DECEMBER, 1904. MONTEELY WEATHER REVIEW. 561
we dare not think of separating them. I f one experiments he
keeps the mathematical laws in mind; if he studies the subject
mathematically he keeps the physical laws in mind. A prob-
lem in one is also a problem in the other; both are rigorous
and develop the reasoning powers, but sometimes i t is easier
to handle the experimental than the analytical method.
I n the MONTHLY WEATHER RETIEW for 1897 will be found a
splendid memoir on the Equations of hydrodynamics  ar-
ranged for the study of the general circulation of the atmos-
phere. This and the corresponding solution of the complex
difEerentia1 equations give the mathematician more than he
can handle a t present, but the suggestive paper by MacRlahon,
read a t the recent International Scientific Congress, on the
n-fold Riemann surface, opens up great hopes for the future.
Meanwhile we must mingle experiment and theory; each
must guide the other. The physicist may, in his laboratory,
carry out some of the following experiments and a t a glance
perceive the resulting atmospheric motions, or the solution
of the differential equations under any given special condi-
tions that the analyst would find i t difficult to attain, but can
easily confirm when once the result is known.
We may experiment on small local motions before proceed-
ing to the larger ones.
In a large room, or in a case with double glass walls, so
that the inside temperature may be controlled, let a shallow
stream of cool air flow along the bottom. By giving this a
slight but adjustable slope the rate of flow may be regulated;
by altering the bottom we may pass from water or smooth
sand to wavy, rolling prairie or ranges of hills and mountains.
We may imitate every variety of ordinary atmospheric motion.
By utilizing a layer of CO, for the bottom me may even study
the flow of upper air currents over lower ones.
We make all these movements visible by introducing a little
smoke, but especially by applying the so-called r Schleier 
method of Foucault, as perfected by Mach and Dubois, which
enables us to photograph the feeblest differences of density,
whether due to pressure or temperature or moisture.
Among other problems in aerodynamics should be mentioned
that more elementary one, the hypsometric formula of Laplace.
Our students and the surveyors and mountaineers use this
with aneroids for determining altitudes, without understand-
ing its derivation or the sources of mistakes in applying it,
especially the uncertainty of our knowleclge of the tempera-
tures of the air. Now the formulas may be deduced analyti-
cally by integration of the simple differential formula or by
algebraic or geometric or arithmetical or graphic method, and
all should be combined as an illustration of tlie unity of logic
in whatever form presented. Science is but logic applied to
material nature.
I will merely mention some other problems that appeal to
us from both analytical and experimental points of view.
The total resistance and the pressure and motions of the air
all around a resisting plate, sphere, or other obstacle.
The action of the wind in producing  suction  a t the top
of an open pipe or chimney.
Among problems that may be handled first by pure mathe-
matics and then by experiment and observation are the deter-
mination of the calibration correction of a thermometer, the
protruding stem correction. and the Poggenclorff Correction.
These belong to elementary physics, but will give your stu-
dents a chance to apply their mathematics to physical problems.
A comples trigonometrical problem involving a slight knowl-
edge of astronomy is the determination of the duration and
intensity of sunshine or the total amount of heat received by
a unit horizontal surface for any moment of the day and the
year. The calculation is to be made for the outside of the
atmosphere, because if we attempt to make allowance for the
absorption by the atmosphere the problem becomes too com-
plex for our present purposes. The simpler problem may be
treated geometrically and graphically and is essentially a mat-
ter of familiarity with  the use of the globes, as it was called
one hundred years ago.
Globes and charts are vital matters in meteorology and are
elegant classics in geometry. Chartography and projections
and the globes themselves are too much neglected-pushed
aside by the crush of new demands for instruction in every
other branch of know eclge; but they are absolutely funda-
mental to astronomy and meteorology, terrestrial physics, and
all geographic relations, and I hope to see them properly ap-
preciated in the schools of pure mathematics and terrestrial
physics. The properties and methods of construction of various
equal surface projections ought to be as familiar to a student as
those of the ordinary stereographic projection. The problems
of chartography are beautiful for the drafting room, but inore
vivid and better adapted to the coniprehension of many per-
sons if worked out on the globe itself; and one does not need
an expensive globe; even a homemade globe or rubber ball
can be very useful.
The globes and conic section iu solido should lie handled by
your students a t some early stage in their education.
But, finally, to return to our aerodynamics. Nothing can
be more attractive to a student than the formation of a water-
spout by Weyhers method and the study of the mind velocity
and pressure, the barometric pressure, the temperature, and
the dimensions of the cloud column.
