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SMITHSONIAN
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TABLE OF CONTENTS

(PuBLicaTIoN 1791). THE. DEVELOPMENT

OF THE

AMERICAN ALLIGATOR (A. MISSISSIPPIENSIS). By

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SMITHSONIAN MISCELLANEOUS COLLECTIONS

PART OF VOLUME LI

TH DEVELOPMENT OF THE
AMERICAN ALLIGATOR

(A. mississippiensis)
WITH TWENTY-THREE PLATES

BY

ALBERT M-REESE

Professor of Zoology, West Virginia University

No. 179]

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1908

WASHINGTON, D. C.
PRESS OF JUDD & DETWEILER, INC.
1908

THE DEVELOPMENT OF THE* AMERICAN ALLIGATOR
(A. MISSISSIPPIENSIS)

By ALBERT M. REESE

(With 23 plates)

INTRODUCTION

With the exception of S. F. Clarke’s well-known paper, to which
frequent reference will be made, practically no work has been done
upon the’ development of the American alligator. This is probably
due to the great difficulties experienced in obtaining the necessary
embryological material. Clarke, some twenty years ago, made three
trips to the swamps of Florida in quest of the desired material. The
writer has also spent parts of three summers in the southern
swamps—once in the Everglades, once among the smaller swamps
and lakes of central Florida, and once in the Okefenokee Swamp.
For the first of these expeditions he is indebted to the Elizabeth
Thompson Science Fund; but for the more successful trip, when
most of the material for this work was collected, he is indebted to
the Smithsonian Institution, from which a liberal grant of money to
defray the expenses of the expedition was received.

The writer also desires to express his appreciation of the numerous
courtesies that he has received from Dr. Samuel F. Clarke, especially
for the loan of several excellent series of sections, from which a
number of the earlier stages were drawn.

The present paper gives a general outline of the whole process of
development of the American alligator (A. mississippiensis), it
being the intention of the author to take up in detail the more spe-
cific points in subsequent researches.

In preparing the material several kinds of fixation were employed,
but the ordinary corrosive sublimate-acetic mixture gave about the
most satisfactory results. Ten per cent formalin, Parker’s mixture
of formalin and alcohol, etc., were also used. In all cases the em-
bryos were stained in toto with borax carmine, and in most cases
the sections were also stained on the slide with Lyon’s blue. This
double stain gave excellent results. ‘Transverse, sagittal, and hori-
zontal series of sections were made, the youngest embryos being cut
into sections five microns thick, the older stages ten microns or
more in thickness.

A SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

THE Ecc
FicurEs I, Ia (Puate I)

The egg (fig. 1) is a perfect ellipse, the relative lengths of whose
axes vary considerably in the eggs of different nests and slightly in
the eggs of the same nest. Of more than four hundred eggs meas-
ured, the longest was 85 mm.; the shortest 65 mm. Of the same
eggs, the greatest short diameter was 50 mm.; the least short diam-
eter was 38 mm. ‘The average long diameter of these four hundred
eggs was 73.74 mm.; the average short diameter was 42.59 mm.
The average variation in the long axis of the eggs of any one nest
was II.32 mm., more than twice the average variation in the short
axis, which was 5.14 mm. No relation was noticed between the size
and the number of eggs in any one nest. Ten eggs of average size
weighed 812 grams—about 81 grams each.

Voeltzkow (18)* states that the form of the egg of the Madagas-
car crocodile is very variable. No two eggs in the same nest are
exactly alike, some being elliptical, some “egg-shaped,” and some
“cylindrical with rounded ends.” The average size is 68 mm. by
47 mm., shorter and thicker than the average alligator egg.

When first laid, the eggs are pure white, and are quite slimy for
a few hours, but they generally become stained after a time by the
damp and decaying vegetation composing the nest in which they are
closely packed.

The shell is thicker and of a coarser texture than that of the hen’s
egg. Being of a calcareous nature, it is easily dissolved in dilute
acids.

The shell membrane is in two not very distinct layers, the fibers of
which, according to S. F. Clarke, are spirally wound around the egg
at right angles to each other. No air-chamber, such as is found in
the hen’s egg, is found in any stage in the development.

In most—probably all normal—eggs a white band appears around
the lesser circumference a short time after being laid. This chalky
band, which is shown at about its maximum development in fig.
Ia, is found, on removal of the shell, to be caused, not by a change
in the shell, but by the appearance of an area of chalky substance in
the shell membranes. Clarke thinks this change in the membrane is
to aid in the passage of gases to and from the developing embryo.
Generally this chalky area forms a distinct band entirely around the
shorter circumference of the egg, but sometimes extends only partly

*The numerical citations throughout the article are to bibliographical refer-
ences at the end of the paper.

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 5

around it. It varies in width from about 15 mm. to 35 mm., being
narrowest at its first appearance. , Sometimes its borders are quite
sharp and even (fig. 1a) ; in other cases they are very irregular. If
the embryo dies the chalky band is likely to become spotted with
dark areas.

The shell and shell membrane of the egg of the Madagascar croco-
dile are essentially the same as those just described, except that the
shell is sometimes pierced by small pores that pass entirely through
it. ‘The same chalky band surrounds the median zone of the egg
(18).

The white of the egg is chiefly remarkable for its unusual density,
being so stiff that the entire egg may be emptied from the shell into
the hand and passed from one hand to the other without danger of
rupturing either the mass of albumen or the enclosed yolk. The
albumen, especially in the immediate neighborhood of the yolk, seems
to consist of a number of very thin concentric layers. It varies in
color, in different eggs, from a pale yellowish white, its usual color,
to a very decided green.

As might be expected, no chalazz are present.

The yolk is a spherical mass, of a pale yellow color, lying in the
center of the white. Its diameter is so great that it lies very close to
the shell around the lesser circumference of the egg, so that it is
there covered by only a thin layer of white, and care must be taken
in removing the shell from this region in order not to rupture the
yolk. The yolk substance is quite fluid and is contained in a rather
delicate vitelline membrane.

The albumen and yolk of the crocodile’s egg, as described by
Voeltzkow, differ from those of the alligator only in the color of the
albumen, which in the crocodile is normally light green (18).

As pointed out by Clarke, the position of the embryo upon the yolk
is subject to some variation. During the earliest stages it may occur
at the pole of the yolk nearest the side of the egg; later it may gener-
ally be found toward the end of the egg; and still later it shifts its
‘position to the side of the egg. It is probable, as Clarke says, that
the position at the end of the egg secures better protection by the
greater amount of white, at that point, between the yolk and the
shell ; while the later removal to the side of the egg, when the vascu-
lar area and the allantois begin to function, secures a better aération
of the blood of the embryo.

Around the embryo, during the stages that precede the formation
of the vascular area, is seen an irregular area of a lighter color and a
mottled appearance. This area is bounded by a distinct, narrow,

6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

white line, and varies in size from perhaps a square centimeter to
one-third the surface of the yolk. ;

During the earliest stages of development the embryo is very trans-
parent; so that, as there is no fixed place upon the yolk at which it
may be expected to occur, it is often very difficult to find. Owing to
this transparency, to the extreme delicacy of the embryo, and to the
character of the white, the removal of an early embryo from the egg
of the alligator is a difficult operation and is accomplished only after
some practice.

Tarr DEVELOPMENT OF THE EMBRYO

As the writer has pointed out elsewhere (13), the embryo of the
alligator is often of considerable size when the egg is laid. This
makes the obtaining of the earliest stages of development a difficult
matter ; so that the writer, as has already been said, like S$. F. Clarke
(5), made three trips to the South in quest of the desired material.
Voeltzkow (18) experienced the same difficulty in his work on the
crocodile, and made several trips to Africa before he succeeded in
obtaining all the desired stages of development.

To obtain the earliest stages, I watched the newly made nests until
the eggs were laid, and in this way a number of eggs were obtained
within a very few hours after they had been deposited, and all of
these eggs contained embryos of a more or less advanced stage of
development. Gravid females were then killed, and the eggs re-
moved from the oviducts. These eggs, although removed from a
“cold-blooded” animal, generally contained embryos of some size,
and only one lot of eggs thus obtained contained undeveloped em-
bryos, which embryos refused to develop further in spite of the most
careful treatment. Voeltzkow (18) found, in the same way, that the
earlier stages of the crocodile were extremely difficult to handle; so
that, in order to obtain the earlier stages, he was reduced to the
rather cruel expedient of tying a gravid female and periodically re-
moving the eggs from the oviducts through a slit cut in the body
wall.

The older embryos are hardy and bear transportation well, so that
it is comparatively easy to obtain the later stages of development.

For the stages up to the formation of the first four or five somites,
I am indebted, as I have already said, to Professor Clarke, and,
since I have had opportunity to examine only the sections and not
the surface views of these stages, I shall quote directly Clarke’s

paper in the Journal of Morphology (5) in description of these sur-
face views.

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 7

STAGE |
Ficurks 2-2f'(Prates I, 11)

The youngest embryo that we have for description is shown in
figures 2 and 2a. Of figure 2 Clarke says:

“The limiting line between the opaque and pellucid areas is clearly
marked, and within the latter is a shield-shaped area connected by
the narrower region of the primitive streak with the area opaca.
The blastopore is already formed near the posterior end of the shield.

““A ventral view of another embryo of the same age (fig. 2a), seen
from the ventral side, shows that the blastopore extends quite
through the blastoderm, in an oblique direction downwards and for-
wards, from the dorsal to the ventral side. The thickened area of
the primitive streak is here very prominent. There is, too, the begin-
ning of a curved depression at the anterior end of the shield, the
first formation of the head-fold.”

Transverse sections of this stage are shown in figures 2b—2f.

Figure 2b, through the anterior region of the blastoderm, shows a
sharply defined ectoderm (ec) which is composed of three or four
layers of cells in the median region, while it gradually thins out
laterally. Closely underlying this ectoderm is a thin sheet of irreg-
ular cells, the entoderm (en).

Figure 2c is about one-fifth of the length of the blastoderm pos-
terior to the preceding and represents approximately the same condi-
tions, except that there is an irregular thickening of the entoderm in
the median region (en). This thickening apparently marks the an-
terior limit of the mesoderm, to be discussed shortly.

Figure 2d represents the condition of the blastoderm throughout
about one-third of its length, posterior to the preceding section. The
somewhat regular folds in the ectoderm (ec) are probably not the
medullary folds, but are such artificial folds as might easily be pro-
duced in handling the delicate blastoderm. The thickening of the
entoderm, noticed in the preceding figure, is here more sharply de-
fined, and as we pass toward the blastopore becomes separated some-
what from the entoderm proper as a middle layer or mesoderm (fig.
2e, mes). It would thus seem, from a study of these sections, that
most of the mesoderm is derived from the entoderm. In fact, all of
the mesoderm in front of the blastopore seems to have this origin,
for it is not until the anterior edge of the blastopore is reached that
there is any connection between the ectoderm and entoderm (fig. 2¢).

Figure 2e is a section through the region just mentioned, where,
medially, the ectoderm, mesoderm, and entoderm form a continuous

8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

mass of cells. Laterally the mesoderm (mes) is a distinct layer of
cells of a fairly characteristic mesodermal type. The notochord is
not yet discernible, though a slight condensation of cells in the middle
line may indicate its position.

Figure 2f is one of the four sections that were cut through the
blastopore (bip), which is a hole of considerable size that opens, as
the figure shows, entirely through the blastoderm. Along the walls
of the blastopore the ectoderm and entoderm are, of course, contin-
uous with each other and form a sharply defined boundary to the
opening. As we pass laterally from the blastopore the cells become
less compact, and are continued on each side as the mesodermal layer
(mes). In this series the sections posterior to the blastopore were
somewhat torn, and so were not drawn; but they probably did not
differ materially from those of the corresponding region of the im-
mediately following stages, which are shown in figures 3m and 61
and will be described in their proper order.

Stace II
Ficures 3-30 (Priates II, III, IV)

The next stage to be described is shown in surface views in figures
3 and 3a. Of this stage Clarke says:

“The head-fold rapidly increases in depth and prominence, as
shown in figure 3, which is a ventral view a few hours later [than
the preceding stage]. The time cannot be given exactly, as it is
found that eggs-of the same nest are not equally advanced when laid,
and differ in their rate of development. The lighter curve in front
of the head-fold is the beginning of the anterior fold of the amnion.
The notochord has been rapidly forming, and now shows very dis-
tinctly on the ventral side, when viewed by transmitted light. A
dorsal view of the same embryo (fig. 3a) shows that the medullary
or neural groove is appearing, and that it ends abruptly anteriorly
near the large transverse head-fold. Posteriorly it terminates at the
thickened area in front of the blastopore, which still remains open.”

Figures 3b-m are drawn from transsections of an embryo of about
this state of development. For a short distance in front of the be-
ginning of the head-fold, there is a mass of cells of considerable
thickness between the ectoderm and entoderm. In figure 3b these
cells appear as an irregular thickening of the entoderm, while in fig-
ure 3c they form a continuous mass, uniting the upper and lower
germ layers. This condition is seen, though in a much less striking.
degree, in the following stage of development. As to its significance
the writer is not prepared to decide.

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 9

Figure 3d passes through the head-fold, which in this embryo was
probably not so far developed as it was in the embryo shown in fig-
ures 3 and 3a. Not having seen the embryo, however, before it was
sectioned, the writer cannot be certain of this point. The ectoderm
and entoderm are here of nearly the same thickness.

Figure 3¢ is a short distance posterior to the preceding. It shows
a marked thickening of the ectoderm in the medial region (ec),
which is continuous posteriorly with the anterior ends of the medul-
lary folds that are just beginning to differentiate (figs. 3/—/).

Figure 3g passes through the anterior end of the medullary plate
or folds (mf), whichever they may be called. The ectoderm of the
folds is thickened and is considerably elevated above the rest of the
blastoderm. ‘There is scarcely any sign, in this region, of a medul-
lary groove. The entoderm (en) is considerably thickened in the
medial region, this thickening being continuous posteriorly, as in the
preceding stage, with the mesoderm.

In figure 3h, cut in a plane at some distance posterior to the pre-
ceding, the medullary groove (mg) is well marked; its bordering
folds gradually thin out laterally to the thickness of the ordinary
ectoderm. The medial thickening of the entoderm is very marked,
but it has not in this region separated into a distinct mesoblastic
layer.

Immediately under the medullary groove is a dense mass of cells
(nt), apparently the anterior end of the notochord in process of
formation.

Figure 37, still farther toward the blastopore, shows the medullary
groove wider and shallower than in the more anterior sections. The
mesoderm (mes) is here a layer laterally distinct from the entoderm.
In the middle line it is still continuous with the entoderm, and at this
place it is the more dense mass of cells that may be recognized as
the notochord (nt). It is evidently difficult to decide whether this
group of cells (nt), which will later become a distinct body, the noto-
chord, is derived directly from the entoderm or from the mesoderm,
which is itself a derivative of the entoderm. There is here abso-
lutely no line of demarcation between the cells of the notochord and
those of the mesoderm and entoderm.

In figure 37 the ectoderm (ec) is nearly flat, scarcely a sign of the
medullary groove appearing. The mesoderm (mes) is here a dis-
tinct layer, entirely separate from both notochord (nt) and entoderm
(en). The notochord is a clearly defined mass of cells, distinct, as
has been said, from the mesoderm, but still closely united with the
underlying entoderm, which is much thinner than the ectoderm.

10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

his condition of the notochord, which is found throughout about
one-third of the length of the embryo, would give the impression
that the notochord is of a distinctly entodermal origin.

In figure 3k there is no sign of the medullary groove, though ecto-
derm (ec) is still much thickened in the middle line. The section
passes, posterior to the notochord, through the anterior edge of the
ventral opening of the blastopore (b/p). The mesoderm (mes) is
here again continuous with the entoderm, around the edge of the
blastopore, but is distinct from the ectoderm.

Figure 3/ represents the third section posterior to the preceding.
The blastopore, which passes upward and backward through the
blastoderm, is seen as an enclosed slit (b/p). It is surrounded by a
distinct layer of compactly arranged cells continuous with the thick-
ened ectoderm (ec) above, with the thin entoderm (en) below, and
laterally with the gradually thinning and scattering mesoderm(mes).

Figure 3m is the next section posterior to the one just described.
It passes through the dorsal opening of the blastopore (b/p), which
appears as a deep, narrow cleft with thick ectodermal borders. The
three germ layers are still continuous with each other, though the
connection of the entoderm with the other two is slight. The sec-
tions posterior to this one will be described in the next stage, where
they have essentially the same structure and are better preserved.

Figures 3n and 30 are sagittal sections of an embryo of about the
stage under discussion. In both figures the head-fold is seen as a
deep loop of ectoderm and entoderm, while the head-fold of the
amnion is seen at a.

The beginning of the foregut is seen in figure 3n (fg), which is
the more nearly median of the two sections, figure 30 being a short
distance to the side of the middle line.

In figure 30 the thin entoderm (en) is separated from the much
thicker ectoderm (ec) by’a considerable layer of rather loose meso-
derm (mes). In figure 3n, which is almost exactly median in posi-
tion, there is, of course, no mesoderm to be seen in front of the blas-
topore, and the entoderm shows a considerable increase in thickness,
due to the formation of the notochord (nt). The blastopore (b/p)
is the most striking feature of the figure, and is remarkable for its
great width in an antero-posterior direction. Its anterior and pos-
terior borders are outlined by sharply defined layers of ectoderm and
entoderm. Posterior to the blastopore the lower side of the ecto-

derm is continuous with a considerable mass of cells, the primitive
streak (ps).

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE II

Stace, III
FIGURES 4, 4a, 5, 5a, and 6-61 (PiatEes V, VI)

“Figures 4 ard 4a are of an embryo removed, on June 18, from an
egg which had been taken out of an alligator two days before. Fig-
ure 4, a dorsal view, is of special interest in that it shows a secondary
fold taking place in the head-fold. This grows posteriorly along the
median dorsal line, forming a V-shaped process with the apex point-
ing backward toward the blastopore. There is quite a deep groove
between the arms of the V. ‘The head-fold on the ventral side, as
seen in figure 4a, made from the same embryo as figure 4, grows
most rapidly on the mid-line, and also becomes thicker at that place.
The medullary folds now begin to form on either side of the medul-
lary groove, ending posteriorly on either side of the blastopore and
anteriorly on either side of the point of the V-shaped process in the
middle of the head-fold. This is seen in figure 5, which is a dorsal
view of an embryo from an egg three days after it was taken out of
an alligator. A ventral view of the same embryo (fig. 5a) repre-
sents the thickened process on the mid-line at its greatest develop-
ment. For some reason the notochord did not show in this embryo,
possibly owing to particles of the yolk material adhering about the
mid-line.

“Tn an embryo a day or two older, the V-shaped fold of the head-
fold is seen to have broken through at the apex, and each of the
arms thus separated from one another unites with the medullary fold
of its respective side. ‘This can be seen in figure 6, wHich is a dorsal
view of part of an embryo a day or two older than the one repre-
sented by figures 5 and sa.

“This is so unexpected a method of formation for the anterior
part of the medullary folds that I have made use of both figures 4
and 5. They were made from very perfect specimens, and the sec-
tions of both of them, and of the specimen from which figure 6 was
drawn, proves that the structure is what it is indicated to be in sur-
face appearance. ‘That is, the transverse sections posterior to the V,
in the embryos shown in figures 4 and 5, show the medullary groove
and the medullary folds; the several sections passing through the
apex of the V show neither groove nor folds, but only a median
thickening ; and in front of the point or apex of the V the successive
sections discover a gradually widening groove between the arms,
which is also much deeper than the shallow groove found posterior
to the V. While I have not seen, and from the nature of the condi-
tions one cannot see, the change actually proceeding from the form

12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 51

of fig. 5 to that of fig. 6, still the explanation given appears to be the
only one possible” (5).

A somewhat extended series of transverse sections of an embryo
of about this age is represented in figures 6a—.

Figure 6a is a section through the head-fold; it passes through the
extreme anterior end of the secondary folds (sf) that were de-
scribed, in surface view, above (figs. 5 and 6). ‘The section was not
quite at right angles to the long axis of the embryo, so that the fold
on the right was cut further toward its anterior end than was the
fold on the left. The pushing under of the head causes a forward
projection of the secondary folds, so that the fold to the right ap-
pears as rounded mass of cells with a small cavity near its center.
On the left the plane of the section passes through the posterior limit
of the head-fold, and shows the cells of the secondary fold contin-
uous with the dorsal side of the ectoderm (ec). As pointed out
above by Clarke, the secondary folds are here some distance apart,
and gradually approach each other as we proceed toward the pos-
terior. The entoderm (em) is here flat and takes no part in the sec-
ondary folds.

In figure 6b, a short distance back of the one just described, the
secondary folds (sf) are much larger and are closer together. On
the right the section passes through the extreme limit of the head-
fold, so that the secondary fold of that side is still a closed circle,
with a few scattered cells enclosed. On the left the section is pos-
terior to the head-fold; on this side the secondary fold is seen as a
high arch of ectoderm, with a thick mass of entoderm beneath it.

Figure 6c represents a section which passes back of the head-fold
on both sides. The secondary folds (sf) are seen as a pair of ecto-
dermal arches continuous with each other in the middle line of the
embryo. The ectoderm of the folds is much thickened and grad-
ually becomes thinner distally. On the right the entoderm shows
the same thickening (en) that was shown on the left side of the
preceding figure. This thickened appearance of the entoderm is
due to the fact that the section passes through the anterior limit of a
tall fold of that layer, which underlies the similar fold of the ecto-
derm that has already been described. This secondary fold of the
entoderm is seen on the left side of the section. It may be traced
through several sections, but soon flattens out posteriorly.

Figure 6d is a short distance posterior to the preceding. The sec-
ondary folds are here much less pronouncedly arched and the deep
groove between them is reduced to a line (1). The entoderm (en)
is no longer markedly arched and is closely adherent, along thie
median plane, to the ectoderm, where there is seen the thickening

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 13

(th) that has been mentioned by Clarke (see above). Springing
from the entoderm on each side of this thickening is a small mass of
mesoderm (mes).

The section immediately posterior to the one just described is rep-
resented in figure 6e. The line (/) which separated the two second-
ary folds in the preceding section is no longer present, so that the
ectoderm (ec) is continuous from side to side, with only a shallow
depression (mg), which may be considered as the extreme anterior
end of the medullary groove. The median thickening (th) is cut
near its posterior limit and still shows a close fusion of the germ
layers. There is no line of demarcation between the gradually flat-
tening secondary folds of the anterior end of the embryo and the
just forming medullary folds of the posterior end, so that it is im-
possible to say whether the thickening of ectoblast in this figure
should be called secondary folds or medullary folds. As a matter
of fact, the secondary folds become, of course, the anterior ends of
the medullary folds. The mesoblast (mes) is here of considerable
extent, and its entodermal origin is beyond doubt, though not well
shown in the figure.

Figure 6f is about one-sixth of the length of the embryo posterior
to the preceding. The medullary thickening of the ectoderm (ec) is
still marked and the shallow medullary groove (mg) is fairly dis-
tinct. The entoderm (en) is medially continuous with both meso-
derm (mes) and notochord (nt), though these two tissues are other-
wise distinct from each other.

Figure 6g is nearly one-third the length of the embryo posterior
to the preceding and passes through the posterior third of the em-
bryo. The medullary thickening of the ectoderm (ec) is marked,
but shows no sign of a medullary groove; in fact, the median line is
the most elevated region of the ectoderm. The notochord (nt) is
larger in cross-section than in the more anterior regions. It is still
continuous with the entoderm (en) and is fairly closely attached to,
though apparently not continuous with, the mesoderm (mes) on each
side.

Figure 6h passes through the blastopore (bl/p). The appearance
of the section is almost identical with that of figure 2f, already de-
scribed.

Figure 67 is five sections posterior to the preceding and has about
the same structure as the corresponding sections in the preceding
two stages, where this region of the embryo was injured, and hence
not drawn. Continuous with the posterior border of the blastopore
(seen in the preceding figure) is the deep furrow, the primitive
groove (pg). The ectoblast (ec) bordering this groove is much

I4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

thickened and may be called the primitive streak. The lower side
of this primitive streak is continuous with the mesoblast (mes),
while the entoderm (em) is here entirely distinct from the mesoderm.
It is evident that the mesoderm posterior to the blastopore is pro-
liferated from the lower side of the ectoblast and not from the upper
side of the entoblast, as is the case anterior to the blastopore. The
primitive groove gradually becomes more and more shallow, as it is
followed toward the posterior, until it is no longer discernible;
back of this point the primitive streak may be traced for a consider-
able distance, becoming thinner and thinner until it too disappears,
and there remains only the slightly thickened ectoblast underlaid by
the thin and irregular layers of mesoblast and entoblast. The prim-
itive streak may be traced for a distance equal to about one-third
the distance between the head-fold and the blastopore.

Stace IV
Ficures 7a-7h (Piatés VI, VII)

No surface view of this stage was seen by the writer, and hence is
not figured. ‘The figures were drawn from one of the series of sec-
tions obtained through the courtesy of Prof. S. F. Clarke. This
series was-marked “3 Urwirbeln,”’ so that the embryo was appar-
ently slightly younger than the youngest stage obtained by myself
and represented in figures 8 and 8a.

Figure 7a represents a section that passed through the head-fold
of the amnion (a) just in front of the head-fold of the embryo; the
amniotic cavity here appears as a large empty space.

Figure 7) is several sections posterior to the preceding; it passes
through the head-fold of the embryo, but is just back of the head-
fold of the amnion. ‘The deep depression of the ectoderm (ec) and
entoderm (en) caused by the head-fold is plainly seen. In this de-
pression lie the ends of the medullary folds, distinct from each other
both dorsally and ventrally. Each medullary fold is made up of two
parts—a medial, more dense nervous layer (nl), and a distal, less
dense epidermal layer (ep). ‘The section corresponding to this one
will be more fully described in connection with the following stage.

Figure 7c is some distance posterior to the preceding, though the
exact distance could not be determined because of a break in the
series at this point. The section passes through the posterior limit
of the head-fold. The medullary groove (mg) is very deep and
comparatively wide; around its sides the germ layers are so closely
associated that they may scarcely be distinguished. Ventral to the
medullary groove the foregut (fg) is seen as a crescentic slit.

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 15

Figure 7d is about a dozen sections posterior to the one just de-
scribed and is about one-seventh the length of the embryo from the
anterior end. ‘The embryo is much more compressed, in a dorso-
ventral direction, and the medullary groove (mg) is correspond-
ingly more shallow. Where the ectodorm (ec) curves over to form
the medullary folds it becomes much more compact and somewhat
thicker. The notochord (nt) is large and distinct, but is still fused
with the entoderm (en). The mesoderm (mes) forms a well-
defined layer, entirely distinct from both the notochord and the ento-
derm. From this region, as we pass caudad, the size of the embryo
in cross-section gradually decreases and the medullary groove be-
comes more shallow.

Figure 7¢ is about one-third of the length of the embryo from the
posterior end, and is only a few sections from the caudal end of the
medullary groove. ‘The ectoderm (ec) is much thinner than in the
preceding figure and the medullary groove (mg) is much more
shallow. ‘The notochord (nt) is of about the same diameter as
before, but is here quite distinct from the entoderm (en) as well as
from the mesoderm (mes).

Figure 7/ is seven sections posterior to figure 7e. ‘The medullary
groove has disappeared and the medullary folds have flattened to
form what might be called a medullary plate (at the end of the refer-
ence line ec), which continues to the anterior border of the blasto-
pore. The notochord (nt) is larger in cross-section than in the
more anterior regions; it is still distinct from the entoderm.

Figure 7g passes through the blastopore and shows essentially the
same structure as was described in connection with the correspond-
ing section of stage I (fig. 2/).

Figure 7h represents the region of the primitive groove (pg) and
primitive streak (ps). The section shows the typical structure for
this region—a thick mass of cells is proliferating from the ventral
side of the ectoderm (ec) and is spreading laterally to form a dis-
tinct mesoderm (mes). ‘The entoderm (ev) is entirely distinct from
the other layers.

STAGE. Vi
Ficures 8-8j (Pirates VII, VIII, IX)

On opening the egg this embryo (figs. 8 and 8a) was found to lie
on the end of the yolk, near the center of the irregular, lighter area
which was mentioned in connection with the description of the egg.
The length of the embryo proper is 3 mm. This was the youngest

16 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL,. 51

stage found in 1905, and approximates quite closely the condition of
the chick embryo after 24 hours’ incubation. ‘The dorsal aspect of
this embryo, viewed by transmitted light, is shown in figure 8. The
medullary folds (mf) have bent over until they are in contact,
though apparently not fused for a short distance near their anterior
ends. As will be described in connection with the ‘sections of this
stage, the medullary folds are actually fused for a short distance at
this time, though in surface views they appear to be separated from
each other. In the Madagascar crocodile (18) the first point of
fusion of the medullary folds is in the middle region of the embryo,
or perhaps even nearer the posterior than the anterior end of the
medullary groove. Throughout the greater part of their length the
medullary folds are still widely separated; posteriorly they are
merged with the sides of the very distinct primitive streak (ps),
which seems, owing to its opacity, to extend as a sharp point toward
the head. Extending for the greater part of the length of the primi-
tive streak is the primitive groove (pg), which, when the embryo
is viewed by transmitted light, is a very striking feature at this stage
of development and resembles, in a marked way, the same structure
in the embryo chick. Clarke (5) figures the blastopore at this stage
as a small opening in front of the primitive streak, but does not men-
tion any such condition as above described at any stage of develop-
ment. Five pairs of somites (s) have been formed and may be
seen, though but faintly outlined, in both dorsal and ventral views of
the embryo; they lie about half way between the extreme ends of the
embryo. The head-fold (h, fig. 8a) shows plainly in a ventral view
as a darker, more opaque anterior region, extending for about one-
fourth the length of the embryo. ‘The still unfused region of the
medullary folds may be seen also in the ventral view at mg. The
head-fold of the amnion (a) forms a very thin, transparent hood
over the extreme anterior end of the embryo. ‘The tail-fold of the
amnion has not made its appearance, and in fact is not apparent at
any stage in the development. ‘This is true also of the Madagascar
crocodile. ‘The notochord (nt) may be seen in a ventral view as a
faint, linear opacity extending along the middle line from the head-
fold to the primitive streak.

Two sagittal sections of this stage are shown in figures 8b and 8c.
The embryo from which the sections were made was apparently
somewhat crooked, so that it was not possible to get perfect longi-
tudinal sections. For example, in figure 8b the plane of the section
is almost exactly median in the extreme posterior and middle regions,
but is on one side of the middle line elsewhere, ‘This explains the
enormous thickening of the ectoblast in the region of the head, where

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE L7
the section passes through one of the medullary folds (mf) at its
thickest part ; and also explains the fact that the ectoblast is thinner
in the middle region (ec), where the section passes through the
medullary groove, than it is farther toward the blastopore, where
the section cut® the edge of the medullary folds. The outlines of
the middle and extreme posterior regions of the ectoblast are much
more irregular and ragged than is shown in the figure. The plane
of the section passes through the notochord (mt) in the posterior
region, but not in the anterior end of the embryo, where a layer of
mesoblast (mes) is seen. The great size of the blastopore (b/p) is
well shown, as is the beginning of the foregut (fg). Comparison of
this figure with the more anterior transverse sections and with the
dorsal, surface view of this stage will make the rather unusual condi-
tions comprehensible.

Figure 8c is cut to one side of ‘the median plane, distal to the
medullary folds. Being outside of the medullary folds, the ecto-
derm (ec) is thinner and less dense than in figure 8); anteriorly it is
pushed down and back as the head-fold, and posteriorly it becomes
thin where it forms the dorsal boundary of the primitive streak (ps).

The foregut (fg), as would be expected, is not so déep as in the
median section (8b). The most striking feature of the section is
the presence of five mesoblastic somites (s). Each somite, especially
the second, third, and fourth, is made up of a mass of mesoblast
whose cells are compactly arranged peripherally, but are scattered
in the center, where a small myocoel may be seen.

A series of transverse sections of the embryo shown in figures 8
and 8a is represented in figures 8d-7.

Figure 8d is through the anterior end of the embryo; the posterior
edge of the amnion is cut only on one side (a). The medullary
folds (mf) are shown as two distinct masses of tissue, separated by
a considerable space from each other, both dorsally and ventrally;
they are underlaid by the ectoderm of the head-fold, through which
the section passes. A mass of yolk (vy) is shown at one side of the
section.

Figure 8¢ represents a section a short distance posterior to the
one just described, and passes through the short region where the
dorsal edges of the medullary folds have fused with each other. The
ventral side of the medullary groove (mg) is, as in the preceding
section, still unclosed. An epidermal layer of ectoblast (ep) is now
distinct from the nervous layer (ml).

Figure 8f is through a region still farther toward the posterior
end. Here the medullary groove is again open above, and is still

2—AL

18 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

open below. A well-marked space is seen between the epidermal
(ep) and nervous (nl) layers of the ectoderm, but no mesoblast is
yet to be seen.

Figure 8g passes through the middle part of the head-fold, and
shows that the medullary folds in this region are fused below, but
are widely separated above, where their margins are markedly bent
away from the mid-line. Between the epidermal and nervous layers
of the ectoderm a considerable mass of mesoderm cells (mes) is
seen. The curious appearance of the preceding four figures, as well
as the first three figures of the next stage, was at first quite puzzling,
until a model of the embryo was made from a series of sections. It
was then plain, as would have been the case before, except for the
unusual depth dorso-ventrally of the head of the embryo, why the
medullary canal should at the extreme anterior end be open both
dorsally and ventrally, while a few sections caudad it is open only
ventrally, and still farther toward the tail it is again open both above
and below. ‘These conditions are produced by the bending under of
the anterior region of the medullary folds, probably by the formation
of the head-fold. It is apparently a process distinct from the ordi-
nary cranial flexure, which occurs later. The fusion of the medul-
lary folds to form a canal begins, as has been already mentioned,
near the anterior end, whence it extends both forward and backward.
Hence, if the anterior ends of the medullary folds be bent downward
and backward, their unfused dorsal edges will come to face ventrally
instead of dorsally, and sections through the anterior part of this
bent-under region will show the medullary canal open both above
and below, as in figure 8d, while sections farther caudad pass
through the short region where the folds are fused, and we have the
appearance represented in figure 8e. In figure 8f is shown a section
passing posterior to the short, fused region of the folds, and we
again have the medullary canal open both above and below. Figure
8g represents a section through the tip of the bent-under region of
the medullary folds, which are here fused below and open above.

Figure 8h passes through the posterior part of the head-fold, be-
tween the limits of the fold of the ectoderm and that of the ento-
derm.. The medullary groove (mg) is here very wide and compar-
atively shallow; its walls are continued laterally as the gradually
thinning ectoderm (ec). The enteron (ent) is completely enclosed,
and forms a large, somewhat compressed, thick-walled cavity. Be-
tween the dorsal wall of the enteron and the lower side of the medul-
lary canal lies the notochord (nt), a small, cylindrical rod of closely
packed cells derived, in this region at least, from the entoderm. In
the posterior region of the embryo it is not possible to determine

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 19

with certainty the origin of the notochord, owing to the close fusion
of all three germ layers. Between, the wall of the enteron and the
lower side of the ectoderm is a considerable mass of mesoderm
(mes), which here consists of more scattered and angular cells than
in the preceding section.

Figure 8 shows the appearance of a section through the meso-
blastic somites, in one of which a small myocoel (myc) is seen. As
is seen by the size of the figure, which is drawn under the same
magnification as were all the sections of the series, the embryo in
this region is much smaller in section than it is toward either end,
especially toward the anterior end. The medullary groove (mg) is
still more shallow than in the more anterior sections, and the ecto-
derm (ec), with which its folds are continuous laterally, is here
nearly horizontal. The mesoblast (mes) is of a more compact na-
ture than in the preceding section and shows little or no sign of
cleavage, although a distinct myocoel may be seen and cleavage is
well marked in sections between this one and the preceding.

The notochord (nt) has about the same appearance as in the pre-
ceding section, but is more distinctly separated from the surrounding
cells.

Figure 8j is through the posterior end of the embryo; it shows the
relation of parts in the region of the primitive streak. Although not
visible in surface views, and hence not represented in figure 8, the
medullary groove is continued without any line of demarcation into
the primitive groove, and the medullary folds into the edges of the
primitive streak, so that it is impossible to set any definite boundaries
between these structures unless the dorsal opening of the blastopore
be taken as the point of division. The medullary groove (mg), if
it be here so called, is proportionately more shallow than in the pre-
ceding figure and is actually much wider. The section passes behind
the posterior end of the notochord, so that structure is not seen.
Though not so well indicated as might be desired in the figure, the
three germ layers are here indistinguishable in the middle line, and
in the center of this mass of cells the blastopore (b/p) or neurenteric
canal may be seen as a small vertical slit. As will be more fully
described in the following stage, this canal opens dorsally a few sec-
tions posterior to the one under discussion and ventrally a few sec-
tions farther toward the head.

In all the sections of this stage the ectoderm and entoderm are
fairly thick in the region of the embryo proper, but become thinner
until reduced to a mere membrane as we pass to more distal regions.
Both layers are composed of loosely arranged cells, with scattered

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

nuclei. Where the ectoderm becomes thickened to form the medul-
lary folds, the cells are much more compactly arranged; hence this
region stands out in strong contrast to the rest of the ectoderm.

Stace VI
FicurEs ga-om (Piates IX, X)

The embryo represented by this series of transverse sections is
intermediate in development between those represented in surface
views by figures 8 and 10. The amnion and head-fold are nearly the
same as in figure 8; the medullary folds are intermediate in devel-
opment, the anterior end not showing so marked an enlargement as
shown in figure 10, v’. There are six or seven faintly distinguishable
somites.

Figure 9a represents a section through the anterior part of the
head-fold; it shows one unusual condition: the head lies entirely be-
neath the surface of the yolk. This condition is quite confusing
when the section is studied for the first time. The pushing of the
head under the yolk is shown at its commencement in figure II.
The process continues until nearly the entire anterior half of the
embryo is covered; but when the embryo attains a considerable size
it is seen to lie entirely above the yolk, as in the chick. According
to Voeltzkow’s figures (18), this same condition is found in the
crocodile, and Balfour (2) also mentions it in connection with the
lizard. The fusion of the medullary folds has made considerable
progress, so that the entire anterior end of the canal is enclosed,
except in the region where the folds are bent down and back, as in
the preceding stage; here the folds are still distinct from each other,
leaving the medullary canal open on the ventral side, as shown in
figures 9 and gb. In the section under discussion the ectoderm (ec)
is a very thin membrane on top of a considerable mass of yolk, while
no entoderm can be distinguished. The amnion (a) completely sur-
rounds the embryo as an irregular membrane of some thickness in
which no arrangement into layers can be seen. ‘The epidermal ecto-
derm (ep) is composed of the usual loosely arranged cells, so that it
is clearly distinguishable from the compactly arranged cells of the
nervous layer (7/), from which it is separated by only a line.

In figure 9b, which shows a section a short distance posterior to
the preceding, the medullary canal (mc) is somewhat deeper and is
still open ventrally. There is a distinct space between the nervous
(nl) and epidermal (ep) layers of the ectoderm, in which space a
few mesoblast cells (mes) may be seen. ‘The section is cut just pos-
terior to the edge of the amnion, so that there is now neither amnion
nor yolk above the embryo.

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESF 21

Figure 9c is about ten sections posterior to figure 9b. The section
passes through the anterior wall of the bent-under part of the medul-
lary canal (mc’), so that the actual canal is shown only on the dorsal
side (mc), where it is completely closed and begins to assume the
shape of the typical embryonic spinal cord. ‘The space between the
superficial (ep) and nervous (ml) layers of the ectoderm is quite
extensive and is largely filled by a fairly compact mass of mesoderm
(mes).

Figure 9d, although only five sections posterior to the preceding,
shows a marked change in structure. The medullary canal (mc) is
here of the typical outline for embryos of this age. A large, com-
pact mass of cells (ent) appears at first glance to be the same that
was noted in the preceding stage at the tip end of the turned-under
medullary canal; it is, however, the extreme anterior wall of the
enteron, which is in close contact with the above-mentioned tip of
the medullary canal. Between this anterior wall of the enteron, of
which wall it is really a part, and the medullary canal is the noto-
chord (nt). The space surrounding the notochord and enteron is
filled with a fairly compact mass of typical, stellate mesoblast cells.
The depression of the ectoderm (ec) and entoderm (en) of the blas-
toderm caused by the formation of the head-fold is here less marked,
and the dorsal side of the embryo in this region is slightly elevated
above the level of the blastoderm.

Figure 9e represents a section passing through the posterior edge
of the head-fold. The epidermal ectoderm is here continuous with
the thin layer of superficial ectoderm (ec) of the blastoderm, while
the entoderm (en) of the blastoderm is still continuous beneath the
embryo. The thick ectoderm of the embryo is sharply differentiated
from the thin layer of ectoderm that extends laterally over the yolk.
The pharynx (ent) is a large cavity whose wall is thick except at
the dorsal side, where it is thin and somewhat depressed, apparently
to make room between it and the medullary canal for the notochord
(nt).

Figure of is about twenty sections posterior to the preceding sec-
tion, and passes through the point of separation of the folds of the
entoderm (en). From this point the entoderm gradually flattens
out, leaving the enteron unenclosed. The medullary canal (mc)
and notochord (nt) are about as in the preceding section, but the
ectoderm (ep) is somewhat thinner and more flattened. The meso-
derm (mes) on the right side exhibits a distinct cleavage, the result-
ing body cavity (bc) being a large, triangular space.

Figure 9g, the twenty-fifth section posterior to that represented in

22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

figure of, shows a marked change in the form of the embryo. While
of about the same lateral dimensions, the dorso-ventral diameter of
the embryo in this region is less than one-half what it was in the
head region. ‘The epidermal ectoderm (ep) is now nearly horizontal
in position and is not so abruptly separated laterally from the thin
lateral sheets of ectoblast. The medullary groove (mg) is here a
very narrow vertical slit. At this stage the fusion of the medullary
folds has taken place over the anterior third of the embryo. For a
short distance, represented in about thirty-five sections, the canal is
open, as in the figure under discussion; for the next one hundred
sections (about one-third the length of the embryo) in the region of
the mesoblastic somites the canal is again closed, while throughout
the last one-third of its length the canal is widely open dorsally. The
enteron is here entirely open ventrally, the entoderm being almost
flat and horizontal. The notochord (nt) is distinctly outlined and is
somewhat flattened in a dorso-ventral direction. The body cavity
(bc) is well marked, but is separated by a considerable mass of un-
cleft mesoblast from the notochord and the walls of the medullary
groove.

A space of about one hundred sections, or one-third the length of
the embryo, intervenes between figures 9g and gi. This is the
region of the mesoblastic somites, and in this region, as has been
above stated, the medullary canal is completely enclosed. It is evi-
dent then that the entire anterior two-thirds of the medullary canal
is enclosed except for the short region represented in figure 8g.
Whether or not this short open region between the two longer en-
closed regions is a normal condition the material at hand does not
show.

Figure 9h represents a typical section in the region of the meso-
blastic somites just described. It shows the enclosed medullary
canal (mc), the body cavity (bc) on the right, and-a mesoblastic
somite with its small cavity (myc) on the left. The entire section
is smaller than the sections anterior or posterior to this region, and
seems to be compressed in a dorso-ventral direction, this compres-
sion being especially marked in the case of the notochord.

Figure gi is through a region nearly one hundred sections pos-
terior to the preceding, and cuts the embryo, therefore, through the
posterior one-fourth of its length. The chief difference between this
and the preceding section is in the medullary canal, which is here
open and is in the form of a wide groove with an irregular, rounded
bottom and vertical sides. ‘The size of the section is considerably
greater than in the preceding, the increase being especially noticeable

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 23

in the notochord (ft), which is cut near its posterior end. There is
little or no sign of mesoblastic cleavage. ,

Figure 9j is about twenty sections posterior to figure gi. The
medullary groove (mg) is considerably larger than in the more an-
terior regions, and its folds are somewhat inclined toward each
other, though still wide apart. The notochord and entoderm are
fused to form a large, compact mass of tissue close under the ventral
wall of the medullary groove. On the ventral side of this mass of
cells a groove (b/p) marks the anterior and ventral opening of the
blastopore shown in the next figure. The mesoblast shows no sign
of cleavage.

Figure 9k shows the medullary groove (mg) in about the same
position as in the preceding section. The blastopore (bip) is here
seen as a small cavity in the center of the large mass of cells that
was noted in the last figure. The entoderm (em) is continuous from
side to side, but is not so sharply differentiated from the other germ
layers as is represented in the figure.

Figure ol is four sections back of the preceding; the wide, dorsal
opening (b/p) of the blastopore or neurenteric canal into the medul-
lary groove (mg) is shown. ‘The blastopore or neurenteric canal,
then, is still at this stage a passage that leads entirely through the
embryo, the medullary canal being in this region unenclosed above.
Ventrally it is seen as a narrow opening through the entoderm;; it
then passes upward and backward, behind the end of the notochord,
as a small but very distinct canal, which may be traced through about
ten sections. The enclosed portion of the canal lies, as has been
stated (figure 9k, blip), in the center of the mass of cells that is fused
with or is a part of the floor of the medullary groove.

The above-described neurenteric canal is essentially like that de-
scribed by Balfour (2) in the Jacertilia. He does not say, however,
and it is not possible to tell from his figures, whether there is a long,
gradually diminishing groove posterior to the dorsal opening of the
canal, as in the alligator. He says that the medullary folds fuse
posteriorly until the medullary canal is enclosed over the opening of
the neurenteric canal; also that “the neurenteric canal persists but a
very short time after the complete closure of the medullary canal.”

In figure 9m, for about thirty sections (one-tenth the entire length
of the embryo), behind the section represented in the last figure,
there is a very gradual change in the embryo, converting the deep
groove, mg in figure 9/, into the shallow slit, pg, figure gm.

There is no line of demarcation between the typical medullary
groove region of figure g/ and the equally typical primitive groove

24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

region represented in figure gm. As was noted in the preceding
stage, the medullary folds are quite continuous with the folds of the
primitive streak, and the medullary groove with the primitive
groove; so that, unless we take the dorsal opening of the neurenteric
canal as the point of separation, there is no line of division between
these structures. The entoderm (en) and the lateral regions of the
ectoderm (ec) and mesoderm (mes) in figure 9m are about as they
were in figure 9g/, but in the middle line is seen a compact mass of
cells forming the primitive streak (ps), with the shallow primitive
groove (pg) on the dorsal side. The cells on each side of the prim-
itive groove and for a short distance below it are compact, as 1s
shown in the figure, but as we pass ventrally and laterally they be-
come looser and more angular to form the lateral sheets of meso-
blast (mes), very much as is the case in the chick and other forms.
For a few sections posterior to the one shown in figure 9m the prim-
itive streak may be seen, then it disappears, and only the ectoderm
and entoderm remain as thin sheets of tissue above the yolk.

Stace VII
FicurEs 10 and toa (Pirates X, XI)

Although of practically the same size as the preceding, this stage
has advanced sufficiently in development to warrant a description.

The medullary folds are apparently still slightly open for the
greater part of their length, though they are evidently fused together
in the head region, except at the extreme end. Transverse sections,
however, of figure 12, in which the medullary folds, from the dorsal
aspect, seemed open (mg) as in figure 10, have shown that these
folds are fused throughout their length.

The first cerebral vesicle (v’) is clearly indicated as an enlarge-
ment of the anterior end of the nervous system, and a slight enlarge-
ment (v”) posterior to the first probably represents the second
cerebral vesicle.

There are now eight pairs of somites (s).

The head-fold (1) now shows in both dorsal and ventral views,
appearing in the former, when viewed by transmitted light, as a
lighter, circular area on either side of the body, just posterior to the
hinder edge of the amnion.

The head-fold of the amnion (@) has extended about twice as far
backward as it did in the preceding stage.

Owing to the opacity caused by the medullary folds being in con-
tact along the middle line, the notochord is no longer visible in sur-
face views.

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 25

The head at this stage begins to push down into the yolk in a
strange way that will be described later.

Stace VIII
-
FicurEs 11-11k (Puates XI, XII, XIII)

This stage is about one-fourth longer than the preceding. The
medullary canal is enclosed throughout its entire length, though it
appears in surface view (fig. 11) to be open in the posterior half
(mc) of the embryo. An enlargement of this apparently open re-
gion at the extreme posterior end (pg) is probably caused by the
remains of the primitive groove or the neurenteric canal, and a
slight opacity at the same point may be caused by the primitive
streak. The anterior end of the neural tube is bent in a ventral
direction (v’), as in the preceding stage. The somites (s) now
number fifteen pairs; they are somewhat irregular in size and shape.

The head-fold is not so striking a feature as in the preceding
stage. The head-fold of the amnion (a) now covers nearly two-
thirds of the embryo. ‘The heart (ht) is seen as a dark, rounded
object projecting to the right side of the neural canal, just anterior
to the first somite. The vitelline blood-vessels are just beginning to
form, but are not shown in the figure.

The depression of the anterior region that was noted in the pre-
ceding stage has advanced so far that a considerable part of the
embryo now projects forward under the blastoderm. In some cases
it is almost concealed in a dorsal view; in other cases it may easily
be seen through the transparent membranes, especially after clearing.

In opening eggs of this stage one is at first apt to underestimate
the size of the embryos, since the anterior part of the embryos cannot
be seen until after they are removed from the yolk and are viewed
from the ventral side.

The embryo from which the series of transverse sections of this
stage was made, while of the same state of development as that
shown in figure 11, was more fully covered by the blastoderm than is
shown in the surface view in question.

Figure Ila passes through the tip of the head. Dorsal to the
embryo is the ectoderm and a thick mass of yolk (vy). The amnion
(a) is seen as an irregular membrane which entirely surrounds the
head. The medullary canal (mc) is entirely closed, except at the
extreme anterior end, which is bent downward so that the opening
is on the ventral side. The nervous (ml) and epidermal (ep) layers
of the ectoderm are in contact throughout, but are clearly distin-
guishable because of the difference in the compactness of their cells.

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

In figure 11D is represented a section, behind the preceding, which
passes through the posterior tip of the turned-under anterior end
(mc’). Here the medullary canal is closed both above (mc) and
below (mc’). The amnion (a) has about the same appearance as in
the more anterior section, but there is here a considerable space,
filled with mesoblast (mes), between the nervous (nl), and epidermal
(ep) layers of ectoderm. ;

Figure 11¢ is twenty sections, about one-tenth the length of the
embryo, posterior to the one last described. ‘The large mass of over-
hanging yolk (y) is still present, as is also the amnion (a), though
the latter no longer passes entirely around the embryo; only the true
amnion could be made out. ‘The thickened walls of the medullary
canal have reduced that cavity to a narrow, Y-shaped slit (mc).
The notochord (nt) is very slender in this region, compared to its
diameter farther toward the posterior end. The enteron (ent) is a
large cavity, whose wall is made up of loosely arranged cells except
around a median, ventral depression where the cells are more com-
pact. This depression may be traced through ten or fifteen sections
and may represent the beginning of the thyroid gland, though this
point was not worked out with certainty. Surrounding the noto-
chord and enteron is a loose mass of typical, stellate mesoblast cells
(mes), which are cleft on either side to form the anterior limit of
the body cavity (bc). Between the body cavity below and the en-
teron above, on each side, is a small blood-vessel (bv) which when
followed caudad is found to open ventrally and medially into the
anterior end of the heart.

