 'whose eastern half receives no direct sun-
light, and is in darkness like the earth, except that its dark
half may receive considerable light from the bright half of
the earth. This so-called earthshine may vary considerably
with the condition of the earth's surface and atmosphere.
When the bright half of the earth is covered with snow or
cloud i t undoubtedly reflects more sunlight than a continent
of forest and vegetation, and much more than an ocean of
mater, and on such occasions the dark half of the moon might be expected to be unusually bright. I t is not often that we
are able to collect data as to the condition of the atmosphere
or of the earth's surface sufficient to satisfactorily explain
the variations in the brightness of the dark side of the old
moon when seen in the arms of the new.
Mr. G. E. Lumsden, President of the Toronto Astronomical
and Physical Society, has requested any information that
may be obtainable relative to the condition of the bright
half of the earth a t G or 7 p. m., eastern time, March 22, 1901, which corresponds to 11 p. m. or midnight, Greenwich
time, or noon in the middle of the Pacific Ocean. By means
of the data given in the Nautical Almanac we ascertain that
at Greenwich midnight the E U I ~ was in the zenith a t about
longitude MOO, latitude Oo 40' north, and the moon was in the
zenith at about longitude 132O west, latitude 1 5 O 7' north.
We have therefore prepared, in Chart S, an orthographic
projection of the western half of the earth upon the horizon
of a point whose zenith is about midway betweeii the sun
and moon a t this time, namely, latitude loo north, longitude
lGOo weet. It would have been more correct to have made
the projection with the nioon in the zenith, but the results
would not have differed appreciably from those here given.
Mr. Lumsden writes as follows:
On the night of the P3d of March the moon, owing to earthshine, vas so bright that a member of the Astronomical Society called me up by telephone, and asked me to make observations with the naked eye and an opera glass, with a view to comparison on other occasions. In- deed, I and other members who took the matter up in the course of the evening were uurprised at the brilliant illumination, which enabled us to identify, even with the naked eye, certain well known lunar for- mations. On thinking the matter over, it occurred to me that this brilliancy might have been due to reflection from a very large area of clouded surface, which possibly at t.he time was true of the western American Continent and the Pacific Ocean, inasmuch as, shortly after midnight, the weather changed, and was succeeded by cloudy skies which lasted for some little time.
Referring to Chart X, and having in mind the positions of
2-2
the sun and moon a t the time specified above, we see that the
sun illuminated the half of the globe from longitude 90 west, across the Pacific to 90 east, while the moon could only
receive light from the earth's equatorial region as far west as
longitude 138O east. Furthermore, while the sun illumined
the earth practically from pole to pole, the moon received no
light from the antartic regions beyond latitude 7 5 O south.
The illumined portion of the earth from which the moon re-
ceived light, may therefore roughly be stated to lie between
latitude 7 5 O south and the North Pole, and longitudes 90
weet and 138O east ; and Chart S shows that it embraces prac-
tically the whole of the Pacific Ocean, the eastern portions
of Australia. Japan, and Siberia, and the larger portion of
North America-an area that does not differ sensibly, in
character or extent, from the normal reflecting surface when
the moon is two or three days old, and observed at about 7 p. 111. from Toronto.
According to Bond,' the quantity of light received at any
point by reflection from a surface may 1x1 represented by the
equation
in which di' niay represent the quantity of light received by reflection from the earth upon an element of the moon's sur-
face, ds', projected as dp' upon a plane perpendicular to a
line joining the earth and moon ; J the distance between the
earth and moon; P the albedo of the earth's surface; i the
amount of light received by the earth from the sun, which
we may assume to be a constant; 6, a coefficient that
varies with the reflecting properties of the reflecting sur-
face. The value of @ is l for a polished sphere, 3 for a flat
opaque disc reflecting equally in all directions on the side
of the hemisphere toward which i t is exposed, 4 for a flat
disc in which the quantity of light reflected to any point
is proportional to the apparent area of the disc as seen
from that point, etc., assuming that the incident rays are
parallel and perpendicular. For any given surface, however,
this coeficient may be considered a constant, and its exact
value does not concern UE in the present investigation, since
we have to do only with the variables of the above equation.
