20 MONTHLY WIEATHER REVIEW. JANUARY, 1906
color for a comparativelylong time, and beside this the colors
which flash out and disappear immediately. A very interest-
ing fact struck me with regard to the latter class. It is gen-
erally known that an auroral arch is often composed of a series
of spear-like shafts of light arranged perpendicularly to the
direction of the arch, which appear to be in constant motion.
A number of these spears will suddenly become brilliant ancl
the lower ends shoot out of the arch into the black sky below.
The brilliancy will then run along the arch like a wave of
light, lighting up all the spears as it goes along. I noticed
that the "front" of such a wave of brilliancy ancl the points
of the spears wheii shooting out were bright red, but as soon as
the motion stopped the color disappeared, while the more
violent the motion the purer ancl brighter the red. It ap-
peared as if some physical process accompanied the passage
of the auroral beam through the air and gave out a red light.
For example, if the air had to be ionized before the dihcharge
could pass through, then the process of ionization produced
red light. If the motion was particularly violent, the pro-
duction of red light woulcl be followed by a produc*tion of
brilliant green light, so tliat if a bright wave passed a l o n ~ an
arch two wares of color would appear to travel along, first a
wave of recl light, closely followed by a green wave, the two
traveling so closely together ith to appear as one wave having :t
two-colored crest. Siiuilarly spears shooting out with a great
velocity would appear to have recl ancl green t i p .
The question of the relation of cloucls to auroras has been
very often ritisecl. Three of my observations bear on this point.
On the evening of October 11, 1903. after a fairly active (lis-
play, the aurora disappeared; but its place \vas taken by a sys-
tem of narrow bands of cirrus clouds stretching right across
the sky, which, being illuminated by the bright moon. hail all
the appearance of the aurora. That they did not form part of
the aurora could only be decided a t first owing to no line
appearing in the spectroscope when pointed at them; but later
there could be no doubt, as they partly obscured the moon.
On October 26 a very bimilar phenomenon tigain appeared;
that which n t first was taken to ])e aiirora, later turned out to
On December 13 the most brilliant nuroral clisplay of iiiy
stay took place. The whole display reached a climax at 9:15,
when a most brilliantly colored corona bhot out from the
zenith. While this final brilliant display mas taking place
the sky suddenly became thinly 01-ercarst. and the aurora was
only risible later as bright patches through the clouds.
It has long been a iiiatter of controversy as to whether tlie
aurora ever extends into the lower legions of the atmosphere.
Several observers positively aflirm that they have seen i t quite
close to the ground. This may be due to an optical illueion.
One evening I was, for a considerable time, in doubt as to
whether the aurora was really under the clouds or not. All
over the sky were detached cloucls, the clouds being (Jf about
the same size and shape as the spaces between them. Right
across the sky a long narrow auroral Leain stretched, showing
bright and dark patches owing to the clouds. I t looked es-
actly as if the auroral beam rnn along under the cloudn
brightly illuminating the patolieu of cloud which i t met. I n
reality the bright patches were the upeniugs and not the
clouds. It took me a long time to inake quite certain of this,
ancl i t was only by a t last seeing a star in the iuiclcile of a
bright patch tliat I could he quite certain.
Lemstroiu strongly eupported tlie idea that the :~iirvra often
penetrates down to the earth's surface, and described how on
one occasion the auroral line appeared in a spectroscope
pointed a t a black cloth only one or two meters away. I was
able to repeat this observation on several occasions, and found
that the line which then appeared in the spectroscope v ns not
due to an auroral discharge in the air between the spectro-
scope and the black cloth, but was clue to reflected light,
be cloud.
which it wae impossible to prevent entering the spectroscope,
as the whole landscape was lit up with the monochromatic
light of the aurora.
All the t h e I observed the aurora I could not detect the
slightest noise accoiupanying the discharge.
THE TIME OF MOONRISE AND MOONSET.'
1 %~ \V\I F. RIW.E, X. J , ( reightciii t~iiir?i\ity, OiiiaIia, Nchr.