Figure 11d is about a dozen sections posterior to the preceding.
The appearance of the overhanging yolk (y) of the amnion (a) and
of the notochord (nt) is about as in the more anterior section. The
medullary canal (mc) is a straight, vertical slit, and the depression
in the floor of the pharynx (ent) is much more shallow. ‘The body
cavity (bc) is much larger and extends across the mid-ventral line
beneath the heart (ht), which is cut through its middle region. The
heart may be traced through about twenty sections (one-tenth the
length of the embryo) ; its mesoblastic wall (mes’) is thin and irreg-
ular, and is lined by a distinct endothelium (en’) whose exact origin
has not yet been worked out.

Figure Ile is just back of the heart, and shows in its place the
two vitelline veins (vv). The depression in the floor of the enteron
(ent) is entirely distinct from the one that has been mentioned
above, and is simply the posterior limit of the head-fold of the ento-
derm ; the fifth section posterior to this shows where this depression

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 27

opens ventrally to the yolk sac. The other structures shown in the
figure are not markedly different from what was seen in figure 11d.

Figure 11f is about one-tenth the length of the embryo posterior
to figure 11e. The chief differences here noticed are in the enteric
and ccelomic cavities. ‘The former is no longer enclosed, a dorsal
fold in the entoderm being all that remains of the cavity that was
seen in the more anterior figures, while the latter is here reduced to.
a narrow cleft between the somatic and splanchnic mesoblast. A
thickening of the mesoblast on either side of the notochord, espe-
cially on the left, represents a mesoblastic somite. The medullary
canal (mc) is more open than in the more anterior sections.

For about one-third of the length of the embryo posterior to figure
tif there is a gradual flattening, in a dorso-ventral direction, with
loss of the amnion, until the condition represented in figure IIg is
reached. The most striking feature of this region is the great
thickness of the ectoderm (ec), which is still made up of scattered,
irregular cells. In the middle line, directly over the medullary
canal (here a nearly cylindrical tube), is a sort of break in the ecto-
derm, as though there had not been a complete fusion of the epi-
dermal layer when the nervous layer came together on the closure
of the medullary groove. This break in the ectoderm may be fol-
lowed back to the region of the primitive streak, and will be men-
tioned again. As has been noted, the medullary canal (mc) is
nearly circular in cross-section, and is closely underlaid by the noto-
chord (nt), which is several times the diameter that it was in more
anterior sections. The mesoblast (mes) is a comparatively thin
layer, intermediate in thickness between the ectoderm and entoderm.
It shows laterally a slight separation to form the body cavity.

Figure 11h is about ten sections posterior to figure 11g, and dif-
fers from it chiefly in that the notochord (nt) is continuous with the
lower side of the medullary canal (mc), though still distinct from
the underlying entoderm (en).

Figure 117, four sections farther from the head, shows the same
greatly thickened ectoderm (ec) with the same break (ec’) in the
middle line. The section is posterior to the notochord and passes
through the anterior edge of the blastopore or, as it may now per-
haps better be called, the neurenteric canal. The cells of the medul-
lary wall are continuous with those of the entoderm. ‘The meso-
derm (mes) is still distinct from the other germ layers.

Figure 11j is the next section posterior to the one just described
and differs from it only in showing the actual opening of the neuren-
teric canal (mc) into the medullary canal (mc). The medullary
canal extends, with gradually diminishing caliber, for about fifteen

28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

sections posterior to the point at which the neurenteric canal empties
into it. ‘The mesoblast (mes) is so closely attached to the lower
wall of the neurenteric canal that it seems to be actually continuous
with it.

For a considerable distance posterior to the end of the medullary
canal we find the structure similar to that shown in figure IIk,
which is about the twentieth section posterior to figure 117. The
break (ec’) in the ectoderm is here seen as a compact group of cells
which at first glance seem to be continuous with a rounded mass of
cells below (ps). Examination under greater magnification, how-
ever, shows that the two groups of cells are distinct. As the sec-
tions are followed back of this region, the upper mass of cells (ec’)
gradually disappears, and after its disappearance the lower mass
(ps), which is already continuous with the mesoderm (mes) on
either side, becomes continuous with the under side of the ectoderm.
The mass of cells (ps) is apparently the primitive streak, though it
is distinct from the ectoderm for a considerable distance posterior
to the neurenteric canal. Just what may be the meaning of the
thickened ridge of ectoderm (ec’) it is difficult to determine.

STAGE IX
FicuRES 12-I12g (Pirates XIII, XIV)

The entire length of the embryo proper is 6.5 mm. from the ex-
treme posterior end to the region of the midbrain (v?), which now,
on account of the cranial flexure, forms the most anterior part of
the body. Besides being slightly longer than the preceding stage,
the embryo has increased in thickness, especially in the anterior
region, where the enlargement of the cerebral cavity is considerable.

Body torsion has begun (fig. 12), so that the anterior third of the
embryo now lies on its right side, while the rest of the body is still
dorsal side up. The direction of body torsion does not seem to be
as definite as it is in the chick, some alligator embryos turning to the
right side, others to the left. Clarke has illustrated this fact in his
alligator figures. He says (5) that embryos lie “more frequently
on the left, but often on the right side.”

The head is distinctly retort-shaped, and at the side of the fore-
brain (v’) a small crescentic thickening is the optic vesicle (e).
The auditory vesicle, though of considerable size, does not show in
this surface view. The head-fold (#) extends for about one-third
the length of the entire embryo, though its exact limit is difficult to
determine in surface view. There is no sign of a tail-fold.

DEVELOPMENT OF THE AMERICAN AI,LIGATOR—REESE 29

About seventeen pairs of somites are present.

The amnion extends over the anterior two-thirds of the embryo.

The above-mentioned increase in the diameter of this embryo
over that of the preceding is evident when the first two transverse
sections of this stage are compared with the corresponding sections
of the earlier stage; in the middle and posterior regions there is not
very much difference in size.

Figure 12a passes through the region of the forebrain. This end
of the embryo lies on its side, as was noted above and as may be
recognized from the relative positions of the head and the overlying
yolk (y). The great size of this and the following figure is due
partly to the increase in size mentioned above and partly to the fact
that the sections pass through the region of cranial flexure. The
present figure (12a) represents the brain cavity as large and dumb-
bell-shaped, with comparatively thick walls of compactly arranged
cells. The ventral end of this cavity (fb) is cut anterior to the
region of the optic vesicles, while the dorsal end (mb) may perhaps
be called the midbrain. In the sections that follow this one the two
cavities are distinct from each other. The medullary canal, as was
stated above, is now completely enclosed, except for the ventral
opening of the neurenteric canal, to be presently noticed. Sur-
rounding the brain is a considerable mass of mesoblast (mes). It
is composed of the typical stellate cells. The ectoderm (ec) is made
up of the same irregularly and loosely arranged cells that have been
seen in earlier stages; it is of unequal thickness in different régions,
the thicker parts being at the sides. The amnion (a) has the usual
appearance, and in this region of course completely surrounds the
embryo.

Figure 12b is ten sections posterior to the section just described.
The width of the embryo is greater in this region, but the dorso-
ventral diameter is about the same as in the more anterior section.

The overlying yolk and blastoderm are not shown in any figure of
the series except the first. In this figure the forebrain (fb) and
midbrain (mb) are widely separated instead of being connected, as
in the preceding figure, where the section passed through the actual
bend of the cranial flexure. The anterior and ventral part of the
cranial cavity, the forebrain (fb), is nearly circular in outline. It
exhibits on one side a well-marked optic vesicle (ov), which is suffi-
ciently advanced in development to show a rudimentary optic stalk.
The outer wall of the optic vesicle is in close contact with the super-
ficial ectoderm, which shows as yet no sign of the formation of a
lens vesicle. The plane of the section being probably not quite at
right angles to the long axis of the embryo, the optic vesicle of one

30 SMITHSONIAN MISCELLANEOUS COLLECTIONS _ VOL. 51

side only was cut. ‘The wall of this part of the forebrain is of about
the same thickness and appearance as in the preceding stage. The
other cerebral cavity (mb) of this section is probably the hinder part
of the midbrain, though it may be the anterior part of the hind-
brain; there is no sharp line of demarcation between these regions
of the brain. This cavity (mb) is much smaller in section than the
forebrain; its walls are of about the same thickness.

Ventral to the midbrain is the anterior end of the notochord (nt),
surrounded by the mesoblast. At various places throughout the
mesoblast irregular open spaces may be seen; these are blood-
vessels. The ectoderm (ec) and amnion (a) have about the same
appearance as in the preceding figure, though the former seems
somewhat thinner.

Figure 12c¢ is just back of the bent-under forebrain represented in
the preceding figure and in front of the main body of the heart.
The plane of the section not being at right angles to the long axis
of the body (as was mentioned above), the figure is not bilaterally
symmetrical. The neural canal, since the section passes through
the auditory vesicles, may here be called the hindbrain (hb). It has
an almond-shaped cavity, surrounded by a wall of medium thickness.
In close contact with the wall of the hindbrain, on each side, is the
inner side of the auditory vesicle (0), which is seen as a deep, wide-
mouthed pit in the superficial ectoderm. On the right side of the
section the auditory pit is cut through its middle region; it is simply
a thickened and condensed area of the ectoderm which has been in-
vaginated in the usual way. Directly beneath the hindbrain is the
notochord (nt), on each side of which, in the mesoblast, is the dorsal
aorta (ao), or rather the continuation of the aorta into the head.
Beneath these structures and extending from one side of the section
to the other is the pharynx (p/) ; its lining wall is fused on each
side with the ectoderm, but there is no actual opening to the. ex-
terior. These points of contact (g) between entoderm and ecto-
derm are of course the gill clefts; they are not yet visible from the
outside. The roof of the pharynx is flat and comparatively thin,
while the floor is thickened and depressed to form a deep, wide pit,
traceable through six or eight sections. This pit may be the thyroid
gland already noticed in the preceding stage. Below the main
cavity of the pharynx and close to each side of the thyroid rudiment
just mentioned is a large blood-vessel (tr). These two vessels
when traced posteriorly are found to be continuous with the anterior
end of the heart, and hence may be called the truncus. They were
noticed in figure 11c, bv. The ectoderm surrounding the lower side

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE ist

of the embryo was so thin and indistinct that it could scarcely be
distinguished from the mesoderm of,that region. The amnion (a)
is still a continuous envelope entirely surrounding the embryo.

Figure 12d, about twenty sections posterior to figure I2c, is in
the posterior heaft region. The spinal cord (sc), as might be ex-
pected, is smaller than in the more anterior region, but is otherwise
not markedly different from what was there seen. The notochord
(nt) also has the.same appearance as before. The enteron (ent)
shows of course in this region no gill clefts; it is a small, irregular
cavity with thicker walls than in the figure just described. The
ventro-lateral depression is entirely distinct from the depression that
was called the thyroid rudiment in the preceding figure. Dorsal to the
enteron are the two dorsal aortz (ao), now smaller and more ventral
to the notochord than in the preceding figure. Ventral to the enteron
is the large heart (ft), projecting below the body cavity, which is no
longer enclosed. The mesodermic wall (mes’) of the heart is still
comparatively thin and is separated by a considerable space from
the membranous endocardium (en’). The extent and shape of the
heart are shown in the surface view of this stage. On the right side
of the section the body cavity extends to a point nearly opposite the
middle of the spinal cord, considerably dorsal to the notochord,
while on the left side the dorsal limit of the body cavity is scarcely
level with the lower side of the notochord. Between the dorsal end
of the body cavity and the side of the spinal cord, on the left, is a
dense mass of mesoblast (s), one of the mesoblastic somites. A few
sections either anterior or posterior to the one under discussion will
show the condition of the two sides reversed—that is, the body
cavity will extend to the greater distance on the left and will be
interrupted by a mesoblastic somite on the right. It is evident,
then, that the upper angle of the body cavity is extended dorsally
as a series of narrow pouches between the somites. The mesoblast
that lines the body cavity, the splanchnopleure (sm), and somat-
opleure (so) is somewhat denser than the general mass of meso-
blast, so that these layers are quite distinct, the former (sm) extend-
ing around the enteron (ent) and heart (ht), and the latter (so)
being carried dorsalward as the mesoblastic part of the amnion (@).
The amnion may be traced through about 130 of the 200 sections
into which this embryo was cut.

Figure 12e is nearly one-fourth the length of the embryo posterior
to figure 12d; it is approximately in the middle region. The diam-
eter of the embryo has been gradually decreasing until now it is
very much less than in the head region. The section being behind
the head-fold the entoderm (en) is nearly flat and the enteron is

32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

=<

quite unenclosed. The canal of the spinal cord (sc) is smaller in
proportion to the thickness of its walls, and the notochord (mt) is
somewhat larger than in the preceding sections. In proportion to
its extent, the ectoderm is very thick. Under the notochord the
dorsal aortee (ao) are seen as two large, round openings in the
mesoblast. On the left side the section passes through the center
of a somite and shows a small, round myocoel (myc). The meso-
blastic layer of the amnion (se) is distinct throughout from the ecto-
blastic layer (@).

The most important structures to be here noted are the first rudi-
ments of the Wolffian ducts (wd). They are seen in the present
section as lateral ridges of mesoblast projecting outward and up-
ward toward the ectoblast, which suddenly becomes thin as it passes
over them. ‘These ridges or cords of mesoblast are as yet quite
solid. ‘They arise suddenly at about the eightieth section of the
series of two hundred and may be traced through about forty sec-
tions, or one-fifth of the length of the embryo. Their exact length
is difficult to determine because, while their anterior ends are blunt
and sharply defined, they taper so gradually posteriorly that it is
hard to tell just where they end. They apparently originate ante-
riorly and gradually extend toward the tail. In a slightly younger
embryo the rudimentary Wolffian duct could be seen as a still
smaller rod of cells extending posteriorly for a few sections, from
the seventy-fifth section of a series of about two hundred. In the
particular series under discussion the left rudimentary Wolffian duct
was about one-fifth longer than the right one.

Figure 12f is just posterior to the head-fold of the amnion, pass-
ing, in fact, on the left side through the extreme edge of its lateral
fold, which is shown as an upward bend in the ectoblast and somat-
opleure.

The ectoblast (ec) shows the same remarkable thickening that
was noted in the corresponding region of the preceding stage. The
spinal cord (sc), notochord (nt), aorte (ao), and entoderm (en)
need no special mention. The mesoderm seems to be separated by
unusually wide spaces from both ectoderm and entoderm, and is
made up of rather closely packed .cells except around the aorte,
where there seems scarcely enough tissue to hold these vessels in
place. The body cavity (bc) is large, and a small myocoel (myc)
is seen on the left.

Figure 12g is through the neurenteric canal (nc), a distinct open-
ing through the floor of the spinal canal. ‘The section is of course
just back of the posterior end of the notochord. The entoderm
(en) along the margin of the neurenteric canal is naturally contin-

DEVELOPMENT OF THE AMERICAN ALTLIGATOR—REESE 33

uous with the wall of the spinal cord (sc). The ectoderm (ec) is
thicker than ever, except in the median plane, where it passes over
the spinal cord. The mesoblast is more abundant than in the pre-
ceding figure, and shows on the left what appears to be a distinct
myocoel (mye), though in surface view the mesoblastic somites do
not extend this far toward the tail.

STAGE X
FIGURES 13-13g (PLatEs XIV, XV, XVI)

This embryo (fig. 13) is about 5 mm. in length, and hence is
slightly smaller than the preceding stage, though somewhat more
advanced in development. The medullary canal is still apparently
unclosed for a short distance at the extreme posterior end; this ap-
pearance is probably due to the neurenteric canal (nc) and to the
thinness of the roof of the medullary canal rather than to any lack
of fusion of the medullary folds. The optic vesicle is more distinct
than in the preceding stage; a somewhat similar, though smaller,
opacity (0) marks the position of the ear. There are now about
twenty pairs of somites, though it is difficult to determine their exact
number on account of the torsion of the body. The amnion is at
about the same stage of development as in stage 1x. The heart
(ht) is a large double mass, whose outlines may be dimly seen when
the embryo is viewed by transmitted light. The vitelline vessels
(vv) are still but faintly outlined in the vascular area; the veins and
arteries cannot yet be distinguished from each other. The gill
clefts, though not visible externally in the embryo drawn, may be
seen in sections of this stage as evaginations of the wall of the
pharynx. |

The transverse sections of this stage are slightly more advanced
in development than was the embryo that has just been described in
surface view. Only those sections have been figured which show a
decided advance in the development of some special structures over
their condition in the preceding stage. The sections of the pre-
ceding stages were drawn under a magnification of eighty-seven
diameters ; those of this and the following stage were drawn under
a magnification of only forty-one diameters. All of the figures have
been reduced one-half in reproduction.

Figure 13a is the most anterior section of this series to be de-
scribed. On account of the cranial flexure, which causes the long
axis of the forebrain to lie at right angles to that of the spinal cord,
this section cuts the head region longitudinally. The ectoderm (ec)

3—AL

34 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

is of varying thickness, the thickest areas being on each side of the
forebrain; it is more compact than in the earlier stages, and, owing
to the low magnification under which it is drawn, it is represented
here by a single heavy line. Under this magnification only the
nuclei of the mesoderm cells (mes) can be seen, so that this tissue is
best represented by dots, more closely set in some places than in
others. The forebrain is an elongated cavity (fb) with thick, dense
walls. Attached to each side of the forebrain is an optic vesicle
(ov), which is considerably larger than in the preceding stage. The
connection between the cavity of the forebrain and that of the optic
vesicle is not seen in this section; it is a wide passage that may be
seen in several sections posterior to the one under discussion. The
beginning of the invagination of the optic vesicle to form the optic
cup may be seen on both sides, but more plainly on the right. On
the right side also is noticed a marked thickening of the ectoderm,
which is invaginated to form a small pit, the lens vesicle (/v) ; on
the left side the section is just behind the lens vesicle. Above the
optic stalk on each side, in the angle between the optic vesicle and
the side of the forebrain, is a small blood-vessel (bv). Several
other blood-vessels may be seen at various places in the mesoblast,
four of them.near the pharynx being especially noticeable. The
hindbrain (/ib) is wider than, but not so deep as, the forebrain; its
walls are very thick laterally, but are thin on the dorsal and ventral
sides. The dorsal wall is reduced to a mere membrane, which, with
the overlying ectoderm, has been pushed into the brain cavity, as is
generally the case with such embryos. Close to the ventral wall of
the hindbrain the notochord (nt) is seen. The character of the
notochord has already begun to change; the cells are becoming
rounded and vacuolated, with but few visible nuclei except around
the periphery of the notochord. Near the center of the section,
close to the ventral end of the forebrain, is the pharynx (ph), cut
near its anterior limit; it is here a small, irregularly rectangular cav-
ity with a comparatively thin wall. On the left side of the pharynx
the first gill cleft (g) is indicated as a narrow diverticulum reach-
ing toward the ectoderm. A few sections posterior to this one the
first gill cleft is widely open to the exterior. As has been said, in
the surface view of this stage above described none of the gill clefts
showed; so that in this respect at least the sectioned embryo was
more nearly of the state of development of the embryo represented
in figure 14, to be described later.

Figure 13b, about forty sections posterior to figure 13a, passes
through the hindbrain in the region of the ears. Being back of the
region affected by cranial flexure, this section is of course of much

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 35

less area than the preceding. The ectoderm shows no unusual
features; it is of uniform thickness except where it becomes con-
tinuous with the entoderm around the mandibular folds (md) ;
there it is somewhat thickened. The most striking feature of the
section is the presence of two large auditory vesicles (0). The sec-
tion being not quite at right angles to this part of the embry6, the
vesicles are not cut in exactly the same plane; the one on the left is
cut through its opening to the exterior, while the one on the right
appears as a completely enclosed cavity. In a section a short dis-
tance posterior to this one the appearance of the vesicles would be
the reverse of what it is here. As may be seen in the figure, the
vesicles are large, thick-walled cavities lying close to the lateral
walls of the hindbrain. The hindbrain itself has the usual trian-
gular cross-section, with thick lateral walls and a thin, wrinkled
dorsal wall. Close to the ventral side of the hindbrain lies the noto-
chord (nt), on each side of which, in the angle between the brain
and the auditory vesicles, is a small blood-vessel (bv). Ventral to
these structures and close to the dorsal wall of the pharynx (ph)
are the two large dorsal aorte (ao). The ventral side of the section
passes through the open anterior end of the pharynx (ph). On the
left is seen the widely open hyomandibular cleft (g’), between the
main body of the section and the mandibular arch (md). On the
right side the plane of the section was such that the hyomandibular
cleft was not cut through its external opening. In each mandibular
fold a large aortic arch (ar) is seen, and also a slight condensation
of mesoblast, the latter probably being the forerunner of cartilage.

Figure 13c passes through the anterior part of the heart about
seventy-five sections posterior to figure 13b. The embryo in this
region is narrow but deep (dorso-ventrally), the depth being largely
due to the size of the heart. The ectoderm (ec) is considerably
thickened on each side of the pharynx (pi); this thickened area
may be traced for some distance both anteriorly and posteriorly
from this point; its significance could not be determined. The
spinal cord (sc) and notochord (nt) need no special description ;
the former is smaller and the latter larger than in the more anterior
sections. The two large blood-vessels (ac) near the spinal cord
and notochord are probably the anterior cardinal veins. The aorte
are cut by the plane of this section just anterior to their point of
fusion into a single vessel. A few blood corpuscles are seen in
the right aorta. The enteron (ent), cut posterior to the region of
the gill clefts, is a large elliptical cavity, with its long axis in a
transverse position. Its entodermal wall is comparatively thin and
smooth, with the cell nuclei arranged chiefly on the outer side, 7. ¢.,

30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

away from the cavity of the enteron. The body cavity (bc) is here
still unenclosed, and its walls, the somatic stalk, are cut off close to
the body of the embryo. The heart (ht), the most conspicuous
feature of this section, is nearly as large in cross-section as all the
rest of the embryo. As seen in such a section it is entirely detached
from the body of the embryo, and in this particular case has about
the shape of the human stomach. The mesoblastic portion of its
wall (mes’) is of very irregular thickness; it forms a dense layer
entirely around the outside, except for the pointed dorsal region,
and is especially thick along the ventral margin, where it is thrown
into well-marked folds, the heavy muscle columns. Lining the
cavity of the heart is the membranous endothelium (en’), and be-
tween this and the dense outer wall just described is a loose reticular
tissue with but few nuclei.

As the series is followed toward the tail the sections diminish in
size until, at a point about one-third the embryo length from the
posterior end, they are of scarcely one-fourth the area of the sec-
tions through the region of the hindbrain.

Figure 13d is about one hundred and twenty-five sections pos-
terior to figure 13c. Although not so small as the sections that
follow it, this section is considerably smaller in area than the one
last described. ‘The amnion (a), which was not represented in the
last three figures, is very evident here. The spinal cord (sc) is
considerably smaller here than in the preceding figure, while the
notochord (nt) is not only relatively but actually larger than in the
more anterior regions. Beneath the notochord is the aorta (ao),
now a single large vessel. ‘The mesoblast on each side of the body
is here differentiated into a distinct muscle plate (mp). These
muscle plates have very much the appearance of the thickened ecto-
derm seen in the younger stages of development. At about its
middle region (7. e., at the end of the reference line ec) each muscle
plate is separated from the overlying ectoderm by an empty space;
this space is still more marked in some other series. Ventral to the
aorta, and supported by a well marked though still thick mesentery
(ms), is the intestine. It is a small, nearly cylindrical tube with
thick walls; the splanchnic mesoblast which surrounds it is more
dense than the general mass of mesoblast; it was somewhat torn
in the section and is so represented in the figure. The urinary
organs have made considerable progress since the last stage. In
the figure under discussion they are seen as a group of tubules on
either side of the aorta. The tubule most distant from the middie
line, on each side, is the Wolffian duct (wd). It extends through
the posterior two-thirds of the embryo and varies in diameter at

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 37

different points; it is usually lined with a single layer of cubical
cells which contain large nuclei. The Wolffian bodies (wt) are a
mass of slightly convoluted tubulés that may be traced throughout
the greater part of the region through which the Wolffian duct
extends. These tubules also vary somewhat in diameter, buz they
are usually of greater caliber than the duct. No actual nepliros-
tomes are to be seen, though the occasional fusion of a tubule with
the peritoneal epithelium, as is seen on the left side of the present
figure, may represent such an opening. A detailed description of
these structures may be given in a subsequent paper.

Figure 13e¢ is about one hundred and forty sections posterior to
the section just described. The embryo is here very slender, so
that the contrast between this and the first figure (13a) of this stage
is remarkable. Except in size, this section does not differ greatly
from the preceding. The spinal cord, notochord, etc., are smaller
than before, but are of about the same relative size. The mesen-
tery (ms) in the section drawn was torn across, so that the intestine
is not represented. Medial to the Wolffian duct is a tubule (wt),
which seems to be the same as those which were called Wolffian
tubules in the preceding stage, but which may be the beginning
of the ureter.

Figure 13f, about two hundred and fifty sections posterior to the
last, passes through the extreme posterior end of the embryo. The
section is nearly circular in outline and is somewhat larger than
the preceding. The amnion (a) completely encircles the embryo.
The ectoderm (ec) is of fairly even thickness, and the mesoblast
which it encloses is of the usual character. The spinal cord (sc)
is nearly circular in outline, as is its central canal. The digestive
tract (ent) is larger in section than it was in more anterior regions;
it is nearly circular in cross-section and its walls are made up of
several layers of cells, so that it resembles to a considerable degree
the spinal cord of the same region. In the narrow space between
the spinal cord and the hindgut is seen the notochord (nt), some-
what flattened and relatively and actually smaller than in the pre-
ceding figure. A few scattered blood-vessels may be seen in the
mesoblast at various places.

A sagittal section of an embryo of this stage, drawn under the
same magnification as were the transverse sections, is shown in
figure 13g. The embryo being bent laterally could not be cut by
any one plane throughout its entire length, so that only the ante-
rior end is represented in the figure. The amnion (a) may be
clearly seen except at certain places where it is closely adherent to

38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the superficial ectoderm. Under the low magnification used the
superficial ectoderm cannot be distinguished from the ectoderm of
the nervous system. The plane of the section being in the anterior
end almost exactly median, this part of the central nervous system
is seen as the usual retort-shaped cavity, while in the region back
of the brain, where the neural canal is narrow, the section passes
through the wall of the spinal cord (sc) and does not show the
neural canal at all. The wall of the forebrain (fb) is quite thick,
especially at the extreme anterior end; the wall of the midbrain
(mb), where the marked cranial flexure takes place, is somewhat
thinner, and it gradually becomes still thinner as it is followed
posteriorly over the hindbrain (ib). Between the floors of the fore-
and hindbrains, in the acute angle caused by the cranial flexure, is
the anterior end of the notochord (vt), the only part of that struc-
ture that lies in the plane of the section. Ventral and posterior to
the notochord is a large cavity, the pharynx (ph), whose ento-
blastic lining can scarcely be distinguished under this magnification
from the surrounding tissues. The stomodeal opening being as yet
unformed, the pharynx is closed anteriorly; posteriorly also, owing
to the plane of the section, the pharynx appears to be closed, since
its connection with the yolk stalk is not shown. In the floor of the
pharynx, almost under the reference line ph, a slight depression
marks the position of the first gill cleft. In the mesoblast ventral
to the pharynx and near the gill cleft just mentioned, a couple of
irregular openings represent the anterior end of the bulbus arteri-
osus, posterior and ventral to which is the heart (/t), a large,
irregular cavity. The dorsal aorta (ao) may be seen as an enlon-
gated opening in the mesoblast, extending in this section from the
middle region of the pharynx to the posterior end of the figure
where it is somewhat torn. T'wo of the eighteen or twenty pairs
of mesoblastic somites possessed by this embryo are shown at the
posterior end of the figure (s), where the plane of the section was
far enough from the median line to cut them.

STAGE XI
FicuRE 14 (PLATE XVI)

Only the anterior region of this embryo is shown in the figure,
which is a ventro-lateral view. While there is some change in the
general shape and in parts of the head, the reason for figuring this
stage is to show the first gill cleft (¢’), which lies at an acute angle
to the long axis of the neck behind the eye (e). The cleft is narrow

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 39

but sharp and distinct in outline; it shows, neither in this nor in
the following stages, the branched, Y-shaped outline mentioned by

Clarke.
OEAGE Xi
FIGURES 15-I5f (Pirates XVI, XVII)

In this stage, also, only the anterior region of the embryo is
figured in surface view. The shape of the head is about the same
as in the preceding stage, but it is drawn in exact profile. Three
gill clefts (g™3) are now present, and are wide and distinct. The
first cleft, as in the preceding stage, lies at an acute angle to the
long axis of the pharynx and nearly at right angles to the second
cleft» The third cleft sends a wide branch (g*) toward the pos-
terior, as has been described by Clarke, from which, or in connec-
tion with which according to Clarke, the fourth cleft will develop.
All three clefts may be distinctly seen to open entirely through the
pharyngeal wall. The outlines of the visceral folds, especially of
the mandibular, begin to be apparent. The nasal pit (7) now
shows as a round depression in front of the more definitely outlined
eye (e). The auditory vesicle (0) is so deep beneath the surface
that it may be seen only by transmitted light.

Figures I5a-e represent transverse sections of an embryo of
about this general state of development, except that the gill clefts
are not so definitely open as in the surface view.

Figure 15a, the most anterior section of the series, passes through
the forebrain (fb) in the region of the eyes, and through the hind-
brain (Ab) anterior to the auditory vesicles. The forebrain is here
a large cavity with a dense wall of a comparatively even thickness.
Owing probably to the section not being exactly in the transverse
plane, the eyes are cut in different regions, that on the left (ov)
being cut through its stalk, while that on the right (oc) is cut near
its middle region and hence does not show any connection with the
forebrain. The almost complete obliteration of the cavity of the
optic vesicle to form the optic cup by the invagination of the outer
wall of the vesicle is shown on the right side of the section (oc).
The lens vesicle (Jv) is completely cut off from the superficial ecto-
derm (ec), which is comparatively thin. The hindbrain (ib) has
the usual shape for that structure. Its ventral wall is dense and
thick, while its roof is reduced to the usual thin, wrinkled mem-
brane. Close to the floor of the hindbrain lies the notochord (it),
which is large and is distinctly vacuolated. ‘To the right of the
hindbrain a large mass of darkly stained cells (cn) is one of the

40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

cranial nerves, which is connected with the hindbrain a few sections
anterior to the one under consideration. The pharynx (p/), which
is cut near its extreme anterior end, is represented by three irregular
cavities near the base of the forebrain. Scattered throughout the
mesoblast, which makes up the greater part of the section, are
numerous blood-vessels (bv).

Figure 15) is twenty sections posterior to figure 15a and passes
through the tip of the bent-under forebrain (fb). On the left the
section is anterior to the optic vesicle and barely touches the side
of the optic stalk, which is seen as a small lump on the ventro-
lateral wall of the brain. On the right the connection of the optic
vesicle (ov) with the forebrain is shown. Dorsal to the optic vesicle
just mentioned is a markedly thickened and slightly invaginated re-
gion of the ectoderm (1) ; this is the nasal pit; on the left side of the
figure the thickening is shown, but the section did not pass through
the invagination. The hindbrain (hb) is somewhat narrower than
in the preceding figure, but is otherwise about the same; the origin
of a cranial nerve is seen on its left side (cw). The notochord (it)
has the same appearance as in the preceding section. A number of
blood-vessels may be seen, the pair lying nearest the notochord
being the aorte (ao), while the two other pairs, on either side of
the fore- and hindbrains, are the anterior cardinals-(ac). The first
aortic arches are shown at ar. On the left the section passes through
the exterior opening of the first gill cleft (g’), so that the mandibu-
lar fold (md) on that side is a distinct circular structure, made of a
dense mass of mesoderm surrounded by a rather thick ectoderm.
The mesoderm of this fold is especially dense near the center, prob-
ably the beginning of the visceral bar. Near the center is also seen
the aortic arch that has already been mentioned. On the right the
section does not pass through the external opening of the first gill
cleft (g’) so that the tissue of the mandibular fold is continuous
with the rest of the head. It is of course the slight obliquity of the
section that causes the pharynx (ph) to be completely enclosed on
the right, while on the left it is open to the exterior both through the
gill cleft and between the mandibular fold and the tip of the head.
The superficial ectoderm shown here as a heavy black line varies
considerably in thickness, being thickest in the region of the nasal
pit already mentioned and thinnest over the roof of the hindbrain.
The amnion (a) in this, as in the other sections of the series, has
the appearance of a thin, very irregular line.

Figure 15c is posterior to the region affected by cranial flexure
and so shows only one region of the embryo, that of the hindbrain
(hb), which is here of essentially the same structure as above de-

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE Al

scribed. On each side of the hindbrain is a large auditory vesicle
(0) ; that on the left is cut through its center and shows the begin-
ning of differentiation, its lower end being thick-walled and
rounded, while its upper end is more pointed and has a thin, some-
what wrinkled*wall. The notochord (nt) is slightly larger than in
the more anterior sections. Numerous blood-vessels (bv, ar) are
seen in the mesoblast. The pharynx (ph) is here open ventrally
and also through the gill cleft of the left side; on the right side the
plane of the section did not pass through the external opening of the
cleft. ‘Ihe mesoblast of the visceral folds is much more dense than
that of the dorsal region of the section.

Figure 15d, as is evident, is a section through the region of the
heart, which appears as three irregular cavities (At) with fairly
thick mesoblastic walls (mes’) lined with endothelium (en’). ‘The
body wall, though consisting of but little besides the ectoderm (ec),
completely surrounds the heart, and the pericardial or body cavity
thus formed extends dorsally as a narrow space on either side of
the foregut, giving the appearance of a rudimentary mesentery,
though no especial development of such a structure would naturally
be expected in this region of the embryo. The foregut (ent) is a
moderately large cavity lined with a very distinct entoderm of even
thickness. Dorsal to the foregut are three large blood-vessels, a
median, and now single, dorsal aorta (ao), and a pair of cardinal
veins (cv). The notochord (nt) is small and is flattened against
the ventral side of the spinal cord (sc), which latter structure needs
no special mention. The muscle plates (mp) are considerably
elongated, so that they now extend ventrally to a point slightly
below the upper angles of the body cavity.

Figure 15e is through the middle region of the embryo, and,
owing to the curvature of the body, is not an exact dorso-ventral
section; this accounts, in part at least, for the unusual diameter in
a dorso-ventral direction of the aorta (ao), which is very large in
proportion to the other structures. ‘The posterior cardinal vein is
shown on the left, but not on the right. The relative sizes of the
spinal cord (sc) and notochord (nt) are very different from what
was seen in the preceding figure. In this section the spinal cord
is considerably smaller than in the preceding, while the notochord
is very much larger; in fact the notochord here seems abnormally
large when compared to corresponding sections of other series. It
is true, however, that while the spinal cord has been diminishing
in diameter the notochord has been increasing. The spinal cord,
notochord, and dorsal aorta are all so large that they are flattened
against each other, the pushing in of the ventral side of the spinal

42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

4

cord being even more marked than is shown in the figure. On
either side of the spinal cord a large spinal ganglion (sg) is seen,
closely wedged in between the spinal cord and the adjacent muscle
plate (imp). As in the preceding stage, there is a marked space
between the muscle plate and the adjacent ectoderm (ec). The
somatic mesoblast at the upper angle of the unenclosed body cavity
is thickened on each side and somewhat bulged out by the Wolffian
body to form what might be termed a Wolffian ridge (wr). In the
mid-ventral line is the considerably developed mesentery (ms),
from which the intestine has been torn. The Wolffian bodies now
consist, on each side, of a group of five or six tubules (wt) of
various sizes, near which in a more ventro-lateral position, close to
the upper angle of the body cavity, is the more distinct Wolffian
duct (wd). The allantois is fairly large by this time, and may be
seen in the most posterior sections as an irregular, thick-walled out-
growth from the hindgut.

A horizontal section through the anterior end of an embryo of
this age is shown in figure 15f. While enclosed of course in the
same membranous amnion (a), the pharyngeal region of the section
is separated by a considerable space from the more anterior region
where the section passes through the forebrain (fb) and eyes. The
spinal cord (sc), notochord (ut), muscle plates (mp), aorte (ao),
and anterior cardinal veins (ac) need no special description. The
appearance of the pharynx (ph), with its gill clefts and folds, is
quite similar to that of the corresponding structures in the chick.
None of the four clefts (g'4+) show, in the plane at which the sec-
tion was cut, any connection with the exterior; in fact the fourth
cleft (g*) would scarcely be recognized as a cleft if seen in this
section alone. One or two of the more anterior clefts are open to
the exterior. Three pairs of aortic arches are seen, and each vis-
ceral fold has a central condensation of mesoblast.

STAGE XIII
FicurEs 16-16g (PLatEs XVII, XVIII)

The embryo (fig. 16) now lies on one side, body torsion being
complete. The curvature of the body is so marked that the exact
length is difficult to determine. The eye (e) and ear (0) have
about the same superficial appearance as in the preceding stage.
The nose is not shown in this figure. About thirty somites are
present; the exact number cannot be determined in surface view.
The amnion is complete, though not shown in the figure, and the
tail (t) is well formed. The umbilical stalk was torn in the removal

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 43

of the embryo, so that it is not shown in the figure. The dim out-
line of the now convoluted heart may be seen if the “cleared”
embryo be viewed by transmitted light; it is not shown in the
figure. The allantois (al) is a rounded sac of considerable size just
anterior to the’ tail. Four gill clefts (g'+) are now present; the
most posterior one is more faint than is represented in the figure,
and it could not be definitely determined from a surface view
whether or not it opened to the exterior. The mandibular fold
(md) is now fairly well outlined, but there is as yet no sign of the
maxillary process.

Figure 16a is the most anterior of a series of transverse sections
made of an embryo of the approximate age of the surface view just
described ; it passes through the tip of the forebrain (fb) and shows
the nasal pit (7) of the right side. The great thickening of ecto-
derm in the region of the nasal invagination is represented by a
solid line. Owing to the obliquity of the section, the left nasal pit
was not cut. The mesoblast is quite dense and contains two or three
small blood-vessels near the roof of the brain. The plane of this
section, owing to the cranial and body flexure, cut the embryo also
in the region of the pharynx; this part of the section was, as a
matter of convenience, omitted from the drawing.

Figure 16) is in reality more anterior in position considering the
entire embrvo, than the preceding; but the region of the embryo
represented is most posterior, so that it is described at this point.
The greatly elongated outline of the brain is due to its being cut
through the region of flexure, so that the forebrain (fb) or, per-
haps, midbrain, is shown at one end and the hindbrain (hb) at the
other. The walls of these cavities are somewhat wrinkled and irreg-
ular and their constituent cells are beginning to show slight differ-
entiation, though this is not shown in the figure. On the left side
are seen a couple of darkly stained masses; one is the origin of a
cranial nerve (cu); and the other is one of the auditory vesicles
(0), which is still more irregular in outline than it was in the pre-
ceding stage. The only blood-vessels to be seen are a.few very

7 7

small ones that lie close to the wall of the brain. The ectoderm is
quite thin at all points.

Figure 16c, the largest section of this series, passes through the
forebrain in the region of the eyes and through the gill clefts. The
forebrain (fb) exhibits on the left a marked thickening of its wall
(ch), the edge of the cerebral hemisphere of that side, which is just
beginning to develop; on its right side the lower part of the fore-
brain is connected by a well-marked optic stalk (os) with the optic

44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

cup (oc), in whose opening lies the lens vesicle (lv), now reduced
to a crescentic slit by the thickening of its posterior wall. The
mesoblast is more dense in those parts of the section adjacent to the
pharynx than in the more distant regions, and the ectoderm thickens
in a marked way as it approaches the borders of the pharynx and
gill clefts. Only a few small blood-vessels (bv) are to be seen in
the region of the forebrain.

Parts of three pairs of clefts (g) are shown in the figure: one
pair opens widely on either side, so that there is a large area of the
section that is distinct from the two still larger portions and con-
tains a small, thick-walled cavity (g) on the right side; this cavity
is a gill cleft that is cut through neither its outer nor its pharyngeal
opening.

No structures other than this small portion of a gill cleft and a
few blood-vessels are to be seen in this middle region of the section.
In the more posterior part of the section, in which the notochord
(nt) is located, a pair of curved clefts may be seen, opening entirely
through the wall on the left, but closed on the right (g). One dis-
tinct pair of aortic arches is shown (ar), and also the dorsal aorte
(ao), which are of very unequal size. The spinal cord (sc) and
muscle plates need no special description.

Figure 16d is in the region of the heart (it) and lungs (Ju). The
former is an irregular cavity whose walls, especially on the ventral
side (mes’) are becoming very thick and much folded. Although
thin, the body wall completely surrounds the heart, as would be
expected, since this was true of the preceding stage. The lung
rudiments (Jw) and the foregut from which they have arisen have
the same appearance as in the chick; they consist of three small,
thick-walled tubes so arranged as to form a nearly equilateral tri-
angle. They are surrounded by a swollen, rounded mass of meso-
blast which almost completely fills the surrounding portion of the
body cavity (bc). The pleural sides of these crescentic portions of
the body (or pleural) cavity—that is, the boundary of the mass of
mesoblast just mentioned—is lined with a thickened layer of cells,
shown by the solid black lines in the figure. ‘The lung rudiments
may be traced through about fifty sections of this series, or about
one-twelfth of the entire series. At the dorsal angle of the part of
the body cavity (bc) just described, near the dorsal aorta (ao), are
two dark, granular masses (ge), which, under a higher magnifica-
tion than is here used, are seen to consist of a small group of blood-
vessels filled with corpuscles; although several sections in front of
the anterior limits. of the kidneys, these are evidently glomeruli.
They may be traced, though diminishing in size, far toward the

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 45

tail, in close connection with the Wolffian bodies. At intervals they
are connected by narrow channels with the dorsal aorta; no such
connection was present in the section drawn. The notochord (nt),
spinal cord (sc), muscle plates (mp), and spinal ganglia (sg) need
no special mefition. The mesoblast is beginning to condense in the
neighborhood of the notochord, and the ectoderm is slightly thick-
ened laterally and dorsally.

Figure 16e¢ is in the region of the liver and the Wolffian bodies ;
it also shows the tip of the ventricular end of the heart. The liver
(li) is a large irregular mass, of a blotchy appearance under this
magnification, lying between the heart (vm) and the intestine (7).
Under greater magnification it is seen to be made up of indefinite
strings of cells; and its still wide opening into the intestine may be
seen in more posterior sections. The intestine (7), which in this
section might be called the stomach, is a fairly large cavity with
the usual thick entodermic walls; it is supported by a comparatively
narrow mesentery. The body cavity on the side next this mesentery
has the same thick lining that was noted in the region of the lungs.
The convolutions of the thick peritoneal lining may easily be mis-
taken in places for parts of the enteron. The Wolffian bodies may
be seen as two groups of tubules (wt) in their usual location. The
heart is cut through the ventricle (vm),as has been said. The section
being at right angles to the long axes of the villi-like growths of
the myocardium, the depressions between these mesoblastic cords are
seen as a number of small irregular areas, each one lined with its
endocardium. The incompleteness of the body wall below the heart
is apparently due to an artificial break and not to a lack of fusion.
The only point that need be mentioned in connection with the struc-
tures of the dorsal part of the section is that the distinctness of the
myocoel (myc) on the right side is somewhat exaggerated.

Figure 16f is in the middle region of the embryo, where both
spanchnopleure and somatopleure are unfused. Owing chiefly to
the unclosed condition of the midgut (7) and to the increase in
length of the mesentery (ms), the section is quite deep dorso-
ventrally. The continuation of the amnion (a) with the somato-
pleure is of course here evident.

The most striking feature of the section is the marked projection
of the Wolffian ridges, though no local enlargements of these ridges
indicate the rudiments of the limbs. A large mass of Wolffian
tubules (wt) is seen projecting into the upper part of the body
cavity on each side; close to each of these masses is the posterior
cardinal vein (pc), and between them is the large aorta (ao). The
other structures are about as in the preceding section.

40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Figure 16g represents a sagittal section of the anterior half of
the body of an embryo of this or possibly a slightly younger stage
of development. The three regions of the brain are clearly indi-
cated, as well as the cavity of the spinal cord (sc). The roof of the
hindbrain has been made too thick in the figure; it should be rep-
resented by a mere line. A little mesoblast is to be,seen at places
between the roof of the brain and the superficial ectoderm. A slight
invagination of the epithelium (p), between the floor of the brain
and the anterior end of the notochord, probably represents the begin-
ning of the hypophysis. No indication of the pineal body is yet
to be seen. Extending from the region of the hypophysis to the
posterior end of the section is the notochord (mt) ; it is much vacuo-
lated and gradually increases in thickness toward the posterior,
though its outline is quite irregular; except at the extreme anterior
end and at one or two other places, it lies in close contact with the
Hoor of the neural tube. Directly under the notochord lies, in the pos-
terior half of the figure, the large dorsal aorta (ao). The pharynx
(ph), opening between the end of the forebrain and the thick man-
dibular fold (across which opening the amnion (a) of course ex-
tends), is a funnel-shaped space which passes out of the plane
of the section toward the posterior end of the figure. Its thick
endodermal lining extends to the mandibular fold on the ventral
side, while on the dorsal side it gradually thins out and becomes
continuous with the thin ectoderm that extends over the forebrain.
Just back of the mandibular fold is the bulbus (b), and back of that
is the edge of the ventricle (vu). Posterior and dorsal to the ven-
tricle the liver (/i) is seen as an irregular mass of cells, and dorsal
to the liver one of the Wolffian bodies (wt) is cut through its ex-
treme edge.

STAGE XIV
FicurEs 17-17g (Piates XVIII, XIX)

Body flexure has increased until now the forebrain and tail are
almost in contact (fig. 17). The eye has developed somewhat; the
ear vesicle, which is not shown in the figure, is small and seems to
lie nearer the ventral side; the nasal pit is much larger and is
crescentic in shape. The hyomandibular cleft (g’) still persists as a
small crescentic slit, while the next three clefts are now represented
merely by superficial grooves separated by distinct ridges, the vis-
ceral folds. No indication of a fifth cleft is seen. The maxillary
process (mx) grows ventralward under the forebrain and is already
longer than the manibular arch (md).

The chief advance in development over the preceding stage, be-

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 47

sides the formation of the maxillary process, is in the appearance of
the appendages (aa and pa) ; they have the characteristic shape of
the rudimentary vertebrate appendage, though the anterior pair
seem to point in an unusual direction at this stage and to be slightly
more developed than the posterior. The curious, anteriorly directed
heart (At) is, perhaps, somewhat abnormal. The umbilical stalk
(w) is comparatively narrow and, like the allantois, was cut off close
to the body.

Transverse sections of an embryo of this stage are represented in
figures 17a-g, drawn under a lower magnification than were any of
the preceding figures.

Figure 17a isin the region of the pharynx, and passes through
the forebrain (fb) and posterior part of the hindbrain (ib). In the
thick walls of both of these structures histological differentiation has
begun, so that even under low power an inner granular and an outer
clear zone may be distinguished. Under greater magnification the
presence of short fibers may be made out among the cells. The
cerebral hemispheres (ch) are well-marked structures, their asym-
metry being of course due to the obliquity of the section. Only one
eye is cut by the plane of the section, and this one shows no con-
nection with the forebrain. The outer wall of the optic cup (oc) is
so thin that under this magnification it can scarcely be seen as a
dark line surrounding the retinal wall. The lens (/1) is now a solid
mass, of the usual type for vertebrate embryos, its front or outer
wall being a scarcely discernible line. The hindbrain (hb) has the
usual form for that region and does not differ particularly from
what was noted in earlier stages except in the histological differ-
entiation that has already been mentioned. As with the eye, it is
only on the right side that the auditory vesicle (0) is shown. It
shows some differentiation, but not so much as would be seen were
it cut in another region. In the center of the section the pharynx
(ph) forms an irregular cavity connected with the exterior on the
left by a gill cleft (g) and by another slit which is simply the ante-
rior margin of the stomodaeum. On the right neither of these
openings are in the plane of the figure, though the gill cleft (hyo-
mandibular), which lies close to the auditory vesicle, is almost an
open passage. A few small blood-vessels are scattered through the
section; one of these (bv), lying between the notochord (nt) and
the floor of the brain, is noticeable from its being very closely packed
with corpuscles, so that at first glance, under low magnification, it
looks more like a nerve than a blood-vessel.

Figure 17) is also through the pharyngeal region, a short distance
behind the preceding section. The growth of the cerebral hemi-

48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

spheres (ch) is better shown than in the preceding figure, as is also
the general form of the optic cup (0c). On the left the nasal cavity
(7) is seen as an elongated slit with thick walls; it is cut near, but
not through, its opening to the exterior. The same gill cleft (g)
that was seen in the preceding figure is seen here as a narrow, trans-
verse cleft, open at both ends. Between the notochord (mt) and the
spinal cord (sc) is the same, though now double, blood-filled vessel
(bv) that was seen in the preceding section. The other blood-ves-
sels are larger here than in the more anterior region. There is a
faint condensation of mesoblast in the neighborhood of the noto-
chord, and a more marked condensation (mp) farther toward each
side is the curiously shaped muscle plate.

Figure 17c is through the heart region, and that organ is cut
through the opening from the lower or ventricular into the upper or
auricular chamber. The thickening of the wall of the ventricle,
which was noticed in the preceding stage, has increased to such
an extent that there is now a marked difference in the thickness of
the ventricular and auricular walls. As in the preceding stage, the
body wall is torn, probably in handling, so that it appears to be
incomplete around the ventral side of the heart. Dorsal to the heart
two small circular holes (ent) with thick walls are the cesophagus
and trachea, cut anterior to the point of bifurcation of the latter into:
the bronchial or lung rudiments. On either side of these struc-
tures is an elongated blood-vessel (ac), the anterior cardinal vein,
its elongation being due to the fact that it is cut at the place where:
it turns downward to empty into the heart. Dorsal to the cesoph-
agus are the aorte (ao), which are here cut just at the point where
the two vessels unite to form one; the next section, posterior to the
one under discussion, shows an unpaired aorta. The notochord (nt)
and spinal cord (sc) need no description, except to note that the
latter shows active histological differentiation, numerous mitotic
figures being seen under higher magnification, especially in the
cells that line the spinal canal. On the right of the cord the edge
of a spinal ganglion (sg) is seen, in connection with which in other:
sections are seen the clearly defined nerve roots. The condensation
of mesoblast around the notochord is quite evident, and in close
contact with this medial condensation are two very characteristic,
S-shaped muscle plates (mp), which extend from the level of the
dorsal side of the spinal cord to the upper limits of the cardinal
veins. In some sections the muscle plates even yet show slight
remains of the myocoel at the dorsal end.