We therefore obtain from equation (1) for the total light re-
ceived a t the moon by reflection from the earth the follow-
ing expression, in which C is a constant:
Similarly, for the light reflected back from the moon to a
point on the earth, by substituting (2 ) for t' in (l), we obtain
the following equation:
(3)
in which cli" represents the quantity of light received upon
zn element of the surface of the earth, projected as dp"
upon a surface perpendicular to a line connecting the earth
znd moon ; tr' is a constant, as in equation (l ), and P' is the
zlhedo for the moon. This albedo must also be a constant,
5ince in the absence of an atmosphere we can not conceive
)f any variation in the reflecting power of the moon's sur-
Face, except the inappreciable variation due to the fact that
3 9 reason of libration a slightly different hemisphere is pre-
iented to UE from time to time. Our final equation for the quantity of earthshine observed
)n the moon from a point on the earth will therefore have
,he following form:
George P. Bond, On the light of the moon and of the planet Ju iter. blemoirs American Academy of Arts and Sciences. 1S61. Vol. $111,
3. ?%5.
210
85 j('louds . . . . 51 0.70
(Water ..... M I 0.@1 Ocean. . . . . . . . -
MON!L'HLY WEATHER REVIEW.
85.70 0.71
MAY, 1901
(4)
in which C' is a constant, and the p and J are variables.
We will now consider the probability of a variation in the
value of p, and its effect upon the intensity of the earthshine
on March 22.
Referring again to Chart S, we estimate that the illumined
disc of the earth, as seen from the moon, consisted of 15 per cent continent and 85,per cent ocean. The normal distribu-
tion of clouds is approximately shown by the lines on Chart
S, which are based on the well known cloud charts of Teis-
serenc de Bort. These show that for the hemisphere we are
considering, under average conditions for March, four-tenths
of the ground is covered with cloud, and probably two-thirds of the remainder with snow. Over the ocean the average
cloudiness is about six-tenths.
The albedos of these various surfaces are not so well de-
termined as we could wish. Bond, in the memoir already
quoted, records comparisons between the light reflected from
various surfaces, determined principally by means of com-
parisons with Jupiter. He found, as did Hersche1,Y that the
albedo of dry earth, or a rock surface, is about one-sixth that
of white paper, or only a little less than that of the moon.
His value for white paper is only 0.410, and is apparently
the same as the value determined by Lambert ;' and his value
for newly fallen snow is a little less than that for white paper.
Zollner,' from direct measurements, has given a more satis-
factory determination of the albedos of various surfaces, as
follows :
Fresh fallen snow, 0.783 ; white paper, 0.700 ; .white sand-
stone, 0.237 ; clay marl, 0.156 ; moist earth, 0.079 ; water,
0.021.
These results were obtained with an angle of incidence of
20. The values vary somewhat with this angle, particularly
for a water surface, for which Tyndall gives the following :
Angle of incidence. p
0 0.018
40 60 80 0.889
89. I 0.721
In the present case we need not concern ourselves about an
angle of incidence greater than 20, except in the case of a
tempestuous sea, when the value of 11 might greatly exceed
that here given, and for cloud surface we inay assume 11 to
have the same value ae for white paper. Zollner's value of
the albedo of the moon is 0.1736, which would make that of
an ordinary ground surface about 0.16. For a anow surface
we can hardly adopt the value he has given, since over North
America and Siberia, where the snow surfaces we are consid-
ering were lying, the reflecting power must have been much
diminished by the presence of forests and bare ground. Fur-
thermore, the surface of the fresh fallen snow soon loses its
whiteness from a variety of cauBes. It will therefore he
safer to adopt for the albedo of a snow-clad continent the
mean between the albedosof the naked ground and snow,
We may therefore deduce the normal average reflecting
powerof this hemisphere for March, as in the following table:
See pages 276 and 2S2 of Bond's memoir, above quoted. See page 282 of Bond's memoir, above uoted. 4Dr. J. C. F. ZGllner, Photometrische (tntersuchungen. Leipzig,
5Prof. John Tyndall. Six Lectures on Light. London, 1573. Page
- ~.
1565.
17.
or an average albedo of 0.44 for the illuminated hemisphere.
The log hooks of westward bound steamers on the Pacific
Ocean on March 23, 1901, are not yet avai.lable to any extent,
but through the courtesy of the Chief Hydrographer, U. 8. N., we have been permitted to examine those of steamers east-
ward bound and find no evidence of any marked storms or
unusual cloudiness over the water at that time. The average cloudiness a t Greenwich inidnight on March 22, as indicated
Iiy these log books, is shown by figures inclosed in circles on
Chart S ; the figures to the right and a little above the circle
indicate the number of oliservations available for determin-
ing these averages. There was, however, an extended area of
cloudiness over the western part of the United States, and
snow had fallen there during the day. We may therefore
increase the cloudiness over the land to seven-tenths and
diminish the naked ground to two-tenths, thereby increasing
the total in the above table to 44.45, or a little more than one
per cent of itself, which would be inappreciable.