We simply set a horizontal disk a t the top of a room or
closed case into rapid rotation. Soon the air beneath is dragged
into rotation clown to the very floor. Below we place a dish of
water, and the yapor from it is drawn up into the inner re-
volving vortex while a t the same time thrown out; eventually
it descends and ascends in regular circulation. As the disk
and air increase their rotary speed, the central vortex climin-
ishes in barometric pressure while increasing in velocity, and
the moist air flowing into it cools liy espansion, forming a
central waterspout column or vortex. Here we begin to be
stirred with a desire to measure. We insert a long Pitot tube
and determine the wind pressure a t many points and chart the
pressure or velocity on ruled paper.
We insert a pair of small plane plates as in my method of
barometic exposure (see Meteorological Apparatus and Meth-
ods), and determine and chart the pressure a t many points.
TSTe send a thermometer or thermoelectric junction exploring
the vortex and plat the temperature, or we use some form of
hygrometer and determine the dew-point,. I n fact we experi-
mentally determine all the elements that enter into the struc-
ture of the waterspout and compare our observations with the
theories that have been worked out by Ferrel and Bigelow.
I have said enough for the present. I hope to elaborate
this effort to help the mathematician and physicist to find a
new field of problems for their students. Thus they will help
us to develop the talents of future meteorologists.
These are but special illustrations of the general law that
thinking, seeing, and doing milst go together. We learn by
doing as much as by reasoning-each helps the other. Every
theory or hypothesis or suggestion should be reduced to esact
formula, exact experiment, exact measurement. Precision irj
the vital essence of all valuable knowledge.
I hope to live and see special schools of meteorology, special
laboratories and mathematical seminaries devoted to this as to
every other profession, but for the present a t least I urge that
you illustrate the value of and enliven the interest in your
mathematical and physical courses by frequently quoting or
proposing problems drawn from meteorology.
THE STORM AND COLD WAVE OF DECEMBER
24 TO 29, 1904.
By WALTER J. RENNETT, Forecast Diviaiun, U. 8. Weather Bureau.
A storm of unusual intensity, closely followed by a marked
562 MONTHLY WEATHER REVIEW. DECEMBER, 1904
cold wave, crossed the United States from the 24th to the 29th.
The weather maps showing the progress of this storm are of
special interest and will be found on Charts XIII-SV.
At 8 a. m. of the 24th the storm center was near Roseburg,
Oreg., with a central pressure of 29.43 inches. It then moved
rapidly due east and a t 8 p. m., was over southern Idaho, with
a barometer reading of 29.56 inches, an area of high pressure
having in the meantime advanced over Alberta. At S a. ni. of
the 25th the storm was central near Denver, Colo., with a pres-
sure of 29.54 inches, and tlie northern high-pressure area had
increased in intensity and moved southward over northern
Montana, where for the next few days i t reinainecl nearly
stationary while increasing in intensity. Baroinetric conditions
were favorable for a sharp fall in temperature to the north
and west of the storm center, and frost, in some places heavy,
occurred in the central valleys of California, while westerii
Montana esperiencecl a cold wave with temperatures of zero or
below.
During the 25th, the storiii center moved in a south-sonth-
easterly direction to the panhandle of Texas with pressure of
29.60 inches, and the cold wave covered Montana, eastern
Wyoming, and western South Dakota. Continuing a south-
southeasterly movement,, the storm center reached central
Texas 11-y S a. in. of the 26th. The cold wave hacl aclvancecl
over South Dakota aiid western Nebraska, and had extended
over Wyoming. northern Nevada, anil southern Iclaho, the line
of zero temperature reaching the southern bounclary of
Wyoming. During the 36th the storm rertchecl the most
southerly point of its path, ancl recurved, changing the direc-
tion of its motion from south-sonthertst to north-northeast,
while i t increased ill intensity anil in rapidity of motion. At
1 1). m. it was central over southwestern Arkansas, ant1 a t 6
p. m. was near Little Rock, Ark. At 8 p. 111. i t was over soutli-
eastern Missouri with a barometer of 39.56 inches. Rain fell
throughout the Mississippi Valley, and was particulrtrly heavy
in its southern portion. The cold wave hacl aclvancecl as far
south as Taylor. Tex., and Hosmell, N. Mes., and covered
Nebraska, Ihiisas. Oklalioma, the eastern portions of Colorado,
New Mexico, the Dakotas, and eastern and central Tesas.
During the night of the 2G-27th. the storin center continuetl
its north-northeastwkrcl~~r~l inovenlent, increasing in intensity,
ani1 by the morning of the 27th hac1 reached northern Illinoiq,
with a barometric pressure of 29.3-i inches. Heavy rains were
general throughout the hIississippi itncl Ohio valleys, and rain
and snow fell quite heavily in the Lake region. These were
the first heavy rains that 11ad occurred in the Ahhissippi
Valley for several months. ant1 were much neeclecl. I n the
rear of the storm, the cold wave extended from North Dakota
to the Texas coast, and from the Rocky Mountains to the
Mississippi River. t8he greatest twenty-four hour temperature
fall, from GO" to G O , occurring a t Springfield, 310. Tempera-
tures of zero or lower were recorded as far south as Concordia,
Kans., and Pueblo, Colo., ancl a minimum of 36" below zero
occurred a t Williston, N. Dak.