Figure 17d is in the region of the posterior end of the heart (ht),
which is cut through the tip of the ventricle, and the anterior end of

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 49

the liver (/i), which has the appearance of a mass of darkly stained
cords or strands of cells surrounding a large blood-vessel (mv).
This blood-vessel may be ca.led*the meatus venosus, though it is not
separated by any line of demarcation from the auricle. A few
sections anterior to this region the meatus venosus opens dorsally
into a large vessel on each side (dc), which at first glance seems a
part of the body cavity, but which is in reality the ductus Cuvieri,
forméd by the union of the anterior and posterior cardinal veins.
An irregular, crescentic cleft (bc), lying medial and parallel to each
of the Cuvierian vessels, is the body cavity. In the upper angle of
this cavity is a granular mass, the glomerulus, that of the left side
being accompanied by the extreme anterior end of the Wolffian duct.
In the rounded mass of mesoblast, between the cleft-lke regions
of the body cavity, the lung rudiments (/w) and the cesophagus (0c)
are seen as three small, circular openings; that of the cesophagus 1s
somewhat smaller than the other two. The notochord (nt), spinal
cord (sc), and muscle plates (mp) have almost the same appear-
ance as in the preceding section. A spinal ganglion (sg) is seen on
each side of the spinal cord; the one on the left shows a well-defined
spinal nerve (sz), which may be traced.ventrally as far as the end
of the muscle plate, along whose medial side it courses. The ventral
nerve root is plainly seen; the dorsal root, in this section, less
plainly. The amnion (a) and abdominal wall are, as in the pre-
ceding figure, torn in the region of the ventricle.

Figure 17e is a short distance posterior to the figure just de-
scribed. The liver is cut through its middle region and forms a
large, darkly staining, reticular mass on the left side of the figure.
The digestive tract is seen at two places to the right of the liver;
the smaller and more ventral of these openings (7) may be called
the intestine, while the larger is evidently the stomach (i’). The
body wall is here unfused and becomes suddenly thinner as it passes
upward into the amnion (a). The Wolffian tubules (wt) form a
very conspicuous mass on either side of the mesentery, in close con-
nection with the posterior cardinal veins (pc). In the mesoblast
between the dorsal aorta (ao) and the notochord are two small,
irregular, darkly stained masses (sy). These are shown in the
preceding two figures, but were not mentioned in the description.
They may be traced through a great part of the length of the embryo
back of the head region; at intervals corresponding in length to the
distance between the spinal ganglia they are enlarged, while between
these enlargements they are very small in cross-section. At certain
points a small blood-vessel is given off by the dorsal aorta to the
immediate neighborhood of each’ of these small areas. Although

4—AL

50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

they show no connection with the central nervous system, these
structures appear to be the rudiments of the sympathetic nerves.

Figure 17f is in the region just in front of the hind legs. The
abdominal walls are here unfused, and into the unenclosed body
cavity projects the intestine (7), supported by a narrow mesentery
and surrounded by a comparatively thick mass of mesoblast. The
Wolffian body and duct form a mass of considerable size on each
side of the mesentery. The Wolffian body is cut near its posterior
end and consists of smaller tubules than in the more anterior regions.
The Wolffian ducts (wd), on the other hand, are very large and are
much more clearly distinguishable from the Wolffian tubules than
in the preceding sections. The Wolffian ridges (wr) are very
marked projections on the sides of the body, and in a region further
caudad become especially developed as the posterior appendages, to
be described in connection with the following section. Both spinal
ganglia are shown in this figure (sg), and in connection with the
left ganglion the spinal nerve (sw), extending ventrally as far as
the level of the Wolffian duct. The sympathetic nerve rudiments do
not extend so far caudad as the plane of this section. The dorsal
end of each muscle plate (mp) is seen, in this and other sections, to
be slightly enlarged to form a round knob; this knob contains a dis-
tinct cavity (not shown in the figure), the myocoel.

In figure 17g, owing to the curvature of the body, the plane of
the section passes through the body at three places: through the
region of the heart and lungs (fig. 17d), through the region of the
posterior appendages, and through the tail. In fact, the plane of the
section represented by each of the preceding figures cut the embryo
in more than one region, but for the sake of simplicity only one
region was represented in each figure. In the figure under discus-
sion only the leg and tail regions have been drawn, though the latter
region (t), being cut through one of its curves, is seen as an elon-
gated body with a section of the spinal cord, notochord, etc., at each
end. Both regions shown in the figure are enclosed in the same fold
(a) of the amnion. Of the structures in the dorsal side of the larger
or more anterior part of this figure nothing need be said. The most
striking feature of the section is the presence of the large posterior
leg rudiments (pa). As was noted in the preceding figure, they are,
as usual, merely local enlargements or projections of the mesoblast
(covered, of course, with ectoblast) of the Wolffian ridge. They
are, as shown in this section and in the surface view of this stage
(fig. 17), bluntly pointed projections from the sides of the body.
The anterior appendage seems to be slightly more developed than
the posterior, as was noted in describing the surface view of the

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE op!

embryo. The digestive tract is cut through its extreme posterior
end, in the region that may be termed the cloaca (c/), for into it at
this point the Wolffian ducts open (wdo). :As the narrow cloacal
chamber is followed toward the tail, it becomes still smaller in diam-
eter, and the ventral depression or cleft seen in this figure gradually
becomes deeper until its walls are continuous with the ectoderm
that covers the ventral projection of mesoderm between the hind
legs; no actual opening to the exterior is present, however. There
is a space of about twenty-five or thirty sections (in a series of eight
hundred) between the posterior ends of the Wolffian bodies and the
cloacal openings of the Wolffian ducts. The body cavity (bc) and
the posterior cardinal veins (fc) are very small in this region, as
might be expected.

STAGE XV
Ficure 18 (Pirate XIX)

Only the head of this embryo is represented, as the general state
of development is about the same as in the preceding stage.

The chief object in making the figure is to show the five gill clefts
(g*°). The fifth cleft, though small and probably not open to the
exterior, is quite distinct in this embryo. The writer would feel
more doubt of its being a true, though rudimentary, gill cleft had
not Clarke (5) found a fifth pair of clefts in his material. The
nasal pit has advanced in development somewhat and shows the
beginning of the groove that connects it with the mouth. In this
figure the crescentic hyomandibular cleft shows its connection with
the groove between the mandibular and the hyoid folds.

Stace XVI
FicurE 19 (PLATE XIX)

This embryo is only slightly more developed than the preceding.
Body flexure is so great that the forebrain and tail nearly touch.
Only the anterior three gill clefts are visible. The maxillary pro-
cess (mx) is longer and more narrow; the mandibular fold has not
changed appreciably. The nasal pit (7) is now connected by a dis-
tinct groove with the stomodaeum. The appendages have increased
in size, the posterior (pa) being the longer. The anterior appendage
(aa) is distinctly broadened to form the manus, while no sign of
the pes is to be seen at the extremity of the posterior appendage.
The heart (ht) is still very prominent. The stalk of the umbilicus
(uw), which is quite narrow, projects from the ventral wall in the
region between the heart and the hind legs. The tail is of consider-
able length and is closely coiled.

52 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Stace XVII
FicurEs 20-207 (PLatEs XX, XXI)

The superficial changes noted in this stage chiefly concern the
head, which has increased considerably in length (fig. 20). The
curvature of the body is slightly more marked, and thestail is more
tightly coiled at the end. There are still signs of three gill clefts.
The maxillary process (ma) is long and narrow, while the mandibu-
lar arch (md) is still short and broad. The fronto-nasal region has
greatly increased and has the acquiline profile noted by Clarke. The
nasal groove has disappeared, and there remains the small opening
(n) at the side of the fronto-nasal region, near the end of the still
separate maxillary process. ‘The umbilicus is in about the same
condition as in the preceding stage, but the heart is less prominent.
The outline of the manus (ma) is more definite, and the extremity
of the posterior appendage is distinctly flattened out to form the
rudimentary pes (pe). The position of the elbow-joint in the an-
terior appendage is seen at the end of the reference line aa.

Typical transverse sections of this stage are shown in figures
20a-).

Figure 20a is a section through the middle region of the head,
cutting the hindbrain on one side and the forebrain on the other.
The walls of the brain show rather more histological differentiation
than was seen in the preceding sections, though this cannot be
shown under the low magnification used. The hindbrain (hb),
which is cut near its anterior border, exhibits the usual membranous
dorsal and thick ventral walls. The forebrain is here seen as three
distinct cavities—a median third ventricle (vt), with a thick ventral
wall, and a thin dorsal wall extended to form a large pineal body
(epi), and two lateral ventricles (ch), the cavities of the cerebral
hemispheres, whose walls are quite thick except on the side next the
third ventricle. The sections of this series being slightly oblique,
the eye is here cut on the right side only, where it is seen as a large,
semicircular cavity (e) with thick, dense walls. The mesoblast, in
which several blood-vessels (bv) are seen, exhibits three distinct
areas—a median, lighter zone, with a more dense area on either
side. The significance of this variation in the density of the meso-
blast is not apparent.

Figure 20b is only a few sections posterior to the section just
described. It is drawn chiefly to show the appearance of the fore-
brain, the other structures being about as in the preceding figure,
except that both eyes (e) are here represented. The section passes
through the wide opening between the third (tv) and the lateral

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 53

ventricles (ch) and cuts the anterior edge of the pineal body (epz).
The pineal body is very large and is directed backward instead of
forward, as is usually the case among the lower vertebrates (if the
alligator may be so classed). It is shown in figure 17a of a pre-
ceding stage and will be again shown in a sagittal section to be
described later. ‘The same areas of more dense and less dense
mesoblast noted in the preceding figure are seen here.

Figure 20c, though still in the head region, shows several features
that were not seen in the preceding figures. On the left of the hind-
brain (hb) the auditory vesicle (0), which is now considerably more
advanced than in earlier figures, is seen as a larger, flask-shaped
cavity and a smaller, round one. Between the larger cavity and
the hindbrain is the root of a cranial nerve (cu), apparently the
eighth, since in another section it comes in close contact with the
wall of the larger part of the auditory vesicle just mentioned. On
the right side, ventral to the hindbrain, another and much larger
merve (cm) is seen. Nearly in the center of the figure is seen a
small, irregular, thick-walled cavity (/), this is the pituitary body,
and its connection with the roof of the pharynx may easily be made
out in another section. The mesoblast in this region of the sections
contains numerous large and small blood-vessels and exhibits certain
denser areas which probably represent the beginnings of the cranial
cartilages. No sign of the forebrain is seen (the plane of the section
passing in front of that region), except that the tip of the wall of one
of the cerebral hemispheres (ch) is cut. The left nasal chamber (7)
is shown: it will be noted again in the following section. The eye
on the right side shows no remarkable features; its lens (Jn) is
large and lies well back of the lips of the optic cup, which may now
be called the iris (ir). A thin layer of mesoblast has pushed in
between the lens and the superficial ectoderm to form the cornea,
and the outer wall of the optic cup is now distinctly pigmented. The
inner wall of the optic cup is beginning to differentiate into the
retinal elements. ‘The eye on the left side is cut farther from its
central region and has a very different appearance from the eye just
described. This unusual appearance is due to the fact that the sec-
tion passed through the choroid fissure, which is very large and
seems to be formed by the pushing in of the walls of the cup and not
by a mere cleft in these walls. This fissure is hardly noticeable in
the stage preceding the present, and in a stage slightly older it has
disappeared ; so that it would seem to be a very transient structure.
It apparently is formed at about the time that the optic stalk, as
such, disappears. It is in the region of the choroid fissure, if not
through it, that the optic nerve (on) enters the eye. Through the

54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

fissure also enters a vascular tuft of mesoblast (pf) which may be
seen projecting into the optic cup after the disappearance of the
fissure. ‘This loop of blood-vessels is doubtless the pecten.

Figure 20d represents a section through the hindbrain (hb),
pharynx (pi), and tip of the snout. On either side of the hindbrain
are a convoluted auditory vesicle (0), and several blood-vessels and
nerves, while ventral to it is seen the anterior end of the notochord
(nt), around which the mesoblast is somewhat more dense than
elsewhere. The pharynx (ph) sends out toward the surface a nar-
row gill cleft (g’) in the neighborhood of each auditory vesicle.
These clefts connect with the exterior by very narrow slits, not seen
in the plane of this section. The opposite end of the pharynx, as
seen in this figure, opens on the left (pm) into the nasal chamber.
The nasal cavity on the right is cut in such a plane that it shows
neither its external nor its pharyngeal opening. The nasal passages
are here fairly long and nearly straight chambers; their lining
epithelium is quite thick in the middle region, but becomes thinner
where it merges into the epithelium of the pharynx at one end, and
into the superficial epithelium at the other end. The unusual appear-
ance of the eye (¢), on the right side of the figure, is due to the fact
that the plane of the section cut tangentially through the extreme
edge of the eye in the region of the choroid fissure.

Figure 20¢ is only a short distance posterior to the preceding. On
the left side the pharynx (pi) is connected with the exterior through
the stomodeaum, and on the right the hyomandibular cleft (g’) is
cut almost through its opening to the exterior. The auditory ves-
icle (0) on the right is cut near its middle region, while that on the
left is barely touched by the plane of the section. The notochord
(nt), with its condensed area of mesoblast, is somewhat larger than
in the preceding section. The nasal canal on the right (m) is cut
through neither anterior nor posterior opening, while on the left
side the canal shows the anterior opening (an).

Figure 20f, which is in the region of the posterior part of the
pharynx and the anterior part of the heart, shows some rather un-
usual conditions.

The spinal cord (sc) and notochord (nt), with the faintly out-
lined condensations of mesoblast in their region, need no special
description. The pharynx (ph) is here reduced to an irregular,
transversely elongated cavity, the lateral angles of which are con-
nected on each side with the exterior through a tortuous and almost
closed gill cleft (g), which must be followed through many sections
before its inner and outer openings may be determined. Dorsal to
the pharynx numerous blood-vessels (bv), both large and small, may

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 55

be seen, while ventral to it is noticed a faint condensation of meso-
blast (Ja), in the form of an inverted T, the anlage of the laryn-
geal structures. The ventral portion of the figure is made up of a
nearly circular, thin-walled cavity, the pericardium (pr). Most of
the pericardial cavity is occupied in this section by the thick-walled
ventricle (vn), above which is the bulbus (b) and the tip of the
auricle (au). The bulbus is nearly circular in outline, though its
cavity is very irregular. A few sections anterior to this, the opening
of the bulbus into the ventricle is seen.

In figure 20g the section represented is only a short distance pos-
terior to the one represented by figure 20f. The mesoblastic struc-
tures in the neighborhood of the spinal cord (sc) and notochord
(nt) will be described in connection with the next figure, where
they are more clearly defined. The cesophagus (oe)—or posterior
end of the pharynx, whichever it may be called—is here a crescentic
slit, with its convex side upward; ventrally it opens by a narrow
glottis into the trachea (ta). The trachea is surrounded by the
same condensed area of mesoblast (/a) that was mentioned in con-
nection with the preceding figure, but the condensation is here more
marked. From the bulbus (b) an aortic arch (ar) extends up-
ward for a short distance on the right side, while to the left of the
cesophagus an aortic arch (ar) is cut through the upper part of its
course. Ventral to the bulbus the ventricle (vm) and two auricles
(au) are seen surrounded by the pericardial wall.

Figure 20h is in the region of the liver (/7), which has about the
same position in relation to the auricles (aw) that was occupied by
the ventricle in the last figure. The auricles are connected with
each other by a wide passage. The trachea (ta) and the cesophagus
(oe) are entirely distinct from each other; the former is a small,
nearly circular hole, while the lumen of the latter is obliterated and
its walls form a solid, bow-shaped mass of cells. Since there is a
narrow space between this mass of cells and the surrounding meso-
blast, it might be thought that the lumen of the cesophagus had been
closed by the simple shrinkage of its walls; higher magnification,
however, fails to show any sign of a collapsed lumen. It is doubtless
the problematic and temporary closure of the cesophagus that is
noticed in other forms. On each side of the cesophagus, in close
relation with the anterior cardinal vein (ac), is noticed a nerve
(cn) cut through a ganglionic enlargement. When traced forward
these nerves are seen to arise from the region of the medulla, and
when followed caudad they are found to be distributed chiefly to the
tissues surrounding the newly formed bronchi; they are doubtless
the tenth cranial nerves. On the right side of the figure the close

56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

.
connection of this nerve with the near-by gill cleft is seen. Above
the paired aorte (ao) the sympathetic nerves (sy) will be noticed.
The mesoblast surrounding the spinal cord (sc) and notochord
(nt) is distinctly condensed (more so than the figure shows) to
form what may be called the centrum (c) and neural arch (na) of
the vertebrae. The arch, owing to the slight obliquity of the section,
shows here only on one side. The spinal cord is not yet completely
enclosed by the neural arches. The muscle plates (mp) are in close
connection with the rudiments of the vertebre just mentioned. The
spinal cord (sc) is here differentiated into three areas—a dense,
deeply stained area immediately around the neurocoel; a less dense
area of cells surrounding the inner area and extending ventralward
as a rounded projection on each side; and an outer layer, with few
or no nuclei, surrounding the inner two layers except on the dorsal
side.

In figure 20: the size and complexity of the figure are due, it will
be easily understood, to the fact that the plane of the section passed
through the curve of the body, thus practically cutting the embryo in
two regions—an anterior, where the lungs (/u) and liver (/1) are
seen, and a posterior, where the Wolffian bodies (wt) are present.
The spinal cord and the surrounding structures have almost the
same characteristics at both ends of the figure, except that the
primitive spinal column is rather more distinct in the posterior end
of the section. The posterior cardinal veins (pc), Wolffian ducts
(wd), and Wolffian bodies (wt) are also prominent structures of
this end of the figure, the last being made up of a great number of
tubules. The extreme anterior ends of the Wolffian bodies are seen
in the other half of the section in the upper angles of the body
cavity, dorsal to the lung rudiments (/u). Filling most of the body
cavity (bc) and making up the greater part of the middle of the
figure are the liver (/1), now a very large organ; the stomach (1’),
also quite large; the pancreas (pan), a small body lying near the
stomach; and the lungs (Jw), which here consist of several thick-
walled tubes, surrounded by lobes of mesoblast. The other features
of the figure need no special mention.

Figure 207 is through the base of the posterior appendages (pa),
in which the cartilages are already being outlined by condensations
of mesoblast. The intestine (7) is cut in two regions—at a more
anterior point, where it is seen as a small, circular hole surrounded
by mesoblast and hung by a narrow mesentery, and through the
cloacal region, the larger and more ventral cavity, into which the
Wolffian ducts (zvd) open a short distance caudad to this section.
The blood-vessels present a rather curious appearance. A short

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 57

distance anterior to this point the aorta has divided into three, or it
might be said that it has given off,two, large branches. These two
branches, one on either side near the posterior cardinal vein, pass
toward the ventral side of the embryo on each side of the cloaca and
end at about the region represented by the present figure. The
small portion of the aorta that remains after the giving off of the
two branches just described continues, as the caudal artery (ca),
into the tail; it is a small vessel just under the notochord, and gives
off small, paired branches at regular intervals toward the vertebral
region. ‘The posterior cardinal veins (fc), posterior to the open-
ings of the Wolffian ducts into the cloaca, unite to form a large
caudal vein lying just ventral to the caudal artery.

STAGE ¥VIII
FIGURE 21 (PLATE XXII)

This embryo, as may be seen, for example, by the form of the
appendages, is slightly further developed than the one represented
in figure 20. The figure is from a photograph of a living embryo as
it lay in the egg, a portion of the shell and shell membranes having
been removed. The embryo, which lies on its left side, is rather
faintly outlined because of the overlying allantois. The allantois
has been increasing rapidly in size, and is here so large that it ex-
tends beneath the cut edges of the shell at all points except in the
region in front of the head of the embryo, where its border may be
seen. Its blood-vessels, especially the one that crosses the head just
back of the eye, are clearly shown in the figure, and in the living
specimen, when filled with the bright red blood, they form a most
beautiful demonstration. As in the chick, the allantois lies close
beneath the shell membranes and is easily torn in removing them.

STAGE SOLS
FIGURE 22 (PLATE XXII)

Figure 22 is a photograph of a somewhat older embryo, removed
from the egg and freed of the foetal membranes. The appendages
show the position of both elbow and knee joints, and in the paddle-
shaped manus and pes the digits may be faintly seen. The tail is
very long and is spirally coiled, the outer spiral being in contact
with the frontal region of the head. The jaws are completely
formed, the upper projecting far beyond the lower. ‘The elliptical
outline of the eyes is noticeable, but the lids are still too little devel-
oped to be seen in this figure. The surface of the embryo is still
smooth and white.

58 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

STAGE XX
FicurEs 23-23b (PLaTe XXII)

In this surface view (fig. 23) several changes are seen, though no
very great advance in development has taken place. The outlines
of the digits (five in the manus and four in the pes) ‘are now well
defined; they even project slightly beyond the general outline of the
paddle-shaped part. The tail has begun to straighten out, and it
now extends across the front of the face. The lower jaw has in-
creased in length, but is still shorter than the upper. The eyelids,
especially the upper, are beginning to be discernible in surface view.
Though still without pigment, the surface of the body is beginning
to show by faint transverse lines the development of scales; these
lines are most evident in this figure in the middle region of the tail,
just before it crosses the nose.

A sagittal section of the entire embryo (except the tail) of this
age is shown in figure 23a. In the head region the section is nearly
median, while the posterior part of the body is cut slightly to one
side of the middle line. At the tip of the now well-developed snout
is seen one of the nostrils (an), cut through the edge; its connection
with the complicated nasal chamber (17) is not here seen, nor is the
connection of the nasal chamber with the posterior nares (pn). The
pharynx (ph) is anteriorly connected with the exterior through the
mouth (mm) and the nares, while posteriorly it opens into the cesoph-
agus (oe); the trachea (ta), though distinct from the cesophagus,
does not yet open into the pharynx. In the lower jaw two masses
of cartilage are seen, one near the symphysis (mk) and one near the
wall of the trachea, doubtless the rudiment of the hyoid. The deep
groove back of the Meckel’s cartilage (mk) marks the tip of the
developing tongue, which here forms the thick mass on the floor of
the mouth cavity. Dorsal to the pharynx a mass of cartilage (se)
is developing in the sphen-ethmoid region. This being a median
section, the ventricles of the fore- (fb), mid- (mb), and hindbrain
(hb) are seen as large cavities, while the cerebral hemispheres (ch)
appear nearly solid, only a small portion of a lateral ventricle show-
ing. The pineal gland (ep) is cut a little to one side of the middle
and so does not show its connection with the brain. At the base of
the brain the infundibulum (im) is seen as an elongated cavity whose
ventral wall is in close contact with a group of small, darkly staining
alveoli (pf), the pituitary body. Extending posteriorly from the
pituitary body is a gradually thickening mass of cartilage (bp),
which surrounds the anterior end of the notochord (nt) and may be
called the basilar plate. In its anterior region, where the section is

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 59

nearly median, the spinal column shows its canal, with the enclosed
spinal cord, while toward the posterior end of the figure the vertebre
are cut to one side of the middle line, and hence show the neural
arches (na) with the alternating spinal ganglia (sg). Near the
posterior end of the figure the pelvic girdle (fl) is seen. The
largest organ of the embryo, as seen in this section, is the heart, of
which the ventricle (vu) seems to be closely surrounded, both in
front and behind, by the auricles (aw). The liver (Jc) is the large,
reticular mass back of the heart. Dorsal and anterior to the liver
is the lung (/w), now of considerable size and development. The
enteron is cut in several places (oe, 7) and its walls are beginning
to show some differentiation, though this cannot be seen under the
magnification here used. One of the Wolffian bodies is seen as a
huge mass of tubules (wt) extending from the pelvic region, where
the mass is greatest, to the region of the lungs. The Wolffian
tubules stain darkly and the whole structure forms a very striking
feature of the section. Dorsal to the posterior end of the Wolffian
body is a small, oval mass of very fine tubules (k), which do not
stain so darkly as do the Wolffian tubules; this mass is apparently
the beginning of the permanent kidney, the metanephros. Its
tubules, though their origin has not been determined, seem to be
entirely distinct from the tubules of the Wolffian body.

A single vertical section through the anterior part of the head of
an embryo of this age has been represented in figure 23b. On the
right side the plane of the section cut through the lens of the eye
(In); on the left side the section was anterior to the lens. The
upper (ul) and lower (/l) eyelids are more evident here than in the
surface view. Owing to the hardness of the lens, its supporting
structures were torn away in sectioning. The vitreous humor is not
represented in the figure. The superior (wr) and inferior (Ir) recti
muscles are well shown on the right side; they are attached to the
median part of a Y-shaped mass of cartilage (se), which may be
termed the sphenethmoidal cartilage. Between the branches of this
Y-shaped cartilage the anterior ends of the cerebral hemispheres
(ch)—better called, perhaps, the olfactory lobes—are seen. Be-
tween the lower end of the sphenethmoidal cartilage and a dorsally
evaginated part of the pharynx are two small openings (pm) ; when
traced forward these tubes are found to open into the convoluted
nasal chamber, while a short distance posterior to the plane of this
figure they unite with each other and open almost immediately into
the pharynx. The rather complicated structures of the nasal pas-
sages of the alligator have been described by the writer in another
paper (12). In the lower jaw the cartilage (mk) is seen on either

60 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

side and several bands of muscle are developing in the mesoblast.
Two deep grooves give form to what may be called the rudimentary
tongue (tn). In both jaws one or two tooth rudiments (fo) may
be distinguished as small invaginations of ectoderm.

STAGE XXI
FicurE 24 (PLATE XXII)

In this stage the curvature of the body and tail is less marked
than was seen in the last surface view. The body has increased
greatly in size, so that the size of the head is relatively not so great.
The size of the eye in relation to that of the head is much diminished
also. The five anterior and four posterior digits are well formed,
and their claws are of considerable size, though of course not present
on all the digits. The outlines of scales may be traced from the
tip of the tail to the skull; they are especially prominent along the
dorsal profile. The skin is just beginning to show traces of pig-
ment, which is, however, not shown in the photograph. The umbil-
ical stalk is seen projecting with a loop of the intestine from the ab-
dominal wall; this is shown more clearly in the next stage. The
embryo now begins to exhibit some of the external characteristics
of the adult alligator.

STrAce DOXIT
Ficure 25 (Piate XXIII)

This embryo needs no particular description. It has reached in
its external appearance practically the adult condition, although
there is still considerable yolk (not shown in the figure) to be ab-
sorbed, and the embryo would not have hatched for many days.
Pigmentation, begun in the last stage, is now complete. The umbil-
ical stalk is clearly seen projecting from a large opening in the body
wall. The long loop of the intestine that extends down into the
yolk sac is here evident, and it is hard to understand how it can all
be drawn up into the body cavity when the umbilical stalk is with-
drawn. No sharp shell-tooth at the tip of the snout, such as is
described by Voeltzkow (18) in the crocodile, is here seen.

STAGE XXIII
FicurE 26 (PLaté XXIII)

This figure shows the relative sizes of the just-hatched alligator
and the egg from which it came. It also shows the position of the
young alligator in the egg, half of the shell having been removed for

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 61

that purpose. The blotchy appearance of the unopened egg is due
chiefly to stains produced by the decayed vegetation of the nest. At
hatching the young alligator is about 20 cm. long, nearly three times
the length of the egg; but the tail is so compressed that, though it
makes up abottt half of the length of the animal, it takes up very
little room in the egg.

SUMMARY :

Owing to the fact that the embryo may undergo considerable
development before the egg is laid, and also to the unusual difficulty
of removing the very young embryos, the earlier stages of develop-
ment are very difficult to obtain.

The mesoderm seems to be derived chiefly by proliferation from
the entoderm, in which way all of that anterior to the blastopore
arises. Posterior to the blastopore the mesoderm is proliferated
from the lower side of the ectoderm in the usual way. No distinc-
tion can be made between the mesoderm derived from the ectoderm
and that derived from the entoderm.

The ectoderm shows during the earlier stages a very great in-
crease in thickness along the median longitudinal axis of the embryo.

The notochord is apparently of entodermal origin, though in the
posterior regions, where the germ layers are continuous with each
other, it is difficult to decide with certainty.

The medullary folds have a curious origin, difficult to explain
without the use of figures. They are continuous posteriorly with
the primitive streak, so that it is impossible to tell where the medul-
lary groove ends and the primitive groove begins, unless the dorsal
opening of the blastopore be taken as the dividing point.

The amnion develops rapidly, and entirely from the anterior end.

The blastopore or neurenteric canal is a very distinct feature of
all the earlier stages up to about the time of closure of the medullary
canal.

Preceding the ordinary cranial flexure there is a sort of temporary
bending of the head region, due apparently to the formation of the
head-fold.

During the earlier stages of development the anterior end of the
embryo is pushed under the surface of the blastoderm, and is hence
not seen from above.

Body torsion is not so definite in direction as in the chick, some
embryos lying on the right side, others on the left.

Of the gill clefts, three clearly open to the exterior and probably
a fourth also. A probable fifth cleft was seen in sections and in one
surface view.

62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The first trace of the urinary system is seen as a dorsally project-
ing, solid ridge of mesoblast in the middle region of the embryo,
which ridge soon becomes hollowed out to form the Wolffian duct.

The origin of the pituitary and pineal bodies is clearly seen; the
latter projects backward.

No connection can be seen between the first rudiments of the sym-
pathetic nerves and the central nervous system.

The lumen of the cesophagus is for a time obliterated as in other
forms.

The choroid fissure is a very transitory but well-marked feature
of the eye.

REFERENCES

1. ANDERSON, A.: An Account of the Eggs and Young of the Gavial (G. gan-
geticus). Proc. Zodl. Soc., 1875.

. Batrour, F. M.: The Early Development of the Lacertilia. Quar. Jour.
Mic. Soc., 1879, vol. xIx, pp. 421-430.

3. Batrour, F. M.: Comparative Embryology, vol. 11.

. Bronn, H. G.: Klassen des Thier-Reichs (vols. on reptiles).

5. CLARKE, S. F.: The Habits and Embryology of the American Alligator.
Jour. Morph., vol. v, pp. 182-214.

6. Denpy, ArtHuR: Outlines of the Development of Tuatara (Sphenodon
punctatus). Quar. Jour. Mic. Soc., vol. xxxxt1r, 1899, pp. 1-87.

7. Ersier, P.: Zur Kentniss der Histologie des Alligatormagens. Archiv. f.
Mik. Anat., vol. xxxIv, pp. I-10, 1889.

8. Horrmann, C. K.: Beitrage zur Entwicklungsgeschichte der Reptilien.
Zeit. f. wiss. Zodl., vol. xxxx, 1884, pp. 214-246.

9. HorrMann, C. K.: Weitere Untersuchungen zur Entwicklungsgeschichte
der Reptilien. Morph. Jahrb., vol. x1, 1886, pp. 176-2109.

10. Parker, W. K.: On the Structure and Development of the Skull in the
Crocodile. London, 1883. Zoél. Soc. London, 1883, vol. x1, pp. 263-310.

11. RatHKe, H.: Untersuchungen iiber die Entwicklung und den Kérperbau
der Krokodile. Braunschweig, 1866.

12. Reese, A. M.: The Nasal Passages of the Florida Alligator. Proc. Phila.
Acad. Nat. Sc., 1901.

13. ReEsE, A. M.: The Breedings Habits of the Florida Alligator. Smithson-
ian Misc. Coll. (Quarterly Issue), vol. xiv, pp. 381-387, 1907.

14. Rorse, C.: Uber die Zahnleiste und die Eischweile der Sauropsiden. Anat.
Anz., 1892, vol. vir, pp. 248-264.

15. STRAHL, H.: Beitrage zur Entwicklung von Lacerta agilis. Archiv. f.
Anat. u. Physiol., 1882, pp. 242-278.

16. STRAHL, H.: Beitrage zur Entwicklung der Reptilien. Jbid., 1883, pp. 1-43.

17. Strant, H.: Uber friithe Entwicklungsstadien von Lacerta agilis. Zool.
Anz., vol. v1, 1883, pp. 347-350.

18. VorLtzKow, ALFRED: Biologie und Entwicklung der ausseren Kérperform
von Crocodilus madagascariensis Grand. Abhandl. Senckenberg. Naturf.
Gesell., vol. xxv1, pt. 1, pp. 1-149, 1880.

19. WIEDERSHEIM, R.: Comparative Anatomy.

bo

aS

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 63

LETTERING FOR ALL FIGURES

a, head-fold of amnion,
aa, anterior appendage.
ac, anterior cardinal vein.

al, allantois. ,
an, anterior nares.
ao, aorta.

aop, area opaca.

ap, area pellucida.

ar, aortic arch.

au, auricle. ,

.b, bulbus arteriosus.

bc, body cavity.

blip. blastopore.

bp, basilar plate.

bv, blood vessel.

c, centrum of vertebra.

ca, caudal artery.

ch, cerebral hemisphere.

cl, cloaca.

cn, cranial nerve.

cp, posterior choroid plexus.

cv, cardinal veins.

dc, ductus Cuvieri.

e, eye.

ec, ectoderm.

ec’, thickening of ectoderm.

en, entoderm.

en’, endocardium.

ent, enteron.

ep, epidermal layer of ectoderm.

epi, pineal body.

es, embryonic shield.

f, fronto-nasal process.

fb, forebrain.

g, foregut.

gts, gill clefts.

gft-6, gill folds.

gl, glomerulus.

Ah, head-fold.

hb, hindbrain.

ht, heart.

1, intestine.

1’, stomach.

tn, infundibulum.

ir, iris.

it, iter.

k, kidney (metanephros).

1, remains of groove between second-
ary folds.

Ja, larynx (cartilages of).

li, liver.

ll, lower lid of eye.

ln, lens.

lr, inferior rectus muscle of eye.
lu, lungs.

luv, lens vesicle.

m, mouth.

ma, manus.

mb, midbrain.

mc, medullary canal.

me’, tip end of medullary canal.
md, mandibular fold.

mes, mesoderm.

mes’, myocardium.

mf, medullary fold.

mg, medullary groove.

mk, Meckel’s cartilage.

mp, muscle plate.

ms, mesentery.

mv, meatus venosus.

mx, maxillary fold.

myc, myocoel.

n, nasal invagination or cavity.
na, neural arch of vertebra.
nc, neurenteric canal.

nl, nervous layer of ectoderm.
nt, notochord.

o, ear vesicle.

oc, optic cup.

oe, cesophagus.

on, optic nerve.

os, optic stalk.

ov, optic vesicle.

p, pituitary body.

pa, posterior appendage.
pan, pancreas.

pc, posterior cardinal vein.
pe, pes.

pg, primitive groove.

ph, pharynx.

pl, pelvis.

pn, posterior nares.

pr, pericardial cavity.

ps, primitive streak.

pt, pecten.

rt, retina.

s, somites.

sc, spinal cord.

se, sphenethmoid cartilage.
sf, secondary fold.

64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

sg, spinal ganglion. u, umbilical stalk.

sm, splanchnic mesoblast. ul, upper lid of eye.

sn, spinal nerve. ur, superior rectus muscle of eye.
so, somatic mesoblast. v’-"-""" first, second, and third cere-
st, stomodzum. bral vesicles.

sy, sympathetic nervous system. va, vascular area.

t tail. vm, vitelline membrane.

ta, trachea. vn, ventricle of heart.

tg, thyroid gland. vv, vitelline blood-vessels.

th, thickening and posterior limit of sf. wd, Wolffian duct.

tn, tongue. wdo, opening of Wolfhan duct.
to, tooth anlage. wr, Wolffian ridge. .

tr, truncus arteriosus. wt, Wolffian tubules.

tv, third ventricle of brain. y, yolk.

tv’, third ventricle of brain.

EXPLANATION OF FIGURES 1-26 ON PLATES I-XXIII

All of the figures, with the exception of the photographs and those copied
by permission from S. F. Clarke, were drawn under a camera lucida.

The magnification of each figure, except those from Clarke, is indicated
below.

The photographs were made by the author, and were enlarged for repro-
duction by the photographic department of the Smithsonian Institution. The
other surface views were made, under the author’s direction, by Miss C. M.
Reese.

With the exception of Stage III, all of the figures of any one stage are
given the same number, followed where necessary by a distinguishing letter,
so that it is possible to tell at a glance which section and surface views belong
together. The transverse sections are all cut in series from anterior to
posterior.

FicurE 1. Surface view of egg. X 2/3.
1a. Egg with part of the shell removed to show the chalky band in
the shell membrane. X 2/3.
FicurEs 2 and 2a. Dorsal and ventral views respectively of the blastoderm be-
fore the formation of the notochord, medullary folds, etc. After
Clarke.
2b-2f. Transverse sections of an embryo of the age represented in
figures 2 and 2a. X 43.
3 and 3a. Ventral and dorsal views respectively of an embryo a few
days older than that represented in figures 2 and 2a. After
Clarke.
3b-3m. Transverse sections of an embryo of the age shown in figures
3 and 3a. X 43.
FicurEs 3n and 30. Two sagittal section of an embryo of the same stage as
figures 3 and 3a. X 43.
4and 4a. Dorsal and ventral views respectively of a slightly older
embryo than the one shown in figures 3 and 3a. Figure 4a
shows only the head region. After Clarke.
5and 5a. Dorsal and ventral views respectively of an embryo of

FIGURE

FIGURES
FIGURES

FIGURES

FIGURES

FIGURE

FIGURES

FIGURE

FIGURES
FIGURE

FIGURES

FIGURE

FIGURES

FIcurE

DEVELOPMENT OF THE AMERICAN ALLIGATOR—REESE 65

almost the same age as the preceding, to show the further de-
velopment of the medullary folds. After Clarke.

6. Dorsal view of an embrye only a day or two older than the pre-
ceding. After Clarke.

6a-Hi. A series of transverse sections of this stage. X 43.

7a-7l A series of transverse sections of an embryo slightly older
than the one shown in figures 4-6. 43. (No surface view of
this stage is figured.)

8 and 8a. Dorsal and ventral views respectively of an embryo with
five pairs of mesoblastic somites. X 20. (Drawn by trans-
mitted light.)

8b and 8c. Two sagittal sections of an embryo of this stage. X 43.

8d-8;. A series of transverse sections of the embryo represented in
figures 8 and 8a. X 43.

ga-gm. A series of transverse sections of an embryo somewhat more
advanced in development than the one represented in the last
Sehicswman~ 43: °

toand toa. Dorsal and ventral views respectively of an embryo with
eight pairs of mesoblastic somites. X 20. (Drawn chiefly by
transmitted light.)

11. Dorsal view of an embryo with fourteen pairs of mesoblastic
somites. The area pellucida and the developing vascular area
are shown, the latter having a mottled appearance. The pushing
of the head under the blastoderm is also shown. X 20. (Drawn
chiefly by transmitted light.)

t1a-1tk. A series of transverse sections of an embryo of this stage.
X 43.

12. Dorsal view of an embryo with about seventeen pairs of meso-
blastic somites. Part of the area pellucida is represented.
(Both transmitted and reflected light were used in making the
drawing.) X 13.

12a-12g. A series of transverse sections of an embryo of this stage.
EAS:

13. Surface view of an embryo with about twenty pairs of meso-
blastic somites. % (about) 15. (Drawn with both reflected
and transmitted light.)

13-13f. A series of transverse sections of an embryo slightly more
developed than the one shown in figure 13. X 20.

13g. A sagittal section of an embryo of about the age of the one
represented in figure 13. X 20.

14. Head of an embryo with one pair of gill clefts; ventro-lateral
view. X 13.

15. Profile view of the head of an embryo with three pairs of gill
clefts. X 13.

15a-15e. A series of transverse sections of an embryo of about the
age of the one represented in figure 15. X 20.

15f. A horizontal section through the anterior region of an embryo of
the age of that shown in figure 15. X 20.

16. Surface view in profile of an embryo with four pairs of gill clefts.
X (about) 12.

5 Ar

66
FIGURES

FIGURE

FIGURES

FIGURE

FIGURE
FIGURES

Ficure

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

16a-16f. A series of transverse sections of an embryo of the approxi-
mate age of the one represented in figure 16. X 20.

16g. A sagittal section of an embryo of the age (possibly slightly
younger) of the one represented in figure 16. X 20.

17. Surface view in profile of an embryo at the time of origin of the
limbs. X (about) 5.

17a-17g. A series of transverse sections of an embryo Of the age of
the one represented in figure 17. X 7. .

18. Surface view in profile of the head of an embryo slightly larger
than, though of about the same state of development as, the one
represented in figure 17. Reproduced here chiefly to show the
gill clefts. X (about) 3.

19. Surface view of an embryo somewhat more developed than the
one just described. XX (about) 3.

20. Surface view of-an embryo older than the one represented in
figure 19; with well-developed manus and pes. X (about) 5.

20a—207. A series of transverse sections of an embryo of the age of
the one represented in figure 20. X 7.

2t. A photograph of a living embryo in the egg, showing the allan-
tois, yolk mass, etc. ‘The embryo is somewhat more developed
than the one shown in figure 20. X 2/3.

22. A photograph of a still larger embryo, removed from the shell
and freed from the fetal membranes. X (about) 1.

23. A photograph of a still more advanced embryo, in which. the
digits are quite evident and the scales are beginning to show.
X (about) I.

23a. A sagittal section of an embryo of the age of the one represented
in figure 23; the tail has not been shown in this figure.
(about) 3.

23b. A vertical section through the head of an embryo of about the
size (perhaps slightly smaller) of the one shown in figure 23.
X (about) 3.

24. A photograph of an older embryo in which the pigmentation of
the scales is evident, though not shown in the figure.
(about) T.

25. A photograph of an embryo in which the pigmentation and the
development of the body form are practically complete. The
allantois, unabsorbed yolk, ete., have been removed. XX
(about) 34.

26. A photograph of a just-hatched alligator, of an alligator egg,
and of a young alligator in the egg just before hatching. X
(about) 3/7.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. |

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DEVELOPMENT OF THE AMERICAN ALLIGATOR

1, za.—The Egg 2, 2a.— Stage I

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51

REESE, PL. Il

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DEVELOPMENT OF THE AMERICAN ALLIGATOR

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. Ill

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL, 51 REESE, PL. IV
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DEVELOPMENT OF THE AMERICAN ALLIGATOR

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51

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DEVELOPMENT OF THE AMERICAN ALLIGATOR

6-61.—Stage III. 7a.—Stage IV

REESE, PL. vi

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE Pl. VII

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. X

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. XVIII

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. XIX

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. XX

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. XXII

DEVELOPMENT OF THE AMERICAN ALLIGATOR

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SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REESE, PL. XXIII

7

DEVELOPMENT OF THE AMERICAN ALLIGATOR

25.—Stage XXII Alligatorembryo. 26.—Stage XXIII Alligator just hatched
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SMITHSONIAN MISCELLANEOUS COLLECTIONS

PART OF VOLUME LI

THE TAXONOMY OF THE MUSCOIDEAN
FLIES, INCLUDING DESCRIPTIONS
OF NEW GENERA AND
SPEGIES

ley

CHARLES H. T. TOWNSEND, B. Sc.

In Charge of Collections of Muscoidean Flies, U. S. National Museum

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1908

udd Hetweiler
7

Woshington
p Cc”

THE TAXONOMY OF FHE MUSCOIDEAN FLIES, IN-
CLUDING DESCRIPTIONS OF NEW
GHNERA AND SPECIES

By CHARLES, EC I. TOWNSEND, By Se.

History

When we review the history of the classification of any highly
specialized group of insects, provided it has attained a considerable
degree of popularity among systematists, we find it to exhibit a
well-marked series of oscillations between the two extremes com-
monly known as bunching and splitting. This is especially true of
the dipterous superfamily Muscoidea.*

The systematists of the eighteenth and nineteenth centuries, ac-
cording to the work they did on this superfamily, mark alternate
periods of action and reaction which fall. conveniently into five his-
torical epochs.

Linné, Fabricius, and Latreille must be considered the pioneers.
The system they established was followed by their immediate con-
temporaries. Very few others concern us here, but Geoffroy erected
the genus Stomoxys, and Scopoli, Rossi, and Panzer did some work
on the superfamily. As a natural result of approaching a quite new
subject, these early workers did not always grasp the real value of
characters. Largely because of the comparative dearth of material
in those initial days of systematic work, they did not clearly discern
anatomical values, and hence did not recognize many characters
whose worth has since been well established.

Meigen introduced a new epoch in 1804, and considerably in-
creased the number of genera by splitting up the original ones estab-
lished by his predecessors. Collections had become richer in mate-

‘It is to be noted that the superfamily Muscoidea, as herein restricted, in-
cludes but a portion of the forms to which the name was applied by its author,
Mr. D. W. Coquillett. As now restricted, it includes practically the old
calyptrate Muscide minus the Anthomyiide, or the same group as that treated
by Brauer and von Bergenstamm—Muscaria Schizometopa, exclusive Antho-
myiide. The Muscoidea is here divided into five families, as follows: (1)
Qistride, (2) Macronychiide (being a part of the old Dexiide), (3) Tachinide
(including the old Gymnosomatide, Phantide, Ocypteride, Sarcophagid, and
most of Dexiide as subfamilies), (4) Muscide, and (5) Phasiide (including
Rutilia and its allies).

2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

rial by this time, and Meigen’s attention was naturally drawn to the
discovery of further characters that could be used in classification.
He was indorsed and followed by his contemporaries, Olivier, Fallen,
Say, Wiedemann, who adopted his genera without proposing new
ones, except that the last-named author erected the single genus
Glossina for the tse-tse flies. Duméril erected the genus "Echinomyia,
and Le Peletier de Saint-Fargeau the single genus Prosena. Mei-
gen’s best work was in genera. His descriptions of species were in
many cases faulty. On the whole, however, he is clearly to be looked
upon as an epoch-maker.

The first really intuitive student of the superfamily was Robineau-
Desvoidy who, in 1830, introduced the third epoch and very greatly
increased the number of genera, besides defining more or less natural
taxonomic divisions for their reception. It must be understood that
very considerable accumulations of material from the Americas, both
North and South, had reached Europe during the early part of the
nineteenth century, besides much material from the African, Ori-
ental, and Australasian regions. ‘To most of this Robineau-Desvoidy
had access. Notable among the accumulations were the rich collec-
tion of the Count Dejean, which had been added to constantly by
Latreille, and the quite extensive material secured from all parts by
the Museum of the Jardin du Roi in Paris. Palisot de Beauvois,
Saint-Hilaire, Bosc, and many others collected in the Americas, and
various representatives of the Jardin du Roi in other parts of the
world. Besides these, many European entomologists sprang up who
began to do much more thorough collecting at home. Thus a com-
paratively great wealth of material in the Muscoidea was brought
together from all parts of the world, both at home and abroad, which
stimulated Robineau-Desvoidy to a detailed study of characters in
this superfamily. His “Essai sur les Myodaires” remains to this
day a monument to his very considerable grasp of Muscoidean rela-
tionships. His posthumous work (1863) can not be considered as
affecting in any way the status of the “Essai.”

Macquart, almost contemporaneous with Robineau-Desvoidy, but
possessed of less discernment, bunched the latter’s genera to a very
considerable extent. However, it must be pointed out in defense of
Macquart that he was eminently a general dipterist, while Robineau-
Desvoidy was preéminently a specialist in the Myodaria.

Zetterstedt erected only two genera in the superfamily, and prac-
tically employed Meigen’s genera for all of his work. Perty, Bouché,
Guérin, and Bremi each erected a single genus in the superfamily.

Robineau-Desvoidy’s system, founded largely on habits, was in a
degree faulty and insecure. Attention should be called to the fact,

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 3

apparently long since lost sight of, that Robineau-Desvoidy origi-
nated the idea of including the Céstride with his Calypterata (al-
though renounced in his posthumous work), and the Conopidz with
the Myodaria (Conopide not included at all in posthumous work).
The founding of the now obsolete division Calypterata is also to be
accredited to him, though it is to be noted that he did not include the
Anthomyiide therewith. The latter family was included in that
division by subsequent authors. In this connection, see Osten-
Sacken for statement that the term “Acalypterata” was interpolated
in Robineau-Desvoidy’s posthumous work by the editors (Berl. Ent.
Zeit., 1896, pp. 329, 335-6). ;

Rondani marked a fourth epoch beginning about 1850. He re-
vised in large part the work of Robineau-Desvoidy, still further in-
creased the number of genera, was altogether a very close student of
relationships, and possessed a remarkably clear insight into the affin-
ities of the Muscoidea, in which he was essentially a specialist. His
system was followed to some extent by his more immediate contem-
poraries, but Schiner, with a fine grasp of dipterous characters in
general and little conception of the needs of the Muscoidea, was espe-
cially active in bunching his genera.

Schiner was a splendid general dipterist, but the method of treat-
ment adapted to other groups of Diptera fails when the attempt is
made to apply it to the Muscoidea. That is where Schiner, Mac-
quart, and all the other conservatists fell. And it is to be noted that
these conservatists were always general dipterists. They tried to
apply the same system throughout the Diptera, but the Muscoidea
need a distinct method of treatment, as will appear further on in this
paper under that heading. Even such conscientious students as
van der Wulp, Loew, Osten-Sacken, Williston, and others, who fol-
lowed Schiner largely, but were somewhat less conservative than he,
nevertheless fell far short of reaching a requisite degree of radical-
ism in their views as to a proper treatment of this superfamily.

Others who entered the ranks during this fourth epoch, Walker,
Bigot, Bellardi, Jaennicke, Thomson, Meade, von Roeder, Kowarz,
Mik, followed Schiner more or less, adopting Réndani and Rob-
ineau-Desvoidy at times on certain points, and gradually increased
the stock of genera as seemed warranted along more or less con-
servative lines.

Robineau-Desvoidy had divided the Muscoidea into many smaller
groups which he called stirpes, corresponding more or less in value
to our present subfamilies. These were not recognized by Rondani,
who grouped all into six stirpes. Neither Robineau-Desvoidy nor
Réndani were really adopted by Schiner, who recognized eight

4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

stirpes, mainly founded, however, on certain of Robineau-Desvoidy’s.
Schiner thus largely adopted Robineau-Desvoidy’s stirpes in those
divisions which he did recognize, but bunched his genera along with
those of Rondani, Robineau-Desvoidy’s reviser. The eight taxo-
nomic divisions adopted by Schiner generally obtained throughout
the epoch.