It will be interesting to note what would be the effect if
the cloudiness over the ocean should be increased materially.
We will suppose i t to average seven-tenths, and in this case
our results will be as follows :
I
Proportiond part#. ! Albedos. Reflecting power.
I
Clonds... 7 0.70 ' 4.90 Continents.. . 15 .inow .... 6 0.47 2.m {Ground.. 2 I 0.16 : 0.88 85 \Clouds ... 59 5 0.70 41.66
(Water ... 25:5 1 0.081 I 0.64 Ocean.. . . . . .. - Totals.. . . . .lo0 />X-
The total reflection in this case is nearly 15 per cent
in excess of the average, hut we have no data that justifies
the assumption of any such increase ia the cloudiiiess on
March 22.
It now remains to investigate the effectof thevariation in -I,
or the distance between the earth and the moon. The mean
distance is about 239,000 miles; the distance a t perigee is
about 221,000 miles, and a t apogee about 253,000 miles.
Equation (4) shows us that the iuteiiFity of earthshine must
vary inversely as the fourth power o f these distances, or as
2355 to 3263 for the moon at meaii distance and at perigee,
and as 4097 to 3263 for the moon at meail distance and at
apogee. In other words, the earthshine 011 the 1110011 is
97 per cent brighter with the moon at perigee t.lian i t i~ with
the moon a t mean distance, and 25 per cent brighter with the
moon a t mean distance than i t is with the moon a t apogee.
There is therefore an estreme variation in the intensity of
earthshine of 52 per cent, due to the eccentricity of the
1110011's orbit. This is certainly a greater variation than we
could expect froin any probable increase or diminution in
the avernge cloudiness over the hemisphere of the earth re-
flecting light to the moon.
From the Nautical Almanac we find that the semidiameter
of the moon a t Greenwich midnight, March 8, 1901, was 14'
45.5''; at noon, March 21, it was 16' 41.9"; and a t midnight,
March 22, 16' 35.7". On this latter date the moon was there-
fore just past perigee, and the aarthshiue should have ap-
peared at least one-fourth brighter than the average.
MAY. 1901 .
HAWAII . m.0.
Walakea .................................... HllO(t0WnJ ................................. Kaumaua ................................... Pe ekeo ............................. Haralau .................................... Honohina ........................................ Laupahoehoe .............................. Ooaala .....................................
Kukaiau ....................................
....
HAPAKUA .
MONTHLY WEATHER REVIEW .
Feel . Bc 1M: 1, 2% lo(
90(
w(1
4CN
25E
211
Honokaa INul?) ............................ Aonokaa (Rickard) ........................ Kukuinaele ...............................
Awini Ranch .............................. Nlulli ....................................... Kohala (Mission) ......................... Kohala (Sugar Co.) ....................... Waimea .................................... Uawi 1111 .................................. Bawi Pill .................................. KONA . Kailua ...................................... Kealakekua ...............................
Naaleha .................................... Honuapo ................................. Riled ....................................... Pahala .................................... Moanla ....................................
Volcano House ............................ Kapoho ................................... Pohoiki ................................. IEalapana ................................... MAUL Dlowalu .................................. Walopae Ranch ............................ [tau o (Mokulau) ..........................
Kipahullai ................................. Namoa Plantatiou ......................... Nahiku ..................................... Nahiku ................................... Elaiku ...................................... Kula [Erehwon) ........................... Puoomalei ................................. Paia ........................................ Haleakala Ranch ........................ LANAI . Keomoku .................................. OAAU . Punahon (Weather Bureau, ............. Lulaokahua .............................. Kewalo Wing street) ..................... Jnited States Nayal Station .............. Rapiolanl Park .......................... Kanoa I Woodlawn D) ..................... Maakiki Reservolr .............................. lchool Street (B.shop) .................... lngane Asylum ............................. Nuuanu (W . W . Hall) .................... Nuuanu (Wpllle Street) .................. Xuuanu (Elec . Station1 , .................. Vuuanu (Luakaha) ........................ dalmamalo ............................... Maunawili ................................ lianeobe .................................... hhuimanu .................................. Bahuku .................................... Waialua .................................. Wahiawa ................................... Ewa Plantation .......................... Walpahu .................................. Yakiki Reservolr .......................... Ralihl-uka .................................. Yoanalua ................................ KAUAI . Lihue (Grove Farm) ....................... Lihue (Molokoa) ........................... Lihue (Kukaua) ........................... liealla ...................................... Roloa ....................................... llllauea .................................... Banalel .................................. Walawa .................................... Wahiawa. Mount ........................... Eleele ......................................