On account of the moon's rapid motion both in right ascen-
sion and in declination, the computation of the tiiiies of the
moon's rising and setting is apt to prove very laborious, since
it can not be done except by successive approximations. The
object of this article is to explain a very rapid method to be
used for this purpose. While i t iiiay be an old one, the writer's
reason for 1)resenting i t is that he has never found i t in print.
The method to be described is a graphic one and requires
in advance the construction of three diagrams, which me may
denote 8, B, and C'. I n order to show their practical use, they
have been prepared for Omaha, Nebr. The problem before
US, therefore, is to find the central [stanclard] times of moonrise
ancl moonset at Omaha.
1. The first thing to be clone is to find the time of the moon's
meridian passage. Tliis is given for Greenwich on page I V
of eiery month in the American Ephemeris.' To reduce i t to
Omaha ancl to central time, we must add to i t 6.4 (the Green-
wich longitude of Omaha being + lib 33.8") times the hourly
clif'Fereiice there given, plus 23.8 minutes. This is done rapidly
by means of diagrani A, whose construction needs no esplana-
tion. Thus for January 13, 19OG, when the time of the moon's
transit over the meridian of Greenwich is l-ih 58.1" and the
hourly difference is 2.13", we find that 2.13 on diagram A in-
dicates souiething oxer 37 minutes, which added to the Green-
wich time gives 15" 36" as the central time of the moon's
transit a t Omalla.
This is
shown on cliagraili B for Oinaha, the latitude being + 41' 16'.
The formula
2. The nest step is to find the moon's hour angle.
COS 7 = - tan 9 tan d
gives the true hour angle,
which must be corrected for refrnction and parallas. For pur-
pose of prediction i t is evident that only the mean refraction
or 36' caii he taken. Special computation will show that this
cliniiuishes the hour angle by 3.1"' for all values of d between
plus and Iuinus 30'. For the parallax the mean value of 57.6'
Many of the Weather Bureau observers, when called into court to
testify as to the state of the weather at a given time, are asked whether
the moon had risen, and they have, therefore, requested the Central
Offiw to furiiish them with t a l k s of nioonrise and moonset. As such tallles, in order to Ire atall accurate, must 1Je computed for each locality,
it is prolier tliat the work should tie done by the astronomers of the Nau-
tical Almanac. But this is not always practicable and the tables given in
the ordinary popular almanacs are not sufficiently accurato or extensive.
A graphic method has just Ireen publisheil By Bev. W. F. Rigge, of
C'reighton Uni\ ersity, Omaha, Nebr., (see Popular Astronomy, Vol. SIII,
No. 10). This will enable any one to compute the times of rising and
setting for a whi)le month or year in a short time, utilizing the data
given in the Nautical Almanac. We, therefore, reprint the following arti-
cle by Professor Rigge, in t h p conviction that inany of our readers will
Page IV o f the American Ephemerib and Nautical Almanac gives the
following itenis in Greenwich mean time:
(1) The semiiliameter of the moon at Greenwich mean noon and (2)
at midnight.
(3) The 1it)rizontal parallas of the in0011 for Greenwich mean noon and
(4 ) nieaii midnight. mith (5) and (6) the lateof changeof each in one hour.
i 7 ) The Greenwich mean time of the upper tranbit of the moon's cen-
ter across tile meriilian of Greenw-ich, and (S) the rate of change of this
titlie for an hour, whence the time of transit over any other meridian
can be computed.
(9) Finally the age or the moon at Greenwich mean noon, counting Prom the moment of conjunction with the sun.
The following are the figures for January 13, 1906 :
(1 ) 15' 44.9' . (9 ) 15' 48.4 ', (3) 57' 43.1V', (4) 57' 54.9' , (5) +l.ll", (6)
__
make use of his Ulethod-EDIToR.
+l.U5". (7) 1 4 h 58.4"', (R ) 2.13m, (9 ) 18.3 days.