Rondani’s system, unlike Robineau-Desvoidy’s, took little note of
habits, and, while less detailed, was more secure from being founded
primarily on external anatomical characters. But these characters
were liable to misinterpretation in certain cases.

Brauer and von Bergenstamm inaugurated the present and fifth
epoch in 1889, which is destined to hold out for a greater degree of
radicalism than its predecessors. They approached the subject
largely in a new way, greatly lessening the difficulties of classifica-
tion in the superfamily by recognizing a large number of sections
which correspond to the subfamilies and tribes of the present paper.
At the same time, they greatly multiplied the number of genera,
whereby they were able to present comparatively concise diagnoses
of these, as well as of their sections.

They adopted Robineau-Desvoidy’s plan of grouping the forms
into many small divisions, but they did not feel bound, as did he, to
adhere to any definite scheme of life habits for indicating taxonomic
limitations. In the main their divisions were made on quite original
lines. However, many of Robineau-Desvoidy’s old stirpes are still
recognizable, now more or less revised, restricted or enlarged, and
they must be considered as the original foundation of our present
subfamilies and tribes. Brauer and von Bergenstamm’s characters
were better chosen and represent a more exhaustive study of the
subject, as would naturally follow from their having enjoyed the
greatly superior advantages derived from marked increase in biologic
progress since the time of Robineau-Desvoidy and Rondani, and
access to the greatly enriched collections of material drawn from all
parts of the globe.

Until quite recently Brauer and von Bergenstamm’s system has
been followed rather indifferently—in some cases enlarged upon, in
some revised—by students of the group contemporaneous with them
and continuing in the work since their time. The general trend of
sentiment now, however, is strongly in their favor, recognizing, as
it does, the necessity of a subdivision of the superfamily into many
subfamilies, tribes, and genera, so as to allow of more careful and
concise diagnoses. While it is true that a middle course between
the two extremes of conservatism and radicalism is usually the best
one to follow, the present superfamily furnishes a notable exception

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 5

to the rule in that it can not be successfully treated on other lines
than what are to be considered as quite radical compared with the
treatment accorded to other superfamilies in the order.

In this historical review, Robineau-Desvoidy, Réndani, and
Brauer stand forth prominently as the greatest students of the Mus-
coidea that the world has produced. Each had a deeper insight into
the peculiar relationships and affinities of the superfamily and a
closer grasp of the subject as a comprehensive whole than any of his
predecessors or contemporaries.

The following is a tabular arrangement of the five epochs, with
the respective students who belong to each, including the approxi-
mate periods during which they were more or less active in work on
the superfamily. The asterisk indicates those authors who estab-
lished one or more genera. The plus sign indicates work continued
to the present time:

EPOCH I (prior to 1804).

Redi, 1671-1712 (general insects).

Réaumur, 1738-1740.

Scopoli, 1760-1763.

*Linné, 1761-1760.

Poda, 1761.

*Geoffroy, 1762 (one genus—Stomoxrys).

*Fabricius, J. C., 1775-1805.

De Geer, 1776.

Schranck, 1781-1803.

Herbst, 1789-1801 (general insects).

Rossi, 1790.

*Latreille, 1792-1805 (Trichopoda, Bucentes, Hypoderma, Ocyptera,
(Edemagena).

Panzer, 1793-1800.

Baumhauer, 1800.

Illiger, 1801-1807 (general insects).

EPOCH II (1804-1830).
*Meigen, 1804-1830.
Schoenher, 1806-1817 (general insects).
Gyllenhal, 1808-1829 (general insects).
Dufour, 1809-1833.
Olivier, 1811.
Germar, 1813-1821 (general insects).
Fallen, 1814-1825.
*Clark, 1815 (one genus—Cuterebra).
Lamarck, 1815-1822 (general invertebrates).
*Leach, 1817 (one genus—Gastrophilus).
Say, 1817-1832.
*Duméril, 1819 (one genus—Echinomyia).
*Wiedemann, 1821-1830 (one genus—Glossina).
*Le Peletier de Saint-Fargeau, 1825 (one genus—Prosena).

6

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOI,. 51

EPOCH III (1830-1850).

*Robineau-Desvoidy, 1830-1863.

*Perty, 1830-1834 (one genus—Diaugia).

Haliday, 1832.

*Macquart, 1834-1855.

*Bouché, 1835-1847 (one genus—Compsilura).

*Guérin, 1835-1850 (one genus—Formosia).

*Zetterstedt, 1838-1855 (Wahlbergia, Cinochira, Gymnopeza).
*Bremi, 1846 (one genus—Amsteinia).

EPOCH IV (1850-1889).

*Rondani, 1850-1865.

*Walker, 1850-1866 (Doleschalla, Schizotachina, Hamma.ia, Saralba,
Toroca, Zambesa).

*Egger, 1856 (Zelleria, Halidaya, Frauenfeldia, Microphthalma).

*Doleschall, 1856 (Spiroglossa, Megistogaster).

*Brauer, 1858-1880.

*Bigot, 1859-1893.

Bellardi, 1859-1862.

*Meinert, 1860-1880 (one genus—Philornis, larva).

*Loew, H., 1861-1872 (Stegosoma, Blesoxipha, Euthera, Himantostoma,
Phylloteles). .

*Schiner, 1862-1868.

*Jaennicke, 1867 (one genus—Archytas).

*van der Wulp, 1867-1903.

*Thomson, 1868 (Glaurocara, Tricharea).

*Osten-Sacken, 1877-1902 (one genus—Urode-ia).

*Pokorny, 1880-1896 (Parastauferia, Sarromyia, Steringomyia, Trigonos-
pila).

*Meade, 1881-1899.

*von Roeder, 1881-1806.

*Kowarz, 1882-1894 (Ctenocnemis, Mikia).

*Mik, 1882-1901 (Crossocosmia, Zygobothria, Microtachina, Microtricha).

*Williston, 1886 + (Melanophrys, Acroglossa, Talarocera, Dichocera,
Melanodexia).

EPOCH V (1889 +).

*Brauer, 1889-1890.

*von Bergenstamm, 1889-1894 (co-author with Heaney’
*Portschinsky, 1890-1902.

*Schnabl, 1890-1902.

*Giglio-Tos, 1891-1897.
*Wachtl, 1891-1895.

*Townsend, 1891 +

*Girschner, 1893-1901.

*Meunier, 1892 +

*Strobl, 1892 + in
Bezzi, 1892 +

*Pandellé, 1894 +

Becker, 1894-1901.

Snow, 1895.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND

N

Corti, 1895-1897.
*Austen, 1895 +
*Coquillett, 1895 +
*Hough, 1898 +

Kertész, 1899 +

Roberts6n, 1901 +
*Bischof, 1901 +
*Grimshaw, I90I +
*Hendel, 1901 +
*Hutton, 1901 +

Villeneuve, 1902 +

Wainwright, 1902 +
*Speiser, 1903 +
*Johnson, 1903 +

TREATMENT

Speaking of the Muscoidea, Dr. Williston has said: “Species,
genera, and even families, show such slight plastic or colorational
differences that only the most patient study will define their limits.
At the present time there is a decided tendency to base the classifica-
tion of even the higher groups upon apparently trivial characters.
Most naturalists have long since abandoned the idea that genera, or
even families, represent anything but the conveniences of classifica-
tion, and the recent writers on this family are probably right in seiz-
ing upon any characters that will satisfactorily group the vast num-
ber of species irrespective of their relative values. But it is very
probable that, in the proposal of so many genera in such rapid suc-
cession, many characters have been employed which future research
will show to be entirely inadequate. We yet know very little about
individual variations in this family, or the real value of many of the
characters now used. The absence or presence of a bristle may be
found to represent a group of species, but we should first learn how
constant the character is in species. * * * Seriously, is not the
stock of Tachinid genera sufficiently large for the present? Would
it not be advisable to study species more before making every trivial
character the basis of a new genus?’’—InseEc?T Lire, vol. v (1892-3),
pp. 238-40.

These words, from the leading authority on American dipterology,
written some fifteen years ago and shortly after the appearance of
the first two instalments of Brauer and von Bergenstamm’s work,
may advantageously be taken as a text for some pertinent consider-
ations at this time.

While the great multitude of forms in the Muscoidea seems at
first sight chaotic and formidable, the student soon perceives that
standing forth from the general mass there- occur certain well-

8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

marked generic types, such as Gistrus, Cuterebra, Dexia, Macrony-
chia, Phasia, Trichopoda, Meigenia, Masicera, Phorocera, Tachina,
Gonia, Belvosia, Plagia, Thryptocera, Phania, Gistrophasia, Milto-
gramma, Pyrrhosia, Ocyptera, Gymnosoma, Echinomyia, Hystricia,
Dejeania, Sarcophaga, Calliphora, Musca, Stomoxys, Glossina, and
at least a hundred others. These types correspond in value to the
more settled genera of the older superfamilies, where intermediate
forms are largely lacking. In the present superfamily, however, it
is quickly seen that massed in between these many typical forms
are numerous intermediate ones, which collectively vary in all direc-
tions and combine certain of the characters of the various types.
These intermediates are the bridges for the passage of genera, so to
speak—the inevitable precursors and resultants in the process of the
evolution of genera. The same holds good of species. Numerous
intergrades are found to group naturally around and between the
various species. That these intermediates and intergrades are pres-
ent is due to the fact that the Muscoidea are now—at the present
day, geologically speaking—in their period of greatest prolificacy, a
period characterized by a condition of multiform development.
After the lapse of a great space of time, many of these intermediate
forms will have dropped out of the struggle, leaving a residue more
or less well defined from each other and thus much more amenable
to taxonomic treatment. This is now the case with the older dip-
terous superfamilies, which have long since passed their period of
greatest prolificacy.

It should be explained that the term “intermediates” is used to
designate forms of generic rank or higher, and “‘intergrades” to
designate those which are only of specific rank. The further term
“intergradants’ may be employed to designate individuals which
connect species, but upon which it is not practicable to bestow names.

The Muscoidea are of very recent evolution—in fact, their evolu-
tion is still going on. Here are species, genera, and families in the
making. The whole superfamily is one enormous assemblage of
thousands upon thousands of forms distinguishable from each other
by only slight differences and exhibiting characters which intergrade
in all directions. That such a multitude of closely similar forms is
exceedingly difficult to classify goes without saying. These forms
can not be classified in the ordinary way, but demand special treat-
ment adapted to the conditions.

The key to the whole situation, when it comes to methods of tax-
onomic treatment in this superfamily, is that we have here the task
of defining not only the numerous well-marked types corresponding
to the existing forms in the older and less specialized dipterous

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 9

superfamilies, but also a great mass of the intermediates, intergrades,
and intergradants that have resulted during the long-continued
process of the evolution of these types.

Brauer and von Bergenstamm recognized these conditions in the
Muscoidea “and treated the superfamily accordingly. As _ being
highly apropos of this subject, the following remarks are quoted
from the translation of these authors’ Introduction (published in
Psyche, vol. v1, pp. 313-16, and 329-32), the whole of which can be
studied with much profit:

“It is a fundamental principle in the development of the whole
dipterous stock that, from the lowest (Orthorrhapha nematocera)
to the most differentiated or highest (Cyclorrhapha schizometopa),
the actual value of the genus, and of the systematic series generally,
becomes less and less. This proposition seems applicable to all
groups of animals—in all cases the most recent forms are more
closely related and more difficult to characterize .than older ones.

The cause lies in the numerous intermediate forms occur-
ring in a group of animals which has just reached its period of great-
est prolificness.”

As the same authors point out farther along in their Introduction,
it is absolutely futile to attempt a classification of these flies along
any other lines than a separation into many comparatively restricted
categories. The authors are also correct in maintaining that the
classification of all animals must be based on the entire develop-
ment—not on the adult alone. The characters of the imago are most
important for genera and species; those of the earlier stages are
most important for families and higher categories, even up through
orders and classes. In studying early stages, it may be pointed out
that some characters will occasionally serve for generic separation,
but much judgment must be exercised in deciding which characters
are of value for this purpose, since conspicuous ones may in some
cases possess less than generic value. Such are those of special
adaptation to peculiar conditions of life.

The fact should be recognized, as suggested in the opening text
to this chapter and emphasized in the quotation just given, that gen-
eric values are not necessarily uniform throughout the organic
world. It is fallacious to attempt to set a standard whereby plant
and animal genera, or animal genera alone, shall be gauged by a cer-
tain fixed measure of difference. This holds good even in different
superfamilies of the same order or suborder of insects. The de-
mands of the group in hand must be considered in each case. A
superfamily in the multiform stage of development, contingent upon
its being still in process of evolution, demands a less generic value

IO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

than an older and well established superfamily whose forms have
become fixed through a long period of conformity to their environ-
ment. If this be not conceded, it becomes impossible to treat the
younger superfamilies by any satisfactory system.

It will be alleged by some that such plan will result in multiply-
ing genera unduly. There is, however, no doubt that the course
adopted is warranted by the conditions. This conclusion has been
reached after full and mature deliberation. The only possibility of
successfully systematizing the superfamily, so that its myriads of
forms can be designated definitely by name, lies in the recognition of
genera founded upon comparatively slight characters—slight com-
pared with those recognized as the standard in the older and less
specialized superfamilies. The differences between genera are less
pronounced in the more specialized than in the less specialized
groups. All are genera, and of equal value systematically; but, as
already pointed out, they can not be measured by a standard gauge.

The writer has always contended that a proper treatment of the
Muscoidea demands the definition of smaller categories and more
carefully restricted genera (see Psyche, vol. V1, p. 313, Sept., 1892).
As the characters of the early stages are investigated, more light
will be thrown on higher divisions in the superfamily. Such a vast
assemblage of closely related forms is not amenable to separation, in
the adults, into divisions conceived on lines of mathematical pre-
cision. Any system of classification must become more or less arti-
ficial if it attempts, in the presence of intermediates and the absence
of a knowledge of early-stage characters, to mark off precise lines of
division between categories of higher value. When the interme-
diates are lacking, or largely lacking, it becomes a comparatively
easy matter to fix the lines of demarcation, and the system appears
extremely natural simply through the absence of the immense mass
of intermediate forms that at one time existed. But when these
numerous intermediates and intergrades are extensively present, any
attempt to apply an arbitrary system of classification to the group
can not but result in disaster. A system can be thoroughly natural
only in so far as it indicates natural types of families, subfamilies,
tribes, and genera, and groups the intermediates and intergrades
around them. Properly conceived and executed, such a system is
the only natural one, since it must accord with the facts as known.
At the same time the fact must not be lost sight of that taxonomy
is at best merely a means to an end, and does not exist in nature. It
is artificial in its original conception, because it is practically in-
tended to ignore numerous steps in the development of life—steps
that have been lost during the evolution of forms now existing, and

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 1

whieh, if still present, would make a taxonomic system simply
impossible. '

Taking these points into consideration, there is evidently but one
course open, Draw lines of demarcation between the best marked
types, and let the others, with their respective coteries of inter-
mediate forms, fall in whatever divisions a preponderance of their
characters in each case indicates. Definitions of characters for the
higher divisions can not be exact, because the forms themselves in
nature do not fall into well defined divisions.

Such a system as outlined would recognize typical forms as genera
and species, and would then intercalate necessary additional genera
and species for the convenient reception of the intermediate forms,
which group around the typical ones and connect them with each
other. The one great difficulty here will be to arrive at the true
relationships of the intermediate forms, for their affinities are often
so complex that it is very hard to decide with what genus or species
they are most closely related. The real truth will ultimately be
attained only after many years of continued research into their
ontogeny, combined with an exhaustive study of the geological his-
tory of the superfamily.

What have been called typical forms, both genera and species, it is
proposed to term fypic. The additional genera and species to be
intercalated between the typical ones it is proposed to term atypic.
We will thus have a system of typic genera and atypic genera for the
reception of typical genera and intermediates respectively, and typic
Species and atypic species for the accommodation of the typical spe-
cies and intergrades respectively. This scheme accords with the
facts, which do not conveniently admit of the employment of sub-
genera and subspecies. The latter concepts are here inapplicable
on account of the nature and intricate relationships of the forms.
To include subgenera, the genera would have to be too loosely char-
acterized. Furthermore, this scheme preserves the binomial nomen-
clature, which is highly desirable. It can be designated in each case
whether a genus is typic or atypic, if this is found desirable.

All the more primary divisions—those above the subfamilies, up
to the very subordinal divisions themselves—can at present be only
imperfectly characterized and defined. Here is where aid will be
derived from early stage characters, when these become known.
Even the Cyclorrhapha and the Orthorrhapha? can not be sharply

‘The writer is aware that Osten-Sacken claims there is a clearer line of
separation between the Nemocera and Brachycera than between the Orthor-
rhapha and Cyclorrhapha, but this is outside our subject.

I2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

differentiated from each other in the adults on account of inter-
mediate forms. Less and still less grows the clearness of limita-
tion as we descend through the series, sections, subsections and
superfamilies to the families. Limitations clear a little in the
families, but it is not until we get to the subfamilies and tribes that
we can, from a study of the adults, begin to draw moderately well
marked lines and set fairly concise limits. A moderate degree of
conciseness is possible here only because we are now concerned with
divisions sufficiently low in the taxonomic scale to allow the exclu-
sion of refractory and disturbing elements, and if necessary put
them alone by themselves. Many subfamilies and tribes are seen to
stand out as natural groups of genera.

At first sight it would appear advisable to ignore the higher divis-
ions, and drop at once to the very considerable number of subfatn-
ilies and tribes necessary to the system outlined. But it evidently
serves a better purpose to recognize these higher categories, however
much their boundaries may be obscured by connectant forms. They
are certainly present, and their existence should not be lost sight of.
Therefore they should be retained’ in any taxonomic system as indi-
cating steps in the evolution of these flies. "They may be kept some-
what in the background, with the caution that they can not be clearly
and concisely defined until the ontogeny of the intermediate forms is
known.

Many genera stand more or less apart and do not fall actually into
any of the subfamilies. Very restricted groups of such genera,
which may be termed refractory on account of either their complex
relationships or their apparent neutrality with reference to the
various subfamilies, will best be treated directly as tribes, without
reference to any particular subfamily.

Some few genera will prove to be quite isolated, and yet not enti-
tled to subfamily or tribal rank. A final system should aim at the
definition of as many well-marked subfamilies and tribes as possible
to concisely characterize, and the consequent reduction of the num-
ber of these isolated forms. A comprehensive table can thus be
prepared, including the subfamilies, the non-referable tribes, and the
non-referable genera in one synoptic treatment, which will be con-
venient for general use. Separate tables can follow defining the
genera within each subfamily and non-referable tribe. No attempt
should be made to force refractory genera into any subfamily or
tribe where they do not fall naturally, or any tribe into any sub-
family where it does not clearly belong, or to antagonize natural
affinities in any way, or to combine refractory forms in one heter-

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 13

ogeneous tribe or subfamily. The refractory elements should rather
be left to stand alone. .

In such manner as the above will it be possible to work out a
serviceable system of classification, which will indicate, so far as may
be, the true relationships, and at the same time preserve approx-
imately the relative values of taxonomic divisions in the Cyclor-
rhapha.

A very important point remains to be noticed: What is a species
in this superfamily? The preceding remarks on intermediate forms
apply especially to the higher divisions, but are also largely true of
genera and species. The difficulties as to genera can be practically
overcome by the erection of a sufficient number to accommodate all
thentermediates. But who can tell what is a species in nature, and
especially what is a species in the Muscoidea? It is clear that we
must have a definition that will answer to the term. In large assem-
blages of insects, where intergrades and intergradants have not been
lost, there is no such thing as a species in the generally accepted
sense. No sharp specific distinctions can be drawn in such cases.
The term is a necessary conception in taxonomy, however, and it is
to be noted that the only reason for its employment is the necessity
for being able to distinguish between assemblages of individuals that
are unlike. Therefore it seems clear that the only safe course to
pursue is to give a name to every assemblage that can be distin-
guished from other assemblages.

It is proposed to use the term
Typic species are already explained. The term atypic species will
be used for recognizable assemblages of individuals grouping around
typic species. The term “forms” may be used interchangeably as

‘species’ in a well-restricted sense.

referring to either or both.

When two atypic species are connected by intergradant individ-
uals, the former should be given names and the latter referred to as
intergradants between the two atypic species. A few words of de-
scriptive matter will serve to fix practically the exact taxonomic
position of these intergradants. Such a course will afford students
of bionomics an opportunity to attain some degree of definiteness in
their investigations. As the names now stand in the Aldrich Cata-
logue, this element of definiteness is totally lacking. Many distinct
forms are bunched under one name on almost every page. Absolute
exactness is impracticable in this phase of nature, where variation
through pressure of environment is constantly at work in the evolu-
tion of new forms. But a reasonable degree of definiteness is possi-
ble of attainment. So long as we can refer by name to recognizable
forms, we may be certain that we are not going wrong. Such forms

14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

should not be bunched merely because it is difficult to distinguish
them. If it is possible to separate them, they should be separated.

The conviction is constantly growing among biologists that we
really do not comprehend species. Multitudes of insect forms have
been confused under one specific name since systematic entomology
began. The scientific concept of the invertebrate species is grad-
ually growing less vague and more restricted. There is practically
no doubt that in most groups of insects, the Coccidz excepted, there
are many times more forms that will eventually be termed “species”
than have heretofore been recognized. Every year new results ob-
tained from a study of the early stages of insects force this convic-
tion upon us. (The Coccide probably form an exception. Mr. J.
G. Sanders is authority for the statement that the species have been
largely split on characters pertaining to different ages of the same
stage.) Without doubt, bunching is infinitely more harmful to a
system of classification than splitting. Splitting, even if inju-
diciously done, does not give rise to actual error, but bunching pro-
duces all kinds of error in the bionomic literature, which errors,
moreover, are irremediable except through a restudy of the speci-
mens originally referred to. It goes without saying, however, that
forms can be properly separated only on constant structural charac-
ters pertaining to the same age or stage of development, and on
color, form, and size only when such are known to be constant. A
plea is herewith entered for judicious splitting,’ up to the limit of
practicability. A reasonable degree of conciseness in the designation
of forms of insects is absolutely unattainable by any other means.

A word is not out of place here bearing upon the causes of varia-
tion which give rise to vast multitudes of forms during the period
of greatest prolificacy of a group in any order of life.

Mr. W. L. Tower, in his paper on Leptinotarsa (Carnegie Institu-
tion of Washington, Publication No. 48), has demonstrated that
variation is not inherent in the germ plasm, but is invariably induced
by external stimuli acting thereon. The demonstration consisted of
several experiments in which the stimuli were directly applied to
pregnant females of Leptinotarsa, so as to reach the germ plasm
within the contained ova. This one point is by far the most im-
portant contribution to science that the author makes in the whole of
his long and highly instructive paper. All variations are directly
caused by the action of external stimuli—such as heat, humidity,

“This term is adopted in a serious sense because it is both apt and expres-
sive. Splitting can be accomplished only along lines of formation or natural
cleavage, and this is true of the proper division of taxonomic groups.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND T5

atmospheric pressure, food, etc——in other words, by the pressure of
environment, which means all»stimuli taken together and acting
together.

It is thus seen that climatic or meteorologic conditions are potent
factors in the evolution of forms of life, and that as a rule one form
does not inhabit two widely different life zones or areas. Few, if
any, forms inhabit both temperate and tropical regions, or both
humid and arid regions. The external stimuli natural to the differ-
ent zones and areas result in the modification of forms coming within
the sphere of their influence, and the consequent production of new
forms. Thus the progeny of individuals of one and the same form,
spreading gradually through areas where they become subjected to
new, sets of stimuli, are gradually differentiated into distinct forms
through the pressure of environment. Dr. Merriam’s exposition of
this law in his address before Section F of the American Association
for the Advancement of Science, at its 55th meeting (Proc. Am. Ass.
Adv. Sci., 1906, pp. 387-9), is an admirable one, and can be studied
with much profit. His observations, as there given, agree perfectly
with the results of the writer's studies in Diptera. For instance, the
arid and humid regions of North America will be found to possess
very few species in common. ‘These very different life areas are
divided and subdivided by temperature as we go north or south, or
ascend above sea level, and again and again subdivided by various
climatic and other environmental factors. The result is many sepa-
rate life areas, more or less restricted, each of which exhibits a dis-
tinct stamp of environment. Intergradations occur along the periph-
eries of the ranges of closely related species, when such lie contig-
uous, as they often do. These intergradants must not be confused
with the normal specimens of the form as exhibited throughout the
more central portions of the area of range. That the intergradants
occur between two such forms does not invalidate the distinctness of
the forms themselves.

It may safely be stated as a theorem in bionomics that, given an
arid area and a humid area contiguous to each other, both originally
stocked with individuals of the same form—whether of Diptera or
any other order of life—the descendants of this form will not remain
identical in the two areas throughout any considerable period of
time. The theorem may be enlarged to include temperate and trop-
ical contiguous areas, and many divisions and subdivisions of these
and of the arid and humid areas as well. The resultant differentia-
tion is brought about by dynamic variation, incited by the respective
sets of external stimuli acting on the germ plasm of the ova con-

2

16 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

tained within pregnant females of the form, already referred to as
demonstrated by Tower.

A careful study of these factors and of the results produced by
them demonstrates the fallacy of the idea that forms from the north
Atlantic coast region of the United States and the south Gulf coast
region of Mexico are identical. In other words, forms originally
described from Vera Cruz are not to be identified in Massachusetts
material. Likewise, forms from arid regions are not to be identified
in humid region material. Furthermore, European species are not
to be identified in American material, except in the few cases of
forms that have been imported through the agency of man. There
exist today practically no Muscoidean forms common originally to
Europe and North America. The Muscoidea did not originate from
circumpolar stock. The forms that immigrated to northern America
from Eurasia during the warm periods that existed in the subarctic
region in interglacial times have long since given rise to new forms,
and no longer persist in their original state.

There are certain more or less cosmopolitan flies, such as Musca
domestica, Stomoxys calcitrans, Lucilia cesar, Calliphora erythro-
cephala, and others, which find their natural environment in the wake
of man. ‘These are not so amenable to the above factors, but even
they show some effects of their agency. A considerable number of
such species doubtless accompanied primitive man in his wanderings
through various parts of the earth. Other species are of compara-
tively recent dispersion through commercial agencies. Both classes
have been involuntarily spread by man. The detection of the second
class calls for extremely careful study and fine powers of perception.
Still another and very recent class has been purposely spread by man
for economic ends.

A word may be said as to the difficulty of distinguishing between
many of the distinct but closely similar forms that occur in the Mus-
coidea. While many of these forms that closely resemble each other.
do so by virtue of their close relationship through common origin, it
is evident that others of more diverse origin have developed a close
resemblance through counterfeitism’ attained by means of natural

*The writer herewith proposes a change from the use of the words mimic,
model, and mimicry. The terms “mimic” and “model” have nothing, except
usage and priority, to commend them. “Mimic” is exceptionally faulty, and
does not nearly convey the intended meaning. In the strict sense of the word
a mimic is one who, by sound or action, imitates another. The word does not
imply any idea of form, color, or size. The word “counterfeit,” however,
embodies the full concept. Again, “model” does not carry the idea of size,
and in an art sense only partially that of form; moreover, it is not necessarily

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 17

selection and the pressure of environment. This may be termed con-
vergent evolution. Somewhat similar are cases of parallelism, or
recurring types of structure in nowise related to one another, which
are to be explained by use and adaptation to external conditions. A
thorough study of larval and puparium characters will determine
such cases beyond a doubt, but in many instances an intimate knowl-
edge of the adults will enable one to separate these forms quite accu-
rately. Parallel series in the adult of forms of common origin will
usually show their distinctness very readily to the experienced eye
without a lens. In this way the writer has often made a preliminary
arrangement of much material, which subsequent study demon-
strated to be correctly separated into distinct forms, many of them
so.closely resembling each other that they were extremely liable to
be confused. A very serviceable guide in distinguishing between
forms of common origin is the character and color of the pollen,
which is present to a greater or less extent in all the forms. This,
strange to say, is extremely constant throughout series of individ-
uals of the same form and the same sex. In those forms which pos-
sess golden pollen on the head, the male as a rule has the golden
shade more pronounced and extensive than the female. The color
of the pollen of thorax, and especially that of abdomen, is very con-
stant in both sexes. A slight difference in the shade of color of the
abdominal pollen, such as that between a silvery cinereous and an
ashy cinereous, will frequently serve to correctly separate closely
related but distinct forms which might otherwise be confused. It is
almost needless to say that reference is here made only to fresh and
well-preserved specimens. Greased specimens must be restored be-
fore attempting to place them.

Illustrative of convergent evolution and parallelism, in which adults
of two or more forms closely resemble each other through causes other

imitated, often has no relation to color, and may even be a miniature or other
representation and not the original at all. “Pattern,” on the contrary, means
the original, to be imitated as to form, size, and color, strictly speaking, and
is the term used in mechanics in the exact sense of our concept.

By using these terms—counterfeit and pattern—we can adhere strictly to the
significance of our diction. We would thus speak of an edible counterfeit
(species) of an inedible pattern (species), which latter has been unconsciously
and involuntarily adopted by the former as a subject for imitation, impelled
thereto by certain accruing advantages. Both words express the sense exactly,
and both can be used without change as either nouns or adjectives. Deriva-
tively, instead of the objectionable term “mimicry,” we have the very sugges-
tive and thoroughly appropriate name counterfeitism to apply to a subject of
rapidly growing importance. It would seem that neither priority nor usage
have any claim to consideration in a case of this kind.

> SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

than those implied in close relationship, the following is an excellent
case in point among the Coleoptera. Mr. W. Dwight Pierce makes
the statement that three species of Anthonomus (A. nigrinus, eneo-
lus, and albopilosus), which breed in the flower-buds of Solanum
spp. (S. carolinense, eleaginifolium, rostratum, and torreyi) in
Texas, resemble each other so closely in the adult that they are often
confused by experienced coleopterists. Yet Mr. Pierce, who has
studied the early stages of these species, has found that the anal
characters of the pupz serve to readily distinguish them. A. eneo-
lus and nigrinus belong in the same group, are distinguished in the
pupa by a slight difference in the proportions of the posterior termi-
nal structures of the anal segment, and in the adult only by color.
But A. albopilosus belongs in a distinct group, is inseparable in the
adult except by leg characters, and markedly different in anal
characters in the pupa. A. albopilosus is thus a case of con-
vergence toward eneolus and nigrinus, which two are closely related
forms. It should also be mentioned that albopilosus has been found
recently breeding in great numbers in buds of Croton spp. Dr.
Chittenden is authority, however, for its former breeding in Sola-
nun spp.

The reasons for such convergent evolution or parallelism are often
difficult to ascertain and are outside our subject. This case is intro-
duced from the Coleoptera merely as paralleling certain very similar
ones in the Muscoidea. For example, the species Achetoneura
datanarum, A. promiscua, and Parexorista futilis seem to form a
group similar to the above species of Anthonomus. ‘The first two are
closely related, and the third furnishes a case of convergent evolu-
tion in their direction. All three forms are entirely cinereous polli-
nose, have the anal segment brassy, and the parafrontals and para-
‘facials golden pollinose. (Achetoneura frenchi has a different
facies, but has been confused with the first two.)

Similar groups will be found in the genera Tachina, Masicera,
Phorocera, etc. Another group is probably exemplified in Myro-
phasia spp., Phasioclista metallica, Ennyomma clistoides, and certain
other species.

Such conditions as the above explain why specimens of tachinids
looking strongly alike and bred from the same «caterpillar, perhaps
issuing on the same date, are at times found to belong to different
forms and ever to different genera. In such of these cases as are
due to convergent evolution and parallelism, the larva and puparia
will be found to exhibit better differential characters than the adults.
No work connected with the taxonomy of the Muscoidea could more

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 19

solidly advance our knowledge of the subject than the careful and
painstaking study and rearing of the early stages. It is a most
promising and inviting field, and one whose problems are intimately
woven with subjects of broad biologic significance.

It may Be pointed out that the well-known promiscuity of ovi-
position with reference to hosts in the Muscoidea is another evidence,
and a necessary result, of the geologically recent evolution of the
superfamily. The Microhymenoptera are of far more remote evo-
lution, as evidenced by the fact that each genus is restricted to a
group of hosts. Microhymenopterous parasites bred from host
larve belonging to different families may safely be pronounced off-
hand to belong to different genera. ‘This demonstrates a fixed habit
of oviposition that has endured through a long period of time. No
such fixed habit is to be found among those Muscoidea parasitic
upon lepidopterous larve, or among any of the superfamily except
the Ci stride.

It has been alleged that much of the so-called synonymy in this
superfamily, as it stands in the Aldrich Catalogue, is due to a mis-
guided erection of species on stunted specimens developed from
underfed larve, through a lack of acquaintance with the breeding
habits of the species. It is well known to all students of the
Muscoidea that the females sometimes, if not frequently, carry the
act of oviposition to an extreme, ovipositing upon larve that are
already overstocked with eggs. This has been observed and recorded
in a number of instances. It has been observed at the Gipsy Moth
Laboratory of the Bureau of Entomology in Massachusetts that
tachinids would oviposit at times upon larve covered with eggs,
while masses of unstocked larve were abundant close by. Some of
the unmolested larvz were dissected and found unparasitized. This,
moreover, was in the open, outside the breeding cages. However
puzzling this may seem, it is certainly unsafe to draw conclusions as.
to habits from observations made in the gipsy moth area, since the
equilibrium of the various forms is in a state of extreme unrest.
This is due not only to the enormous increase of comparatively
newly introduced host elements in the fauna, but also to the more
recent introductions of new parasitic species, both tachinid and
microhymenopterous. These agencies have so disturbed the balance
between species that the resultant conditions have become highly
artificial. Similar conditions could hardly arise except through
man’s interference. Had the gipsy and browntail moths and their
parasites spread into Massachusetts from a contiguous area, the
change of equilibrium between them and the resident fauna would

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

have taken place more gradually, and the balance between species
would not have been so suddenly upset. It is not at all likely that
tachinids oviposit so heedlessly as above observed, provided they are
subjected to thoroughly normal conditions.

As far as the recognition of stunted and underdeveloped individ-
uals of a form is concerned, there is rarely any difficulty provided
one is familiar with the characters. The stunted specimens always
exhibit practically the same characters, and if there is any exception
the true status of a specimen is quite recognizable.

CHARACTERS

The following outline of the construction and development of the
head capsule in Calliphora, principally drawn from Lowne (Anat.
Blowfly, pp. 114-16), forms a fitting introduction to a consideration
of characters, inasmuch as those of the head take precedence over all
others in the taxonomy of the Muscoidea.

The MreracEPHALON comprises the segmented post-oral portion of
the head.

The PARACEPHALON, which is formed of the two paracephala, or
two lateral procephalic lobes of the nymph, comprises the pre-oral
portion of the head.

The paracephala bear the compound eyes and antenne.

They are united in front and below and form the epistoma and
labrum.

The portion of the facial paracephalon behind the epistoma shows
three distinct parts. These are two bladder-like swellings, the
anterior and posterior cephaloceles, and the antennal ridge between
them. The last is developed by a process from each of the two
lateral procephalic lobes.

The anterior and posterior cephaloceles correspond with the thin
portion of the blastoderm which intervenes between the two lateral
lobes or paracephala.

The posterior cephalocele is the forehead (Vorderkopf) of the
German embryologists. It bears the ocelli, and the front is devel-
oped from it.

The anterior cephalocele develops into the facial region.

Behind the front there are two plates which extend forward from
the metacephalon; these form the eficephalon (parafrontal-occipital
ridge).

That portion of the procephalic lobe which lies in front of the
antennal ridge unites with its fellow, and curves downward and
backward over the mouth to form the prefacial region.

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 21

When the posterior cephalocele is closed by plates of chitin, these
are the triangular median epifrdéntal, and the two frontals (frontalia
or frontal vitta).

The frontal sac or ptilinwm consists of a great part of the pos-
terior cephalocele withdrawn into the interior of the head between
the frontals and the antennal ridge.

The /unula is thus an anterior chitinized portion of this sac or
ptilinum.

The anterior cephalocele is the vesicle of the olfactory lobes.

The posterior cephalocele is the vesicle of the cerebral hemispheres
and their median ventricle.

In the nymph the median parts of the head capsule lie in a deep
cleft between the two lateral lobes or paracephala, and in close prox-
imity to the ganglia with which they correspond, so that the head
appears to be open on the median line. Sections show this to be a
deep infolding of the inner edges of the paracephala (Lowne).

The two paracephala (two lateral procephalic lobes), having
united on the median line, become the paracephalon of the imago.

The paracephalon is opened transversely by a horseshoe-shaped
suture running up from the cheek border on each side and passing
between the antennal ridge and the frontals, bridged by a widely
distensible membranous tissue (the ptilinum), on the forward me-
dian portion of which is the lunula somite. This suture ends on
each side at the cheek groove, which is formed in the integument by
the mechanical strain on it when the suture is opened to thrust forth
the ptilinum. The suture may be properly called the paracephalic
suture, but the writer prefers to employ the term Ptilinal suture.

The following is a detailed statement of the external anatomical
parts to be studied in the superfamily Muscoidea, arranged primarily
in the order of their importance, and severally in the order of their
relative position. The characters of the superfamily are to be found
in the various features exhibited by these anatomical parts, and are
pointed out so far as possible under each head. The parts preceded
by 1) afford characters of family, subfamily, tribal, and partly gen-
eric value, and those preceded by 2) characters of mainly generic
value. The terminology is made to conform so far as possible to
that already in use. New terms are introduced only in such cases
as demand their use for reasons of clearness, conciseness, and per-
manence, and for such few parts as had no name and afford charac-
ters of taxonomic value.

The figure here introduced is diagrammatic and intended to show
the main sclerites of the front aspect of the head, the characters
afforded by which take rank over all others for taxonomic use within
this superfamily.

22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Front view of head of a Muscoidean fly (half in diagram), much enlarged.
(Original, from drawing prepared by the Bureau of Entomology.)

The heavy black line indicates the ptilinal suture. O=Ocellar plate.
FF = Frontalia. PP=Parafrontals. Pfc Pic =Parafacials.§ CC =Cheeks.
EE = Compound eyes. L = Lunula (postfront of larval insects). A= Antennal
ridge (mesofront of larval insects). Fp Fp=Mesofacial plate (plus facialia
equals prefront of larval insects). Fa Fa=Facialia. (Parts from lunula to
facialia both inclusive taken together constitute the homologue of the front of
larval insects.) Ep=Epistoma. Cl=Clypeus. Pl Pl= Palbpi.

EXTERNAL ANATOMICAL PARTS AND CHARACTERS
(Heap)

1) PTILINAL suTURE (through which is protruded the ptilinum of Robineau-
Desvoidy) evenly rounded and widened above, narrowed above, subangular at
top; its sides parallel, divergent, convergent; its termini high or low where
they join the cheek grooves; position of its termini with relation to lower eye-
border, epistoma and vibrissal angles.

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 23

[Before ptilinal suture]

1) PYrimLINAL AREA (area enclosed,by ptilinal suture= facial depression of
descriptions plus antennal somite plus lunula; front of Berlese) of what form,
width above and below compared with adjacent parts of parafacials and para-
frontals. .

1) FactaL PLATE (clypeus of Brauer and von Bergenstamm; face, facial
plate, mesofacial plate of Lowne plus epistoma; facial depression of authors,
prefront of Berlese, transverse impression of face of Hough—in each case
minus facialia and plus epistoma) produced and swollen in middle like the
bridge of the nose, merely swollen nose-like below, tube-like, projecting for-
ward in profile below, flat, even, elongate, reaching almost to lower margin of
head, extending obliquely downward and posteriorly, reaching straight down
between vibissal angles, widened below same; shortened in front view, ending
high above lower margin of head; widened below, oval, triangular, compara-
tive width above and below, narrowed high or low by the facialia or by the
vibrissal angles.

1) MESOFACIAL PLATE (do. of Lowne; facial plate minus epistoma).

1) Fossa OF FACIAL PLATE (fovee plus foveal sinuses) long, short, wide,
narrow, deep, shallow, curved, straight.

2) FovEa% (fovee of Robineau-Desvoidy; antennal grooves of descriptions;
simply depressions in the facial plate) deep, shallow, elongate, short, double,
single, and confluent.

1) FovEAL sINUSES (more or less linear grooves which in certain cases
form outlets of the fovee anteriorly) linear, widened, deep, faint, convergent,
divergent, etc.

2) Factal CARINA (keel of descriptions) present, absent, developed only
above, weak, strong, high, sharp, knife-like, thin, thick, flattened, rounded,
widened, canaliculate or furrowed on its median line, or simple.

1) Factatia (facialia of Robineau-Desvoidy and Osten-Sacken; facial
ridges of descriptions; facial edges of paracephalon of Lowne; Vibrissenleisten
of Brauer and von Bergenstamm; vibrissal ridges of Hough) parallel, gradually
convergent below, short, long, bare, ciliate, narrow, sharp, widened, flattened,
divergent, or absent.

1) FacraL BRIsTLES (those on facialia; Vibrissen of Brauer and von Ber-
genstamm) ascending less than half way on facialia, or half way, or to point
opposite lowest frontals, or nearly or quite to base of antennz; in one or two
rows, bushy, in irregular position, short, weak, long, represented by many
rows of fine hairs, normal with hairs among the bristles, only one or two
above vibrissz, or wholly absent.

I) VIBRISSAL ANGLES (Vibrissenecken of Brauer and von Bergenstamm;
angles or corners where the facialia and peristomalia meet) pronounced,
weak, high above the lower margin of head, set low, rounded, sharp, or absent.

2) VIBRISSAL PAPILLA (Vibrissenwiilste of Brauer and von Bergenstamm;
sometimes present at vibrissal angles) prominent, pronounced, flattened, weak,
inconspicuous, or absent.

1) Vipriss# (the two longest or strongest bristles, one at each vibrissal
angle; Vibrissen of Brauer and von Bergenstamm) approximated, widely
separated; their insertion on, close to, well removed from the oral margin, or
on, close to the under margin of the head, or on the upper edge of the oral
margin when this is turned up and broadened, or on or near end of facial plate,

24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

on a level with uppermost front edge of oral margin, or above or below same.

1) PertstoMaLiaA (lateralia of Robineau-Desvoidy; peristomal ridges, the
ridges on lower edges of peristoma or cheeks, extending to vibriss@) with one
or many rows of bristles, extending how far up; parallel above oral margin,
divergent, convergent; parallel, divergent, convergent posteriorly below oral
margin; effect on epistoma.

2) PERISTOMAL BRISTLES (those on peristomalia) strong, weak, in one or
more rows, or few and with row of hairs.

1) Eprstoma (epistoma of Rob.-Desv.; Mundrand of Br. and v. Berg.; the
portion of facial plate below vibrissal angles and enclosed between the peristo-
malia, its point of junction with the mesofacial plate being indicated by the
vibrissal angles) projecting nose-like, prominent in profile, retreating, set
back or removed, produced downward or anteriorly, turned up, drawn out
tube-like, transversely cut off, broad, narrow, thin; thickened, widened on
edge, callous or indurated, projecting forward and downward below vibrisse;
drawn up in middle to form anterior part of narrow oral slit, its sides thereby
becoming nearly parallel; square, or curved in front outline. [The characters
of the epistoma are usually best included in those of facial plate, of which it
forms a part.]

ORAL MARGIN (the anterior edge of the oral cavity, being the lower edge of
epistoma).

1) OraL cavity covered over transversely in front with an oblique pos-
teriorly-extending skin or membrane developed probably from the clypeus,
open, elongate, short, wide, narrow, deep, shallow, slit-like, or closed.

1) Crypgeus (clypeus of Rob.-Desv., Lowne, and Berlese; the anterior or
dorsal plate of the cephalopharyngeal skeleton, or fulcrum, of the rostrum)
distinct, rectangular, triangular, developed into a plate closing oral cavity, or
vestigial.

1) MoutH parts normal, vestigial, immovably fixed at base of shallow oral
cavity, hidden in a narrow deep oral slit, or wanting.

2) Progoscts short, fleshy; not longer than head height, shorter or longer
than same; very elongate, bristle-like, twice geniculate, once geniculate, slender
and horny, large, stout, vestigial, or absent.

2) LABELLA well developed, large, broad, small, vestigial.

2) Papi absent, vestigial, filiform, club-shaped, strongly elongate, normal.

1) LONGITUDINAL AXIS OF HEAD at oral margin longer than that at insertion
of antennz, or the two equal, or the former shorter. —

1) FAcIAL PROFILE advancing thereby, or more or less straight or concave,
or receding or convex.

1) FACIO-PERISTOMAL PROFILE angular, rounded, strongly or gently convex.

1) ANTENN# (arising from antennal ridge of Lowne; from antennale or 2d
somite of front of Berlese) inserted above, on, or below a line drawn through
middle of eyes; above or below middle of extreme head height, widely sepa-
rated or closely approximated.

1) SECOND ANTENNAL JOINT strongly elongate compared with first, longer
than shortened third joint, normal, with or without strong bristles on front
edge.

2) THIRD ANTENNAL JOINT entire, fissiform in one or both sexes, elongate,
narrowed, widened, enlarged, with curved point on front apical corner, normal.

1)2) Arista bare, microscopically pubescent, hairy, pectinate, partly or
wholly plumose, geniculate, flattened, thickened in what part of its length; first

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 25

and second joints elongate, short, strongly elongate; or only second joint
strongly elongate, its length compared, with its width or with the third joint.

1) LunuLa (postfront of Berlese) enlarged in middle inferiorly and supe-
riorly into a more or less diamond-shaped or rounded plate, like an extension
of the facial plate into a secondary one; elongated below between the antenne
into a keel-like prolongation, widely separating the antenne, or normal.

Note.—The lunula reaches its greatest development in the Syrphoidea.

(N. B—MESoFACIAL PLATE [=2 mesofacials of Lowne + carina if present,
since latter is formed by inner edges of the two mesofacials] + 2 FACIALIA +
ANTENNAL RIDGE + LUNULA = homologue of FRONT of larval insects [= PTILINAL
AREA |).

[Behind ptilinal suture]

2) Eyes absolutely bare; thinly microscopically hairy, sometimes distinctly
so, sometimes indistinctly so; thickly pubescent, sometimes more so in male,
less So in female; reaching as low as vibrissz, or lower, or only to middle of
face, or very short. [N. B.—In comparisons last mentioned, hold head in full
profile with plane of posterior aspect of occiput perpendicular. |

2) VERTEX wide, narrow, comparative width in sexes.

2) VERTICAL BRISTLES present or absent, or present only in female; pro-
clinate, reclinate, divergent, convergent.

2) POSTVERTICAL BRISTLES (+ postocellar bristles =lesser ocellar bristles of
Hough) large or small, separated or approximated, how many pairs.

1)2) FRONT prominent in profile; flattened, or only anteriorly so; bulging,
narrow, wide, widened anteriorly, conically produced, of equal width, or
not so.

1) OCELLAR PLATE (stemmata of Rob.-Desv.; epifrontal of Lowne) triangular,
rounded, large, small.

1) OcELLI separated, approximated.

1)2) OCELLAR BRISTLES (Ocellenborsten of Brauer and v. Berg.; greater
ocellar bristles of Hough) strong, weak, proclinate, reclinate, divergent,
vestigial, or absent.

1)2) POSTOCELLAR BRISTLES (a second or posterior pair sometimes present on
ocellar plate just behind the two posterior ocelli; + postvertical bristles =
lesser ocellar bristles of Hough) present, absent, or represented by fine hairs
only.

2) PREOCELLAR BRISTLES (do. of Hough; small pair on frontalia in front of
anterior ocellus) present or absent.

2) FrontaLia (frontalia of Rob.-Desv.; frontals, mesofrontals of Lowne;
frontal vitta of descriptions) polished, opaque, wide, narrow, long, short, equi-
lateral; widened or narrowed anteriorly or posteriorly, or in middle; square in
front, notched in front or behind.

2) PARAFRONTALS (optica frontis of Rob.-Desyv.; parafrontals of Lowne;
sides of front of descriptions; geno-vertical plates of Hough) swollen, dilated,
bare except for frontal and fronto-orbital bristles, hairy, bristly, short, long,
wide, narrow, equilateral; widened before or behind, or both; prolonged
anteriorly.

1) FRONTAL BRISTLES (those inserted on the inner edges of the parafrontals,
always convergent, often extending posteriorly only to point about half way
between ptilinal suture and vertex; transfrontal bristles of Hough) in a single
row, in two or more rows; descending below base of antennz, continuation

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 51

below represented by row on parafacials descending nearly as low as oral
margin, or about half way down, or less than half way, or not descending
below base of antenne; or represented only by one or more rows of weak
bristly hairs on parafrontals.

2) UPPER FRONTO-ORBITAL BRISTLES rchaee on posterior portion of para-
frontals immediately in front of the vertical bristles and often appearing as a
continuation of frontal rows posteriorly, always reclinate; ascending frontal
bristles of Hough) in line with frontal bristles, or with middle fronto-orbital
bristles; position, direction, number; or absent.

2) MIppDLE FRONTO-ORBITAL BRISTLES (Orbitalborsten of Brauer and vy. Berg.;
fronto-orbital of Osten-Sacken; orbital bristles of descriptions; they are
usually a little nearer the orbit than the preceding, and always proclinate)
present in both sexes, or in female only, strong, weak, divergent, convergent ;
one, two, three, or a row, or represented only by weak hairs; or absent in
both sexes.

2) LOWER FRONTO-ORBITAL BRISTLES (lower fronto-orbital of Osten-Sacken
and Williston; occurring occasionally in the Acalypterata, but rarely in the
Muscoidea) present or absent, number.

1)2) PARAFACIALS (optica faciei of Rob.-Desv.; Wangen, gene of Brauer
and v. Berg.; sides of face of descriptions; gene of Hough) widened above,
or not so; bare, hairy, bristled; widened below and narrowed above, more or
less swollen, very wide, very narrow, elongate, short; or narrowed, shortened,
or abbreviated below.

2) FACIO-ORBITAL BRISTLES (those on parafacials) present or absent, number,
position, direction.

1) CHEEKS (peristoma of Rob.-Desyv.; Backen, peristoma of Br. and v.
Berg.; bucce of Hough) wide, narrow, very narrow; width equaling or ex-
ceeding eye height, or equaling what proportion of eye height; naked, hairy,
bristly, or so only below or behind. [N. B.—Br. and v. Berg. give apparent
height (not width) of cheeks as seen in profile, with eyes included. Their
actual greatest width (distance from peristomal margin to eye) should be
compared with eye height, as seen in front view. ]

1) CHEEK MARGINS (portions bordering on parafacials and ptilinal area)
ascending, encroaching on face, more or less circumscribing the facial plate.

2) CHEEK GROOVES (mediana of Rob.-Desv.) present, well defined, curved,
wide, deep, shallow, position, vestigial.