KOHVLA .
KAU .
PUNA .
Kahfkinni .................................
The local conditions of the atmosphere have a noticeablf
effect upon the brightness of the celestial bodies. particulnrlj
when they are near the horizon. but apparently only averagc
Conditions prevailed a t Toronto on the evening of March 22
The air over the United States and Canada had just been
cleared of dusk by a passing snow and rain storm. but then
must have been considerable water vapor present. since the
weather became cloudy shortly after midnight. as stated by
Mr . Lumsden . In conclusion. while it is possible that an increase in the
cloudiness over the Pacific Ocean may have slighty increased
the earthshine 011 the night in question. we may gafely at-
tribute the increased brightness observed to the comparative
nearness of the moon a t the time . The new moon will not again be favorably situated for
]night earthshine until April. 1902 .
Since writing the above article. I find that in the Annals of
Harvard College Observatory. Vol . S V I I I . p . 75. in an article
C . Pickering has computed the actinic albedo of the moon by the following process. as an illiistratioii of a method that he
proposed to apply more completely hereafter :
Two photographs were taken on February 18. 1855. giving for the region of Oceaniis Procellarum 0.000015 units or 15 micro.units. if we may use the term . (The unit of light employed is that given out by a Carcel lamp burnin pure colza oil and shining through n hole of 1 millimeter radius at t i e distance of 1 meter for 1 second.) This isequal to 0.000013 times the brightness of the same region during full moon when it is similarly illuminated by the sun. The relative brightness then of the sun and of the gibbous earth one day after it is on the quarter is as 1.000. 000 to 13 . Adopting Lamberts formula for the illumination of a smooth sphere L =l /r (sin Q -9 cos 0 ) where B is the hase angle. we have for the date in question o=lOl 15. whence
E=O.X!. [This. therefore. is the relative brightness of the moon for this phase angle regarding the brightnessof the earth as unity when it is in opposition; adifferent result would have been obtained if Professor Pickerin had used Ziillners modification of Lamberts formula.] From &e above it folJows that the brightness of the sun is to that of the full earth. as seen from the moon (on February 18. 1885). as
1.000. 000 is to 31 . The brightness of the sun has been variously esti- mated visually at from 350. 000 to CiClO. 000 times that of the full moon . A hotographic determination of mine (Science. VI. p . 133) gave the vafue as 760. 000 or in the ratio of 1.31 to l.O(W1.OOO . Adopting the latter figure. we find the full earth 23.6 times as bright. photographically. as the full moon . But the area of the earth is 13.5 times that of the moon. hence its albedo is 1.7 times as great . The portion of the earth illurninatin the moon at the time consisted almost exclusivcl of that portion of t i e Pacific Ocean east of 160 east longitude. whicg is gen- erally represented as occupying the Western Hemisphere . As the time of the observations was an afternoon of the rainy season in the South Pacific. it is presumable that a large amount of cloud occupied the visible portion of the torrid ..... while the extreme northern and southern regions were encased in snow and ice; it is therefore not surprising that the factor obtained is so large . Professor Pickerings actinic albedo for February 15. 1855.
when the moon is one day past its quarter. is not essentially
opposed to my normal average albedo for March and for the
moon three days before the quarter .
-
.. the Total eclipse of the moon. January 28. lS88. .. Prof . E .
485
1.3
1.100
90(1
5811 234
2.720 Bw 3w
950 1. 5fW
650
15 810
850 1. Mo
4. OOO 110 10 8
15 500 283 1.660
800 60 1100 130 500 4 500
180 2. OOO
6
60 60 15 6 10 L85
60 80 !io 2W 450 Iuo 25 800 100 340 b w)
800 80 300 1w) !250
15
300 800 Loo0 15 850 3% 10 88 2. 100 200
1:4m
HAWAIIAN ULIMATOLO@ICAL DATA FOR APRIL AND
By CUI~TIF J . LIONS . Terrltorlal Meteorologist .
GENERAL NOTE .
MAY. 1901.
The mean temperature a t sea level was 74.S0, or O.Go above
normal; the highest. 84O. and the lowest. 64O (at sea level) .