JANUARY, 1906. MONTHLY WEATHER REVIEW. 21
FIG. 1.-Rigge's method o f finding the time of iiioonrise and moonset.
may always be used, since the extreme values cliffer oiilg 3.7'
from it or lesK than one-fifteenth of its amount. As the 1):~-
allax increases the hour angle while refraction diminishes it,,
the combined effect of both is to increase the moon's hour
angle by two minutes. Accordingly all the hour angles on
diagram B have been increased by this amount. No rariativiis
from the mean values of the refraction and parallax, used in
the construction of this iliagram, can ever change the hour
angle one-third of a minute. No correction for semidiameter
has been applied. This mould diminish every hour angle a t
Omaha a minute and a half for the upper limb, or increase it
as much for the lower. [Hence the computed times refer to
the center of the moon.-En~~o~.]
Entering the Ephemeris' on pages V-SI1 of the nionth with
the central time of the moon's meridian passage a t Omaha in-
creased by six hours (that is, the Greenwich time, lTih 36" + Gh =
21b 3G'"), on January 13, 1906, we find the moon's declination
to be about 9t'north. I say "about,"because a t this stage the
fraction of a degree is of no importance. With this argument
of 9i0 north, we find that on diagram B the moon's approxi-
mate hour angle is G" 37"'. This is written under the time of L,he
moon's transit, 15h 36", and then subtracted for rising but aclded
for setting. With the results, Sb 59"' and 2 P 13'", increased Ly
six hours (to obtain the Greenwich times, lib 5!)"' and 3Sh 13"')
we make a second approximation and apply to the chgrain
the moon's declination a t these times as found in the Ephein-
eris. We write down under 8' 5!1" and 3db 13" only the differ-
ence between the first and the second hour angles found on
diagram B, vie, - 4" and - 4'" in the present instance. Experi-
ence will soon show what fraction of a degree of the inoon's
declination it is necessary to take in order to get the hour
angle correct to the minute. I f any care a t all has 1)een taken
about the first value of the moon's declination, the corrections
- 1" and - 4lU to the first approximate hour angle will agree
Pages V-XI1 of the Ephemeris give the right ascension and declina-
tion of the moon for each hour of Greenwich mean time. astronomical reckoning, in which the zero hour corresponds to noon of the civil clay
of the same date.
~~ ~ ~
uuiiierically within two minutes, and will have the saiiie sign,
which will 1)e plus when the moon is going north and minus
when going soutli.
3. The tliiril step is to correct tlie time of the moon's rising
and setting for its motion in riglit ascension. This is done
by means of diagraiu C', mhich is merely a graphic method of
niultiplication. The vertical lines marked4, 6, 6, 7. 8, indicate
the moon's hour angles, and the oblique ones 1.50, 2.00, 2.50,
3.00. the hourly ditYerence of the times of the moon's meridian
pabsage as given on page IT of the inonth in the Ephem-
eris. With these two as arguiiients, viz, Gh 37" and 2.13'"
in tlie example selected, we find from the horizontal lines
marked 5, 10, 15, 30, t8he correction sought, which here is
fourteen minutes. This is to be subtracted for rising and
aildecl for setting, and is the same numerically for both.
As tlie correction given by diagram C mag amount a t times to
twenty minutes and more, a third approximation would seen1
to 1)e necessary. I n tleclination this is inappreciable, since
the maximum change of the moon's declination is less than
one-third of a degree in an hour. and in tmeuty minutes it
woulcl never affect the moon's hour angle on diagram B to a
noticeable fraction of n minute. I n right ascension, however,
a first correction of twenty minutes when added to the hour
angle that was used to fiucl i t b y inenns of clingrain C would entail
a second correction of a full minute if the 110urly difference were
3.00. a limit which it never reaches. But as this second correc-
tion often exceeds half n minute. tlie hour angle may a t once be
increased by the amount of the first correction and another
found from the diagram. It would not be advisable to recon-
struct diagram C for the purpose of avoiding this additional
labor, since, as will be said later, this error affects only the
time of the moon's setting a t Omaha, and never that of its
rising.