2) CHEEK BRISTLES (strong bristles which sometimes occur on cheeks near
lower border, slightly outside of peristomalia) present or absent, number,
direction, position.

2) POSTERIOR ORBITS (bare space between posterior eye margin and row of
hairs fringing occiput) widened below, narrowed above, of even width, wide,
or narrow.

2) LOWER MARGIN OF HEAD (lower border as seen in profile) straight, bulged
downward or outward posteriorly, long, short.

2) OccrpuT (all the portion of the head behind the plane which defines the
limit of the posterior orbits, as marked by the fringe-like row of small bristles
or hairs bordering same and called by Hough and others cilia of posterior
orbit) evenly swollen, flat; flat above and swollen below, bulging the cheek
profile posteriorly.

I)2) PARAFRONTAL-OCCIPITAL RIDGE (ridge-like sclerite formed by what
seems a continuation of parafrontals over vertex on occiput and which bifur-

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 27

cates above great central foramen; cerebrale of Rob.-Desv.; epicephalon of
Lowne).

1)2) OCCIPITO-CENTRAL BRISTLE (do. “of Hough; small bristle on parafrontal-
occipital ridge just below inner vertical bristle before bifurcation of ridge)
present or absent, character of.

1)2) OccIPITO-LATERAL BRISTLE (do. of Hough; small bristle on occiput just
below outer vertical bristle) present or absent.

2) OccrPIraL AREA (the characteristic hairy area of occiput which some-
times invades the cheeks posteriorly) invading cheeks, or restricted to occiput.

2) LONGITUDINAL DIAMETER OF occIPUT (shows its degree of swelling at any
specified point) above or below compared with eye width in profile.

2) Brarp (pilosity arising and depending from lower portion of occiput,
and in certain cases clearly defining a portion of cheeks invaded by occipital
area) long, short, thick, thin.

. (THORAX)

1)2) STERNOPLEURAL BRISTLES One, two, three, or more, in what arrangement.

1) HyYporLEURAL BRISTLES strong, weak, or represented only by hairs.

1) PTEROPLEURAL BRISTLES strong, weak, or hair-like.

1) MESOPLEURAL BRISTLES very strong, or normal.

1) PROPLEURAL BRISTLES strong, weak, number, direction.

1) NOTOPLEURAL BRISTLES (posthumeral of Osten-Sacken) strong, weak,
number.

2) PosTsUTURAL BRISTLES (dorsocentral of Girschner behind suture; outer
dorsocentral of Osten-Sacken behind suture) strong, weak, relative strength,
number, position.

2) DorsocENTRAL BRISTLES (dorsocentral of Girschner before suture; outer
dorsocentral of Osten-Sacken before suture) strong, weak, relative strength,
number.

1)2) AcROSTICHAL BRISTLES (2 middle rows both before and behind suture)
strong, weak, number, position. e

2) HUMERAL BRISTLES strong, weak, number, direction.

1) INTRAHUMERAL BRISTLES (posthumeral of Girschner) present or absent,
number, position.

I) PRESUTURAL BRISTLES (+ posthumeral of Girschner =intrahumeral of
Osten-Sacken) strong, weak, position in relation to preceding.

1) INTRAALAR BRISTLES strong, weak, whether one in front of suture.

2) SUPRAALAR BRISTLES (+ postalar=supradlar of Osten-Sacken) strong,
weak, number.

2) POSTALAR BRISTLES strong, weak, number.

1)2) ScUTELLAR BRISTLES strong or weak, comparative strength of the vari-
ous pairs, number of lateral pairs; a weaker apical pair present or absent,
erect, suberect, directed posteriorly, decussate, or divergent; discal pairs
present or absent.

(WIncs)

2) Wrncs broad, long, narrow, short; costal margin swollen or dilated in
male, or in both sexes, or normal.

2) CosTAaL SPINE distinct, strong, weak, double, or absent.

2) LONGITUDINAL VEINS bristly, to what extent, or bare.

28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

1)2) FourTH LONGITUDINAL VEIN incomplete, straight, not forked, reaching
neither the wing margin nor the third vein, normal, ending at or before wing-
tip, angular or rounded at bend, bowed or not beyond bend, bend approximated
to or removed from hind margin of wing; last section forming petiole of
apical cell when latter is petiolate, or third vein in such case forming petiole;
or forked and main vein represented beyond apical crossvein by only a short
stump, or by a mere wrinkle or fold in the wing-integument, or by a long
stump.

2) APICAL CROSSVEIN (this term should be employed only when the fourth
vein is furcate, or shows indication of previous furcation in a stump, fold or
wrinkle) bent in, straight, oblique, long, short, absent.

1) FIFTH LONGITUDINAL VEIN bent up to fourth vein, not forked; or furcate,
giving off posterior crossvein; represented beyond latter by a short stump, or
a long one, or only by a wrinkle, or partly by stump and wrinkle, or continu-
ous to wingborder.

1)2) POSTERIOR CROSSVEIN (term not to be employed in the few cases where
fifth vein shows no sign of furcation) oblique, in line with apical crossvein or
with last section of fourth vein, or still more oblique than latter, or normal;
nearer to bend of fourth vein (or to origin of apical crossvein) than to small
crossvein, or nearer to latter, or about in middle between the two; trisinuate,
bisinuate, singly curved, straight.

2) SMALL CROSSVEIN on, before, or behind middle of discal cell; short, long,
straight, oblique, direction.

1)2) APICAL CELL (first posterior of descriptions) ending near wingtip, or
far before; open, closed in margin, or long or short petiolate, or extremely
short petiolate; wide, narrow, short, elongate, tapering equilaterally at apex.

2) TrcuLa# large, small, relative size of two scales; deeply smoky or in-
fuscate, or white, or yellow; bare, pubescent, or hairy.

(ABDOMEN )

1)2) AspoMEN (shape of whole) linear, cylindrical in one or both sexes,
widened on some portion, conical or oval in both sexes, swollen, convex dor-
sally, concave ventrally, flattened in one or both sexes, or laterally compressed.

1) ABDOMINAL SEGMENTS apparently four, or how many visible from above;
how many actually present, which ones shortened, and relative development
of their respective dorsal and ventral plates. [See notes on Gymmnosoma,
Trichopoda, Rhachoépalpus, etc., under head of Descriptions. In many cases,
at least, there are more segments in the Muscoidean abdomen than have here-
tofore been recognized, an undeveloped basal segment being quite hidden from
view, and only visible with difficulty on the sides below. Its dorsal and ventral
plates are easily seen on detaching the abdomen. In order to avoid confusion,
the old terms “first,” “second,” “third,” and “fourth” segments are retained as
referring to those apparent from above in the undetached abdomen. ]

2) ABDOMINAL MACROCH ET# present or absent, bristle-like, true, very strong,
thorn-like, discal and marginal, or only marginal; discal present on second and
third segments (counting apparent segments from above), or only on third
and fourth, or only on fourth; marginal present on all, or absent on first, or
absent on both first and second segments.

1) VENTRAI, MEMBRANE (membrane connecting the ventral and dorsal plates
of the abdominal segments) visible, concealed by the sides of the dorsal
sclerites or plates, or apparently absent.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 29

1) VENTRAL PLATES free, or not so; or that of second segment in both sexes
with its edges upon and covering the edges of the corresponding dorsal plate,
the other ventral plates free, or this true of only one sex; how many ventral
plates, last one in male deeply or weakly Y-cleft or V-cleft, or entire.

2) VENTRAL CARINA present in female, absent, rudimentary, more or less
developed, emafgination of plates of same, or latter entire.

2) Oviposiror elongate, short, tapering, stout, furnished with terminal hooks,
appressed, exserted; directed downward, or forward, or posteriorly; integu-
mental, membranaceous, or horny.

2) Hyporycium prominently exserted, elongate, appressed, directed down-
ward, short, rounded, bulb-like, tube-like, of what formation and character-
istics.

(Lrcs)

1)2) Lkcs strongly elongate, only moderately so, short, or only one pair
elongate, relative length of pairs; bristly, bare, shaggy-haired, with or without
macrochete.

2) Hrnp FEMorA ciliate or not so, character and position of the cilia.

2) Hinp Trista completely and densely feather-barb-ciliate, only comb-ciliate,
subciliate, with some longer bristles; cilia flattened and widened, scale-like,
bristle-like, or of what character.

2) MippLeE Tipta with or without strong bristles or macrochete on outer
side, or on any portion.

2) Tarsi slender, swollen, compressed, short, elongate, relative length of
pairs in each sex; last joint or more Of which pairs oval, thickened, swollen,
or compressed, in one or both sexes.

2) Meratarst short, elongate, comparative length with relation to other
tarsal joints of same pair, comparative length of pairs, slender, stout.

2) Front Tarst widened in female, or widened and flattened, or only flat-
tened, in one or both sexes.

2) CLAWS AND PULYILLI elongate in male, or in both sexes, or short in both,
or only anterior ones elongate in male; claws stout, slender, curved, shape and
character; pulvilli of what shape and character.

While the foregoing enumeration of anatomical parts affording
characters of taxonomic value in the superfamily is not necessarily
complete, it is believed that it brings out practically all the characters
requisite to a proper separation of the forms in the adult.

Of all these characters, those of the head take first rank. For this
reason much space has been devoted to their consideration—in fact,
nearly twice as much as to all the other characters together. It is
conceded that the Schizophora are the most specialized insects, the
most highly developed from the standpoint of ontogeny, as evidenced
by their remarkable and practically complete reorganization of larval
parts within the nymph. Everything points to the Muscoidea as the
most highly organized Schizophora, and this is emphasized by their
acute sensory development. It is therefore naturally to be expected
that certain non-functional parts of the head, which is the chief seat

30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

of the specially developed senses, should afford the most important
characters for taxonomic use.

Here, and practically here alone in the Muscoidean anatomy, are to
be found certain useful atavic characters pertaining to organs not of
any functional importance in the economy at present, but possessing
phylogenetic significance as indicating origin and _ relationships.
These are of especial value for the separation of families and sub-
families. It has long been recognized that rudimentary organs in
recent forms bear a significant relation to those of their allied prede-
cessors. Such are physiologically non-functional now, and appear in
more or less developed condition only in the embryo, but were func-
tional throughout life in the early fossil forms. They have been lost
through disuse, involving a process of degeneration or retrogressive
development. If, then, these organs present sufficient variation, their
rudimentary presence is of much importance to us in the prepara-
tion of a natural taxonomic system. Atavic characters, to be of use,
must be exhibited by parts which vary sufficiently to offer con-
veniently distinguishing marks. To be of use in the separation of
higher, or family, divisions, the parts must present just enough
variation to offer distinctive characters that will hold throughout
considerable aggregations of forms.

Such are the characters afforded by the facial plate in its lower
extent, and by the facialia, vibrissal angles, and peristomalia. ‘The
parts in question present sufficient variation to afford distinguishing
characters. These are all atavic, and possess in consequence a high
phylogenetic significance. They are connected with the portions of
the head whose development in the nymph is not influenced by the
coincident development of functional parts. While the development
of the highly. sensory third antennal joint affects in a degree the
upper portion of the facial plate and determines the character of the
fovez, its influence does not extend below the-vibrissal angles.

Atavic characters are afforded by the wing veins in a remarkable
degree, but the general plan of venation is too uniform to afford us
good family characters. They can be used in higher and lower
divisions. It may further be noted that, since the wings are so
highly functional in a mechanical (not sensory) way, the characters
derived from lesser variations in venation would in any event be sec-
ondary in importance to the head characters just mentioned. It
must be borne in mind that the wings are of great functional im-
portance, and the veins bear the mechanical strain incident upon
their use, while the special head characters above pointed out, whose
importance as affording distinctions for higher divisions has been
dwelt upon, are in nowise connected with any present function,

ae

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 31

either mechanical or sensory, in the economy of the adult insect.
The type of venation furnishes atavic characters of value in sepa-
rating higher divisions. The bristles or hairs of certain thoracic
plates likewise furnish atavic characters of high value here.

Atavic characters also occur to a limited extent in the abdomen,
chiefly in the atrophied basal segment, which can be clearly made out
only by detaching the parts. These are also too uniform to be of
use for the separation of the larger divisions, so far as we yet know.
But their comparative study offers promising results.

Practically all the other portions of the Muscoidean anatomy are
preéminently functional, even including the halteres, tegule, etc.,
and the parts of the head other than those enumerated above. The
frontalia and lunula may be practically non-functional, but they like-
wise do not present sufficient variation to offer any useful characters
for family separation. The second antennal joint is probably not
functional, although in the Nemocera it is the seat of the so-called
“Johnston’s organ,” whose function is supposed to be auditory. This
organ does not appear to be developed in the Cyclorrhapha. Prac-
tically the only character afforded by the second antennal joint,
however, is that of relative length compared with the first joint, and
this is at best available only for subfamily and generic separation.
The arista is doubtless functional. A consideration of certain char-
acters of functional parts, and especially of the physiological func-
tions of certain of these parts whose characters have in the past been
largely used in taxonomy, is now taken up.

Antenne proper.—tThe first and second antennal joints are prac-
tically non-functional. The third joint is highly functional, and
hence does not afford reliable taxonomic characters for higher
divisions than species, and within certain limits for genera. The
relative length of third joint to second affords no valid character,
and especially gives a wrong impression in those forms having the
second joint elongate. The first joint is almost universally short,
but the second is often more or less elongated, and in some cases
strongly so. The relative length of second joint to first affords a
good generic character. The third joint affords excellent specific
characters, so far as its relative length and size go, with proper
recognition of sexual variations. Its shape may furnish characters
of generic, or even of tribal, value.

The olfactory sense is very highly developed in the Muscoidea.
Blow flies will come for miles to decaying, and even to fresh, meat
shortly after its exposure to the air. Most other members of the
superfamily possess this high olfactory sense, though in some it is
developed in a varying degree. The sense of smell in these flies is

a
ao

32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

located in the third joint of the antennz, which contains numerous
olfactory pits communicating with the main nerve trunk by means of
minute nerve-ends.

According to Gustav Hauser (Zeitschr. f. Wissens. Zool., Xxx1Vv,
pp. 367-403, 1880), who studied over sixty species of Diptera in this
connection, the Muscoidea and other cyclorrhaphous Diptera, and
also the Brachycera, have the olfactory pits without exception con-
fined to the third antennal joint. Their number varies greatly in
different forms of Cyclorrhapha. Certain syrphids, as Helophilus
florens, have only one pit on each disk of the third joint, while
Echinomyia grossa has two hundred. In certain forms the pits are
compound, containing from ten to one hundred olfactory hairs aris-
ing from the coalescence of the several original pits. No compound
pits occur in the Tipulide, but only simple ones with a single olfac-
tory hair, such as are found in the brachycerous (s. str.) forms only.
The latter have also compound pits, containing from two to ten
nerve-terminations.

The olfactory pits are sac-like invaginations of the external chit-
inous integument, and are of various shapes in different forms of
diptera. They are always open externally, and never closed by a
membrane. In the Cyclorrhapha, and the Muscoidea especially, the
pits differ but little in the various forms. Hauser (1. c.) figures and
describes at length those of Muscina stabulans as generally typical
of not only the Cyclorrhapha, but the Brachycera s. str. as well. He
gives a figure of the third antennal joint in longitudinal section
showing simple and compound pits, the pits themselves being shown
in both transverse and longitudinal section and from above. The
main nerve trunk, accompanied by the much smaller tracheal trunk,
passes through the second antennal joint entire and without division,
but on entering the third joint gives off a very small branch to the
arista, to which also runs a small branch of the trachea. The bulk
of the nerve trunk continues undivided and undiminished into the
mass of the third antennal joint, where it branches in all directions,
but especially apically and inferiorly (opposite the edge bearing in-
sertion of arista), the main trachea following it with less branching.
This centralization of nerve-branches, nerve-ends, and olfactory pits
in the apical and ventral tracts of the third antennal joint—that is to
say, outside the aristal area—bears out the conclusion that the arista
was originally terminal and that the highly functional extra-aristal
area of the joint has simply grown away from it as fast as more
space was required by the advancing development of the olfactory
sense.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 33

It has been conclusively proved by the experiments of Hauser and
others that the sense of olfaction is located exclusively in the an-
tenne.in Sarcophaga, Calliphora, and Cynomyia, and not at all in
the palpi. This has also been demonstrated in many Hymenoptera,
Lepidoptera, Orthoptera, and Staphylinide; but in certain Hemip-
tera experimented ‘with it was found that the loss of their antennz
did not affect in any way their sense of smell. Certain Coleoptera
were only partially affected by the excision of their antennz.

The olfactory organs of the Muscoidea consist of (1) a thick
nerve trunk arising from the brain and passing into the antenne;
(2) a sensitive apparatus at the end, consisting of rod-like modified
hypodermis cells, connecting with the nerve-fibre terminations; (3)
a supporting and accessory structure consisting entirely of pits. The
same is true of the other Diptera, the Lepidoptera, Orthoptera, and
probably the Hemiptera; but in the Neuropteroid orders, the Coleop-
tera, and the Hymenoptera, the accessory structure consists of peg-
like projecting epidermal invaginations filled with a serous fluid.
Both pegs and pits occur, however, in the Coleoptera and Hymen-
optera, while only tactile hairs were found by Hauser in Pyrrhocoris
of the Hemiptera, though Lespés has recorded the presence of pits
in that order.

It should be mentioned here that another sense, capable of distin-
guishing between various degrees of atmospheric pressure, is be-
lieved to reside in certain sensory structures, like the sensillum placo-
deum, found in the antennal joints of bees and wasps. It is evident
that insects have some means of perception, through certain sense-
organs, of approaching changes in meteorologic conditions.

Arista.—The arista is the persistent rudiment in the Cyclorrhapha
of the terminal antennal joints still to be found in many of the lower
groups of Orthorrhapha. In the development of the third antennal
joint of the Muscoidea as a special olfactory sense organ, the arista
has become dorsal or basal, being left to occupy a position to one side
~ during the extraordinary development of the joint away from it. It
is invariably situated close to the base of the front edge of the joint.
Its persistent retention in this position indicates that it is to some
extent functional.

It is a rule in nature, which carries no exception, that there is a
reason for everything that exists. Therefore there is some cogent
reason for the pubescence, plumosity, and nudity of the arista, as
well as for its presence. The arista has become subordinated to the
third joint, but retained as an accessory. It therefore must be func-
tional. ‘The point is to discover its function, which must be the key
to the explanation of its varying degrees of pubescence and plumos-

34 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

ity. The joint is mainly olfactory, and certainly highly sensory. As
such it is highly important to the insect. The arista is directed for-
ward, outward, and downward from its insertion on the anterior
basal edge of the joint. This would indicate that it is primarily
functional as a tactile sensory organ for the protection of the highly
functional third joint. Such an indispensable organ in the economy
of the insect as the third antennal joint would naturally demand the
presence of some tactile sense organ extended before its exposed sur-
faces, to serve aS a warning against contact with foreign objects.
In other words, the arista has taken to itself the original function of
the antenna, on account of the latter being practically turned into an
olfactory sense organ. ‘The bristles of the facial and frontal areas
protect the other parts of the head from injurious contacts.

What light does this function of the arista throw on the question
of its nudity, pubescence, or plumosity? Simply that the separate
hairs have a tactile function, pointing in all directions from which
danger may come. It is to be noted that the plumosity is always
stronger on the upper or outer than on the under or inner side.
Those forms which have the basal joints of the arista elongated lack
the plumosity. This elongation of the basal joints indicates an in-
creased freedom of movement of the arista. When bare of plumos-
ity the arista either is long and tapering, indicating a somewhat
restricted movement in the comparatively short basal joints, or it is
short, stout, and geniculate, with greatly elongated basal joints, indi-
cating much freedom of movement. The nudity of the arista may
be generally taken to indicate greater freedom of movement in its
basal joints, and its shortening, when combined with geniculation,
still further increase of movement. In any case, the function of the
organ is seen to be a tactile one, intended to guard the highly sen-
sory olfactory pits and nerve-ends located in the third antennal joint.

Those forms which have the arista more or less atrophied doubt-
less have the third antennal joint less highly olfactory and more
tactile in function.

From this functional nature of the arista we can only conclude,
in accordance with the general and almost invariable rule, that it
possesses little value for the definition of subfamilies and higher
groups, but that its characters may well be employed in the separa-
tion of tribes, genera, and species.

Eyes——The organs of vision are with little doubt more highly
developed in the Muscoidea than in any other superfamily of non-
aerial insects. These flies possess, on the whole, a distinctively
terrestrial life-habit, in contradistinction to an aérial one. The rela-
tively small percentage of achetophorous and subachztophorous

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 35

forms, and even the few of these possessing the aérial or hovering
habit, maintain practically the same type of eye-structure, extensive
holopticism of the type obtaining in the Bombyliidze and Tabanidz
being present in none of them. Partial holopticism is present in
very few, atid there is a considerable approach to this condition in
certain others, but dichopticism is practically the rule. In no other
group of insects of a generally terrestrial life-habit is there so rela-
tively large an area of the head occupied by visual surface.

This and other facts further argue for an average higher develop-
ment in the Muscoidea of the visual sense per se than in any other
equally extensive group of insects, or perhaps in any other group
whatever. The Odonata, Hymenoptera, Lepidoptera, brachycerous
and,nemocerous Diptera, and some other insects which equal or sur-
pass them in relative visual area ef the head, do so by virtue of the
correlative evolution of visual surface and aerial life-habit. But
their eve structure is less highly developed. While the number of
facets in general in the Muscoidea is not nearly so great as in Odo-
nata, certain Lepidoptera, and even Coleoptera, their eye is of a
higher order of organization. The Muscoidea possess what is called
the pseudocone eye, which is the most highly evolved type of the
facetted eye.

It is generally conceded that insects possess what may be termed
microvision. Their ability to perceive certain minutiz approaches
that of the human eye supplemented with the microscope. The pres-
ence of this microvisual sense in insects is the cause of the mar-
velous beauty of coloring and sculpture exhibited by their external
parts, and which is revealed to us in detail only by the use of a lens.
In other words, the facetted insect eye gains impressions from light
rays by which the unaided vertebrate eye is unaffected. Most birds,
especially the condor and other birds of prey, and some mammals, as
the big-horn sheep of our western mountains, have a specially devel-
oped far-sight, approaching in a degree the power of the human eye
aided by the telescope. Contrasted with this is the extreme near-
sight of insects, which do not see in general more than a few feet,
and which see best at very close range.

Johannes Muiller’s mosaic theory of insect vision, which gained
such wide credence, especially as modified by Huxley, really seems
untenable and quite at variance with well-known facts. It presup-
poses a very imperfect vision, which can not be the case. Lowne’s
dioptric theory, which indicates a perfect microvision, with sharpness
and clearness of sight, would appear to be the correct one. Yet sub-
sequent investigators, notably both Hickson (1885) and Hewitt
(1907), hold that Lowne’s interpretation of the functions of the

36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

compound eye structures is incorrect. However this may be, it
seems certain that insects possess a clear and perfect vision.

Mouth parts—tKraepelin has recorded taste-pits, with hairs or
pegs arising from them, on the proboscis of Musca (Zeitsch. f.
Wissens. Zool., Xxx1x, 1883).

The palpi are probably not generally gustatory in function in the
superfamily. In certain of the forms they are with little doubt prac-
tically non-functional, and some forms have in consequence more or
less completely lost them. In others their very considerable, some-
times extreme development, indicates some function, which may be
either gustatory or tactile. In certain insects they are olfactory in
function, but probably not in the Muscoidea. They furnish charac-
ters of not more than generic value.

Wings.—The venational characters are in the main quite constant.
The wings themselves are highly functional, but this does not neces-
sarily imply that the style of venation is functional. However, as
already pointed out, the plan of venation is so comparatively uniform
in the superfamily that it yields no characters for separation of fam-
ilies. The venational characters are of very great importance in
separating this superfamily from the Anthomyioidea, but do not be-
come again available for taxonomic use in the Muscoidea until we
descend to tribes and genera.

It is reasonable to attach high importance to the main features of
the dipterous wing venation, since the wing system of Diptera is a
very highly specialized type. The hind pair has undergone atrophy,
its rudiments being diverted to another function, and the entire
flight function, at least so far as propelling power goes, has been
concentrated in the front pair. As a natural consequence of this
high wing specialization, the venation is a practically non-functional
system of long standing, extending over a sufficient period of time to
allow its systemic features to become well fixed and quite constant.
There are a few minor venational characters that can not be relied
upon in certain restricted groups. The last section of fourth vein
(or apical crossvein) may vary in degree of curvature, but not in
kind. The hind crossvein may vary in strength of sinuosity, but the
double curve is never entirely lost in the same form.

There is some ambiguity involved in the term “apical crossvein,”
as it has been used in the past. In certain genera it is impossible to
decide its true limits. The use of the term should therefore be re-
stricted to those cases in which its entire course is exactly defined.
The apical crossvein has resulted from a bifurcation of the fourth
vein at its point of flexure. In those genera showing what has been
called a “stump, or a wrinkle, at bend of fourth vein,” the point of

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 37

bifurcation, and therefore the true origin of the apical crossvein, is
apparent. In such cases the term should be used. It should not be
used in those other genera in which no point of bifurcation is indi-
cated, this having not arisen during their development. In such
cases the term “fourth vein” is correctly applicable to the whole,
whereas the term “apical crossvein” can not be so applied, especially
in Hyalomyia, Phorantha, Alophora, Beskia, Sciasma, Stomatode.ia,
and many other genera. The latter class of genera represents a
lesser specialization than the class showing a stump or wrinkle, and
therefore is an older type, and indicates a more ancient assemblage
of forms. Following Williston, the last three sections of fourth vein,
when latter exhibits no furcation, but is more or less angularly bent,
may very appropriately be termed the antepenultimate, penultimate,
and ultimate.

Halteres and tegule——vThe sense of audition is acutely developed
in insects, at least in the majority of the forms, as evidenced by the
sounds they produce. There is nothing to indicate that the Mus-
coidea are in any way an exception. Air waves which produce no
effect whatever upon our ears doubtless register impressions upon
the auditory nerve-ends of Diptera. Auditory organs are located
near or at the base of the wings in Diptera, Coleoptera, Lepidoptera,
Neuroptera, Orthoptera, and Hemiptera. They are less perfect in
the Lepidoptera, Neuroptera, and Orthoptera, and only faintly repre-
sented in the Hemiptera, in which four orders other chordonotal
structures have succeeded and more or less supplanted them. In the
Culicide, and perhaps in other of the nemocerous groups, the an-
tennal hairs are auditory. This has been established in the male
mosquito.

In the Diptera the nerve supplied to the halter is next in size to the
optic nerve, the latter being the largest nerve in the body. At the
base of the halter is a number of vesicles arranged in four groups,
to each of which groups the nerve sends a branch. These vesicles
are perforated and contain a minute hair, and the vesicles of the
upper groups are protected by chitinous hoods.

Sharp (Cambridge Nat. Hist., v1, p. 448) says of the halteres:
“They possess groups of papillae on their exterior surface, with a
chordotonal organ inside the base. Each halter is provided with
four muscles at the base, and can, like the wings, execute most rapid
vibrations. Seeing that they are the homologues of wings, it is
remarkable that in no Diptera are they replaced by wings, or by
structures intermediate between these two kinds of organs.” This
is because they have taken on special functions.

38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 51

E. Weinland (Zeitschr. f. Wissens. Zool., L1, pp. 55-166) has con-
cluded from his studies of the halteres that these organs are func-
tional in determining the direction of flight. They can be used to
steer a course in the vertical plane as well as in other directions.
He also concluded that the chordotonal structures in the base of the
halteres allow the perception of the steering movements of these
organs. But it is highly probable that the great nerve trunk sup-
plied to the halter is not primarily subservient to this dirigible func-
tion, but rather to that of audition, at least in the higher families.
In the Nemocera the halteres may be mainly dirigible or equilibratory
in function, since the auditory organs are located in the antenne.
In the Cyclorrhapha, however, it seems safe to assume that their
function is primarily auditory. As Lowne suggests, the halteres are
doubtless microphones of a most efficient nature, capable of perceiv-
ing sound waves of such low intensity that they do not affect the
vertebrate ear. ‘They possess a function of codrdination, similar to
that of the semicircular canals of vertebrates, and thus are organs
combining the functions of equilibration and audition.

The tegule of the Schizometopa and some other Diptera are very
likely functional in collecting sound-waves, increasing the perceptive
power of the chordotonal organs of the halteres, thus being ana-
logues of the external cartilaginous ear-lobes of the mammalia.
They also doubtless serve secondarily as a protection to the highly
sensory halteres. It seems safe to assume that in those dipterous
groups having no tegulz the halteres perform chiefly a function of
equilibration, but that in those groups furnished with tegulz the hal-
teres are mainly organs of audition. In other words, the presence of
well-developed tegulz indicates the presence of a highly developed
auditory sense in the halteres. Mere protection to the latter would
not demand such structures as the tegulz, while it can not be denied
that they are admirably adapted to such a function as the collection
of sound-waves.

Whatever may be finally determined as to their functions, it is
certain that the halteres are highly specialized organs. The tegule,
without doubt accessory to them, are by inference equally functional
and of coincident evolution with some function pertaining to them.
The latter, therefore, can not be accepted as affording characters of
value for the separation of large groups, but are rather of decidedly
inferior rank in this respect to the veins of the wings. They occur
in other groups entirely outside of and removed from the Schizo-
phora, and even from the Cyclorrhapha. Their presence in the An-
thomyioidea is therefore not necessarily to be construed as indicating
a close relationship between that superfamily and the Muscoidea.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 39

The Acroceridz, for instance, are to be noted as an extra-cyclor-
rhaphous group which has developed very large tegule, wholly con-
cealing the halteres and probably accessory to a highly developed
auditory sense in the latter. It seems to be chiefly groups contain-
ing a large "percentage of endoparasitic forms which are provided
with tegulee, and it is possible that a greatly increased auditory per-
ception is necessary to these forms as an aid to them in the search
for and ultimate detection of their hosts.

The validity of the time-honored separation of the Calypterata and
Acalypterata on the characters of the comparative presence or absence
of tegule alone may well be open to serious doubt. The unflexed
fourth vein, which from its doubtless far greater age should be a
much more valid character, would indicate a closer relationship of
the Anthomyioidea with the -Acalypterata than with the Muscoidea.
Yet this does not appear to be the proper and natural grouping. It
rather seems preferable to adopt Brauer’s names Schizometopa and
Holometopa as founded on characters of greater value than either
those afforded by relative development of tegule or those of wing
venation, and to recognize therefore the Anthomyioidea as a super-
family of the Schizometopa. While the result is mainly the same,
the divisions become founded on valid rather than on mutable char-
acters. The tegule have developed, though not uniformly, in the
Schizometopa. They have also developed to a certain extent in
some of the Holometopa. This fact demonstrates their unfitness for
taxonomic use in these divisions. There is a distinction between the
characters of a functional organ and the character of the presence
or absence of such organ. Moreover, it may be noted that Robineau-
Desvoidy’s division Calypteratz was applied by him to the super-
family Muscoidea of the present paper in the main sense, as is
further brought out under the head of Synopses.

Abdomen.—The number of abdominal sclerites should be of sub-
family significance at least, and the form of the abdomen is almost
invariably of generic value.

Macrochete and bristles —Chetophorousness in the Diptera finds
the climax of its development in the tachinoid stock of the Muscoidea.
While chetophorous characters are, evolutionally, of recent origin,
vet the arrangement of the macrochetz of the head, thorax, abdo-
men, and legs becomes highly important in separating tribes, genera,
and species. The characters to be derived from the macrochete of
the head rank even higher and serve for the separation of subfamilies
in certain cases. In one or two groups, the Gymnosomatine and
Phasiinz, the peculiar chzetotactic characters of the head are cor-
related with an absence of macrochzetze on the abdomen, while in cer-

40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

tain other groups, as the Hystriciine, a different type of them is
correlated with a true spinose development of the abdominal macro-
chete. The cephalic bristles are uniformly present in the super-
family, though sometimes weakly developed, whether the abdominal
ones are present or absent. The same is usually true of those of the
thorax and scutellum. The function of the macrochete and bristles
of the abdomen is doubtless tactile. They are capable of movement
in life.

In most insects the antennz, and to a less extent the palpi, are the
main seat of the tactile sense. The cyclorrhaphous Diptera, however,
have the antennze so modified as to preclude this function. It is
probable that the vibrissee are functionally tactile, and the frontal
and vertical bristles as well. The vibrisse project. straight out in
front near the ends of the ptilinal suture, and naturally serve as
anterior tactile organs for the protection of the lower portion of the
head. Likewise the frontal bristles serve as anterior and superior
cephalic, and the vertical bristles as superior and posterior cephalic
tactile organs. The fact that the vertical bristles are almost invaria-
bly stronger and longer than the frontal bristles strengthens this
view. The inner vertical bristles correspond in development to the
vibrissee.

The macrochete of the thorax, scutellum, and abdomen serve as
lateral and dorsal tactile organs, those of anal and preanal segments
always being the strongest of the abdomen and those of scutellum
the strongest of the thorax. The scutellar are doubtless the main
dorsal tactile organs, and the anal the main posterior ones. The
abdominal macrochetz, when dense and of spinose character, pos-
sibly serve also as a defense against insectivorous animals, as in
Dejeania, Paradejeania, Bombyliomyia, Hystricia, Hystrichodexia,
and others. ;

The macrochetz, especially those of the abdomen, constitute the
most recent form of specialization in the Myodaria, and are especially
characteristic of the Muscoidea. As such, and considering further
their probable functional character as tactile sense organs, those of
the abdomen at least can not be expected to furnish valid characters
for the separation of higher categories in these flies than species,
genera, and at most tribes.

The macrochetz of the head, thorax, and scutellum appear to be
of far longer standing than those of the abdomen. With the excep-
tion of most of the Cistride, they are present not only in all Mus-
coidea, many of which lack abdominal macrochetz, but also in prac-
tically all of the Myodaria except the Céstride already named and
Conopide, which two families stand well apart from the other Myo-

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 41

daria. The bristles of certain of the thoracic plates are here used as
main atavic characters for separating the Muscoidea from the An-
thomyioidea, as will appear later on under Synopses, accessory sup-
porting atavic characters being furnished by the type of venation.

An extra-tactile function is no doubt discharged by certain of the
cephalic bristles in the Muscoidea. The orbital bristles (middle
fronto-orbital especially) of the females, which are usually wanting,
or of less number, in the males, have probably arisen in those forms
where present for the purpose of enabling the males to recognize the
opposite sex. They are especially conspicuous in profile, when the
strongly proclinate middle fronto-orbital are prominently contrasted
with the reclinate upper fronto-orbital bristles. A front view would
reveal the female in the wider front in most of the forms. The fact
that in some forms the males as-well have the orbital bristles does
not militate against this view, but is explained by a transference of
the female character to the male through heredity. The breast nip-
ples of male mammals furnish an example of such hereditary trans-
fer of a female character to the male, with absolutely no functional
cause.

The bristles of the facialia and the frontal bristles possibly serve
for the recognition of forms among themselves. They are most
developed in the more inconspicuously colored forms, which run
closely together in general habitus. Further confirmatory evidence
is found in the fact that conspicuously colored and otherwise striking
species often have the cephalic bristles but little developed. It is to
be noted, however, that certain of the latter lack abdominal macro-
chetz as well. An absence of abdominal bristles is usually cor-
related with a weakness of cephalic bristles, doubtless due in these
cases to the marked development of an aérial life-habit.

Secondary Sexual Characters——These should be accorded generic
rank when they can be correlated with equally constant characters in
the opposite sex. The secondary sexual characters in the Muscoidea
are to be found in the comparative width of front, presence or ab-
sence of orbital bristles, size and length of third antennal joint, some-
times form of latter, varying degrees of holopticism or dichopticism,
comparative length of claws, ventral carinze, and certain anal pro-
cesses of abdomen; also often in the shade of coloration and distri-
bution of pollen, especially on the parafrontals and parafacials, less
often on the thorax, and sometimes in the distribution of ground
color and even of the pollen of the abdomen.

42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

SYNOPSES

It seems desirable to state at the outset that the subject of tax-
onomic divisions is approached in this paper entirely without preju-
dice. The main lines of interest in all departments of biology lie in
problems of descent, distribution, and bionomics, and the only de-
sirable point as regards classification is to secure a correct delimita-
tion of forms so that they can be definitely referred to by name.

This paper also distinctly disclaims any attempt or intention to
present a taxonomic system that is entirely original, likewise any
attempt to follow any particular author or authors—in either case to
the exclusion of any useful and valid characters already pointed out
by previous authors. This is not intended to be a revolutionary
scheme of classification in any sense, nor one that will upset any
previously conceived ideas of recognized taxonomic value. Rather
have all available characters been used that could be brought together
for a clear definition of the various divisions in each case, those of
value being adopted wherever they were to be found, whether old,
recent, or newly worked out. Asa matter of fact, the present paper
is naturally based largely on Brauer’s extensive and careful work,
but the latter is not by any means followed blindly or undeviatingly,
and points are at the same time drawn from Robineau-Desvoidy and
Rondani. Brauer based his work to a very considerable extent upon
the work of the latter authors, and Rondani drew many valuable
ideas from the work of Robineau-Desvoidy, whose reviser he be-
came. As already pointed out, these three students are the ones to
whom we owe most for our present knowledge of the Muscoidea,
and of these Brauer naturally accomplished the most, since he en-
joved the greatest advantages. Any one who will conscientiously
study this superfamily can not fail of the conviction that Brauer and
von Bergenstamm’s work, while not by any means perfect, is by far
the best that has ever been produced on these flies. The object of
the writer of the present paper has uniformly been to sift the entire
subject, retaining the good, discarding the useless, and adding such
ideas of value as it has been possible to develop independently.

The following tabular arrangement of taxonomic divisions is in-
tended to convey at a glance an idea of the system of classification
adopted :

Order Diptera. Family Tachinide.
Suborder Cyclorrhapha. Subfamily Tachinine.
Series Schizophora. Tribe Tachinini.
Section Myodaria. Genus Tachina.
Subsection Schizometopa. Species larvarim.

Superfamily Muscoidea.

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 43

The suborder Cyclorrhapha is without doubt one of the most nat-
ural divisions of the Diptera, and,yet its line of demarcation from the
Orthorrhapha is obscured by intermediate forms. For details on the
limitation of the suborders of Diptera the student is referred to the
works of Brater, Osten-Sacken, and Williston.

As to the limits of the series Schizophora, and the final conclu-
sions to be reached regarding the forms which naturally belong
within its boundaries, a word may be said with special reference to
the Pupipara. It seems quite evident that some, at least, of the latter
are simply degradedly specialized Schizophora. There are strong
points of resemblance, both in structure and in reproduction, between
Ornithomyia and Glossina. The venation is fundamentally of the
same plan. In Ornithomyia the hind crossvein has been lost. The
apical crossvein is absent, and probably never was present. In
Trichobius the apical crossvein is not present, but the posterior one
is, and there is even a second posterior crossvein which has been
developed between the fifth and sixth veins. Tvichobius has lost all
but a trace of the auxiliary vein. All the winged Pupipara show a
venation which indicates evolution from a Myodarian prototype.
Many of them seem quite closely allied structurally with the Myo-
daria, and it is also to be noted that we have as yet no proof of any
pupiparous habit in either the Streblide or the Nycteribide. In
fact, it is highly improbable that such exists. Kolenati, as long ago
as 1863, stated that the larve of Streblidz live in bats’ excrement.
If this is true, it is probable that the Nycteribidz also have a copro-
phagous larval habit. Miuggenburg has investigated the morphol-
ogy of the Nycteribide, and asserts that they possess no trace of a
ptilinum. On the other hand, he asserts that in Braula a ptilinum
exists, and that the mouth parts are essentially similar to those of the
Hippoboscide. It is probable that the Streblide and Nycteribide
are derived from an extra-myodarian cyclorrhaphous stock. Mutg-
genburg states that the Hippoboseide and Braula are descended
from genuine muscid stock, and that the Nycteribidz are probably
derived from some* other stock within the Cyclorrhapha. He
strongly indorses Brauer’s judgment of the Pupipara as being nearly
related to the Myodaria.

Robineau-Desvoidy’s name Myodaria is adopted for the Eumyidz
of Brauer, the Muscidz s. lat. of authors. In the sense in which
it is here used, it includes both the Cistride and the Conopide.
Both Robineau-Desvoidy and Brauer were correct in their views on
the inclusion of these families in the section. It seems that Brauer
did not study Robineau-Desvoidy’s Essai sufficiently to know that
the latter author had, in 1830, included the Ci#stridz with his Calyp-

44 SMITHSONIAN MISCELLANEOUS COLLECTIONS. VOL. 51

terate. Brauer claimed that the idea was original with him, and
probably arrived at his conclusions on both the Céstride and the
Conopidee quite independently (see Psyche, vol. 6, p. 259. The au-
thor was unaware at that time of the above facts). Brauer claimed
to have studied Robineau-Desvoidy,s posthumous work exhaustively,
and probably neglected the Essai. In the former the *Cistride are
separated entirely from the Myodaria, which would explain the
above oversight on Brauer’s part.

Reference has already been made to the advisability of employing
the subsection name Schizometopa. Robineau-Desvoidy, when he
wrote his Essai, had practically the same idea of the limits of the
superfamily as those here arrived at quite independently. He ex-
cluded the Anthomytide from his Calypterate, which division thus
coincides in the main with the present superfamily Muscoidea, as
here restricted. Latreille originally applied the name Creophilz to
these flies, and Macquart and Westwood used this name. The
division Calypteratze of Robineau-Desvoidy was later made to in-
clude the Anthomyiidz on account of the presence of tegulz in that
family. As has been already pointed out, the tegule do not afford
characters of sufficiently high value to be applied to these divisions.
Therefore, for several very cogent reasons, which are self-evident, it
becomes not only advisable, but necessary, to drop both Creophilze
and Calypterata as subsection names. The superfamily name Mus-
coidea covers the field to which they were originally applied, and the
name Schizometopa designates the subsection.

The failure heretofore, chiefly on the part of Schiner and his fol-
lowers, to properly define the grand divisions of the Myodaria, and
especially the families of Muscoidea, has been due to the attempted
application, in a case demanding primary, constant, and approxi-
mately well-defined characters, of two secondary and gradating char-
acters—namely, the presence or absence of tégulz and aristal pubes-
cence. These two characters are unserviceable, both because they
intergradate to such an extent as to preclude the drawing of any
natural lines of separation, and, further, because the parts exhibiting
them are so functional that they afford characters of only secondary
value or less. It was inevitable that a system founded on such
characters could not stand, for the natural boundaries do not exist
where it was endeavored to set them.

In the present paper the Muscoidea and Anthomyioidea are sepa-
rated in such a manner, on atavic chaetotactic and venational char-
acters, as to throw a few forms heretofore classed with the old
Muscidz s. str. into the Anthomyioidea, which arrangement is be-
lieved to represent their relationships more truly.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 45

It is also believed that the five families into which the Muscoidea
are divided will ultimately be found to closely correspond in value
with the families now recognized in the other divisions of the
Cyclorrhapha. .

Professor “J. H. Comstock published a very able paper in the
Wilder Quarter Century Book, setting forth certain suggestions as
to taxonomic work. ‘The idea is there elaborated that, in order to
determine the proper taxonomic system for a given group of insects,
the forms should be arranged independently on each one of their
many characters in turn, and the final mean between all these sepa-
rate arrangements should then be determined. This mean* would
indicate the correct taxonomic system. It is understood, of course,
that the varying values of the various characters should be taken
into consideration in such a procedure. It has been the aim to pre-
sent a systematic arrangement in this paper to agree quite closely
with the results that might be obtained from such a final average
between characters in this-superfamily.

In the following synoptic treatment of taxonomic categories a plan
is followed which has been devised and perfected by Dr. A. D. Hop-
kins, to whom thanks are due for an exposition of it. This synoptic
plan possesses decided advantages over any scheme of the kind yet
devised, and ‘is really a perfected system on the lines of that used by
Brauer and von Bergenstamm, and some other European system-
atists. The present synopses are carried down to families only, and
do not exhibit the plan in detail. It will be a labor of years to per-
fect the arrangement of the forty or more subfamilies, the numerous
tribes, the two or three hundred American typic genera and five
hundred or more additional atypic genera in this superfamily, to say
nothing of the multitude of typic and atypic species. The synoptic
plan referred to is carried out in detail by employing the following
system of characters in turn: I, IT, ITI, etc.; A, B, C, etc.; a1, a2, a3,
cic pw, b2..3, cbc. > Cl, C2, C3, etc.

. Order DIPTERA
NB tanta lpm Seite wires oe ei rts eect hares nis. fe 0 Peer tendeae ote Suborder OrTHORRHAPHA
IP Ott Dee SMe yiate eV eee clcial «yeleie sp tral etie, weaaane won saees Suborder CycLorRHAPHA
Suborder CYCLORRHAPHA
2tilinalesittine mans ents weet tet ctsiae ciciencke oc eee ae eras Series ASCHIZA

EitialeeStIttIne yPReSEtitsakiicin obs. icone Ses cose ve ee ohne ieee Series SCHIZOPHORA

Series SCHIZOPHORA

Head closely united to thorax or folding back into dorsal groove on same.
Section PuPIPARA
Head separated from thorax by a free neck. ............... Section Myoparia

40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Section MYODARIA

Front in both sexes of equal width, or if wider in female the greater width is
due to a widening of the frontalia and the tegule are absent; tegule never
well developed (includes Conopide)............. Subsection HoLoMETOPA

Front in male narrower than in female, the wider front of female never due
to a widening of the frontalia, tegule never absent; if the front is not
wider in female the tegule are well developed. .Subsection SCHIZOMETOPA

Subsection SCHIZOMETOPA

Hypopleural and pteropleural bristles and hairs always absent, fourth longi-
tudinal vein lying partly in the hind margin of the wing behind middle of
extreme wing-tip, proboscis never adapted for bloodsucking, if three
sternopleural bristles present their formula is 1:2.

Superfamily ANTHOMYIOIDEA

Either hypopleural or pteropleural bristles or hairs always present, fourth
longitudinal vein rarely continuous with hind margin of wing behind mid-
dle of extreme wing-tip except when proboscis is adapted for bloodsuck-
ing, if three sternopleural bristles present their formula is either 2:1
MURA eg Piety tk) s, stave 3.9.6) aos SiC ies Ie EMS ESTES Superfamily MuscorpEa

Superfamily MUSCOIDEA

Facial plate strongly produced below vibrissal angles like the bridge of the
nose, the produced portion convex laterally and not flattened, the vibrissz
separated by this bulging and situated high above the oral margin; the
mesofacial plate and epistoma completely fused into one piece.

(PHastp Stem) Family PHasmpa

Facial plate not so produced, at most projecting nose-like below with flattened
slope, or if latter is somewhat convex (Gymnosomatine) the vibrissz
are inserted quite near oral margin.

I

Facial plate always receding below vibrissal angles and oral margin never
prominent, thus giving the facio-peristomal profile an evenly and gently
convex outline; vibrissal angles situated at or above the lower two-thirds
point between oral margin and base of antenne, always very much higher
above median oral margin than length of second antennal joint, at least
twice as high, the mesofacial plate in consequence greatly shortened, never
widely produced downward, if not completely cut off by vibrissal angles.
then at least very strongly constricted thereby, the peristomalia either
approximated and forming parallel lines for a considerable distance or
bowed outwardly and more or less widely separated so as to enclose the
epistoma as a more or less distinct sclerite of the facial plate between
them; antennz almost always very short. .(Cstrrp-Macronycurp Stem)

A

“Mesembrina and Eumesembrina are the only exceptions known to the
writer, aside from the bloodsucking forms.

TAXONOMY OF MUSCOIDEAN . FLIES—TOWNSEND 47

Facial plate below vibrissal angles never receding conspicuously, the oral
margin always more or less prominent, the facio-peristomal profile in con-
sequence never evenly and gently convex; vibrissal angles approximated
to oral margin and never placed much higher above its median portion
than length, of second antennal joint, distinctly below two-thirds point of
face, the mesofacial plate elongate, never very strongly constricted, if
constricted at all the constriction is close to oral margin; antennz usually

NOM, See yfat eed ts Reet ct AN ate tele Negeri tee se see (Tacutnip-Muscip Stem)
B
A
Vibrisse and macrochaete absent; mouthparts wanting or rudimentary, non-
EULER EAD ITA ec et sec a cetavac bate arc Gt ar Mier acncta ee One Se A ota Family QstTripa

Vibrissee and macrochete present, mouthparts functional.
Family MacronycHIDa
B

Macrochetze developed, or if not (Gymnosomatine only) then the more or
less red abdomen highly swollen or inflated and covered with very short,
fine, black, bristly hairs; ovipositor never Musca-like.

Family TAcHINIDA

Macrochete not developed, or if so (Reimwardtia only) then no fronto-
orbital bristles present and ovipositor integumental, long and Musca-like ;
abdomen never swollen or inflated......,..2--...:4..«- Family Muscipa

The series Aschiza (Becher and Brauer) includes the Phoridz,
Pipunculide, Platypezide, and Syrphide. The series Schizophora
(Becher and Brauer) includes all the rest of the Cyclorrhapha.

The section name Pupipara might well be replaced with Nym-
phipara. (Réaumur), which has priority. The section Myodaria
(Robineau-Desvoidy) corresponds to the Eumyide of Brauer, and
to the Muscoidea of Coquillett plus the Conopide.

The subsection Holometopa (Brauer) includes the Malacosome,
Palomyde, Phytomyde, etc., of Robineau-Desvoidy, and corre-
sponds in the main to the Acalypterate of authors plus the Cono-
pide. The subsection Schizometopa (Brauer) corresponds in the
main to the Calypterate of authors, not of Robineau-Desvoidy.

The superfamily Anthomyioidea (Townsend) corresponds to the
Mesomyde of Robineau-Desvoidy; and to the Anthomyiden of
Girschner minus most of the Muscinen of Girschner. The super-
family Muscoidea (Townsend) corresponds to the Creophile of
Latreille, Westwood, Macquart; to the Calypterate of Robineau-
Desvoidy; to the Muscaria Schizometopa (exclusive Anthomyiide)
of Brauer and von Bergenstamm; and to the Tachiniden of Girsch-
ner plus most of the Muscinen of Girschner.

For detailed characters defining the suborders, series, and sub-
sections, see the works of Brauer, Becher, Williston, and Girschner.

4

48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

From the section Myodaria inclusive down to the families, and in
some cases the subfamilies, the divisions are particularly difficult of
exact definition, from adult characters alone, on account of the
numerous intermediates. A study of the characters of the early
stages is needed to determine beyond question the location of certain
intermediate forms.