During the 37th tlie storm moved in a northeasterly clirec-
tion over northern Illinois and southan Lake Michigan. The
center was near Chicago, Ill.. a t 1 p. m., and a t 8 p. m. was over
southern Lske Michigan. Milwaukee, Wis.. recorded the un-
usually low barometer reading of 2H.S-i inches. High winds
were experienced a t all Lake stations and throughout the Ohio
and upper lUississippi valleys, Chicago recording a wind Teloc-
ity of 74 miles an hour from the southwest. The high winch
caused niuch damage to property along the Lake shores,
houses were unroofed, and telegraph and telephone lines fiuf-
ferecl severely. Telegraphic cominnnication was entirely cut
off over the Lake region and the Ohio and upper Mi
valleys for twenty-four hours, and several days elapsed before
the lines could be put into good working order. The heavy
snow that accompanied this storm in many sections blocked
trains and street cars. The cold wave covered the Mississippi
Valley from Minnesota to Louisiana and extended to the Texas
coast.
During the night of the 27-28th, high minds continued over
the Lakes, while the storin center was pasbing over the Michigan
Peninsula and Lake Huron. At H a. m. of the 28th i t was near
Rockliffe, Ont.; a seconclary center hac1 developed over the At-
lantic coast near Long Island, and high winds mere reported
from all coast stations. Several vessels were wrecked near
Hatteras, N. C. The cold wave extended from the Mississippi
Valley nearly to the Atlantic coast, the line of zero temperature
reached as far south rts Iieokuk, Iowa, aucl freezing tempera-
ture< were re1,ortecI from all Gulf stations except in southern
Flori(1a aiid extreiiie southern Texas. During the day the
storm center 1)at"seecl clonn the St. Lawrence Valley and high
nincls nitli snow contiiiuecl on the New England coast and in
the lower Lake region. The cold u ave covered the lower Lake
region ancl the iuicldle ancl south Atlantic coast. but no very
low temperatweb were recorded in those clistricts. On the
29th the storiii paswd off to sea, colder weather followed iu
the Atlantic coast States, and the cold wave reached central
Florida, with killing frost a t Jacksonville and Tampa and a
temperature of 3s" at Jupiter.
~~
SOME RELATIONS BETWEEN DIRECTION AND VELOC- ITY OF MOVEMENTS AND PRESSURE AT THE CENTER OF ELLIPSOIDAL CYCLONES.
BJ HT%NI\L%Y HANILIK 1'11 I), Prague
Loomis in his " Contribution to Meteorology," Chapter I, on
areas of low prebsure. tried to find out the causes that produce
the different velocities of progrebsion of lows. He selected
for that 1~urpose those lows moiiiig more than 1000 miles
nnd less than 240 miles in twenty-four hours whose pressure
a t the center changed rery little c.02 inch) or not a t all dur-
ing the twenty-four hours considerecl. He tabulated rain,
wiiicl, preswre of the following high, and changes of pressure
in twenty-four hours at the first station anil also a t the second
station; the first btation being the location of the low when
first olJservec1, the second station its location twentyfour hours
later. One of the results of tliih investigation was to show
that the rate of Ilrogress o f low pressure areas is proportional
to the changes of pressure on the first ancl second stations.
Whether the lows that lie coiiiparecl exhibited any similarity,
such. for instance. as similar forms (Jf isobars, or whether they
were primary or seconclary, Loomis does not inention.
I n this paper I have taken for investigation the opposite
case; learing the changes of pressure a t the first and second
stations out of consideration, I tried to fiud out whether there
are any relations between the rate of progress ancl the change
of pressure in the center of the respective lows, and how far
i t depends upon the azimuth toward mhich the low moves. I
selected for that purpose. from the seiniclailg iuannscript
weather maps of the Forecast Dil ision of the Weather Bureau,
cyclones of different velocities, ranging from 50 to 900 miles in
tnelre hours, having a t least two well shaped, closed iso-
liars, ellipsoidal or circiilar (of 0.100 inch of difference).
These lows are, of course, not strictly comparable in all re-
spects, as they are of different dimensions. gradients, and ratios
of axes, ranging from big circular low^ extending from the
Rockies to the Atlantic Ocean ancl from the Gulf up to the
Lakes, on the one hand, to lows of long oval isobars on the other:
lint all are comparable in one respect; they are all primary.
Their total number for the period lS93-1903 for fi1.e months,
November to AIarcli. inclusive, amounts to 288. A list of all
these, classified according to direction of movement, with a
su1)classificatioii by months of occurrence, is given in Table
1. For instance (under east-northeast, December), will be
found SIII, (November) 21' .01. referring to the cyclone track
No. SIII, from 8 p. m. on the 2d of December, 1'301, to 8 a. m.