4. Adding up our quantities algebraically, we obtain Sh 41"
and 3ah 23" as the astronomical central [atandarcl] times of the
these to civil central [standard] times, we find that the in
moon's rising and setting a t Omaha on January 13.
22 MONTHLY WEATHER REVIEW. JANUARY, 1906
rises on January 13 a t 8:41 p. m. and sets on January 14, at
10:23 a. m. A day will be found to drop out for rising as
well as for setting whenever the time changes from 1). 111. to
a. ui., viz, when it crosses inidnight.
January 13, 1906.
Rising. Setting.
15h 36 1!P 36 Meridian passage, central time, by A.
- 6 37 +6 37 Approximate hour angle, by B.
- -
R 59 22 13 Approximate times.
-4 - 4 Correction for change of declination, Lg B.
-14 +I4 Correction forchange of right ascension.bj C.
8 41 22 23 Astronomical central [stanclard] times.
__ ___
136 8:41 p. m. lid 10:23a. in. Uixil central [standard] times.
8 h 40 39 10h 21 5L+ Numerical computation ah check.
Accicrnc!y.-The diagrams. especi:tlly A and C. may be used
to tenths of a fiinute, if desired. But, the nearest whole min-
ute is sufficiently accurate in practise. since often the horizon is
obstructed by terrestrial objects or climiiied 11s smoke, or the
weather is unpropitious, :tud iiiost of the tinies of iuooiirise
and moonset occur during the daytime or at inconvenient
hours during the night, so that only such a sindl percent-
age of the compnted tiiues are actually observed that more
accurate and time-consuming coniputation moulcl seeiii to 1 le
only so much labor wasteel. As three dingrains are used. and
the nearest minute is taken in each one, i t niag happen that
in each case nearly half a iiiiuute is neglected always in the
same direction, and, therefore, the results limy be errciiieoiis by
more than a full minute. This is certaiuly possible am1 must
occur a t times, but i t is just as likely that these fractions of a
minute may linve contrary h i p s and sunn1 one another.
No account ueed ever be taken of second c1ifferenc:es in tlie
times of the moons mericlian passage. For Oiuaha tlie iiioon
dways rises withiu two hours and a qmrter of its upper trnn-
sit at Greenwich, so that tlie errorb of thehe cliagrams 9 ancl
C counteract one itnother. Biit as tlie time of the moons set-
ting occurs within two hours :tnd a quarter of the inotins
lower transit the errors of these clingrams are adclitiw. An
examination of the Ephemeris of lS94, when the moous its-
cending node was near the vernal ealuinox am1 the mooii,
therefore, reached a declination o f over 2So, showed tlie inaxi-
inuui second clifierence between two successive days to be 0.24
minute. For an interval its great a s sixteen hours from the
time of tlie moons upper transit at Chwenwicli, only one-third
of this, or 0.08, would be effective, and this amount for the
masiinuiu hour angle (eight hours) woulcl be only about 1.2
minute. As this is a most exoeptiou:tl case, i t is safe to ~i i y
that, in general, this method is accurate enough to give the
times within a minute. This estiiiiate was confirmed by a iiiore
rigorous numerical coiiiputiction of this sitiue example of Jim-
uary 13, 1906, which mas selected a t randoin, and in which the
moons riglit ascension aucl declin:ttion, the sidereal time, :tiid
other neceshary quantities were used and the saiue result mas
obtained przwtically within a minute.
&wed.-Tlie speed is such that I generally compute the
times of both rising a d setting fur a whole iflonth in less than
an hour, and sometimes even in less than 15 minutes.
_____
A POSSIBLE EXTENSION OF THE PERIOD OF WEATHER FORECASTS.
Ry E. B. GinnIiwT, Proh.sm of hIrteamloK.). Ilated relmnr) 15, l!lOG.