The family Macronychiide includes those forms approaching the
Qéstride in the character of the facial and peristomal development
of the head, and which have heretofore been classed partly with the
true tachinids and partly with the true dexiids. It corresponds prac-
tically to the group Macronychiide of Brauer and von Bergen-
stamm, but it should be noted that Megaprosopus, and not Macro-
nyciua, is the real type of the family.

The old family Dexiide can not be maintained. With the excep-
tion of the few just mentioned as included in the Macronychiide,
its forms all fall in the Tachinidz, of which they constitute several
subfamilies and tribes.

Concerning the three types to be distinguished in the Muscoidea,
it may be pointed out that the most generalized type seems to be the
Phasiid. ‘The primeval stock was the possessor of a Phasiid-like
facial-plate development, in all probability, more or less after the
Syrphoidean style. From this stock sprang the three present stems.

Phasiid—Facial plate of the primeval type practically preserved, the meso-
facial plate and epistoma becoming solidly anastomosed into one piece, retain-
ing the characteristic bridge-of-the-nose production below. Both antenne and
mouthparts, especially the latter, well developed.

Tachinid-Muscid—Mesofacial plate much increased and epistoma more or
less reduced from the preceding, losing the bridge-of-the-nose production, but
retaining a more or less prominent oral margin, the mesofacial plate gaining a
length and width sufficient to accommodate the greatly developed antenne.
The epistomal development is largely retained to accommodate the very func-
tional mouthparts.

(Estrid-Macronychiid—Mesofacial plate much reduced and epistoma (except
in Hypodermatine) greatly narrowed and rounded off, losing the prominent
oral margin entirely. Antenne and mouthparts approaching atrophy from
disuse.

The following detailed notes on the connectant forms appearing
to lie more or less between the superfamilies Muscoidea and Antho-
myioidea will be useful for comparison with the synoptic table just
given. The former superfamily includes the bulk of the old Mus-
cide, the Sarcophagide, Dexiide, Tachinide, et al. (Phasiide, Gym-
nosomatide, Ocypteride, Phaniide), and the Céstridz; the latter
superfamily includes the Anthomyiide as herein accepted. The

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 49

forms which are here referred to the latter, and upon which there
has in the past been any question_as to position, are:

ANTHOMYIOIDEA

Myiospila Pickin tir pin et spp—No hypopleural nor pteropleural bristles or
hairs. Sternopleural bristles 1. 0. 2. A weaker sternopleural bristle below first
one, so as to appear 2.0. 2. Venation like Stomo-xrys.

Muscina stabulans et spp—No hypopleural nor pteropleural bristles or hairs.
Sternopleural bristles 1. 0. 2. WVenation like Stomo-rys.

Muscina cesia (det. Coquillett)—No hypopleural nor pteropleural bristles
or hairs. Sternopleural bristles I. 0. 2. Venation typical anthomyiid.

Cyrtoneura podagrica, gluta, et spp.

Pararicia pascuorum et spp.

Clinopera frontina et spp.—No hypopleural nor pteropleural bristles or hairs.
Sternopleural bristles 1. 0. 2.

These forms have heretofore been Classed in the old Muscide s. str. by
Williston, van der Wulp, and Brauer. It is believed they should be excluded
from the Muscoidea on the general averages of their characters.

MUuSCOIDEA

The following forms here included in the Muscoidea were referred
by Girschner to his Anthomyiden :

Musca domestica, corvina, et spp.——No hypopleural hairs. Distinct ptero-
pleural hairs. Sternopleural bristles 1. 0. 2, but in some the last two bristles
are separated so as to appear almost like 1. 1. 1. Typical Muscoidean venation.

Stomoxys calcitrans et spp—Hypopleural hairs, also pteropleural hairs.
Sternopleural bristles 0. 0. 1. Fourth vein bent, arcuate, partly continuous with
hind border. Proboscis adapted for bloodsucking.

Lyperosia irritans et spp—No hypopleural bristles. Pteropleural hairs pres-
ent. Sternopleural bristles none, 0. 0. 0. Aberrant venation; fourth vein
hardly bent, yet apical cell narrowly open at wing-tip; third vein bulged up-
ward, convex in front or above. Proboscis adapted for bloodsucking.

Hematobia stimulans et spp.—No specimens for study.

Graphomyia maculata, americana (det. Coquillett), et spp.—Hypopleural
hairs present. No pteropleural bristles or hairs. Sternopleural bristles o. o. 2.
Fourth vein arcuate at bend.

Synthesiomyia brasiliana et spp.—Hypopleural hairs strong, quite bristly
No pteropleural hairs. Sternopleural bristles 1. 0. 2. Fourth vein arcuate at
bend.

Glossina longipalpis et spp—No hypopleural hairs or bristles. Distinct black
pteropleural bristles, with yellowish hairs also. Sternopleural bristles 1. 0. 2.
Venation aberrant, in C#strid direction; apical crossvein continuous with pos-
terior crossvein, fourth vein deeply arcuate before. small crossvein so that
latter appears continuous with the section of fourth vein following it.

Morelha violacea (det. Coquillett, Brazil), micans Macquart (det. Coquillett,
Maine), et spp.—No hypopleural hairs. Pteropleural hairs present, bristly
hairs in micans. Sternopleural bristles 1. 0. 2. Fourth vein arcuate at bend.

50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Mesembrina mystacea et spp—No hypopleural hairs or pile. Pteropleural
black pile present. Sternopleural bristles 1. 0. 1, but often hard to distinguish
from the black hairs or pile. Venation like Stomoxrys, also like Mytospila,
fourth vein partly continuous with hind border. This and the five following
genera have the inner side of middle tibiz furnished with one or more strong
bristles.

Metamesembrina (gen. nov.) meridiana Linné (det. Brauer and von Bergen-
stamm, Alaska).—No hypopleural hairs or bristles. Pteropleural bristly hairs
present. Sternopleural bristles 0. 0. 1. Fourth vein reaching front margin of
wing before tip and arcuate at bend.

Eumesembrina (gen. nov.) latreillei Robineau-Desvoidy, et spp.—No hypo-
pleural hairs. Pteropleural hairs present. Sternopleural bristles I. 0. 2.
Venation as in Mesembrina, but fourth vein more continuous with hind margin.

Dasyphora pratorum et spp.—No specimens. Venation of Lwucilia (ace.
Brauer and von Bergenstamm).

Pyrellia cadaverina (1 spm. det. Brauer and von Bergenstamm), serena
Meigen (det. Coquillett), et spp—No hypopleural hairs. Pteropleural hairs
present, bristly and short in cadaverina. Sternopleural bristles 1. 0. 3 (some-
times 4); in the single specimen of cadaverina I. 0. 2 on one side and I. 0. 4
on the other, but probably normally 1. 0. 3. Fourth vein arcuate at bend.

Pseudopyrellia cornicina et spp—No hypopleural hairs. Pteropleural hairs
present. Sternopleural bristles 1. 0. 2, but the hind pair with anterior bristle
placed nearly as high as the posterior one. Fourth vein arcuate at bend.

Phasiophana obsoleta et spp.

Cyrtoneura sp. (det. Brauer, N. C. and Cala.) —No hypopleural hairs
Pteropleural bristles present. Sternopleural bristles 1. 0. 2. Fourth vein
arcuate at bend, apical cell narrowly open. Morellia micans (det. Coquillett)
and hortorum have nearly these characters, and it is likely that the present
North Carolina and California specimens belong to Morellia.

Auchmeromyia spp.—This genus evidently belongs here. It probably has
either hypopleural or pteropleural hairs or bristles.

Ochromyia jejuna J. C. Fabricius (N. W. India) et sp. (Amboyna).—
Hypopleural bristles present. No pteropleural bristles, but yellowish pile
present. Sternopleural bristles 1. 0. 1. Venation typical.

It will be at once seen from the above notes that the characters of
the presence of one or other or absence of both the hypopleural
and pteropleural bristles or hairs are the final determining test in
the separation of the two superfamilies.

Metamesembrina, Graphomyia, and Synthesiomyia do not have
the fourth vein continuous in any part of its extent with the hind
margin of wing, but all show a more or less distinct posterior inclina-
tion of fourth vein where it joins the wing margin, this being less
distinct in Synthesiomyia. The genera with this venation might be
considered by some students to form an aberrant group of the
Anthomyioidea, exhibiting a transition toward the Muscoidean type
of venation; but, considered from all points of view, their relation-
ships are mainly with the Muscoidea.

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 5!

Synthesiomyia has strong hypopleural hairs, which can hardly be
considered true bristles, yet they serve as a character of equal value.
It has also a bare arista. It lacks the pteropleural hairs and bristles.

Musca, Glossina, Pseudopyrellia, Pyrellia, Morellia, and Dasy-
phora (?) have the Muscoidean type of venation strongly marked
(except Pyrellia), but possess no hypopleural bristles. Glossina and
Musca, however, possess distinct pteropleural bristles like the other
Muscoidea, while Pseudopyrellia, Pyrellia, Morelia, and Dasy-
phora (?) possess a tuft of more or less bristly hairs in their place,
directly beneath the wing bases. Morellia hortorum has _ ptero-
pleural bristles approaching those of Glossina and Musca in strength,
and is doubtless not a true Morellia, which has only a tuft of ptero-
pleural hairs. All these genera are more or less intermediate, but
they can be distinguished by the above characters.

Some doubt may arise with Mvyiospila, ete., which belong in the
Anthomyioidea. They have neither hypopleural nor pteropleural
hairs, which will always distinguish them, and it may be seen that
the fourth vein is continuous with wing margin behind the middle
point of the rather widened apex of wing.

In connection with the characters given for the Muscoidea in the
table, it is to be noted that the fourth vein is incomplete in certain
genera, as Roeselia, Phytomyptera, Thrixion, Gastrophilus, Sylle-
goptera, Euryceromyia, Dichetoneura, etc.

Finally it may be pointed out that certain species of the old genus
Cyrtoneura, referred to Pararicia by Brauer and von Bergenstamm,
and belonging to the Anthomyioidea, show the gentle removal of the
fourth vein from the wing margin which is characteristic of the
forms whose position has been heretofore misunderstood. These
forms were considered by some authors as belonging to the old
Muscide s. str., and by others as belonging to the Anthomyiide, but
the characters pointed out by Girschner serve to reveal their true
position. They are distinctly to be considered as a genealogical
group descended from forms with a wholly straight (as far as wing
margin) fourth vein. The extensive removal of the fourth vein
from the wing margin in Pyrellia, Mesembrina, et al. must be con-
sidered as a further step in the development of the venation toward
the Muscoidean type. The Muscoidea are without question more
specialized than the Anthomyioidea; and since the form normal in
the latter exhibits the type of venation universal in the Holometopa
(excepting the Conopide), the last named subsection is less special-
ized than the Schizometopa. The Conopide stand evidently to one
side as a large group rather closely related to both the Schizometopa
and the Holometopa, but with a preponderance of affinities for the

52 ‘ SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

latter. They doubtless represent a branch which sprung from the
proto-Myodarian stem during its period of multiform development.
They should be considered as one of the primary divisions of the
Holometopa, probably equal in taxonomic rank to all of the other
Holometopa taken together. They stand in practically the same
relation to the Holometopa as do the Cistridz to the Sehizometopa,
the Cistridz also being a group apart from the other Schizometopa
and of older origin. Moreover, the Qéstride is a polyphyletic
group showing affinities with various subfamilies and tribes of Mus-
coidea, but owing to its present preponderance of characters due to
mode of life it is best treated as a family. For similar reasons the
Conopidz are also best treated as of family rank.

While on the subject of the relationships and extreme specializa-
tion of the Schizophora in general and the Muscoidea in particular,
it becomes highly significant to note that the Muscoidean stock has
originated three separate and distinct types of parasitism on mam-
mals, all having the same end in view—that of nourishing their
larve at the expense of Mammalia—but each of the three attaining
this result in radically opposite ways.

Cuterebra and its allies attain this end by their well-known sub-
cutaneous larval endoparasitism, in which the larva does all the
feeding, the imago taking no nourishment whatever, this peculiarity
being developed even to the extent of the adult mouthparts having
become atrophied and nonfunctional.

Glossina secures the same result by a supracutaneous imaginal
ectoparasitism, in which the adult does all the feeding, by actual
mechanical blood-letting, and retains and nourishes the larva within
the oviduct until it is fully grown, when it is extruded and becomes
a pupa almost immediately and absolutely without feeding. This is
the exact antithesis of the preceding.

But the Muscoidea must be credited with developing yet a third,
and still more remarkable method, because wholly unique and unpar-
alleled among dipterous larve of this description, of living at the
expense of mammals. Auchmeromyia produces a_bloodsucking
larva, and thus furnishes a case of supracutaneous larval ectoparasit-
ism, since the larva sucks blood externally by mechanical means.
This is the so-called Congo floor-maggot, which has recently
attracted some attention in the literature. It possesses an extended
range on the West African coast and has also been reported from
Uganda. The maggot-like larva pierces the skin of sleeping per-
sons with its small but sharp jaws, and sucks their blood. It is an
unique habit, because the larva is a footless maggot with extremely
small jaws and no means of attaching itself to the skin of its host

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 53

other than by its mouthparts. It can not cling during the act of
piercing by any structure except its mouth-hooklets. The acquire-
ment of such a habit has been possible through the fact that the na-
tives of the region inhabited by it have from time immemorial slept
on mats spread upon the earthen floors of their dwellings. The
larve probably originally fed on fermenting juices and liquids, as
evidenced by the fact that they are especially common beneath the
urine-stained mats which have been occupied by sleeping children.
The flies are attracted by sour-smelling liquids, and doubtless ovi-
posit beneath the sleeping-mats of young children.

The peculiar mode of reproduction of Glossina is carried even
farther by the Hippoboscid genera of mammal ectoparasites (Lipop-
tena, Melophagus, Hippobosca, Ortholfersia). The larva in these
forms is retained and nourished within the oviduct of the female
until full grown, but upon being extruded is incapable of movement.
The Glossina larva upon extrusion is capable of only sufficient move-
ment to find a suitable place for pupation, whereupon its integument
undergoes chitinization to form the pupal envelope. The Hippo-
boscid larva upon extrusion forthwith undergoes this process of ex-
ternal chitinization. The Hippoboscid female therefore extrudes
the larva in a situation and position suitable for it to remain during
its pupal period. It is thus evident that some relationship exists
between Glossina and the Hippoboscidz, doubtless to the extent of a
not very remote common origin. ‘The Hippoboscidz are probably an
offshoot from the old muscid stock on the one hand, and the Gés-
tride are likely an earlier offshoot in a quite opposite direction from
several stems of the same stock.

The Géstrid habit of parasitism seems the oldest, the Glossina and
Hippoboscid habit next, while the Auchmeromyia mode is evidently
very recent.

54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

DESCRIPTIONS

But little need be said in preface to the following descriptions of
genera and species. In addition to the treatment of new forms,
there is given considerable supplementary descriptive matter on
forms already described.

As a basis of operations in determining the North American Mus-
coidea, the recent Smithsonian Catalogue of North American Dip-
tera, by Professor Aldrich, will be found quite indispensable. Its
value lies in its references to descriptions. It will be necessary to
use it with much caution so far as the synonymy is concerned. It
should also be pointed out that the sequence of genera there em-
ployed is unnatural and misleading. This is not the fault of the
cataloguer, but is due to the present unsatisfactory state of the litera-
ture of the North American forms.

The sequence of subfamilies and tribes here adopted is as nearly a
natural one as is possible of attainment in the present state of our
knowledge. No doubt further study will modify this arrangement
in certain details.

It is to be noted that the tribes which appear in center heads are
independent of the subfamilies preceding them, except those in
italics under the families Muscidz and Phastide.

Family MACRONYCHIIDA

Tribe TRIXODINI

Genus Trixodes Coquillett

Trixodes Coquillett clearly exhibits in its weakly developed mouth-
parts, peculiar facial plate, and weak macrochetze a close affinity
with the Céstride. The type species is obesa Coquillett, described
from a specimen collected by the writer in the Sierra Madre of Chi-
huahua. A second specimen was collected by the writer on the
West Fork of the Gila, in New Mexico.

Subfamily MEGAPROSOPIN
Genus Microphthalma Egger.

Microphthalma trifasciata Say—Tachina disjuncta Wiedemann
may be a small specimen of this species.

The genus Microphthalma is distinct from Dexiosoma, from which
it differs in its relatively small eyes, almost bare and much shortened

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 55

arista, more compressed third antennal joint, and almost bare para-
facials. The antenne are inserted on eye middle.

M. michiganensis Townsend is a large northern form, distinct
from trifasciata or disjuncta in its red face and cheeks, third anten-
nal joint hardly longer than second, facial profile more flattened, sil-
very pollen of abdominal segments general and not restricted into
basal fasciz.

Tribe NEoPHYTOINI

NEOPHYTO, gen. nov.

The genus is like Megaprosopus in the formation of the facial
plate, epistoma, and facial ridges, but the vibrissze are distinct from
the peristomal bristles below them, and the parafacials have an
oblique well-marked row of thinly set bristles (not thickly placed as
in Macronychia). Frontal bristles not strong. Peristomalia quite
closely approximated. Cheeks more than one-half as wide as eye
height, sometimes appearing almost as wide in female. Front prom-
inent, facial profile strongly receding and slightly convex. Antenne
inserted distinctly below middle of eyes. . Apical cell closed in mar-
gin considerably before wing tip; fourth vein bent at angle, without
stump but with slight wrinkle, hind crossvein in middle between
small and apical crossveins. Male without, female with two middle
fronto-orbital bristles. Type, Phyto setosa Coquillett.

Neophyto anomala, sp. nov.
Syn. Phyto clesides CoguILLErt (non Walker).

Length, 6 to 8 mm. Grayish cinereous. Facial plate narrow,
oval, acute below, the vibrissal angles but little more approximated
than the peristomalia below them, the facial profile strongly convex.
Face, parafacials and parafrontals silvery; palpi, cheeks, frontalia
and antennz light reddish brown, third antennal joint brown. An-
tenn very short, third joint no longer than second, second about
three times as long as the very short first joint. Male front much
narrower than eyes, female front wider than eyes. Male cheeks
two-thirds eye height in width, female cheeks fully equal to eye
height. Mesoscutum cinereous, with three dusky vitte in male,
almost obsolete in female. Abdomen dusky cinereous, with anterior
portions of second and third segments and most of anal segment
silvery-cinereous. In the female especially the dusky portion is
more variable, appearing in some only on narrow hind margins of
second and third segments. Discal macrochzte on all the segments
except the first. Male abdomen long-subconical, female abdomen

56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

oval and flattened. Legs blackish. Wings clear, veins brown. A
strong costal spine present, apical cell sometimes extremely short
petiolate. Tegule white.

Missouri to Louisiana.
Type.—Cat. No. 11,646, U. S. N. M- (Missouri, Riley Coll.).

Family TACHINIDA
Tribe Mi,rocRAMMINI
Genus Senotainia Macquart

Senotainia rubriventris Macquart.—The writer retains Senotainia,
of which this species is the type, as distinct from Miltogramma in
having a more evenly rounded facio-frontal profile, narrower cheeks,
bare parafacials, distinct vibrissee, and longer antenne.

Miltogramma and Senotainia, with certain other forms yet to be
described, constitute a tribe by themselves. ‘The writer can not fol-
low Brauer and von Bergenstamm in grouping Metopia, Araba,
Hilarella, etc., with them. The latter genera have the vibrissal
angles close to oral margin.

Tribe My1opHASIINI
Genus Myiophasia Brauer and von Bergenstamm

Myiophasia of Brauer and von Bergenstamm has the eyes bare;
cheeks in female more than one-third eye height in width, in male
scarcely one-fourth eye height; both sexes with short but strong
claws, the front claws of male being the only ones that are somewhat
longer than last tarsal joint; no macrochetz on first and second
abdominal segments; arista thickened only at extreme base, second

joint short.
It is hardly possible that the Uruguayan and United States forms

that have been referred to this species are identical. Several other
well-marked forms have been confused here. MM. @nea has the
apical cell distinctly though narrowly open

Myiophasia setigera, sp. nov.

Differs from M. enea in having a median marginal pair of macro-
cheetee on second abdominal segment in both sexes. Male with rows
of hairs on parafacials, female with same rows somewhat less de-
veloped.

Texas, New Mexico, Nevada, Oregon.

T ype.—Cat. No. 11,647, U. S. N. M. (Male, Beulah, New Mex-
ico, 8,000 feet, August, Cockerell.)

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 57

A female specimen received from the Cotton Boll Weevil Labora-
tory (Hunter) was collected on an acorn of Quercus alba at Ruston,
Louisiana, October 31, and was apparently ovipositing on a weevil
larva within.

A female specimen from New Mexico (Santa Fé, Cockerell) has
a pair of small macrochetz on anterior border of second and third
abdominal segments, and a submarginal posterior pair on third seg-
ment. It may be a distinct form.

These forms are placed in Myiophasia tentatively, and may need
to be removed on further study.

Genus Phasioclista Townsend

The genus Phasioclista ‘Townsend also has the eyes bare, but
the cheeks are almost or quite one-half eye height in width in
both sexes; male claws long, all being distinctly longer than last
tarsal joint; female claws very short; arista bulbous at base, indis-
tinctly jointed; first and second abdominal segments without macro-
chetze, apical cell closed or sometimes very narrowly open, hind
crossvein nearly straight.

Mytophasia differs from Phasioclista in having a loosely set,
oblique, fringe-like row of bristly hairs on parafacials, in addition to
the shorter irregularly arranged hairs above them; the cheeks are
not so wide, as above pointed out, a double costal spine is present,
and the antennz reach almost to insertion of vibrissz.

Whether the specimens with apical cell open and closed represent
different forms of Phastoclista is still a question, but the fact is re-
corded in Psyche (June, 1893, p. 467) that specimens bred from dif-
ferent hosts differed in this character. A specimen bred from
Leucania unipuncta had the apical cell open, and another bred from
Sphenophorus parvulus had same closed. The radical difference
between a parasitic habit involving a lepidopterous larval host with
soft skin, and one affecting an adult coleopterous host, would easily
imply the distinctness of these forms.

Phasioclista metallica 'Townsend.—Both sexes have perfectly bare
eyes. Female with more or less suggestion of pollen on mesoscutum
in front. No macrochetz on first two abdominal segments. Male
with rows of hairs on parafacials, female practically without.

Florida, Georgia.

Genus Ennyomma Townsend
Ennyomma, at least in the male, has the eyes thickly pubes-

cent; arista distinctly three-jointed, not so bulbous at base as in
Phasioclista; second abdominal segment with marginal macrochete ;

58 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

apical cell open, sometimes narrowly so; hind crossvein strongly
sinuate. The genus may be at once distinguished from both Myio-
phasia and Phasioclista by its thickly hairy eyes. M. robusta Co-
quillett belongs to Ennyomma.

Ennyomma robusta Coquillett—Eyes thickly pubescent (at least
in male). Last two abdominal segments and anterior border of sec-
ond segment thickly pollinose. Large species.

California, Mexico.

Ennyomma globosa 'Townsend.—Eyes thickly pubescent in male,
bare in female. Male with purplish shining mesoscutum, showing
no pollen. Female showing pollen at least anteriorly and on humeri.
Small species. The species was described in the male only, and
referred to Loewia. Numerous male specimens agree perfectly
with the description. The female is without macrochetz on first
two abdominal segments, the male having them as in the description.

White Mountains, New Hampshire; Maryland, Georgia, Florida,
Louisiana, Missouri, Sierra Madre of Chihuahua, Mexico City,
Nicaragua.

Two specimens, male and female, bred from Anthonomus grandis,
Alexandria, Louisiana (Hunter, No. 1326, W. 6).

Tribe EUMEGAPARIINI
EUMEGAPARIA, gen. nov.

This genus may be considered intermediate between Megaparia
and Dexia, but must be classed with the Tachinidz in the neighbor-
hood of the Dexiinee. The oral margin is only slightly prominent
and the facio-peristomal profile approaches that of the Megaproso-
pine, but the oral margin is nevertheless sufficiently prominent to
destroy the evenly convex outline characteristic of the Megaproso-
pine profile. The antennz are short and the mouthparts much re-
duced, the proboscis being very short. The mesofacial plate, how-
ever, is of good width and length; the vibrissal angles are widely
separated and only feebly convergent, about as high above oral mar-
gin as length of second antennal joint. Ptilinal suture terminating
well above vibrissal angles. Claws of male very long. Type, Meg-
aparia flaveola Coquillett (No. 6236, U. S. N. M.), Colorado.

Subfamily DExIrIna
Genus Ptilodexia Brauer and von Bergenstamm

Clinoneura and Ptilodexia—Ptilodevia has parafacials hairy,
more than one pair of discal macrochztz on middle abdominal seg-

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 59

ments, and male claws very long. Clinoneura has parafacials bare,
only one pair of discal macrochetz on middle abdominal segments.
The species described by Robineau-Desvoidy as Estheria tibialis is
neither a Ptilodexia nor a Clinoneura, since it has the apical cell
petiolate.

Ptilodexia has cheeks (male) about, or slightly over, one-half eye
height; antennz inserted low, so as to give a long frontal profile;
vibrissee inserted high above oral margin; no strong or other recli-
nate vertical bristles; second antennal joint elongate and_ third

shortened.
DOLICHOCODIA, gen. nov.

Near Myiocera, from which it differs as follows: Head conspic-
uously elongated anteriorly, apical cell open. Antennz inserted on
or above middle of eyes; proboscis slender and horny, with long fili-
form palpi which are but slightly thickened apically and bear very
long bristles ; parafacials wider; long axis of head at antennal inser-
tion fully equal to that at epistoma; head longer than high. Type,
Myiocera bivittata Coquillett, described from specimens collected by
the writer on the Rio Ruidoso, in the White Mountains of New
Mexico.

EUCHZAETOGYNE, gen. nov.

Like Chetogyne, but proboscis rather stout and only a little longer
than head height ; hind tibize completely ciliate on outer edge, with no
bristles among the cilia. It agrees with Chetogyne in having the
carina wide, flattened on its edge and conspicuously furrowed on
median line. Type, Hystrichodexia roederi Williston (Kansas Univ.
Quarterly, 1, pp. 77-78), described from Arizona (1 male). For
purposes of comparison, the following characters are given for cer-
tain allied genera:

Hystrichodexia has proboscis shorter than head height.

Paraprosena has carina narrow and thin.

Chetogyne has proboscis very long and slender, hind tibiz with
long macrochetz among the cilia.

Phorostoma has only a weak rudimentary facial carina.

Euchetogyne roedcri Williston—Three males in U. S. N. M.;
two collected by the writer in Meadow Valley, Sierra Madre of
western Chihuahua, head of Rio Piedras Verdes, about 7,300 feet,
August 30 and September 2; and one labeled “Mexico, 400, Phoro-
stoma.”

Williston says in his description: “Third, fourth, and fifth seg-
ments opaque golden yellow.” The so-called fifth segment shows

60 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

very narrowly, being the base of the hypopygium. It is in reality
the sixth segment, since there is a very abbreviated basal segment
present. What appears to be the fifth segment is only the portion
of the fourth behind the transverse row of submarginal macro-
chete. The scutellum shows practically no yellowish on apex.
The third segment (called second heretofore) has, in addition to the
Six approximated macrochztz on hind border in middle, three or
four (usually four) approximated lateral ones on each side. The
second segment (so-called first) has one lateral macrochzta on each
side. The apical decussate pair of scutellar macrochetz is quite as
strong and long as any of the others of scutellum. The narrow
linear yellow of hind margin of third segment is continued in a
slight anterior prolongation on the median line in the two Sierra
Madre specimens. In addition to the two large silvery spots of
third segment of venter, there are two smaller ones on the second
and fourth ventral segments in the above specimens.

Genus Myxodexia Brauer and von Bergenstamm

Syn. Tropidomyia Braver & von BERGENSTAMM (preocc.).
Neotropidomyia TOWNSEND, nom. nov. (Dec., 1891), Trans. Am. Ent.
OG, XVII, py 2o2:
The type of this genus is M. macronychia Brauer and von Ber-
genstamm, of Syria.
Subfamily Trrxina&

EUCLYTIA, gen. nov.

This genus is herewith proposed for the species Clytia flava
Townsend (Tr. Am. Ent. Soc., xvii, pp. 372-373). It may be
known by the two rows of weak frontal bristles on each side of
frontalia, the outer row weaker and somewhat irregular. The epis-
toma is but slightly prominent. Specimens in U. S. N. M. have
been referred by Brauer and von Bergenstamm to Redtenbacheria,
but the species certainly can not be included in that genus.

It is distinct from the old genus Clytia, now to be known as
Clytiomyia, of which the European C. helvola is to be taken as the
type. Clistomorpha also is a very different genus. Both Clisto-
morpha and Clytiomyia belong in the Phasiide.

Tribe PHASIOPTERYGINI
Genus Phasiopteryx Brauer and von Bergenstamm

Phasiopteryx bilimeki Brauer and von Bergenstamm.—The re-
marks on this species in Ann. and Mag. Nat. Hist., x1x, pp. 33-34,

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 61

indicate differences between Phasiopteryx and Neoptera, the signifi-
cance of which did not appeal to the writer at the time. It seems
quite certain that several forms are confused here. The specimens
that the writer has seen of related forms in the C*strophasiinz in-
cline him to the belief that large series of material will demonstrate
the distinctness of Neoptera and Phasiopteryx. It must be remem-
bered that only a fraction of the neotropical fauna is yet known.

Besides the differences, pointed out below, between Cistrophasia
and Phasiopteryx, the following may also be noted: Cstrophasia
and Cenosoma have the facial plate flat or subcarinate; antennz in-
serted distinctly below middle of extreme head height, almost as
low as lower margin of eyes; arista very short and bare, and third
antennal joint only about as long as second. Phasiopteryx has the
facial plate more strongly, often quite strongly, carinate; antennz
inserted but little below middle of eyes, distinctly above middle of
extreme head height; arista very long, very distinctly but finely and
thinly hairy (looks bare in some specimens, apparently from the fine
hairs being lost or rubbed off), and the third antennal joint always
twice as long as second.

Subfamily CistRoPHASIINA

Genus CEHstrophasia Brauer and von Bergenstamm

(Estrophasia clausa Brauer and yon Bergenstamm.—This is a
northern species. The specimens from Cuautla, Mexico, referred
here by Giglio-Tos, doubtless represent another form. Cuautla is
thoroughly tropical, and clausa is a transition and boreal form.

The ultimate section of fourth vein in Cenosoma signifera and
calva is normally rather deeply bowed in, but not so in G4. setosa
and clausa, both of which have the apical cell very short petiolate,
while setosa has third vein bristly nearly to small crossvein.

The antenne of Gstrophasia and Cenosoma are widely separated
by a characteristic median enlargement of the lunula in both sexes
of all the species. This is absent in Phasiopteryx, which has the
antenne closely approximated.

Genus Eucestrophasia Townsend

Euestrophasia aperta Brauer and von Bergenstamm.—This South
American form seems generically distinct from the species of Gs-
trophasia in its open first posterior cell, as pointed out in Trans. Am.
Hint. Soc., XIX .(18092),.p: 133.

62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Genus Cenosoma van der Wulp

Cenosoma signifera van der Wulp.—lIt is likely that this tropical
species will prove generically distinct from both Cistrophasia and
Euestrophasia, when sufficient material is studied. Two species are
probably confused in the catalogue under the name of signifera.
The Canadian and New England specimens are probably a northern
form distinct from the tropical one. QU. calva may be considered
congeneric with signifera.

Subfamily PARAMACRONYCHIIN

Genus Pachyophthalmus Brauer and von Bergenstamm

Pachyophthalmus aurifrons Townsend.—This species is quite
distinct from the European signatus Meigen, which probably does
not occur in America. It differs from signatus in the golden pol-
linose sides of front and face, third antennal joint about the length
of second, hind crossvein very slightly bowed, front quite strongly
produced, etc. P. signatus has pollen of front and face silvery
white with blackish reflections but without golden, third antennal
joint about twice as long as second, hind crossvein strongly bowed,
front scarcely protruded, etc. Both aurifrons Townsend and flori-
densis Townsend are best assigned to this genus.

Genus Sarcomacronychia Townsend

Sarcomacronychia unica 'Townsend.—This species, S. sarcopha-
goides, and S. trypoxylonis are to be considered as three valid
forms. The genus Pachyophthalmus differs from Sarcomacrony-
chia in having the ptilinal area wider in comparison with parafacials,
being three-fifths to almost three-fourths width of face; cheeks as
wide as one-sixth to one-eighth eye height, or less; eyes descending
but little lower than vibrissz, as seen in profile. Sarcomacronychia
has facial plate very small and restricted, being two-fifths to one-
third width of face, parafacials proportionately wider, often nearly
as wide as facial plate itself, but sometimes appearing narrow in
profile; width of cheeks from little less than one-fourth to about
one-fifth eye height; eyes descending far below vibrisse, and even
below epistoma, nearly as low as lateral oral margins, as seen in
profile. Pachyophthalmus has the vibrisse inserted but little above
epistoma, and the antenne are inserted below middle of eyes. Sar-
comacronychia has vibrisse inserted much farther above epistoma,
and the antennz are inserted on eye middle.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 63

Tribe MELANOPHRYONINI

Genus Atropharista Townsend

The affinities of Melanophrys and Atropharista are uncertain.
One can hardly agree with Brauer and von Bergenstamm’s refer-
ence of them to the Paramacronychiine. They seem rather to be-
long in the Tachinide.

Atropharista jurinoides Townsend.—The writer has previously
considered this genus synonymous with Melanophrys, but it appears
after all to be distinct. Melanophrys has the second antennal joint
short, the third joint being three to five times as long as second,
according to sex. Atropharista has second antennal joint elongate,
the.third joint same length or a little longer, probably never twice
as long even in the male.

The species jurinoides is distinct from Walker’s Tachina insolita,
if any reliance is to be placed on the description of the latter. T.
insolita is described as having the third antennal joint fully twice as
long as second, third aristal joint very stout, and a white oblique
stripe on each side of head, presumably (from the connection) oppo-
site the antenne. The last character agrees with Mel. flavipennis,
but the other characters only partially agree. None of them seems
to agree with Atropharista, as the second antennal joint does not
appear to be elongate in insolita.

A. jurinoides differs from both in having a broad, elongate silvery
crescent bordering the orbit on each side of the head, partly on the
parafrontals and partly on the parafacials. It is quite certain that
the elongate second antennal joint will prove Atropharista to be a
valid genus, as genera will ultimately go in this superfamily.

Subfamily PHyToInz
EUPHYTO, gen. nov.

Differs from Phyto (Robineau-Desvoidy) Brauer and von Ber-
genstamm in having parafacials absolutely naked, tegulae small and
rounded, cheeks not widened posteriorly, apical cell quite long petio-
late, hind crossvein in middle between small crossvein and bend of
fourth vein, and no discal macrochetz on abdomen.

Differs from Stevenia Robineau-Desvoidy in parafacials being
wide, same width above and below, their width being equal to that of
cheeks, which are over one-third eye height. Cheeks bare, same as
parafacials.

Type, Leucostoma subopaca Coquillett.

5

64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Tribe METoPIINI
Genus Hilarella Rondani

The cheeks in this genus are about one-fourth eye height, para-
facials with a row of bristles to lower eye margin, arista pubescent
or hairy, front sharply produced in profile. Opsidia is much closer
to Hilarella than is Eumacronycha. |

Tribe EUMACRONYCHIINI

Genus Eumacronychia Townsend

Eumacronychia decens 'Townsend.—This species is the type of
the genus, which has cheeks about one-half eye height in width,
parafacials bare of bristles, frontal bristles stopping at base of an-

tenne.
Genus Gymnoprosopa Townsend

Gymnoprosopa polita, argentifrons, and clarifrons are perfectly
distinct, in spite of the note in the catalogue. They may be recog-
nized by the descriptions.

SPHENOMETOPA, gen. nov.

This genus is proposed for Araba nebulosa Coquillett. The speci-
mens from which this species was described were collected in the
vicinity of Meadow Valley, six or eight miles south of Colonia Gar-
cia, in the Sierra Madre of western Chihuahua, on the head of the
Rio Piedras Verdes, in the pine zone, about 7,000 to 7,500 feet
(Townsend). The form is not referable to Araba.

The genus may be known by the front being conspicuously nar-
rowed anteriorly, the parafacials very narrow and bare, the vibrisse
quite distinct, and the front not produced conically like Metopia and
Araba. It comes near to Metopodia in the latter character. The
wings are slightly clouded on the veins.

Subfamily PsEUDODEXIIN a

EUCALODEXIA, gen. nov.

This genus is proposed for Homodevia flavipes Bigot. It may be
recognized from the characters pointed out by Brauer (Sitzungsber.
Kais. Akad. Wiss., cv, 1, p. 515), who failed to give it a name.

Genus Atrophopoda Townsend and allies

The following new genera are here proposed:

DIAPHOROPE7ZA, gen. nov.
Type, Atrophopoda braueri Williston.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 65

C2DEMAPEZA, gen. nov.
Type, Atroph. townsendi Williston.

CATEMOPHRYS, gen. nov.

a,
Type, Vanderwulpia sequens Townsend.

BRAUERIMYIA, nom. gen. nov.

Type, Wulpia Brauer and von Bergenstamm (1892), preoce. by
Bigot in Dipt. (1886). The genus is a valid one. The new name
is proposed as a tribute to the memory of Friedrich Brauer, the
one student who has most advanced our knowledge of the Mus-
coidean flies.

Below is a table of these and certain allied genera. All of them
except Vanderwulpia, Brauerimyia, and Catemophrys have the para-
facial bristles continuous with frontal row. ‘This character, how-
ever, does not seem to indicate close relationship in all cases, as it is
probable that Ceratomyiella, Metacheta, Dichocera, and Atropho-
palpus, all here included, belong in other subfamilies from the rest.
Hypertrophocera and certain other genera not included in the table
possess this character.

Frontal bristles stopping short at insertion of antenne, apical cell end-
ing well before wing-tip, stump of vein at bend of fourth, hind cross-
vein nearer bend of fourth, cheeks about one-third eye height, eyes
bare, arista pubescent basally, abdomen slender and rather conical,
MACTOCM ete MOMbys MiatSdNall oss vere sel yee cies ene ie tetera ete 2
Frontal bristles descending to middle of second antennal joint, apical
cell ending well before wing-tip closed or extremely short petiolate,
a black wrinkle but no stump at bend of fourth, hind crossvein nearer
to bend, cheeks about one-half eye height, eves bare, arista pubescent
basally, abdomen elongate, macrochete only marginal.
TWPes MaONAEr. SCQUENS, o.ci kc cc deeb ia noses css Catemophrys, gen. nov.
Frontal bristles descending on parafacials to lower border of eyes..... 3
2. No costal spine, apical cell long petiolate, parafacials bare.
pes AU OPRORODOIEES «2. cnn cinss wie Saxe eh goon camera Vanderwulpia
A costal spine present, apical cell narrowly open or closed in margin,
parafacials distinctly very short pilose.
Eigen PY lpi PETG... no cic: 0'.icce ee Ac ee oe ee ee Brauerimyia
3. Palpi atrophied, minute, apical cell closed in border at wing-tip, hind
crossvein nearer bend, eyes almost bare.
AVMs ONSUSHCOIIIS 125. oo oa ale aarctacs O52 Re a oe Atrophopalpus
HSU MOTI dso ote ea SoS wnlale use ee eee Sa de ee es 4
4. Eyes bare, a costal spine, cheeks not over one-fourth eye height; apical
cell ending well before wing-tip, long petiolate; claws of both sexes
atrophied and tarsal joints compressed and swollen, arista pubescent

66 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

in female, hind crossvein is middle between small crossvein and bend
of fourth vein, macrochete only marginal.

PYyPe, FOTUNSOMEL. 0.6 ic oka on ees Hoe Sm one melee (Edemapeza, gen. nov.
Eyes bare, a costal spine, cheeks one-half eye TCHR cc ccsis ie wis Serum 5
Eves HOUY. ce fe aetes Uae Sees ss send Somerely Cerne anet ences 6

5. Apical cell long petiolate, ending well before wing-tip; hind crossvein
in middle between small crossvein and bend of fourth vein.
VDE, GIVE aise Cas fon ates Stee pean WS Sa ie als tin ae Metacheta
Apical cell very short petiolate, ending but slightly before wing-tip;
hind crossvein a little nearer to bend of fourth vein.
yp eSri COMICS, Ble, bcireen oie dk Os ws eae ees et ee Ceratomyiella
6. Apical cell open and ending well before wing-tip, bend of fourth vein
with long stump, male antennez with third joint lyriform cleft.
ype; WTAE? Sox he ais > sss ede te ee ee ome eee Dichocera
Apical cell ending well before wing-tip, a costal spine, hind crossvein
much nearer to bend of fourth veiri, macrochete only marginal
(except,.on arial Segment )is.c te ete ee tsa sun oe os ce xk eee are 77
Apical cell ending at or but slightly before wing-tip, eyes thinly hairy.. 8
7. Apical cell closed in border (or narrowly open, or very short petiolate),
eyes thinly hairy, cheeks fully one-half eye height.
VDE: PELICAN Ce «se ceas Patten eaten aioe cat clon aE Microchira
Apical cell moderately long petiolate, eyes thickly hairy, cheeks nearly
one-half eye height.
WOE, ANDRIES INS. , ue aes Ses oe oa Ges is nace oe Lachnomma
8. Apical cell narrowly open, a costal spine, hind crossvein nearer to bend
of fourth vein, cheeks not over one-fourth eye height, eyes very
sparsely hairy, all the male claws and pulvilli much elongated, female
claws atrophied and tarsal joints compressed and swollen, macro-
chet only marginal.
PYDE BKOMEVT. 2 teh aia oe an ee eae eee. Kee Diaphoropeza, gen. nov.
Apical cell closed in border (or very narrowly open or very short
petiolate), double costal spine, hind crossvein much nearer to bend
of fourth vein, cheeks fully one-half eye height, macrochztz discal on
last segment only, claws and pulvilli of both sexes atrophied (?)
and tarsal joints swollen.
LyDe) SHE SLGTNS’:,..v ae, Renee on ee On nee Nee Atrophopoda
Apical cell open, cheeks nearly one-half eye height, hind crossvein near
middle, no discal macrocheete (acc. v. d. Wulp) or present on last

segment only (acc. B. & v. B.), maie claws and pulvilli of anterior
tarsi elongated.

‘Type, validinerdis, *...,00en eacee eee eae ee Paradidyma

Note To TABLE.—The group of Pseudomintho, Olivieria, etc., has the front
tarsi of female plump and swollen, with very small claws. The group of
Mintho, Actinocheta, and Euantha has the last tarsal joint of all the feet in
both sexes swollen, and claws very short. But the frontal bristles do not
descend half way to vibrissz in any of these forms, and they are thus easily to

* distinguished from the above genera in the table, having somewhat similar
eer:

Cholomyia inequipes Bigot—One specimen bred at the Cotton
Boll Weevil Laboratory, Dallas Texas, from Conotrachelus elegans,
issued May 29 (Hunter).

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 67

NEAPORIA, nom. gen. nov.

This name is proposed for Aporia (Macquart) Brauer and von
Bergenstamm, which is preoccupied. The type of the genus is
quadrimaculata Macquart, of South America. The species lima-
codis Townsend seems to belong here also. The latter is distinct
from Dexia pristis Walker in its practically bare arista. D. pristis,
so far as can be judged from the description, is not a, Wacquartia
s. str. Mr. E. E. Austen has referred it to Aporia (Ann. Mag. N.
Fi set. 7, vol. XIX, p. 344).

RONDANIMYIA, nom. gen. nov.

This name is proposed in honor of Camillo Rondani for his genus
Gymnopsis (Dipt. Ital. Pr., 111, 1859, pp. 90-91), which is pre-
occupied by Rafael in Pisces (1815). The type is Macq. chalconata
(Wiedemann, Meigen, Zetterstedt) Rondani, of Europe. Brauer
and von Bergenstamm retain the species in Macquartia, but it seems
preferable to maintain it separately on the characters pointed out by
Rondani.

METHYPOSTENA, gen. nov.

This genus is proposed for the type of Hypostena barbata Coquil-
lett, which can be referred to neither Hypostena, Tachinophyto. nor
Pseudomyothyria. ‘There are no bristles on the third longitudinal
vein, the small crossvein is almost opposite to the end of the first
vein, hind crossvein is in middle between small crossvein and bend
of fourth vein, apical cell ends in exact wing-tip. The wings are
narrow, their width being much less than one-half their length. The
parafacials are narrowed below to a mere line next the lower border
of eyes, the facial profile is very oblique and receding, the lower
margin of head short, the arista strongly curved.

Subfamily PyRRHOSUN.E
Genus Leskia Robineau-Desvoidy
Syn. Pyrrhosia pt. (R6ndani) Brauer and von Bergenstamm.
Type, aurea Fallen.
Genus Pyrrhosia Rondani (restricted)
Syn. Myobia (Schiner) Brauer and von Bergenstamm.
Type, inanis Fallen.
Genus Anthoica Rondani

Syn. Myobia Robineau-Desvoidy (preoce.—non Schiner, Brauer and
von Bergenstamm).

Type, atra Réndani.

68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

It is clear that the name Leskia Robineau-Desvoidy can not be
properly substituted for 1yobia Robineau-Desvoidy (preocc.), inas-
much as the species referred to Leskia by that author are not typical
Myobia in his sense.

Rondani proposed the name Anthoica for this very purpose, and
it must therefore be employed. Leskia should be recognized as
distinct.

Genus Aphria Robineau-Desvoidy

Aphria ocypterata Townsend.—One female, Massachusetts (No.
142, Riley Coll.). Length, 7 mm. Agrees with original descrip-
tion. The stump of fifth longitudinal vein does not quite reach
margin of wing. The hind crossvein is nearly in middle between
the small crossvein and bend of fourth vein, the bend being quite
rounded. ‘The third antennal joint is distinctly and evenly rounded
on both apical corners.

Aphria occidentale, sp. nov.

One female, Colorado (No. 120, Riley Coll.) ; one female, Beulah,
N. Mex., August (Cockerell) ; one male, Roswell, N. Mex., August
(Cockerell).

Length of female, 7% to 8 mm.; of male, 9 mm. Differs from
ocypterata in being more robust, larger, the abdomen more broadly
red on sides, the red extending length of first segment and half or
more length of third segment; third antennal joint in both sexes dis-
tinctly angular on front apical corner, rounded on posterior apical
corner, widened in male; stump of fifth vein extending to margin of
wing; hind crossvein more noticeably approximated to bend of
fourth vein, which bend is abrupt.

The greater size, the character of third antennal joint, and the
more widely red abdomen will at once distinguish the species.

Type.—Cat. No. 10,900, U. S. N. M. (Colorado, Coll. Riley).

Aphria georgiana, sp. nov.

Two females, Georgia (Riley Coll.), (==? Ocyptera triquetra
Olivier et ? Ervia triquetra Robineau-Desvoidy ).

Length, 10 mm. This is a distinct species from both of the pre-
ceding. It is not so typical of Aphria as are the other species, being
much larger and wider-bodied. Frontal bristles descend but slightly
below insertion of antennz, hardly more than to base of second
antennal joint. The third vein is spined only one-half or three-
fourths way to small crossvein, hind crossvein is nearly in middle

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 69

between small crossvein and bend of fourth vein, stump of fifth vein
extends to wing border ; first and second antennal joints and base of
third reddish yellow, arista and rest of third antennal joint black or
brownish; third antennal joint rounded on posterior apical corner,
subangular on anterior apical corner. Palpi brownish yellow, or
with a reddish tinge. Front fully one-half width of head, frontalia
brownish yellow; face and front silvery white, parafrontals slightly
cinereous. ‘Thorax, scutellum, and pleure quite thickly silvery
pruinose over the black ground color. Abdomen obscure light
brownish red, obscurely blackish on median line, broadening on hind
portions of second and third segments and nearly covering fourth
segment; anterior borders of second to fourth segments broadly
silvery pruinose, but more faintly so than thorax; legs blackish;
wings clear, slightly tawny at base. Tegule white, very slightly
tinged with yellowish.
T ype.—Cat. No. 10,901, U. S. N. M.

PHOSOCEPHALA, gen. nov.’

Form rather Lucilia-like, narrow, abdomen round-oval, head yel-
low, wings slightly smoky, palpi absent, thorax and abdomen me-
tallic.

Head and thorax about same width, abdomen slightly wider.
Front (female) not prominent in profile, distinctly more than one-
half width of head, flattened anteriorly, steeply sloping on anterior
two-thirds, ocelli marking summit, vertex lower; parafrontals wide,
not swollen, clothed with some fine black hairs; vertex not nar-
rowed; frontal bristles descending in a single row about to middle
of second antennal joint, the four front pairs decussate and widely
divergent below; two strong reclinate frontal bristles next behind
these and between them a pair of weak bristles also directed back-
ward, the outer one outward; two reclinate vertical bristles of equal
strength on each side, the outer one directed also outward, these

*’ This genus and several others were purposely described in detail in order to
furnish a forcible illustration of the length of a full generic description in
these flies, mentioning all the characters, such as would be necessary to enable
the student to absolutely place the form in its proper tribe or subfamily with-
out reference to the specimen. Such a description is far too long for practical
use, and demonstrates the inadvisability of attempting systematic work in this
superfamily without a great amount of previous study and access to a large
central collection where all types are to be permanently preserved. Especial
attention is here called to the fact that all these characters require to be
studied and compared in order to determine the final location of a genus of
these flies.

7O SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

being strongest of all; postvertical bristles small, of same size as the
black border row of occiput; ocellar bristles strong, proclinate, diver-
gent; postocellar bristles represented only by weak hairs; two strong
proclinate orbital bristles; lunula normal; frontalia differentiated
only by being bare of hairs; facial plate elongate, ovate, widened
below, about as high as parafacials, greatest width just above vibris-
sal angles and taking up three-fifths the facial width at that point,
quite flat, slightly advancing below, reaching quite to lower margin
of head; facial carina absent, antennal grooves hardly developed at
all; facialia divergent inferiorly to point just above vibrisse, then
feebly convergent ; facial bristles about two above vibrissz ; vibrissz
quite widely separated, inserted just a little above the oral margin;
vibrissal angles only moderately pronounced, rather rounded, sit-
uated moderately close to oral margin; parafacials not quite twice as
wide at base of antennz as on lower orbits, flattened anteriorly, with
some fine black hairs next lower eye-margins; epistoma moderately
prominent, narrowed, showing a cut-off flattened edge below
vibrisse; mouthparts normal, proboscis when extended about as
long as head height, moderately fleshy, only once bent, labella mod-
erately developed; palpi entirely absent, showing no trace; oral
cavity moderately narrow and elongate; peristomalia with a row of
seven or eight black bristles, which are continued around edges of
occiput; longitudinal axis of head at oral margin practically same
as that at insertion of antennz, the facial profile being slightly con-
cave, and profile of parafacials straight but obliquely receding; an-
tennz inserted about on a line drawn through middle of eyes and
about on upper three-fifths of head height, closely approximated ;
second antennal joint slightly elongate, fully twice as long as first
joint; arista bare, moderately long and slender, a little thickened on
basal one-third, basal joints short and indistinct; third antennal joint
about twice the length of second, moderately wide and of equal
width, rounded on both apical corners; eyes bare, not large, set
rather high, not extending as low as vibrissz, about twice as long
as wide; cheeks about as wide as one-half of eye height, clothed with
very fine light hairs, cheek grooves absent; lower margin of head
nearly straight, but rounded behind; occiput slightly swollen on
lower two-thirds.