Through the kindness of M r . Curtis J . Lyons. a general statemelit of weather conditions on the Hawaiian Islands may be espected to be furnished regularly for the MONTHLY WEAT1w.R REVIEW . His memo- randum for the current month is contained in the followiiig lines . The rainfall data for the Hawaiian Islands is published quite fully in the Honolulu newspapers in a form that will lead to interestin com arisons between the departures from nornial in those islands an! the Separtures in other parts of the world . We reprint the data for April and May. 1901. in conjunction with the annual rainfall for 1900. and hope to give similar tables in the future.-&.
Statlons .
M d
. E
u
w .......
Paaullo ........................ ............I l. E Paauhau (Mopre. Glbb) ................... 80(1
Paauhan (Greia) ...........................
Rainfall .
Annual .
Vormal
Incher . 188.00 140.00
154.80 116.00 18.00 180.00 105.00
75.00 76.00
65.00 84.00 78.00
64.00
61.00 65.00 56.00
88.40
........
........
........
........ .........
58.80 61.00
........ ........ 84.00
42 . ro ........ ....... 80.00 81.5%
........
........ ....... ,
........ ....... ,
........ To . 00
........ , ....... ,....... . ,....... . 55.00
84.w ........
........
58.40 80.80
1.10
40.60 41.20 40.00 63.40 81.80 132.50
16.20
16.90 32.10
22 . R
a1.40
........ ........ .......
p . w
$.lo
........ ........ ....... ........ ........ ........
42.80 48 . 80 ........ ........ ........ 76.60 93.00
........ ........ .......
.
1W)o . .
InCh . 1ll.W 117.41
87.1: la2 . o!
84.42
T2.N
w . 5% 48.8 67 . Fi 66.06
74.96 62.M
T8.M 46.M 45.m
47 .I 87 . 74 40 . w
56 .a 64.86
25.a 20.00
81.76
63.88 80.44 75.10 55 .OB
18.48
82.84
61.p9
1rn.18 60.84
71.99 45.97 51.77
21.00
87.85 118.81
2% 86
17.8 1(w . 58
46.85 88.55 46.85 89.40
129.21 46 . (18
m.30 64.21 9T.41 81.21
16.88
........
iia.ia
........
........
........
......
........ ........ ........
........
.......
........
........
......
........ ....... ........ ........ , ....... ........
80.86 87.30 64.45 22 . 32
56.88 88.88
* .......
....... , ....... , .......
I ril 1Ll.l
nclbr 12.8 12.28 17.31 8.94 6.48 8.47 6.16
2.88 4.81
2.84 2 . T8
2.18
4 . w 6.62 8.69
6.04 8.82 4.51 4.02
10.23 8.86
8.28 1.92 8.10 8.78 8.10
6 . 18 6.12
5.04
2 .a 8.54
14.21 2.88 10.18 6 . 88 10.78 1.N 2.51
1.10
0.68
8.11 2.15 2.20 0 . BB 0 . %i
6.49 0.81 8.28 8.41 3.99 6.15 5.87 11.40 2.41 8.99
8.49
8.89
2.25 8.08 2 . 82 0.71
1.94
8.18 8 . 54 6.W 2.41 2.00 9.01
4.74 0 .8 11.90 0.64
......
......
.....
.......
......
.....
......
......
...... ......
7%
.
!mher . 8.68
8.10
2.16 1.61 1.66
0 .I
0.80 0.14 0.T6 0.17 0.47
0.40
0.W 0.44
1.41
.......
1.01
.......
.......
....... ....... ....... ....... 12.61
4.18 3.16 3.10 8.64
8.18 3.41
5.98
5.w 8.5-9 7.08 4.98 1.W 8.82 2 .8 0.80 8.10 0.18
1.m
1.16
. 8.98
2.45 2.61 1.41
7.88
8.1 2.45
8. ffl
18.W
5.80 11.69 10.01
8.64
8.14 2.98 3.08 8.49
4.85 2.46
8.56 9.76 17. o& 7.80
7.84 6.50 5.18 %J . n 8.88
.......
.......
.......
.......
I
......
.......
.......
I
......
.......
a.19
, ......
The precipitation on the island of Oahu was about normal
For most sections. 3.23 inches a t Honolulu. 13.57 inches at
Luakaha. near the Pali. The humidity was the highest
average for May in twelve years . On the island of Hawaii.
the sugar districts of the northeast coast. Hilo. Hamakua.