Periods of escessive heat or cold, and of drought or fitress
of rain, are invariably associated with marked irregularities
in the location and inovement or in the character and inten-
sity of the great continental and oceanic areas of high ancl
low barometric pressure. During periocls of abnorinal heat
or drought in any part of the Xorthern Hemisphere, there is
an undue and staguated accumulation of air in ancl about one
of the great anticyclonic areas, and a corresponding deficiency
in and about one of the great cyclonic areas. Periods of cold or
of excessive precipitation are due either to (1) abnormally rapid
changes in the greater atmospheric areas, whereby a rapid
progression of the lesser areas of high and low barometer
produces n succession of cold waves and rains, or to (2) a per-
sistent abnornial distribution or development of one or more of
the greater areas whereby esisting conditions of cold, or of wet,
are prolonged. It is also true that abnormalities of weather
over some portions of the globe, or of the Northern Hemisphere,
are counterbalanced by opposite tendencies over other por-
tions. Thus inontlis that are exceptionally warm or cold, wet
or dry, over the United States east of the Rocky Mountains
h:~\ e Siinilitr ch:tracteristics over Europe and at least a part of
western hi:&, and exhibit opposite tendencies over the United
States weht of the Rocky RIountains and oyer Southeastern
Asia. An explanation of this fact is found in a study of the
greater areas of high auil lowbaroiiietric pressure or 6 centers
of action  of the Northern Hemisphere.
These centers of nction appear to control tlie character and
ruoreineut8 of the areas of high and low barometer that appear
on our daily weather iuaps,nud in efforts to coorclinate the causes
that coutrilmte to produce weather effects in the hemisphere
ns :i whole or iu any of its parts, all causes are important and
none can I)e neglected. Professor Hann has foiind that prestmre
chaiig,es in tlie Azores liigh area and the Iceland low area are
iuterrelatecl and of au opposite character, and that these
c h m g p :we ashocintecl with certain phases of weather in cen-
t r d aud northwestern Europe. He has discovered that rising
baronietrr over tlie Azores is usuitlly attended by falling
lxtrozneter (J W ~ Icelaiicl, and, ~9 i i .t . wrsu, that falling barometer in
the h o r e s high area is attencled by rising barometer in the
Ice1:tncl lox iirea. Also that falling baronieter in t8he Iceland
area prrduces armer weather over central and northwestern
Europe, and that rising barometer over lceland is followed by
falling temperatmre over iiort>hn astern Europe. It appears,
tlierefore, that marked changes in the Azores high area, regard-
ing which idvices are cabled daily, afford an index of the
rhnracter of the weather that will prevail for several days over
a considerable portion of Europe.
A merely preliininary and general consideration of the whole
proldeiu places the dominating centers of atmospheric action
of the Northern Hemisphere over Siberia and Bering Sea, ancl
an exaniination of these areas prehents an interrelation similar
to that noted for the north Atlantic high and low areas. It
has been observed, furtheriiiore, that the effects of changes
in the Asiatic high and the Bering Sea low are rastly greater
and iiiore widespread than those t,h:tt msy be associated with
the north dtlitntic areas, and that when pressure abnormalities
within and about the Asiatic-Bering centers of action are
iuarkecl, persistent and well-defined types of abnormal weather
are experienced throughout the circuit of the Northern Hem-
isphere.
Among well-remeinbered dJUOrmd seasom, or parts of sea-
sons, when the influence of the dominating  centers of atiuos-
pheric action  was conspicuous, were the mild months of the
ninters o f lsS9-90 and 1905-6, and the cold months of the
winters of 1$#);<-1 and lg(J4-5. The months of the winters of
1%9-90 and 1905-6 that were wariii over great portions of the
United States and Europe showed an unusual depression in
tlie Bering Sea low area. The cleepeued Bering Sea area es-
tended and overlapped the uorthmestern liart of North Amer-
ica, ancl oEshoots therefroin niove(1 eastward in abnormally
high htitudes. The resultant8 abnormal clepression of the
baroineter over northwestern British America caused an un-
usual prevalence of southerly winds over uorhhern portions of
the United States and apparently prevented the formation of
the areas of high lmrometer over British America that are essen-
tial to the origin ancl propagation of American cold waves.