Sternopleural bristles 3, the middle one inserted lower than the
others and about equally distant from them; hypopleural bristles
moderately strong, about 5 in number; 2 pteropleural bristles, the
posterior one very strong, curved, reclinate; mesopleural bristles in
a posterior fringe of 7; propleural bristles 3, curved upward and
forward; notopleural bristles 2, strong, curved, reclinate ; postsutural

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 7%

bristles 4, the posterior one on each side reaching beyond hind bor-
der of scutellum, the others mutch less strong ; 3 dorsocentral bris-
tles; 4 short acrostichal bristles before suture, one strong one next
scutellum (if, more behind suture, the pin has destroyed them) ;
6 humeral bristles, moderately short; 3 intrahumeral bristles; 1 pre-
sutural bristle nearly in line with last; 3 intra-alar bristles, one in
front of suture; 3 strong reclinate supra-alar bristles; I strong post-
alar bristle reaching middle of second abdominal segment, 2 weak
ones below it; scutellar bristles consisting of 3 strong and 2 weak
pairs, an apical decussate weak pair, a weak, more separated sub-
discal pair in front of last, a strong subapical pair reaching almost
to base of third abdominal segment, a shorter pair outside these, and
the strongest macrocheetz of entire body being a lateral pair inserted
on border in front of last, and which reach nearly to base of third
segment; some other bristly hairs on scutellum appearing more or
less like weak macrochete.

Wings not large, rather narrow, extending about length of anal
segment beyond end of abdomen, normal; costal spine distinct but
short; third longitudinal vein with about five bristles at base; other
veins not spined; fourth vein ending in wing-tip, straight to bend,
which is sudden (but hardly angular) and very obtuse, last section
straight, the whole vein so gently bent as to distinctly narrow the
apical cell, bend without stump or wrinkle and slightly more re-
moved from hind margin than any part of the vein beyond it; fifth
vein running half way from hind crossvein to wing border, rest
being wrinkle; apical cell closed in margin, hind crossvein distinctly
trisinuate, a little nearer to bend of fourth vein than to small cross-
vein, but not greatly removed from middle, the axis of its anterior
half at almost a right angle to fourth vein; small crossvein slightly
before middle of discal cell.

Abdomen of 4 segments, broad-oval, almost round, strongly con-
vex above, subflattened below, first segment shortened ; macrochetz
weak, only marginal except on last segment, first segment without
any, second segment with a weak median pair and a weak lateral
one, third segment with a marginal row of 8, anal segment with
some marginal ones and a row of 6 subdiscal; ovipositor withdrawn
inside the subcircular anal orifice on ventral side of last segment.

Legs short (only the hind pair present), femora with short black
bristles ; hind tibize not ciliate, with sharp bristles on posterior side
and some shorter ones on front side; tarsi not stout, moderately
slender, short, about same length as tibize, metatarsi fully as long as
the other joints taken together; claws and pulvilli short, a little
shorter than last tarsal joint. Type, the following species:

72 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Phosocephala metallica, sp. nov.

One female, Tucurrique, Costa Rica, collected by Messrs. Schild
and Burgdorf.

Length of body, 8 mm.; of wing, 6 mm. Head entirely pale yel-
lowish, face and cheeks with a faint silvery bloom; parafrontals,
frontalia, and two basal antennal joints unicolorous with a faint
brownish tinge; third antennal joint, arista and proboscis pale yel-
lowish brown; eyes dark purplish brown. Thorax, scutellum, and
abdomen shining metallic dark purplish, the abdomen hardly more
of a purplish black, humeri yellowish; presutural part of mesonotum
deep golden pruinose, through which run only two linear vitte, the
pruinose covering thickest on sides and in front, extending back-
ward behind suture very faintly on sides of mesonotum; scutellum
faintly silvery pruinose; metanotum faintly silvery, pleure silvery
gray ; abdomen very faintly silvery, not obscuring the metallic sheen,
most noticeable on bases of segments, particularly second segment,
least so on anal segment. Wings distinctly smoky throughout, a
little more so on costal border, extreme base of costa narrowly vel-
lowish. ‘Tegule appearing almost white in some lights, but with a
smoky yellowish tinge, much whiter than the wings, halteres pale
yellowish. Legs brownish yellow, tarsi hardly darker, but appear-
ing blackish from the many short black bristles, cox lighter yel-

lowish.
T ype.—Cat. No. 10,902, U. S. N. M.

Paranaphora diademoides, gen. nov. et sp. nov.

This new genus and species are proposed for Ervia triquetra of
Mr. Coquillett’s Revision of the Tachinide (1897), page 66. The
species is not to be identified with Olivier’s Ocyptera triquetra,
which is probably an Aphria. It does not fit- Robineau-Desvoidy’s
Ervia triquetra, nor does it belong to his genus Ervia. The species.
looks some like Stomatodexia diadema, from which it may be at
once known by the bare arista, the very elongate second antennal
joint, and the atrophied palpi.

PARANAPHORA, gen. nov.

The salient characters of the genus are the elongate second an-
tennal joint and the atrophied palpi, as just mentioned. Front at
vertex one-third width of head in female, one-fourth in male. Palpi
extremely small, cylindrical, like a minute grass seed, with a long,
delicate apical hair. Apical cell narrowly open a little before wing-
tip, sometimes almost closed in margin. Bend of fourth vein angu--

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 73

lar, with slight wrinkle, sometimes with slight stump. Hind cross-
vein much nearer to bend of fourth vein than to small crossvein, the
latter on middle of discal cell. First vein ending well beyond small
crossvein. A,long costal spine present. Macrochete only mar-
ginal, except some submarginal on last segment.

Second antennal joint about four times as long as first, about equal
to third. Frontal bristles descending only two below base of an-
tenne. Arista and eyes bare. Front prominent; parafacials mod-
erately wide, about one-half width of facial plate. Face receding,
epistoma slightly prominent; facialia bare, except two or three short
bristles above vibrissee in male, but practically absent in female.
Vibrissee strong and inserted a little above oral margin. Cheeks
about one-half eye height. Antenne inserted above line drawn
through middle of eyes. Occiput swollen inferiorly. Male with-
out, female with two orbital bristles.

Scutellum with a very short apical decussate pair of bristles, and
two strong lateral pairs with a weaker bristle between them. Abdo-
men composed of five segments, first short, second shorter than those
following. Male abdomen elongate-conical, last segment laterally
compressed ; female abdomen ovate with apex conical. Legs rather
long, tarsi of male very elongate; male claws very long. ‘Type,
the following species:

Paranaphora diademoides, sp. nov.

Five females, four males, Mississippi, Louisiana, Texas.

Length, 7 to 12mm. _ Head, thorax, and scutellum of male golden
pollinose, most thickly so on thorax and scutellum. Same parts of
female brassy gray, extending over abdomen. Antenne of male
reddish yellow, those of female brownish yellow. Frontalia red-
dish brown. Palpi minute, pale yellowish. Mesoscutum with a
median pair of linear vittz interrupted at suture and obliterated
shortly behind same; a lateral triangular blackish marking just in
front of suture outside these, and a longer, narrower, posteriorly
pointed one corresponding to it behind suture. Abdomen of male
reddish yellow with base, median line and broad hind borders of last
three segments brown, a golden bloom over the lighter portions.
Female with narrow hind borders of last three segments brown,
with brassy gray bloom, the second segment faintly yellowish.
First segment without macrochetz; second with anterior and pos-
terior lateral, and a median marginal pair; third with two lateral
pairs and a median pair; fourth with 8; anal segment of male with
about 8 marginal and 6 or more submarginal, those of female less in

74. SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

number and more nearly apical. Legs reddish yellow, tarsi brown-
ish, hind tibiz brownish, and sometimes the femora less so. Tibiz
of female all reddish or yellowish. Wings distinctly yellow along
narrow front border, the submarginal cell clear. Tegule slightly
tinged with yellowish, mostly on borders.
Type.—Cat. No. 10,903, U. S. N. M. (Mississippi, H. E. Weed).
It is possible that further study will show the distinctness of some

of the above specimens.

PARAFISCHERIA, gen. nov.

This genus is proposed for the type of Demoticus venatoris Co-
quillett, which is not a Demoticus. (Latter genus has the epistoma
not at all produced, and furthermore has a short and fleshy pro-
boscis.) The present genus approaches both Demoticus, Rhino-
tachina, and Fischeria, but agrees with neither, though it is clearly
more closely related to the latter, as shown by its produced epistoma.

There are orbital bristles in the male, all the claws of the male are
short, and the epistoma is strongly produced noselike (as in Fisch-
eria) ; second aristal joint is short but distinct, and arista is short-
pubescent; macrochzetze discal and marginal, though only weak
discal ones (if any) are present on third abdominal segment. The
proboscis is elongate and horny (also as in Fischeria), the portion
below geniculation equal to head height (also equal to lower margin
of head). Cheeks wide, fully one-half of eye height, hind crossvein
nearer to bend of fourth vein than to small crossvein. Washington
State (O. B. Johnson).

NEOFISCHERIA, gen. nov.

This genus is founded on the specimen from Philadelphia, Pa.,
mentioned on page 120 of Mr. Coquillett’s “Revision” as Demoticus
venatoris. It is related to Parafischeria, from which it differs as
follows:

Male: Discal macrochete well developed on last three abdominal
segments, consisting of a transverse discal row on last segment and
a single discal pair on intermediate segments; basal segment with a
lateral marginal, but no median marginal; next segment with both;
last two segments with a marginal. row. Hind crossvein nearly in
middle between small crossvein and bend of fourth vein; no orbital
(middle fronto-orbital) bristles in male, and male claws elongate.
Cheeks about one-third eye height, proboscis elongate. Front tarsi
(male) much longer than front tibie. Type, the following species:

TAXONOMY OF MUSCOIDEAN FLIES—-fTOWNSEND 75

Neofischeria flava, sp. nov.

One male, Philadelphia, Pa. * Coll. Coquillett.

Length, 11 mm. General color yellowish. Antennz reddish yel-
low; arista and third antennal joint, except base, blackish. Head,
thorax, and scutellum dark in ground color, thickly light golden
pollinose, the face more silvery. Palpi light reddish yellow. Abdo-
men and legs light reddish yellow, the tarsi quite blackish ; abdomen
thickly light golden pollinose, under which shows faintly a broad
median stripe that widens on next to last segment into a triangular
marking spreading along hind border, anal segment tinged with
blackish only on the broad median line. Venter tinged with darker
apically. Wings clear, very slightly yellowish at base; tegulz tinged
with yellowish; halteres yellowish, including stalks. Pulvilli rather
smoky ; claws brownish, with black tips.

Type.—Cat. No. 10,904, U. S. N. M.

EUDEMOTICUS, nom. gen. nov.

This name is proposed for Plagiopsis Brauer and von Bergen-
stamm (1889), which is preoccupied in Hemiptera by Bergroth
(1883). Type, Demoticus soror Egger, of Europe.

APACHEMYIA, gen. nov.

This genus is proposed for Demoticus pallidus Coquillett.

Only marginal macrochetz, front tarsi much longer than front
tibiz ; proboscis only moderately elongate, horny, with large labella,
cheeks fully one-half eye height, male without orbital bristles.
Claws of male elongate. Hind crossvein nearer to bend of fourth
vein than to small crossvein, apical cell narrowly open before wing-
tip, bend of fourth vein without wrinkle. Frontal bristles descend-
ing to middle of second antennal joint, latter being more than twice
the length of the somewhat elongate first joint, second aristal joint
short, some fine hairs on parafrontals outside the frontal bristles,
facialia bare, epistoma strongly produced. Palpi well» developed,
elongate, a little thickened apically, slightly curved.

Represented in U. S. N. M. by two male specimens collected on
the Rio Ruidoso, White Mountains, New Mexico (Townsend), on
flowers of Rhus glabra, 6,500 to 6,700 feet, July 25 and 20, and by
type of D. pallidus, male, Denver, Colo. The species is large and
robust.

All three specimens may be considered as A. pallida Coq.

76 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
EUPHASIA, nom. gen. nov.

This name is proposed for the Australian Neophasia Brauer and
von Bergenstamm, which is preoccupied in Lepidoptera.

Genus Drepanoglossa Townsend

The genus Drepanoglossa (type, lucens Townsend) has the cheeks
one-third or more of eye height. Epigrimyia is distinct in having
extremely narrow cheeks and parafacials; the eyes long and extend-
ing low, fully to insertion of vibrissze; proboscis shorter, parafacials
hardly widened above, front not prominent, epistoma strongly pro-
duced below, face perpendicular, and tarsal joints short.

Drepanoglossa amydrie, sp. nov.

Three specimens, bred from masses of pupz of a tortricid, Amy-
dria sp., sent by Prof. A. L. Herrera, Cuernavaca, Mexico.

Length, 6 to 7mm. _ Differs from /ucens in whole coloration being
darker; wings slightly infuscate, with a faint yellow tinge in the
marginal cell; the mesoscutum cinereous pollinose with a faint tinge
of brassy; abdominal segments, except anal, with a narrow hind
margin of brown. Proboscis black on apical half.

T ype.—Cat. No. 10,905, U. S. N. M.

Drepanoglossa lucens Townsend.—This species has the wings per-
fectly clear, the mesoscutum pale flesh tint with silvery-white pollen,
the abdomen pale clear yellowish except median line and more or
less of anal segment, no dark hind margin on first segment and only
faint ones on middle segments.

Tribe EpmicRIMYIINI
.

Tribe Epigrimyiini is close to Phaniine, but best retained as a
separate tribe not actually coming within that subfamily. It in-
cludes Epigrimyia only. The genus Drepanoglossa clearly falls
within the subfamily Pyrrhosiine.

Tribe LEUCOSTOMINI

Genus Leucostoma Meigen

Leucostoma nigricornis 'Townsend.—The species nigricornis and
senilis are distinct, and may be recognized by the characters given in
the descriptions. L. nigricornis is essentially a southwestern and
western species, and senilis an eastern and northeastern species.
The former has the antenne more uniformly blackish, the second

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND iy)

and third joints equal in length; the latter has them more rufous,
the third joint being distinctly longer than the second as a rule.
L. nigricornis has the sides of abdomen somewhat reddish at base,
and the femora and tibiz more or less so as well. Both species
belong in Leweostoma. ‘The genus Phyto has the cheeks and para-
facials much widened, the cheeks about one-half eye height.

The species atra Townsend and neomexicana Townsend are like-
wise distinct forms, and do not belong to Phyto. It is doubtful if
they can be properly referred to Leucostoma.

Leucostoma analis Meigen.—This species should not be recorded
from America, as van der Wulp was presumably in error in his
determination of it in Mexican material.

Subfamily PHANIINA

Genus Hemyda Robineau-Desvoidy

Hemyda aurata Robineau-Desvoidy.—The males of this species
have the yellow of third segment wider than the females, but only
slightly so, and nowhere nearly approaching in that respect the form
described below from New Mexico. There are eight specimens of
this form in the U. S. N. M., from Missouri, Kansas, Illinois, and
Wisconsin, one of them being labeled “attracted to light, July, 1876”
(Riley Coll.).

It is interesting to note that one of the above specimens, from
Milwaukee, Wis., has the small crossvein of both wings practically
absent; frontal bristles long, numerous, and thickly placed, and
vibrisse distinct, as in several others of the specimens.

Hemyda sp.—One male, Rio Ruidoso, White Mountains, New
Mexico (Townsend), about 6,500 feet, August I, on flowers of
Monarda stricta. Length, 12mm. Differs from all the above speci-
mens by having the yellow of third segment taking up anterior two-
thirds of length of segment except a median triangular prolongation
anteriorly of the black of hind portion, which stops well before
anterior edge of segment: The femora.have only a faint trace of
the black of aurata in a tinge of brown before apex. The yellow of
second abdominal segment is more extended forward also. The
specimen shows only microscopic vibrissze, invisible save ‘with a
high-power lens.

This specimen probably represents a distinct form, but it is not
deemed wise to name it as such without first securing a considerable
series of specimens to substantiate its claim to distinctness.

78 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Hemyda (Ancylogaster) armata Bigot—It is highly probable
that this is a good species. It may even be a good genus. Bigot
states that the second antennal joint is longer than the third. If it
develops that the second joint in Bigot’s type is strongly elongate,
more so than is aurata, that is to say more elongate as compared
with the first joint (not the third), then it is likely that Ancylogaster
should be retained. ;

Genus Penthosia van der Wulp

Penthosia satanica Bigot.—In this species the fourth longitudinal
vein is slightly rounded at bend, and often bears a very short stump
which can not be considered as the prolongation of the fourth vein
beyond the apical crossvein, since no wrinkle is present in its ab-
sence. It always points straight away from the bend, like the stem
from the arms of a Y, and is to be regarded perhaps as indicating
an original sharp bend of the vein back upon itself for a short dis-
tance, the two approximated parts having later coalesced, finally dis-
appearing more or less completely. The writer knows of no other
tachinid which exhibits this peculiarity in the same devree.

Genus Cercomyia Brauer and von Bergenstamm

Synonyms are Uromyia Meigen (preocc.) and Neouromyia
Townsend, nom. gen. noy. (Trans. Am. Ent. Soc., December, 1891,
to) ’ ’
p. 382).

Subfamily GyMNOSOMATIN.A

Genus Gymnosoma Meigen

The following description of the external anatomy of the male
abdomen will be of interest as throwing light on the taxonomic posi-
tion of the genus.

The male of Gym. fuliginosa Robineau-Desvoidy has six abdom-
inal segments besides the genitalia. The first segment is very short,
and its width is equal to about one-half the greatest width of abdo-
men. It consists below of a small, much shortened, subquadrate,
basal ventral plate, wide in front and somewhat incurvate on front
edge where it joins metathorax, rapidly narrowed posteriorly, its
hind margin much shorter than its front margin. The second ven-
tral plate is a smaller replica of the first, its front edge being the
same length as the posterior edge of first, its sides converging pos-
teriorly on same lines, its posterior edge being correspondingly
shortened. The first and second ventral plates together thus appear
much like a right-angled triangle in outline, with the hypothenuse

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 79

representing the front margin and the right angle cut off truncate
to represent the hind margin.

The first segment consists above and on sides of a strip-like dorsal
plate evenly depressed between its lateral edges, which are tucked-up
rounded folds of the plate, the latter ending ventrally on each side
in a short, pointed strip that does not meet the ventral plate, the ven-
tral membrane intervening between them. A small spiracle, smaller
than any of the others of abdomen, is present in the extreme point of
the first dorsal plate on each side where it joins the ventral mem-
brane, and each one of the other five dorsal plates has a similar but
larger spiracle on its inner edge, these being in each case quite well
removed from the lateral margin where it joins ventral membrane.

The third ventral plate is nearly rectangular, a little broader than
long, about as wide as mean width of second plate. The fourth ven-
tral plate is considerably broader than the third and much shorter,
thus looking like a narrow transverse strip set in the ventral mem-
brane. The fifth ventral plate is much wider than fourth, about
same length, and its median portion (about middle one-third) ap-
pears to be crowded under the fourth plate by the walls of the
sheath-like genital opening, partially retracted within which lies the
hypopygium. Thus only the lateral one-third of the fifth plate is
visible on each side, and these two portions form the narrow visible
strips of the curved plate, bordering the edge of the genital opening
on each side, and each pointed at its outer extremity.

The sixth abdominal segment is not apparent from a dorsal view.
It is a shortened anal segment that has been pushed over and
crowded beneath the extremity of the abdomen. It lies just under
the posterior edge of the abdomen, is rather crescent-shaped, sub-
semicircular on posterior (appearing anterior owing to inverted posi-
tion) edge where it encloses the basal segment of the hypopygium,
slightly squared on anterior lateral corners. It little more than half
surrounds the orifice of the genital cavity, and bears a spiracle on
each side at some distance before the pointed end of its tapering
lateral portion. The basal sclerite or plate of the hypopygium bears
another spiracle, which is one of the largest in the abdomen, on its
basal edge, near the spiracle of the sixth segment and appearing as
if it belonged to that segment. This basal plate of the hypopygium
represents another abdominal segment, and it should be considered
as forming a seventh segment of the abdomen rather than the base
of the hypopygium.

The ventral membrane is widely apparent and extensive, the ven-
tral plates all lying free within it so far as contact with the dorsal
plates is concerned. The area in which the ventral membrane, with

6

80 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the enclosed plates, is visible occupies more than one-third the width
of the ventral aspect of abdomen.

The plates, both ventral and dorsal, are at once distinguished
throughout their extent from the membrane by being clothed with
bristly hairs.

The above description was drawn from a specimen .collected by
F. C. Pratt, at Poolesville, Maryland, July 9. The abdomen was
detached and put under the microscope.

CZDEMASOMA, gen. nov.

This form (male) agrees with the description of Wahlbergia
brevipennis H. Loew, except that the fourth vein is bent at a
rounded angle, and hind crossvein is not strongly oblique. The
hind crossvein is straight, almost at right angles to the fourth vein,
hardly nearer to bend of latter than to small crossvein, and at right
angles to fifth vein. ‘The petiole of apical cell is slightly longer than
small crossvein, but not twice as long—about one and one-fourth
times as long. The abdomen is swollen and strongly convex above,
wider than the thorax, exactly oval in outline from above, the wider
end forward, absolutely without macrochetz. Palpi are extremely
small, almost atrophied, very slender and quite short. Antenne
as long as face, second joint almost as long as third. No orbital
bristles. Wings very short and narrow. The claws are about as
long as last tarsal joint. Type, the following species:

(£demasoma nuda, sp. nov.

One male, Ormsby County, Nevada, July 6, C. F. Baker, Coll.

Length, 6 mm.; of wing, 4 mm. Face, parafacials and para-
frontals from above silvery white pruinose, blackish from in front,
the silvery extending on cheeks. Frontalia silvery white pruinose,
with a faint brassy tinge or a golden reflection. Abdomen densely
covered with moderately short and fine brown or black hairs, and
entirely without bristles, wholly yellowish red or brownish red. The
mesoscutum is silvery pollinose in front of suture, but it does not
show well in some lights. Tegule white. Palpi pale reddish
brownish in color. All the rest of insect is black, except the clear
wings, which are yellowish at base. Otherwise agrees with Loew’s
description of Wahlbergia brevipennis.

This form apparently belongs in the neighborhood of Gymnosoma,
indicated by the absence of macrochete and the possession of a
swollen abdomen. Wahlb. brevipennis H. Loew is this genus, but
a different species. Loew’s specimen is a female from Nebraska,

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND SI

length 42 mm., of wing 3 mm. The writer has examined the type
in Cambridge. The hind crossvein does not form a right angle with
fifth vein, the petiole of apical cell is fully twice as long as small
crossvein, the head is black and shining except face, and the meso-
scutum does not show silvery before suture.

Type.—Cat. No. 10,898, U. S. N. M.

Subfamily OcyPprEeRIn a

Genus Ocyptera Latreille

Ocyptera euchenor \Walker—While it seems probable that this
form and epytus Walker are the same, there can be no certainty in
the. matter until the types are compared. Probably O. caroline
Robineau-Desvoidy is distinct. Some of Bigot’s species may also
prove distinct. It seems probable that caroline is a southern form,
and that euchenor is the more northern large form, having the
cheeks and parafacials narrow, and the eyes elongate, descending
low. Further study may also show the distinctness of dosiades.

Genus Beskia Brauer and von Bergenstamm

Beskia cornuta Brauer and von Bergenstamm and allies——B. cor-
nuta is the South American form. ‘The type is from Brazil. The
figure of the head given by the authors (fig. 276, Muse. Schiz., 1)
is not typical of Southern States specimens in U. S. N. M. There
is a marked difference in the third antennal joint. Williston’s figure
of his St. Vincent specimen shows the third antennal joint same as
the Brazilian. Beskia and Ocypterosipho may be separated on this
character.

Genus Ocypterosipho Townsend

Our species may be known as Ocypterosipho elops Walker. Al-
though Walker says “palpi black,’ and does not mention the slen-
der and elongate proboscis, Mr. E. E. Austen’s statement that @lops
belongs here (Ann. Mag. N. H., Ser. 7, vol. 19, p. 345) must be
accepted. This is the Georgia and Southern States form, and has
the third longitudinal vein bristly to small crossvein (Georgia, Lou-
isiana, and Texas specimens in U. S$. N. M.). Santo Domingo
specimens agree with those from the Southern States in having the
third antennal joint strongly convex on under border and concave
on upper, presenting a curved outline like that of a pruning-knife
blade with cutting edge upward, the anterior distal corner of the
joint being produced in profile into a sharply pointed prolongation.

82 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Van der Wulp’s figure (in the Biol. C. A. Dipt., 11, pl. 13, fig. 12) of
Mexican specimens gives somewhat the same impression. ‘Two
specimens from Mexico (one Tehuantepec, Sumichrast) show this
character markedly, the third antennal joint not being truncate at
tip as in the figures given by Brauer and von Bergenstamm and by
Williston. It therefore seems evident that not only is willistoni a
good species, but the genus Ocypterosipho may be retained, O. wil-
listoni being the West Indian and Central American form, while
O. e@lops is the more northern form occurring in our Southern
States. It is to be noted that St. Vincent belongs to the South
American fauna, while Santo Domingo belongs to the Central
American, which includes parts of Mexico and the Southern United
States.
ICHNEUMONOPS, gen. nov.

Bearing much superficial resemblance to Ocyptera, but differing
radically in the structure of the basal portion of the abdomen, and
in head characters as well. Elongate and narrowed in form. Head,
thorax, and abdomen of almost equal width, but the head distinctly
wider than the thorax, the abdomen constricted basally into a pedicel
formed principally by the base of second segment, which shows
more constriction than any other part.

No vibrisse that can be differentiated from the bristles of peristo-
malia. Second antennal joint rather elongate, about three times as
long as first; third joint elongate, narrowed, about two and one-half
times as long as second. Arista not distinctly jointed. Front at
vertex narrower than eye width, but about equal to latter at base of
antenne. One row of weak frontal bristles extending only to base
of antenne. One pair of weak ocellar bristles, slightly proclinate.
One pair of vertical bristles longer than frontal bristles, directed well
backward. No orbital bristles (male). Cheeks about two-fifths of
eye height. Face receding, facial profile straight, epistoma promi-
nent. Facialia bare, not divergent below, ptilinal area about as
wide as eye width, parafacials about half as wide above, but nar-
rower below. Facial plate elongate, not narrowed below, produced
on lower edge. Antennz inserted above eye middle, rather above
three-fourths of head height. Eyes bare, descending about three-
fourths way to lower margin of head, which is long. Seen from in
front, the space between lower angles of eyes is more than twice that
between upper angles, the frontofacial area evenly widening from
middle of front to cheeks. Proboscis below geniculation hardly as
long as antennz, labella well developed. Palpi extremely small and
short, atrophied. Occiput convex, swollen on lower three-fourths.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 83

Three postsutural bristles, no acrostichal bristles either before or
behind suture. Only one sternopleural bristle (possibly one has
been lost anteriorly on both sides).

Scutellum with a weak apical pair of bristles that are strongly
decussate. Also a much longer marginal subapical pair, and a weak
marginal pair behind last.

Abdomen strikingly Jchnewmon-like in outline, consisting of five
segments: visible from above. Basal segment narrow, but little
wider than base of scutellum, narrowed behind. Postbasal or sec-
ond segment still narrower on basal portion, the greatest constric-
tion being at about anterior three-fourths of the segment where the
abdomen is narrower than scutellum. The second segment grad-
ually widens posteriorly from the point of its greatest constriction,
until on hind border it is twice its anterior width. The third seg-
ment widens posteriorly at not quite same angle, the fourth or pre-
anal segment narrowing posteriorly about as rapidly as the third
segment narrows anteriorly. Anal segment still narrowing pos-
teriorly and evenly rounded on apex. ‘The basal and anal segments
are about same length, the second segment nearly twice as long.
The third and fourth segments are equal and each is a little over
twice as long as anal.

Second, third, and fourth segments with a median marginal pair
of macrocheetz quite removed from posterior border of segment,
also a lateral marginal one on each side. Anal segment with only
an outer pair on each side near hind margin. Second segment with
a lateral one in middle on each side.

Ventral plates not visible, except that the basal plate shows
plainly with adjacent ventral membrane rather widely surround-
ing it.

Wings elongate and narrow, reaching about to end of abdomen.
No costal spine. Small crossvein nearly opposite end of first vein,.
distinctly beyond middle of discal cell. Hind crossvein in middle
between apical crossvein and small crossvein, strongly bisinuate.
Apical crossvein still more strongly bisinuate, quite S-shaped.
Fourth vein produced beyond apical crossvein in a short stump.
Petiole of apical cell half as long as apical crossvein, reaching an-
terior wing border well before wing-tip. No veins spined, not even
third vein at base.

Tegule of moderate size, inner portion subsemicircular in out-
line, so transparent (except narrow borders) that the halteres be-
neath are almost as clearly seen through them as through glass.

84 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

Legs moderately long, but quite normal. Claws and pulvilli
elongate, but not longer than the last tarsal joint, which is itself
elongate. Type, the following species:

Ichneumonops mirabilis, sp. nov.

One male, Beulah, N. Mex., August 17. Prof. T. D. A. Cocker-
ell, Coll.

Length, io mm.; of wing, about 7mm. Wholly dull black, abdo-
men very slightly shining. Antenne light yellowish brownish on
second joint and base of third. Face and parafrontals slightly sil-
very, extending on occipital orbits. Thorax and scutellum thinly
silvery pollinose. Abdomen still more thinly silvery pollinose, the
narrow hind margins of first three segments pale brownish with a
yellowish tinge, that of first segment twice as broad as those of the
- others. ' Legs largely brownish reddish on femora, and especially
on tibiz. Wings on costal half deeply smoky, tinged with yellow-
ish, including basal cells. Tegule and portion of wing behind fiith
and sixth veins clear hyaline; discal and apical cells faintly clouded,
the latter more so.

Type.—Cat. No. 10,899, U. S. N. M.

Tribe CorRoNIMYIINI

Genus Coronimyia Townsend

Coronimyia and Epigrimyia are distinct genera, belonging to and
representing distinct tribes. Coronimyia has the arista short and
geniculate, with very long second joint. Epigrimyia has the arista
elongate, with basal joints short.

EUCORONIMYIA, nom. gen. nov.

This name is proposed for the genus Jsoglossa Coquillett (Can.
Ent., 1895, pp. 125-126), which is preoccupied by Casey in Coleop-
tera (Annals New York Acad. Sci., 1893, p. 304). The characters
are sufficient to retain the genus.

Genus Olenocheta Townsend

Olenocheta kansensis 'Townsend.—This form, Pseudogermaria
georgie Brauer and von Bergenstamm, and Distichona varia van der
Wulp are all generically distinct.

Genus Chztoglossa Townsend

Chetoglossa nigripalpis 'Townsend.—This species differs from
viole ‘Townsend in having black palpi and discal macrochetze on
third abdominal segment. It is also twice the size of viole. By

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 85

some error the words “palpi black” were omitted from the descrip-
tion (Tr. Am. Ent. Soc., x1x, p. 126). C. viole has palpi light
orange, and third abdominal segment is without discal macrochete.

¥ Subfamily THryPTocERATIN
Genus Ceratomyiella Townsend

Ceratomyiella conica Townsend.—This genus may be known by
the apical cell ending but slightly before wing-tip, usually if not
always short petiolate; bend of fourth vein not sharply angular,
third vein bristly not quite to small crossvein, fifth vein not at all
bristly, and costal spine very small. The face is so elongate and
retreating in profile below eyes as to bring the insertion of vibrissz
neatly or quite into the transverse plane of the hind margins of
eyes; the cheeks are one-third’ to one-half eye height in width
(nearly one-half in C. conica).

Chetoplagia has the apical cell narrowly open or closed in border.

Metacheta greatly resembles Ceratomyiella in facial characters.
The facial profile is very receding and elongate below, so as to
bring the insertion of vibrissz close to or nearly into the transverse
plane of hind border of eyes (as viewed in full profile).

ACRONARISTA, gen. nov.

Allied to Schizotachina Walker, from which it is at once distin-
guished by the remarkable characters of the third antennal joint.
This is biramose in the female, being split into an anterior and a
posterior ramus, the two rami almost meeting apically and showing
in profile like an imperfect zero. The inner or under ramus is a
little widened apically; otherwise the profile width of both is prac-
tically the same throughout, even including the base of the joint
where the rami join. The arista is inserted in the anterior edge of
the upper ramus well before its apex, but much nearer the apex than
the base, being at a distance from the apex equal to one-third the
length of the joint. The second aristal joint is only about twice as
long as wide, the first about as long as wide, and the third about
three times as long as second. Front equilateral, about one and
one-half times as wide as one eye, two middle fronto-orbital bristles
in female, facial plate very wide, parafacials reduced to a mere line,
facialia practically bare. Apical cell closed in margin near wing-
tip, last section of fourth vein bent in; hind crossvein distinctly
nearer to small crossvein than to bend of fourth vein, but not nearly
so approximated to small crossvein as in Schizotachina. ‘Third vein

86 _SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
\

with a few bristles at base only, costal spine present. Type, the
following species:

Acronarista mirabilis, sp. nov.

One female, Palm Beach, Florida. Dr. H. G. Dyar, collector.

Length, 4 mm. Blackish, with gray pollen. Antenne reddish
brown, becoming more or less reddish yellow at base. Face, front,
thorax, and scutellum silvery gray pollinose. Abdomen blackish,
narrow anterior margin of second and third segments and all of
fourth segment silvery gray pollinose. Legs quite blackish. Teg-
ulz whitish. Wings faintly tawny at base.

Type.—Cat. No: 11,685, U. S. N. M.

It is strongly probable that the male of Acronarista has the third
antennal joint much more elaborate in structure than that above de-
scribed for the female, and it will be very interesting to look for the
male in South Florida material.

In Talarocera female the location of the arista approaches in a
measure that of Acronarista female, but is not nearly so apical.
Acronarista female seems to be a farther development of Talarocera
female in this regard, in that the ramus of third antennal joint bear-
ing the arista has become elongated and enlarged into almost the
counterpart of the other ramus, the elongation taking place at the
base of the ramus, and thus making the arista subapical thereto. It
is probable that in the male of Acronarista the arista will be found
to be apical to one of many rami, as in the male of Talarocera.
However, this would indicate no near relationship, since Talarocera
is a large form belonging to the Hystriciine.

LIXOPHAGA, gen. nov.

Differs from Gymnostylia by having macrochete of abdomen
only marginal; parafacials and parafrontats bare except for the
frontal and orbital bristles. Male cheeks hardly one-fourth eye
height ; no orbital bristles in male, but a row of six or seven minute
bristles between frontalia and eye margin on the parafrontals.
Apical cell closed in margin just before wing-tip. Hind crossvein
in middle between small crossvein and bend of fourth vein, the latter
rounded and bent at an obtuse angle. Front about one-third head
width, widening on anterior portion. Face fully one-half head
width. Type, the following species.

Lixophaga parva, sp. nov.

One male bred from Lirus scrobicollis, Hunter No. 219, Dallas,
Texas, issued August 15, 1907.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 87

Length, 3.5 mm. Face, cheeks, parafacials, and parafrontals sil-
very, the parafrontals tinged with cinereous. Frontalia, antenne,
and legs blackish. Third antennal joint about three and one-half
times as long as second. Thorax silvery pollinose with tinge of
cinereous abéve; four narrow linear black vitte, the outer ones in-
terrupted at suture, the inner ones abbreviated just behind suture.
Scutellum silvery pollinose. Abdomen blackish, the second to
fourth segments thickly silvery-cinereous pollinose leaving a median
vitta and the hind margins blackish or brown, the vitta not so
marked on anal segment. ‘The pollen of abdomen is flecked with
numerous small dots marking insertion of bristly hairs. Macro-
cheetze in a median marginal pair and a lateral one on first two seg-
ments, weaker than the marginal rows on third and anal segments.

T ype-—Cat. No. 11,648, U. S. N. M.

Subfamily BAUMHAUERIINA

Genus Euthyprosopa Townsend

Euthyprosopa petiolata Townsend.—There are two pairs of
ocellar bristles in this genus, the posterior pair being about same
length as frontal bristles. The anterior pair is strongly proclinate,
almost appressed; the posterior pair is slightly reclinate, suberect,
and inserted between the two posterior ocelli.

Subfamily PLacuna

Genus Plagia Meigen

Plagia aurifrons 'Townsend.—This species is from the northeast-
ern United States, and is not conspecific with the Mexican ameri-
cana van der Wulp.

Genus Plagiprospherysa Townsend

Plagiprospherysa valida Townsend.—It is possible that the
Presidio specimens referred by van der Wulp to his species parvi-
palpis may be conspecific with this species, but the others are likely
to prove distinct.

Genus Heteropterina Macquart

Heteropterina nasoni Coquillett—This form seems, from an ex-
amination of the type, to be quite typical of the genus Heterop-
terina. The cheeks are very narrow, not over one-tenth eye height,
and the few fine hairs of the normal row on parafacials are almost
imperceptible with an ordinary low-power lens, but they are present.

88 | SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Subfamily PHOROCERATIN A

Genus Acheztoneura Brauer and von Bergenstamm

Achetoneura.—This genus is characterized by having the second
antennal joint but little longer than the first, and thus is easily dis-
tinguished from Tachina s. str., to which it otherwise bears a strong
resemblance. ‘Type is hesperus Brauer and von Bergenstamm, of
North America. T. aletie Riley belongs to this genus.

HEMIARGYRA, gen. nov.

Form Pollenia-like, eyes pilose, facialia and hind tibiz ciliate.
Ptilinal suture bent at a rounded angle in middle superiorly, its ends
divergent inferiorly, making the ptilinal area almost triangular in
shape and about one-third head width below. Facial plate elongate,
not narrowed below, depressed, but not produced anteriorly on lower
portion, fosse running full length of plate; fovee shallow, but
marking length of third antennal joint; a low, sharp, narrow carina
fading out before reaching inferior end of fovee. Facialia sharp-
edged, narrow in front outline from being set on edge, with a row of
strong bristles running fully half way up and marking the edge,
which is nearly straight in outline save for a slight curve inward at
lower end, and is closely approximated to suture until it begins to
curve. Vibrissal angles quite distinctly removed from oral margin,
very faintly pronounced, but slightly more approximated than the
rows of bristles above them, the vibrisse strong and decussate.
Peristomalia subparallel in epistomal region, divergent posteriorly,
with a row of black bristles extending to beard. Epistoma not
prominent, not showing in profile. Proboscis very short and fleshy,
part below geniculation hardly as long as eye width, but about as
long as the palpi; labella large, with long hairs; palpi rather elon-
gate, moderately slender, but thickened on apical half. Axis of
head at insertion of vibrisse distinctly less than that at insertion of
antenne, facial profile very gently receding, but nearly straight.
Antenne inserted about on eye middle, at about three-fifths of head
height; second joint rather short, but about twice as long as first;
third joint elongate, not wider than second, sides nearly parallel,
subtruncate at apex. Arista thickened on hardly more than basal
one-third, finely short-hairy, basal joints distinct but short. Eyes
thickly pilose, extending not quite to vibrissal angles, inner outline
appearing slightly bulged on middle by reason of a faint incurvature
below. Front (female) not prominent in profile, at vertex (seen
from in front) about one-fourth of head width, gradually widening

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 89

anteriorly to distinctly more than one-third head width at base of
antenne. No ocellar bristles, but some long fine hairs on and in
front of ocellar area. Frontal bristles in a single row on each side
close to frontalia, but widely divergent at an angle anteriorly, the
foremost two Being out of line with main row and the only ones
inserted below first antennal joint. Vertical bristles consisting of a
moderately strong inner and a very weak outer one, the latter but
slightly longer than the row forming occipital fringe. Two strong,
lightly reclinate upper fronto-orbital bristles inserted close to fronta-
lia, in profile showing same strength and curvature as inner vertical,
all three being same distance apart in profile. Two strong middle
fronto-orbital bristles, strongly curved and proclinate, outside line
of preceding, the posterior one being inserted midway in profile be-
tween the two upper fronto-orbital bristles, the anterior one about
half way between foremost frontal bristle and vertex. Parafacials
wide, only gently narrowed below, fully two-thirds as wide on
lower portion as opposite base of antennz, bare. Width of cheeks
equal to about one-fourth eye height, cheek grooves well marked.
Lower margin of head arcuate, evenly bulged and rounded. Occi-
put considerably swollen below, behind eyes.

Two sternopleural bristles, strong, formula 1:0:1; hypopleural
bristles in a curved row, long but slender; one moderately strong
pteropleural bristle with some fine hairs; three postsutural bristles,
supra-alar bristles stronger. Scutellar bristles in three strong mar-
ginal pairs and a weak apical decussate pair; subapical pair longest,
reaching nearly to base of preanal segment; a widely separated
discal pair about as strong as the apical.

Wings decidedly longer than abdomen, rather broad, with very
small but distinct costal spine. No veins spined, except a few
bristles at base of third vein. Fourth vein bent roundly at an ob-
tuse angle, ultimate section slightly and evenly crooked, no wrinkle
or stump at bend. Hind crossvein bisinuate, slightly more than
one-half as far from bend as from small crossvein, which is on
middle of discal cell and about half way between ends of auxiliary
and first veins. Apical cell well open, ending on front border well
before wing-tip. Tegule very large, antitegulze one-third as long.

Abdomen broadly oval, rounded anally, only four segments vis-
ible from above, with almost equally short marginal and discal
macrochete. Ventral plates not visible. Anal segment with a ven-
tral median cleft, within which is the retracted ovipositor.

Legs not elongate, normal, the hind tibize quite thickly ciliate with
a slightly stronger bristle near middle. Claws and pulvilli (female)
short, not as long as last tarsal joint. Type, the following species:

go SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Hemiargyra nigra, sp. nov.

One female, San Carlos, Costa Rica, collected by Schild and
Burgdortf.

Length, 8.5 mm.; of wing, 8 mm. Blackish, or brownish black.
Palpi reddish yellow, quite thickly black-hairy, blackish at base.
Space from anterior fronto-orbital bristle to cheek grooves con-
spicuously silvery white pruinose as seen from above, covering
whole area of parafacials and anterior half of parafrontals, but ap-
pearing dead black when seen from below. Facial plate silvery
from above, blackish from below. Epistoma yellowish. Third an-
tennal joint three and one-half times as long as second. Cheeks
brownish, clothed with black hairs; cheek grooves and edge of
parafacials bordering suture slightly golden in some lights, brown-
ish or reddish in others, the golden continued on occipital orbits.
Frontalia, thorax, scutellum, and basal abdominal segment soit
black with slight brownish tinge, apex of scutellum silvery. Two
middle segments of abdomen heavily golden silvery pollinose seen
from in front, behind, ar above, but nearly lost when seen from
side ; the coating showing broadly on venter, anteriorly on each seg-
ment at least. Sides of middle segments slightly reddish under the
pollen. Anal segment black, with some golden pollen on sides and
base. Macrocheete as follows: A median and lateral marginal pair
on basal and postbasal segments, a median discal pair on postbasal
and preanal segments, the latter with a marginal row, anal segment
with only bristly and fine hairs. Wings slightly infuscate along the
veins, chiefly on costal half, rest subhyaline. Tegule smoky, with
smoky yellowish borders widening in oblique lights. Pulvilli
whitish, with a slight smoky yellowish tinge. Halteres rufous,
knobs fuscous.

Type.—Cat. No. 10,907, U. S. N. M.

POLIOPHRYS, gen. nov.

Ptilinal suture rounded subangular in middle, its ends divergent
below, giving ptilinal area an oval outline that is quite narrowed
above and fully one-third head width below. Facial plate elongate,
not narrowed below, depressed, produced anteriorly on lower por-
tion; fossee running full length of plate, fovee deep and marking
length of third antennal joint; a distinct narrow carina between the
fovee, with a linear median furrow on its edge. Facialia wide, but
with rather sharp edge, latter gently curved in outline, well inside
suture and furnished with bristles extending more than half way up.
Vibrissal angles quite distinctly removed from oral margin, not

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND OI

sharp, conspicuously more approximated than the rows of facial
bristles above them, the vibrissz strong and decussate. Peristomalia
almost straight, nearly parallel, with bristles extending to beard.
Epistoma prominent, but not showing greatly in profile owing to
strong depression of facial plate. Proboscis short, fleshy, part
below geniculation about as long as eye width (in front view),
labella well developed; palpi elongate, rather slender, more atten-
uate on basal one-third. Axis of head at insertion of vibrisse very
noticeably less than that at insertion of antennz, facial profile gently
receding, but quite straight. Antennz inserted above eye middle,
at about three-fourths of head height; second joint about twice as
long as first, with a pair of bristles on lower front edge; third joint
elongate, wider than second, sides nearly parallel. Arista bare,
thickened on more than basal one-half, conspicuously jointed; first
joint slightly elongate; second joint elongate, two or three times as
long as first, and one-fourth to one-fifth as long as third joint. Eyes
thickly pilose, not extending as low as vibrissal angles, inner out-
line S-shaped in front view in male, straight in female. Front not
strongly prominent in profile, but flattened and sloping straight to
base of antennz; at vertex (seen from in front) one-third head
width in both sexes, in male suddenly swelling in lateral outline an-
teriorly, in female gradually widening anteriorly, almost one-half
head width at base of antennz. A strong pair of proclinate, diver-
gent ocellar bristles. Frontal bristles in two rows, the inner rows
strongly curved and widely divergent below, the outer rows nearly
straight; the lowermost bristle on each side sometimes in line with
both rows so as to appear (male) as belonging to either, but belong-
ing (as shown in female) to inner row, which descends strongly to
point somewhat below insertion of arista. Short fine hairs on para-
frontals, long hairs on and in front of ocellar area. The usual
strong inner and weaker outer vertical bristles, both reclinate, latter
also divergent; two lightly reclinate upper fronto-orbital bristles,
the frontal bristles extending only about half way back from base of
antenne to vertex. No middle fronto-ofbital bristles in male, two
strong, decidedly proclinate ones in female nearly in line with the
posterior one of the upper fronto-orbital bristles. Parafacials wide,
narrower below than opposite antennal insertion, least width about
equal to length of second antennal joint, greatest width bordering
parafrontals and not twice as much. Facio-orbital bristles in a
median row of about five or six, not so strong as frontal or facial
bristles, some fine hairs outside them. Width of cheeks equal to
one-third eye height, cheek grooves faint. Lower margin of head

Q2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

nearly straight, about two-thirds as long as axis of head at antennal
insertion. Occiput swollen below, behind eyes.

Four sternopleural bristles, formula 2: 1:1; hypopleural bristles
in a curved row, strong; pteropleural bristles several, one strong;
four postsutural bristles. Scutellar bristles strongly developed;
apical pair decussate, suberect, weaker than the other marginal ones,
a weak discal pair in front of them; three strong marginal pairs, the
subapical longest and reaching nearly to middle of preanal segment
(male), or only to base of same (female).

Wings a little longer than abdomen, moderately broad, with very
small but distinct costal spine. No veins spined, except third vein
with two or three bristles at base. Fourth vein bent at nearly a
right angle, with very slight (almost imperceptible) wrinkle at
bend, latter not sharp, apical crossvein well bowed in near origin,
hind crossvein slightly bisinuate and approximated to bend of fourth
vein, small crossvein half way between end of auxiliary and end of
first vein. Apical cell widely open, ending far before wing-tip.
Tegule large, antitegule overlapping them for one-third of their
length.

Abdomen rather broadly oval, quite pointed at apex, only four
segments visible above, with strong marginal and short, weak discal
macrochete. Ventral plates not visible. Anal segment in both
sexes with a median ventral slit for protrusion of genitalia, which
are retracted.

Legs not elongate, middle tibiz with three strong bristles in mid-
dle, hind tibize weakly ciliate with a long bristle in middle of ciliated
edge; tarsi normal; male claws and pulvilli elongate, longer than
last tarsal joint; female claws about as long as last tarsal joint.
Type, Poliophrys sierricola sp. nov.

This genus is proposed for what Mr. Coquillett has identified as
Gediopsis mexicana, represented by four male specimens from
Organ Mountains, New Mexico, about 5,300 feet, September 4—5
(Townsend), on flowers of Lippia wrightii; and two specimens,
male and female, from Sierra Madre of western Chihuahua, head of
Rio Piedras Verdes, about 7,000 feet, July 19(/Townsend), on flowers
of Rhus glabra. The Sierra Madre specimens are distinct irom.
the Organ Mountains species, and probably represent two species.
The male from the Sierra Madre, P. sierricola, is made the type,
and the Organ Mountains species is called P. organensis.

The genus differs from Phrissopolia chiefly in having the eyes
pilose. The genus Gediopsis differs from Chetogedia chiefly in
having the eyes hairy. G. setosa Coquillett belongs close to if not
in the genus Poliophrys.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 9

io)

Poliophrys sierricola, sp. nov.

One male, Sierra Madre, Chihuahua, collected by Townsend.

Length, 9 mm.; of wing, 74% mm. Blackish, clothed with silvery
cinereous. Parafrontals with a golden tinge (male), which extends
very faintly on parafacials and cheeks. Facial plate silvery.
Frontalia seen from in front silvery, seen from behind brownish.
Antenne brownish, third joint blackish and three times as long as
second, arista blackish. Palpi yellowish. Thorax silvery pollinose,
with four moderately wide vittee, which are blackish seen from be-
hind, but salmon colored seen from in front. Scutellum light
brownish reddish, blackish at base, silvery. Abdomen silvery,
slightly marmorate above, with a faint golden tinge which is strong
on anal segment, where it is about the same as on parafrontals.
Sides of abdomen faintly reddish under the pollen. Wings clear,
tegule whitish. Legs blackish, femora silvery; tibiae reddish or
brownish yellow, except at ends; pulvilli slightly smoky.

Type.—Cat. No. 10,908, U. S. N. M.

A female from same locality differs only in second antennal joint
being clear reddish yellow, the third joint little more than two and
one-half times as long as second, and the sexual characters given
above under the genus. It may prove to be a distinct species, but
more material is needed to make sure of this.

Poliophrys organensis, sp. nov.

Four males, Organ Mountains, New Mexico, Townsend, Coll.

Léngth, 8 to 10 mm.; of wing, 6 to 7.5 mm. Front fully one-
third head width at vertex, cheeks more than one-third eye height
in width. Differs further from P. sierricola in having hardly a
tinge of golden to the pollinose covering of head, which is silvery
white throughout face and with only a slight tinge of golden on
parafrontals not extending on facial plate at all. Antenne black,
third joint nearly four times as long as second (male). Abdomen
more noticeably reddish on sides; anal segment less distinctly
golden, about the same as other segments.

Type.—Cat. No. 10,909, U. S. N. M.

PHRISSOPOLIA, gen. nov.

This genus is proposed for Prospherysa crebra van der Wulp,
which was included in Chetogedia by Brauer and von Bergen-
stamm. It is characterized by a double row of frontal bristles, the
outer row nearly or quite as strong as the other, and especially by a
row of strong bristles on parafacials close to orbit, the facio-orbital

04 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

bristles, of same strength as frontal bristles, and, except for their
downward curve, appearing like a continuation of latter to lower
eye border. The second aristal joint is long, the third much shorter
than in Chetogedia, and the whole arista is widened and flattened,
usually geniculate or subgeniculate. Eyes bare.

Phrissopolia desertorum, sp. nov.

Las Cruces, New Mexico, Cockerell, No. 4,952. Specimens from
Beulah, New Mexico (Cockerell), and Santa Clara County, Cali-
fornia, may also be referred to this species.

Length, 9 to 10 mm. The species differs from van der Wulp’s
description of crebra as follows: All the tibiz rufous (male) or yel-
lowish (female). Face, including parafacials, silvery roseate white
in male without yellowish tinge, which is confined to front; in fe-
male with a faint yellowish white tinge spreading over face. Third
antennal joint of male four times as long as second, of female three
times as long. Arista thickened nearly to end in both sexes, only
the apical one-third or one-fourth appearing slender from certain
viewpoints due to flattening; second joint very distinct, elongate,
fully one-fourth as long as last joint, the articulation geniculate in
some cases. Hind tibiz rather weakly ciliate, with a long bristle in
middle. Wings faintly yellowish tinged at base.

Type.—Cat. No. 10,910, U. S. N. M. (Las Cruces, N. Mex.).
Genus Chetogedia Brauer and von Bergenstamm

Chetogedia acroglossoides 'Townsend.—This is a good species.
It is neither a Frontina nor a Baumhaueria, but is apparently to be
referred to Chetogedia. Frontina has the parafacials bare, and the
second aristal joint is not elongate. Bauwmhaueria has the front
greatly produced, the parafacials hairy and of exaggerated width,
much wider than,the eyes, and the cheeks as wide as eye height.

The identification of this species with Bawmh. analis van der Wulp
is quite out of the question, if the description agrees with the type.
The second antennal joint is elongate, the third is not over four
times as long in male and less than three times as long in female as
second joint. The description was of the female.

Chetogedia vilis van der Wulp, the type of the genus, has the
frontal bristles in two rows, the outer row usually weaker, and the
parafacials are clothed only with fine bristly hairs.

Genus Gediopsis Brauer and von Bergenstamm

Gediopsis cockerelli Coquillett—This species appears to be cor-
rectly referred to the genus Gediopsis. ‘The material from which it

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 95

was described was all collected by the writer in the White Mountain
region of New Mexico (not New Hampshire, as given in the Cata-
logue), at about 8,000 feet, on the head of Eagle Creek, a stream
which takes its rise on the upper slopes of the peak known as Sierra
Blanca (altittide, 10,050 feet).

TREPOPHRYS, gen. nov.

Head in profile almost half round. Antenne inserted about at
eye middle. Front flattened, rounded in profile, showing just the
same width beyond eye margins as do parafacials. Eyes bare, reach-
ing quite to vibrisse. Cheeks very narrow, not over one-tenth of eye
height. Front about one-third of head width, or slightly less, the
inner outline of eyes but slightly divergent below base of antenne.
Parafrontals a little wider than frontalia, parafacials gradually
narrowing from base of antennz until they become almost linear
at lower eye margin. Prtilinal suture inverted V-shaped, the median
angle a little rounded. Ptilinal area elongate, about one-third head
width below. Facial plate elongate, not narrowed below, depressed,
with a distinct and sharp but low median carina full length, not
produced at lower margin. Facialia edge-like, bristly more than
half way up, vibrissal angles hardly perceptible. Vibrissee inserted
close to oral margin, well developed.

Frontal bristles in a single row close to frontalia and extending
back to ocelli, all curved inward, more or less decussate, descending
in front to insertion of arista. The usual strong inner and weak
outer vertical bristles. ‘Two upper reclinate fronto-orbital bristles
set well forward, almost far enough forward to occupy the usual
place of insertion of the middle or proclinate ones. These two
fronto-orbital bristles are of exactly the same strength, length,
curvature, and direction as the inner vertical bristle, and look like
two replicas of it in profile. They are also quite in line with it, and
the three in profile are seen to be an equal distance apart. Two
proclinate middle fronto-orbital bristles in female, outside the upper
ones; none in male.

Proboscis short and fleshy, palpi slender and normal. Second an-
tennal joint about twice as long as first; arista indistinctly jointed
and minutely pubescent, slightly thickened on basal one-third. Third
antennal joint about two and one-half times as long as second.
Occiput slightly swollen behind on lower one-fourth, the lower mar-
gin of head short, long axis of head at vibrissz but little over one-
half that at base of antenne.

Three sternopleural bristles, 1. 1. 1, the middle one weakest, the
posterior one strongest. Three postsutural bristles. Scutellar

7

96 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

bristles in five pairs, one decussate apical, three lateral, of which
anterior and posterior are longer and stronger, and one separated
discal pair.

Abdomen above of four visible segments, macrochztz only mar-
ginal.

Wings reaching well beyond end of abdomen, apical cell narrowly
open just before and almost in wing-tip, ultimate section of fourth
vein bowed in about the middle so as to attenuate the terminal por-
tion of apical cell. Hind crossvein slightly curved, not quite in
middle between small crossvein and bend of fourth vein, distinctly

nearer latter.

None of the veins spined, the small crossvein slightly

or distinctly before middle of discal cell.
Legs normal, hind tibiz weakly ciliate, with a bristle or two

among the cilia, claws and pulvilli very short.

n. Sp.

Type, T. cinerea,

Comes near Pseudocheta Coquillett, with which it agrees in the
arrangement of the upper and middle fronto-orbital bristles, and

from which it differs as follows:

Pseudocheta

Antenne inserted distinctly above
eye middle in both sexes, but es-
pecially so in the male.

Two sternopleural bristles.

Four postsutural bristles.

Apical cell ending not far but very
distinctly before wing-tip.

*Hind crossvein almost in middle,
male; nearer bend of fourth vein,
female.

*Small crossvein nearly in middle of
discal cell, male; before middle,
female.

Wings very short and broad, hardly
more than twice as long as wide.
Head distinctly widened.

Trepophrys cinerea, sp. nov.

Trepophrys

Antenne inserted practically on eye
middle in both sexes.

Three sternopleural bristles.

Three postsutural bristles.

Apical cell ending slightly before,
almost in, wing-tip.

* Hind crossvein distinctly nearer bend
of fourth vein, male; almost in
middle, female.

*Small crossvein well before middle
of discal cell, male; nearly in mid-
dle, female.

Wings elongated beyond end of ab-
domen, at least two and one-half
times as long as broad.

Head hardly wider than thorax.

Three specimens bred from masses of pupe of a tortricid, Amy-
dria sp., sent by Prof. A. L. Herrera, from Cuernavaca, Mexico.

Length, 4.5 to nearly 6 mm.

Blackish, parafrontals and para-

facials golden, extending on occipital orbits; frontalia, antenne, and

face blackish, latter with a slight silvery reflection.
Pleurz very faintly silvery.

golden.

Cheeks slightly
Dorsum of thorax and abdo-

* These characters represent the average of the specimens.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 97

men cinereous pollinose, with a distinct golden tinge most noticeable
on scutellum. First abdominal segment, narrow hind margins of
second and third, and apical half of anal blackish, the black surface
of anal segment shining. Wings clear, tegule whitish with a tawny
tinge. Legs black.

Type.—Cat. No. 10,911, U. S. N. M.

Subfamily MASICERATIN AS
Genus Exorista Meigen and allies

The genus E-vorista, as restricted, has the cheeks wide, one-third
to one-half eye height; second antennal joint somewhat elongate,
and abdominal macrocheetz discal and marginal.

Parexorista differs from E.vorista in cheeks being not over one-
fourth eye height, second antennal joint not elongate, second aristal
joint usually elongate; abdominal macrochetze usually only mar-
ginal, but long discal bristles present, those on third segment ap-
proaching macrocheete in character.

The genus Carcelia Robineau-Desvoidy may be known by hav-
ing no long discal bristles on abdominal segments, all being short
and of even length. Macrochetz only marginal. Cheeks not over
one-fourth eye height. Type, gnava Meigen.

Nemorilla has cheeks not over one-fourth eye height, second an-
tennal joint elongate, second aristal joint short, macrocheetz discal
and marginal, hind tibiz weakly ciliate.

EUSISYROPA, gen. nov.

Proposed for Exorista blanda Osten-Sacken. Differs from Parex-
orista in possessing regularly arranged discal macrochetze on ab-
dominal segments, without the erect and usually long bristly hairs
of that genus, and especially in the peculiar form of the abdomen in
both sexes. The latter is high, somewhat arched, slightly wedge-
shaped ventrally in female, and obliquely truncate downward and
forward at apex in profile. The female has these abdominal charac-
ters more marked, but the male also possesses them in a hardly less
degree. The female has the venter quite distinctly carinate.

Eusisyropa blanda Osten-Sacken.—This species has the legs and
second antennal joint more or less deeply blackish or brownish,
with usually only faint suggestions of yellowish or reddish. The
palpi have a reddish tinge. Both sexes have the parafrontals with
a slight golden tinge, and anal segment very distinctly golden.
There are two sternopleural bristles only.

Sire SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

New Jersey, New York, Massachusetts, and south to District of
Columbia.

This species has been bred from Cymatophora pampinaria Guenée,
one specimen issuing from a larva collected on cranberry at Cotuit,
Massachusetts, by J. B. Smith (Riley Notes, Bureau of Entomol-
ogy) ; also from Hyphantria textor, at Washington, D. C. (No. 78%
Riley Notes).

One female specimen was bred at the Gipsy Moth Parasite Labo-
ratory, North Saugus, Massachusetts, issued July 29, 1907, which
may have come from native Euproctis chrysorrhea.

Eusisyropa boarmie Coquillett—This is a Florida and Southern
States form closely allied to blanda. It reaches Arkansas and Mis-
souri. It has light reddish yellow legs and second antennal joint,
these being quite concolorous with the reddish yellow palpi, and
possesses a small third sternopleural bristle.

The type specimen was bred from a larva of Aletia argillacea,
received from Oxford, Mississippi, issued November 14, 1882 (No.
468 L,°, Riley Notes, Bureau of Entomology). ‘The species has not
been bred from Cymatophora (Boarmia), the Boarmia-bred speci-
men mentioned by Coquillett being E. blanda.

Genus Argyrophylax Brauer and von Bergenstamm and allies

The following is a table of Argyrophylax and the forms closely
related to it:

1. Ocellar bristles wanting (type, albincisa Wd.).......... Argyrophylax B.B.
Weellar bristles presenta Mi pew ale .c wisn sng dow RE BR Pe 2

2. Apical pair of scutellar bristles much stronger than those next to them,
hind tibial cilia dense (type, pupiphaga Rdi.)............. Sturmia R. D,
Apical pair of scutellar bristles much weaker than those next to them.. 3

3. Third abdominal segment of male with two shining or pilose black spots

on ventral surface, a distinct longer bristle in cilia of hind tibiz near
middle (type, Gimacwlata Ete. Vis... sec tk es 6 oe aa Zygobothria Mik.

' Third abdominal segment of male without such spots, hind tibial cilia
dense and without longer bristle (type, scutellata Rdi.)...Blepharipa Rdi.

Argyrophylax piperi, nom. sp. nov.

This name is proposed for Sturmia schizure Coquillett, which is
an Argyrophylax. The specific name is preoccupied by Argyr.
schizure Townsend.

Pullman, Washington State (Piper). Bred from Schizura ipo-
mea.

Length, 10.5 mm. Much larger than type of A. schizure Town-
send, with which it at first seemed identical. Agrees with descrip-

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 99

tion of A. schizure Townsend except as follows: The facial plate
shows no appreciable tinge of golden, fourth vein is quite abruptly
bent, first abdominal segment has one lateral marginal macrocheta,
second segment has a lateral marginal pair of macrochete, pulvilli
are smoky blackish, and size is larger.

Genus Zygobothria Mik.
Zygobothria nidicola, sp. nov.

Male.—Fifteen specimens. ‘Thirteen bred at the Gipsy Moth
Parasite Laboratory, North Saugus, Massachusetts, as follows:
Four bred by E. S. G. Titus, in 1906, from Euproctis chrysorrhea
imported from Germany (Erfurt, Munich, and Fuhlsdorf, received
from Marie Ruhl) ; nine bred by W. F. Fiske, in 1907, from hiber-
nated larve of Euproctis chrysorrhea from imported nests received
from Vienna and other parts of Nieder-Oesterreich, and from sum-
mer importations of larve of same species from South Tirol and
Carniola. ‘Two bred at Simferopol, Russia, by S. Mokschetsky,
from Euproctis chrysorrhea, June 7, 1905, and July, 1907.

Length, 7 to 9 mm. Eyes very faintly hairy, appearing bare.
Antenne blackish, third joint more or less reddish or lighter colored
at base, palpi light yellow. Face and front silvery, parafrontals
darker in some lights, but not golden. No middle fronto-orbital
bristles. Frontalia slightly, if any, wider than one parafrontal.
Parafrontals with fine hairs outside the row of frontal bristles.
Front anteriorly hardly as wide as one eye, half as wide as one eye
at vertex. Facialia with some bristles extending about one-third
way up. Arista thickened on less than proximal half, first two
aristal joints short. Cheeks hardly one-third eye height. Thoracic
dorsum thinly silvery pollinose. Scutellum testaceous except ex-
treme base, apical pair of bristles weak, almost erect, decussate.
Abdomen with more or less red on sides, first segment and narrow
hind borders of second and third segments shining black, rest
thickly cinereous pollinose leaving a more or less distinct median
line. A median marginal pair of macrochetz on first and second
segments, also three lateral marginal ones on each side of same seg-
ments, third segment with a marginal row of twelve or fourteen.
Anal segment with only bristly hairs. Legs wholly black, claws
and pulvilli very elongate, hind tibize thickly ciliate, but with a
longer bristle near middle. Tegule white. Four sternopleural and
four postsutural bristles, a few specimens showing a fifth weaker
sternopleural bristle.

100 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

A specimen of this series sent to Dr. K. Kertész, at Budapest, was
returned by him as Argyrophylax galu Brauer and von Bergen-
stamm. As gali has the male vertex one and one-third times the
-eye width and female vertex twice the eye width, this can not be
that species. Two specimens sent to Dr. A. Handlirsch, at Vienna,
‘were returned as unknown to him, and indicated with a query as
American.

Female.—Fourteen specimens. ‘Twelve bred at the Gipsy Moth
Parasite Laboratory, North Saugus, Massachusetts, as follows: Five
bred by E. S. G. Titus, in 1906, from Euproctis chrysorrhea im-
ported from Germany (Baden and Dresden, received from Marie
Ruhl and Schopfer, respectively) ; seven bred by W. F. Fiske, in
1907, from summer importations of Euproctis chrysorrhea from
Germany. Two bred at Simferopol, Russia, by S. Mokschetsky,
from Euproctis chrysorrhea, June 10, 1905, and July, 1907.

Length, 7 to 8 mm. Differs from the male as follows: Thickly
yellowish-cinereous pollinose all over, including front and. first ab-
dominal segment. Face more silvery. Thoracic vitte fine, outer
ones broken at suture and somewhat widened. Scutellum yellowish
on margin. Middle fronto-orbital bristles two in number. Front
from more than one-third to about two-fifths width of head, hardly
narrowed from facial width. Abdominal macrochetze same as male,
but the second segment rarely has four median marginal macro-
chetz more or less well developed from the long marginal hairs on
each side of the original pair. Hind tibiz sparsely but distinctly
ciliate, a long bristle near middle. Four sternopleural and four
postsutural bristles.

A specimen of this series sent to Dr. K. Kertész was returned un-
determined; another sent to Dr. A. Handlirsch was ‘returned as
unknown to him, and probably American. The two sexes were not
suggested by either Kertész or Handlirsch as belonging together,
but it seems highly probable that they are the same species. Both
are positively European, as conclusively demonstrated not only by
the breeding records of the Gipsy Moth Parasite Laboratory, but
also by Mr. Mokschetsky’s breeding of both at Simferopol, Russia.

Types—Cat. No. 11,803, U.S. N. M. (2 types: male from Nieder-
Oesterreich, issued July 29, 1907; female from Central Europe,
issued July 10, 1907).

Mr. W. F. Fiske has bred this species (male specimens) from
cages containing hibernated larve of Euproctis chrysorrhwa under
circumstances indicating that the female tachinids oviposit in the
Euproctis nests in the fall, the tachinid larve remaining through the
winter in the nests and issuing from the host larve or pupz in the

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND IOL

summer. ‘This is a remarkable habit of oviposition among tach-
inids, and credit is due to Mr. Kiske for the discovery of it.

Genus Comatacta Coquillett
Comatacta nautlana, sp. nov.

The material upon which the genus Comatacta Coquillett was
founded was collected at San Rafael, near Jicaltepec, Veracruz
(Townsend). ‘The specimens were erroneously identified with
Brachycoma pallidula van der Wulp (Can. Ent., 1902, pp. 199-200),
which is to be considered the type of the genus Comatacta.

The present species differs from van der Wulp’s description of
pallidula as follows: Facial plate silvery like parafacials; frontalia
honey yellow, parafrontals silvery with a golden shade. Frontal
bristles descending but one or two below base of antenne. Beard
very short, grayish. Antenne reaching two-thirds to three-fourths
way to oral margin. Arista rufous, concolorous with antenne.
Anal segment hardly at all rufous.

T ype-——Cat. No. 10,906, U. S. N. M.

PARADEXODES, gen. nov.

Wings longer than Devodes (type spectabilis Meigen), abdomen
very bristly like Derodes, with many discal macrochzte and erect
hairs, apical pair of scutellar bristles weak but long and markedly
divaricate. Eyes bare; male front narrow, about or nearly equal-
ing eye width anteriorly, vertex about or more than one-half eye
width. Frontal bristles in male closely placed, descending three to
four below base of antennz. Ocellar bristles present. Vibrissz
close to oral margin, facialia with a number of bristles above
vibrissee. Parafacials quite narrowed below, widening above. An-
tenn inserted on eye-middle. Second antennal joint nearly three
times as long as first; third joint narrow, two or.more times as long
as second, equilateral in profile, subtruncate at tip. Second aristal
joint short but distinct, arista thickened on proximal fourth. Legs
rather long, male claws and pulvilli elongate. Wings long and nar-
rowed in male, apical cell open well before wing-tip, hind crossvein
approximated to bend of fourth vein, small crossvein on middle of
discal cell. Abdomen elongate, conico-cylindrical in male. Type,
the following species:

>

Paradexodes aurifrons, sp. nov.

One male, North Saugus, Massachusetts (Gipsy Moth Labora-
tory, bred in Cage FE, 14 July, 1906. No. 698, E. S. G. Titus. Host
unknown).

102 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Length, 1o mm. Blackish, gray pollinose. Entire face and front,
even including cheeks and orbit, deep golden pollinose. Frontalia
quite black, nearly as wide as one parafrontal. Antenne blackish.
Palpi reddish yellow. Thorax and scutellum very thinly pollinose,
humeri thickly so. Abdomen quite uniformly pollinose except first
segment, thickly bristly and hairy. Legs entirely black, femora
pollinose on under side. Claws long and black, pulvilli smoky.
Tegule whitish, with narrow yellowish edge.

T ype.—Cat. No. 11,686, U. S. N. M.

Paradexodes albifacies, sp. nov.

One male, White Mountains, New Hampshire, Morrison. This
specimen is figured in Dr. Howard’s Insect Book, pl. 22, fig. 7, as
Hypostena variabilis Coquillett, but is not congeneric with the type
of that species.

Length, 9.5 mm. Face and front, cheeks and orbits silvery white.
Frontalia reddish brown, wider than one parafrontal. Antenne
reddish brown. Palpi yellow. ‘Thorax, scutellum, and abdomen
shining black, very thinly bluish silvery pollinose, most thickly so on
humeri and bases of last three abdominal segments. Legs blackish
brown, femora silvery beneath, pulvilli yellowish white, claws pale
reddish brown. Tegule white, with narrow yellowish edge.

T ype.—Cat. No. 11,687, U. S. N. M.

i
Genus Ceromasia Rondani
Ceromasia aurifrons, sp. nov.

Three females and one male, New Hampshire (2 females and the
male from Canobie Lake, Dimmock).

Length, 7.5 to 10 mm. Differs from the European C. florum
Meigen (determined by Brauer and von Bergenstamm) by having
whole of parafrontals, parafacials, and orbits deep golden in both
sexes, even the cheeks showing golden in fresh specimens; the pollen
of thorax and abdomen whitish gray, without the brassy tinge of
florum ; anal segment in both sexes with a noticeable tinge of golden,
and scutellum testaceous only on apical half.

Type.—Cat. No. 11,649, U. S. N. M. (female).

Two males of this species were bred at the Gipsy Moth Parasite
Laboratory, North Saugus, Massachusetts, by E. S. G.. Titus, from
unidentified lepidopterous larve.

Ceromasia auricaudata, sp. nov.

Two females and one male, Harrison, Idaho (male and female),
and Pullman, Washington (female, July 16).

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 103

Length, 7 tog mm. Differs from C. aurifrons ‘Townsend by hav-
ing the anal segment wholly deep golden, same shade as para-
frontals, etc.; humeri with a faint, abdomen with a more distinct
golden tinge, scutellum hardly more narrowly testaceous, and thorax
more distinctly vittate.

Type.—Cat. No. 11,650, U. S. N. M. (female, Harrison, Idaho).

EUDEXODES, gen. nov.

This genus is proposed for Dexodes eggeri Brauer and von Ber-
genstamm, of Europe. The characters of the facial plate throw the
species into a different tribe (if not subfamily) from Devrodes, of
which the type is spectabilis Meigen.

Subfamily WILLISTONINA

Genus Belvosia Robineau-Desvoidy and allies

Dr. Williston published a plate of Belvosia and allies in Insect
Life, vol. v (1893), facing p. 238, exhibiting the difficulties to be en-
countered in separating the forms. By studying this plate, it will
be seen that there is a correlation between length of second antennal
joint and bristles on the facialia, also between former and distance
of vibrissze from oral margin.

The more elongate the second antennal joint is, the less bristles
there are on the facialia. Conversely, the shorter the second joint,
the more strongly are the facialia ciliate. In all cases, the distance
of the vibrissz above the oral margin is about equal to the length of
the second antennal joint.

The forms having facialia not ciliate have the second antennal
joint long, vibrissze inserted far above oral margin, and fourth vein
angular at bend. ‘Those having facialia ciliate have the second joint
much shorter and vibrissz inserted only a little above oral margin;
they fall into two categories by the character of the bend of fourth
vein. We thus have the following table:

1. Facialia not ciliate, fourth vein angular at bend; second antennal joint
strongly elongate, nearly as long as third joint; vibrissz inserted high
above oral margin, male claws normally very elongate, female claws
less elongate. (Sto. Domingo, Brazil, California, New Mexico,
Mexicos Jianialcde re cere sericis cic eiaare Belvosia bicincta Robineau-Desvoidy

attired FAN CAIALE Meaty eae 6 shies Pe otha oe a mee eR a's 2

2. Fourth vein bent at a sharp angle, with or without stump, but often
V-shaped and with stump; claws of male normally elongate, of female
not; second antennal joint not strongly elongate, vibrissz inserted
normally above oral margin. (Brazil.)...Wéllistonia esuriens J. C. Fabricius

104 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Fourth vein rounded at bend, second antennal joint short or only appre-
ciably elongate; vibrisse inserted close on or only appreciably above
oral margin, about as far above as length of second antennal joint;
male claws usually not elongate, but longer than the short female

GLOWS tees ee woe Latreillimyia, nom. nov. (Latreillia preoce.) 3
=, Waibrese itiserted: close om the ‘oral imateini«. 2 ane cele vse bases oe 4
Vibrissze inserted appreciably above the cral margin, male claws
strongly elongate. (Brazil, Pennsylvania.)........... L. (aberrant form)
4. Second antennal joint appreciably elongate, female claws rather’ short.
(QM DESH GYERTO EA) se ws at et aoe Re eau ARES rc LL. (intermediate form)
Second antennal joint short, not at all elongate. (Brazil, Mexico, New
GIES Niche thst saad 4 arsts Bob asd vee Ieee mae Latreallimyia (typical forms)

bifasciata J. C. Fabricius, leucopyga (van der Wulp) Williston.

The character of the ciliate facialia is more important than the
venational character and the same holds good of the vibrissal charac-
ter and the elongation of second antennal joint. As already pointed
out in a previous section of this paper, the relative length of the sec-
ond and third antennal joints will not hold for generic separation,
since the length and size of the third joint in these flies is largely a
sexual character. But the actual length of second joint taken inde-
pendently furnishes a good character. Only a few genera have the
second joint elongate. It may be compared in length with the first
joint. The first two joints do not vary sexually.

Brauer and von Bergenstamm state that the claws of male are
elongate in Wullistonia and short in Latreillimyia. It is doubtful
how far these characters can be relied upon, since they are also
sexual. The same authors also give as a character of Willistonia a
stump at the angular bend of fourth vein and the angle more ap-
proximated to hind margin of wing. These may hold good, espe-
cially the latter, but are not necessary for the separation of the forms
at present known to us. Further material will probably call for
their use.

The writer pointed out in 1892 (Trans. Am. Ent. Soc., xIx, p.
89) that bifasciata has the facialia strongly ciliate and bicincta has
not; that five specimens of bicincta from New Mexico had the third
antennal joint scarcely longer than the second, which means that the
second joint was strongly elongate; that three specimens from New
York were easily referable to bifasciata, and one from Jamaica to
bicincta; and that, while the parafacials are bare in both species, the
whole anterior aspect of head is altogether more bristly in bifasciata,
which possesses also greater hairiness of cheeks.

The elimination of Belvosia, argued for by Brauer and von Ber-
genstamm, is not permissible under the rules of the International
Code. Its maintenance fortunately does not conflict with the genus
Villistonia, since bicincta differs generically from esuriens.

ia.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 105

Belvosia and Latreillimyia show no ventral plates or ventral mem-

brane. :
LATREILLIMYIA, nom. gen. nov.

This namesis proposed for Latreillia Robineau-Desvoidy (1830),
which is preoccupied by Roux in Crustacea (1827).

GONIOMIMA, gen. nov.

This genus is proposed for Belvosia luteola Coquillett. Bears a
striking resemblance to Gonia. Second antennal joint short, third
joint very long and narrow; arista long and flattened whole length,
in front view appearing as a mere line, but in lateral view showing
itself to be uniformly widened nearly to apex; frontal bristles in one
main inner row bordering frontalia, with a row of weaker bristles
outside, and orbital bristles (female) outside these; second aristal
joint very short, front not widened and swollen, facialia ciliate
almost to base of antenne. Abdomen appearing conical from above,
but laterally appressed on apical portion, fully as thick dorso-
ventrally for its whole length as its greatest width, which is at base.
The body and wing characters agree perfectly with Gonia, but the
head characters are totally different, and it is the latter which place
the genus in the Willistoniinz.

The genus appears to come near Thelymorpha Brauer and von
Bergenstamm, but is at once distinguished by having no discal
macrochetz on abdomen. ‘The head is almost the same, and the
abdomen is described as very similar.

TRIACHORA, gen. nov.

°
This genus is proposed for Latreillia unifasciata Robineau-Des-
voidy, of which E-vorista flavicauda Riley is a synonym. Differs
from Latreillimyia in having three rows of frontal bristles on each
side of frontalia, besides the fronto-orbital bristles of female. The
arista is flattened, and the antennal characters are similar to those of
Goniomima. ‘The main or strongest row of frontal bristles, of the
three rows on each side, is in the middle, the inner row being de-
cidedly weaker, and the outer row but little weaker than the main or
middle row.
Genus Rileymyia Townsend

(Ent. News, 1893, p. 277)

This name was proposed by the writer in 1893 for Rileya Brauer
and von Bergenstamm, which is preoccupied in Hymenoptera. The
type of the genus is Blepharipeza fulvipes Bigot, according to Brauer

106 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

(Sitzungsber. Math.-Naturwiss. Cl. k. Akad. Wiss., cv1, 1, p. 348),
who says that R. americana Brauer and von Bergenstamm is a
synonym of Bigot’s species. B. adusta H. Loew is also typical of
the genus, which may be distinguished from Blepharipeza by the ab-
sence of apical scutellar bristles and thornlike macrochete.

Rileymyia albifacies Bigot.—Brauer (1. c.) says this is a synonym
of fulvipes Bigot, but in view of the widely removed type localities
it would seem that the point needs verification. i. albifacies was
founded on a specimen from Brazil, while fulvipes is from Washing-
ton State. FR. americana is from California.

Subfamily MErIcENUN aA:
Genus Viviania Rondani

It must be noted that this genus is characterized quite fully by
Rondani on p. 53, vol. 1v, of Dipt. Ital. Prod., where the imperfectly
erected Biomyia (1. c., vol. 1, p. 72) is given as a partial synonym.
Biomyia does not cover the same forms, so far as any one knows,
and its one-line characterization entitles it to no notice in the face of
its author’s subsequent rejection of it. It is therefore quite out of
the question to attempt to use it, especially since we have no defini-
tion of it.

Viviania mutabilis Coquillett, ete—Biomyia mutabilis is a Viv-
tania. So also is B. aurigera Coquillett. B. genalis Coquillett does
not belong anywhere near this genus.

Viviania lachnosterne, sp. nov.

One female, Urbana, Ill. (No. 36,817, Forbes). “Supposed to
have bred in Lachnosterna adults.”

Length, 10 mm.; of wing, 8 mm. Gray-cinereous, more or less
silvery. All three antennal joints and arista wholly reddish yellow,
the frontalia same color posteriorly, but darker in front. Para-
frontals blackish, thinly silvery. Parafacials more distinctly silvery.
Ptilinal area blackish, the lower portion of facial plate broadly yel-
lowish on oral margin. Palpi light reddish yellow. Mesoscutum
with five vitte, the middle one narrow behind and obsolete in front
of suture, the outer ones more or less triangularly widened, shorter
and more triangular in front of than behind suture. Wings wholly
hyaline, tegulz white. Legs wholly blackish, femora silvery below,
pulvilli smoky. Abdomen black, thickly cinereous pollinose.

Type.—Cat. No. 10,913, U. S. N. M.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 107

Genus Tachinomyia Townsend

Tachinomyia robusta Townsend.—The genus differs from Tachina
in the vibrissz being inserted higher above oral margin, cheeks one-
half eye height in width, and abdomen very elongate.

Genus Emphanopteryx Townsend

Emphanopteryx ewmyothyroides Townsend.—This genus differs
from Cryptomeigenia by having the abdomen large; claws and pul-
villi of female elongate, those of male very long and strong; arista
finely pubescent, strong subdiscal and discal macrochetz (at least
on second segment), fourth vein rather angular at bend and usually
represented beyond apical crossvein by a short stump.

Subfamily TAcHININa
Genus Tachina Meigen

Tachina clisiocampe Townsend.—Achetoneura fernaldi Williston
is very probably a synonym. The strongly marked wrinkle at an-
gular bend of fourth vein, the elongate second antennal joint which
is about three times as long as first, the frontal bristles descending
low on parafacials, and the strongly ciliate facial ridges, whose
bristles ascend at least to opposite the lowest frontal bristles, make
the species typical of Tachina s. str. The third antennal joint is
about twice as long as second. Achetoneura has the second anten-
nal joint hardly longer than the first, the third joint thus being easily
five or six times as long as the second.

This species can not be identified with T. mella Walker, if the de-
scription of latter is to be depended on, since it states that the
second antennal joint is ferruginous apically, third joint three times
as long as second, arista much longer than third antennal joint,
second aristal joint moderately long, large ferruginous spot on each
side of second segment. ‘The venational characters also do not
agree. In clisiocampe there is at most in either sex only a very
faint tinge of reddish, hardly perceptible in fact, on sides of second
abdominal segment. The antennze are wholly blackish, the third
joint, even in male, hardly more than twice as long as second, arista
but little longer than third antennal joint, apical crossvein well
bowed in, hind crossvein quite strongly sinuate.

Tachina orgyiarum, nom. sp. nov.

This name is proposed for T. orgyie Townsend, which is preoccu-
pied by 7. orgvie Le Baron. Both species belong in the genus
Tachina, as here restricted.

108 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Tachina utilis, sp. nov.

Length, 6to8mm. Differs from 7. Jarvarum in its much smaller
size, vertex of male not wider than one eye, thoracic dorsum not so
thickly pollinose, abdomen more shining, with pollinose bands not
so distinct, and anal segment not thickly hairy. The male in some
specimens shows signs of reddish on sides of abdomen.

The anal stigmata of puparium also show important differences,
the median slit being much abbreviated.

Germany, Bavaria, and Carniola. Bred at the Gipsy Moth Para-
site Laboratory, North Saugus, Massachusetts, by E. S. G. Titus, in
1906, and W. F. Fiske, in 1907, from both Euproctis chrysorrhea
and Porthetria dispar larve received as summer importations from
above localities; and also bred by W. F. Fiske, in 1907, from native
larve of both species collected in field colonies near Boston (Oak
Island and Woburn), Massachusetts, where European specimens of
this tachinid had been previously liberated, showing that this species
has gained a foothold.

Type.—Cat. No. 11,804, U. S. N. M. (male, length 6 mm.; Dres-
den, Germany, from Euproctis larve collected and shipped by
Schopfer ).

This type specimen was submitted to Dr. K. Kertész, and by him
determined as Tachina glossatorum Rondani. It can not be that
species, which is described by Réndani as having the second aristal
joint four tinies as long as wide, and belongs to the genus Micro-
tachina established on that character. Tachina, including the pres-
ent species utilis, has the second aristal joint no longer than wide.

Genus Euphorocera Townsend
Euphorocera slossone, sp. nov.

One female, Franconia, N. H. (Mrs. A. T. Slosson). Syn. £,
cinerea Coquillett (non van der Wulp), Rev. Tach., p. 102.

Differs from van der Wulp’s description of Phorocera cinerea
(Biol. C. A., Dipt., u, pp. 81-82) as follows: Frontalia as broad or
broader than the parafrontals. Lowest frontal bristles not close to
the eyes. Face very distinctly yellowish. Second antennal joint
two and one-half times as long as first, the third joint a little more
than twice as long as second. Arista thickened on basal third only.
Palpi somewhat swollen, evenly clothed with black hairs. No trace
of dorsal stripe on second and third abdominal segments. Two
discal macrochztze on second segment as well as on third. Anal
segment only moderately beset with bristles. Small crossvein

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 109

slightly before the middle of discal cell. Fourth vein bent at an
obtuse angle. Posterior crossvein gently bisinuate.

Type.—Cat. No. 10,912, U. S. N. M.
Subfamily EcHINOMYIIN
Genus Varicheta Speiser

The name Varicheta has been proposed by Speiser for Erigone
Robineau-Desvoidy (1830), which is preoccupied by Savigny in
Arachnida (1827). The type species is V. radicum Fallen.

Varicheta aldrichi 'Townsend.—This species, described under
Hystricia, belongs in the genus: Erigone (Robineau-Desvoidy )
Brauer and von Bergenstamm, and must thus be known as lari-
cheta aldrichi. It is quite distinct from V. radicum. The latter has
only three postsutural macrochete, while aldrichi has four or five.
There are also differences in the abdominal macrochete.

Genus Elachipalpus Rondani

This genus is characterized by Rondani as possessing palpi,
though small; and having apical cell appendiculate by reason of the
continuation of fourth vein beyond apical crossvein. The type
cited for it by Réndani is Wicropalpus longirostris Macquart, from
the Cape of Good Hope. The species is figured by Macquart as
having a proboscis like Spanipalpus, but with distinct filiform palpi,
and venation like Spanipalpus and Deopalpus, except that, instead
of a wrinkle, there is a distinct stump representing fourth vein be-
yond apical crossvein. Brauer and von Bergenstamm indicate E.
longirostris Rondani as type of Elachipalpus, but throw doubt on
Réndani’s longirostris being the same as Micropalpus longirostris
Macquart. However this may be, it is certain that the American
species ruficauda van der Wulp and macrocera Wiedemann do not
belong to Elachipalpus, since they have absolutely no palpi, the pro-
boscis is much shorter, and the venation markedly different. The
new genus Copecrypta is therefore proposed for Schineria ruficauda
(van der Wulp) Williston. The species was referred to Cuphocera

by Williston.
COPECRYPTA, gen. nov.

Distinguished by a characteristic narrowing of the apical cell at
the end, the ultimate section of fourth vein being crookedly bowed
in and for the last one-third or one-fourth of its extent parallel with
the third vein and very closely approximated to it, thus forming a
narrow handle-like tip to the apical cell. The proboscis beyond

110 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

geniculation is shorter than head height. Palpi absent. Two orbi-
tal bristles in female, none in male. Some extra bristles outside the
frontal row, but these do not form a definite second row except
anteriorly in some males. No ocellar bristles. Claws of female
short, those of male as long as last tarsal joint.

The genus differs from Trichophora by having the abdomen elon-
gate, subconical or subcylindrical, reaching nearly to end of wings.
Trichophora has abdomen much shorter than wings and rounded.

SPANIPALPUS, gen. nov.

This genus is proposed for Trichophora miscelli Coquillett. It
differs from Copecrypta in possessing a strong pair of ocellar
bristles ; proboscis long and slender, much longer than head height;
abdomen considerably widened (female). Male not known. Fe-
male with two strong orbital bristles; only one row of frontal
bristles; inner pair of vertical bristles very long and strongly
curved, decussate, reclinate. Apical crossvein normal, not crooked,
evenly bowed in near origin; apical cell widely attenuate on terminal
portion, widely open. A distinct wrinkle at origin of apical cross-
vein.

DEOPALPUS, gen. nov.

Differs from Spanipalpus only as follows: No ocellar bristles.
Two very definite rows of frontal bristles on each side of frontalia.
No orbital bristles (male), claws of male not elongate. Parafacials,
parafrontals, and cheeks evenly and thinly pilose with rather long
fine black hairs. Parafrontals not metallic or blackish, silvery
white. Venation and proboscis like Spanipalpus. Abdomen about
like Copecrypta. The head bristles, like those of all the rest of the
body, are strong. The inner frontal rows are decussate, extending
only half way back between base of antennz and vertex. The outer
row on each side is composed of lightly reclinate bristles of nearly
equal strength, nearly as strong as the vertical bristles. Both rows
descend well below base of antennz, the outer row slightly lower
than the inner and to base of third antennal joint. Two facio-
orbital bristles as strong as the frontal bristles. Facial plate strongly
produced below. Second antennal joint elongate, about as long as
third. Second aristal joint strongly elongate, slightly geniculate.
Cheeks nearly equal to eye height. Type, the following species:

Deopalpus hirsutus, sp. nov.

One male, Meadow Valley, head of Rio Piedras Verdes, about
7,300 feet, Sierra Madre of western Chihuahua, July 29 (Town-
send).

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND WAbAL

Length, 9.5 mm. Bears considerable superficial resemblance to
Copecrypta ruficauda, but may *be distinguished therefrom by the
generic characters above given. Head entirely silvery white, fron-
talia showing very faintly pale brownish, first two antennal joints
light brownish yellow, third joint hardly darker, but with anterior
terminal border and arista blackish. Proboscis black, shining.
Thorax cinereous pollinose, with two interrupted heavy outer dark
vittee, and two narrow inner vitte stopping a little behind suture.
Scutellum tawny yellowish, darker at base, silvery, with two very
strong pairs of lateral macrochetz reaching beyond base of third
abdominal segment, a moderately strong but shorter apical decussate
pair, and two lateral weak pairs besides discal bristles. Abdomen
faintly blackish on dorsum, pale reddish or brownish yellow on
sides, anal segment wholly reddish. All of abdomen more or less
thickly silvery pollinose, showing most on basal half or more of last
three segments. Macrochetz as follows: One lateral marginal on
first segment; one lateral marginal, and one median marginal pair
on second segment; eight strong marginal in a row on third seg-
ment; anal segment with about twenty in marginal, submarginal,
and discal rows. Legs black, tibiz reddish, especially hind ones,
pulvilli only faintly smoky. Wings clear, tegulz white, third vein
bristly to small crossvein.

I ype.—Cat. No. 10,914, U. S. N. M.

EUPELETERIA, gen. nov.

Erected for Echinomyia fera Linné, magnicornis Zetterstedt,
preceps Meigen, etc. Differs from Peleteria Robineau-Desvoidy in
lacking the two or three facio-orbital bristles (macrochztz on para-
facials next orbit and separated from descending frontal bristles).
Differs from Echinomyia Duméril, as restricted, by having abdom-
inal macrochetz not closely set and thorn-like. Body Peleteria-
like, not Jurinia-like.

EUFABRICIA, gen. nov.

Second antennal joint strongly elongate, fully four times as long
as first, much longer than third; third joint strongly convex on
front border in profile. Second aristal joint elongate, fully four
times as long as wide. Palpi widened and flattened on distal one-
third or so, somewhat spatulate. No ocellar bristles. Parafacials
wide, front not specially prominent in profile. Cheeks about two-
thirds eye height in width. Anterior tarsi of female not more
widened than those of other legs.

8

L12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Differs from Fabricia, to which it is most nearly related, in the
absence of ocellar bristles, and form of palpi and third antennal
joint.

Type, the following species (to be figured in the forthcoming new
edition of Dr. S. W. Williston’s Manual of Diptera, fig. 157).

Eufabricia flavicans, sp. nov.

One female, Brazil, H. H. Smith, Coll. Received from Dr. S. W.
Williston.

Length, 14mm. General yellowish or rufous yellowish in ground
color. Head silvery whitish, frontalia and first two antennal joints
reddish yellow, third joint and arista light brown. Palpi yellow.
Parafrontals with a faint tinge of brassy yellow. Thorax and scu-
tellum brassy yellow pollinose. Abdomen rufous yellow, first seg-
iment brown on depressed median portion, other segments more
tinged with rufous on median line, third segment wholly so tinged.
Narrow anterior margin of second and third and all of anal segment
yellowish silvery pollinose. A median marginal pair of macrocheetze
on second segment, a marginal one on each side of first and second
seginents, a median marginal pair and three lateral marginal ones
on third segment (eight marginal in all), anal segment with a discal
and marginal row. Legs blackish or brown, the tibiz more or less
rufous, hind tibiz especially so. Claws reddish or yellowish brown,
tips darker, pulvilli yellowish. Wing bases broadly yellow, tegulz
whitish.

T pe.

Cat.. No. 11,805, U.S: N.-M.

Subfamily Hystrictin#
Genus Dejeania Robineau-Desvoidy and allies

Dejeania vexatrix Osten-Sacken and Paradejeania rutilioides
Jaennicke.—Speaking of Dejeania vexatrix, Osten-Sacken said: “It
is very remarkable that Dejeania, a South American and Mexican
genus, should occur so commonly at high altitudes in the Rocky
Mountains among alpine forms, and it would be worth the while to
investigate on what insect (probably Lepidopterous) it preys as a
parasite’ (Western Diptera, p. 343). At the close of his paper
(1. c., p. 354), he again referred to the same matter, and included a
reference to P. rutilioides, not, however, mentioning it by name.

These instances of a tropical group of tachinids developing boreal
forms is paralleled in birds by the parrot genus Rhynchopsitta, pecu-
liar to the pine region of the Sierra Madre of western Chihuahua.
The tropical bird group of parrots has here developed a sub-boreal

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND I1l3

genus peculiar to the pine region, and which both passes the winter
and nests there. Likewise a speties of trogon occurs, belonging to
the monotypic genus Euptilotis, also peculiar to the same region and
breeding there,

Paradejeania may be considered as more or less of a boreal off-
shoot from Dejeania, and D. vexatrix Osten-Sacken is a boreal and
distinct form from the tropical corpulenta Wiedemann. Osten-
Sacken was mistaken in taking Wiedemann’s type to be the same as
vexratrix.

PTEROTOPEZA, nom. gen. nov.

This name is proposed for Chetoprocta Brauer and von Bergen-
stamm (1891), which is preoccupied by Nicéville in Lepidoptera
(1890). Type is Blepharipeza tarsalis Schiner, of South America.

Genus Gymnocheta Robineau-Desvoidy

Gymnocheta alcedo H. Loew.—This species is not typical of the
genus Gymnocheta. ‘The type of the genus is viridis Fallen, which
has second antennal joint elongate, second aristal joint elongate, an-
tennz inserted a little below middle of eyes, and cheeks one-half
eye height.

EUJURINIA, gen. nov.

This genus is proposed for Hystricia pollinosa van der Wulp. An-
tenn, frontal bristles, arista, and palpi like Jurinia, but resembling
Hystricia in having the eyes hairy and the cheeks not so wide. It
differs from Jurinella in the narrower cheeks and wider parafacials,
and from Pseudohystricia in the first of these characters and the less
produced front.

The cheeks of Jurinia are nearly equal to eye height, and the eyes
are bare. Hystricia has the third antennal joint truncate at tip,
second joint not so elongate, but attenuated at origin; frontal bristles
weaker, straighter, descending lower, and all directed forward; no
macrochetz on lower border of cheeks, second aristal joint not
strongly elongate.

A female specimen in U. S. N. M., collected by the writer July 3,
at San Rafael, near Jicaltepec, Veracruz, is apparently to be identi-
fied as Eujurinia pollinosa, although van der Wulp says “arista
indistinctly jointed,” which, it seems, must be an error, and not
intended by the author. ‘The first two aristal joints in above speci-
men are elongate and distinct. Also there are some fine strong
bristles on under side of middle femora. Length, 16 mm.

II4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

RHACHOEPALPUS, gen. nov.

This genus is proposed for Saundersia testacea van der Wulp.
Mr. van der Wulp has remarked on the striking resemblance which
this species bears to Paradejeania rutilioides.

Rhachoepalpus olivaceus, sp. nov.

Two specimens, male and female, collected on the head of Rio
Piedras Verdes, about 7,000 feet, Sierra Madre of western Chihua-
hua (Townsend), one on flowers of Rhus glabra, July 15, the other
August 16.

Length of male, 18.5 mm.; of female, 19 mm. Thorax with an
olive green tinge. Frontalia with much the same tinge, but darker.
Second antennal joint with a strong bristle on front border near
distal end, sometimes a pair of them. Third joint only a little longer
than second, hardly one and one-half times as long, same size in both
sexes. Arista thickened on rather more than basal half, distinctly
jointed, second joint elongate. Scutellum with at least four rows of
spines. The male shows a median dorsal stripe on abdomen,
widened in front on second segment, where it is marked by an area
of spines, narrower on third segment, and narrowest, but still dis-
tinct, on anal segment. This stripe shows only on anal segment in
female, but the area of spines is present on second segment. The
anal segment in both sexes is gently emarginate in middle on hind
border, presenting a double curve like a pair of buttocks. Wings
evenly infuscated. Color of scutellum is same in both sexes—quite
yellowish. Abdomen of male is of a distinctly more reddish shade,
female abdomen being of nearly same shade as scutellum, if any-
thing, slightly lighter. Claws of female are yellow, with black tips.
Front of female is wider, with three proclinate fronto-orbital bristles
on one side and only two on the other. Front tarsi of female not
dilated.

Iype.—Cat. No. 10,915, U. S. N. M.

Rh. olivaceus bears the same striking resemblance to Paradejeania
that Rh. testaceus does; perhaps even more so, since in the latter
there seems to be no posterior emargination of anal segment on the
median line. Mr. van der Wulp’s figure shows none, and his text
mentions none.

Rhachoépalpus shows broad ventral plates in both sexes, but ven-
tral membrane in female is not visible. There are five abdominal
segments, the first very short and barely discernible from the side.
The female shows ventral plates, bearing thick bunches of spines,
corresponding to second to fifth dorsal plates, the lateral edges of

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND TES.

latter overlapping sides of former, and a sixth ventral plate, or
sclerite appearing as such, at base of ovipositor. The latter bears
only hairs. The male with second and third ventral plates bearing
thick bunches of spines as in female, but fourth with only hairs and
free, the ventfal membrane showing widely on sides of fourth only;
fifth ventral plate much narrower, longer than wide, bare, not free;
what seems a sixth ventral plate in female represented in male by a
paired process articulating with the hypopygium.

EUEPALPUS, gen. nov.

Differs from Epalpus in having third antennal joint elongate and
convex in profile on anterior edge, front and epistoma much less
prominent, face less deeply concave in profile. Eyes absolutely
bare. Parafacials very wide, black-hairy. Cheeks about equal to
eye height. Second aristal joint hardly twice as long as wide.

Differs from NXanthozona (type, melanopyga Wiedemann) in hay-
ing no discal macrochetz on abdomen.

Type, the following species (to be figured in the forthcoming new
edition of Dr. S. W. Williston’s Manual of Diptera, fig. 156).

Euepalpus flavicauda, sp. nov.

One female, Brazil, April, H. H. Smith, Coll. Received from Dr.
S. W. Williston.

Length, 15 mm. Black; face, cheeks, and beard silvery white.
Frontalia and parafrontals blackish, quite concolorous. Antenne
and arista brown. Thoracic scutum metallic black with greenish
tinge, thinly silvery pollinose, more thickly so on anterior edge,
humeri, and pleure. Scutellum and abdomen metallic brown with
a hardly purplish tinge, the anal segment with a conspicuous sub-
triangular (from above) yellow area defined by the discal row of
macrochetz and extending under so as to narrowly surround the
genital opening. A comb of median marginal thorn-like macro-
chetze on ventral segments, and discal row on ventral side of anal
segment. A single lateral marginal macrocheta on first and second
segments, two median marginal pairs on second, a marginal row of
ten on third, the discal row on anal; and only a row of weak bristles
on posterior edge of anal, appearing like bristly hairs compared with
the other macrochete. Legs brown or blackish; claws and pulvilli
rufous yellow, tips black. Wings entirely and evenly infuscate,
tegule decidedly smoky.

T ype.—Cat. No. 11,806, U. 8. N. M.

116 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

XANTHOZONA, gen. nov.

This genus is proposed for Tachina melanopyga Wiedemann.
Two female specimens in U. S. N. M., Campinas, Brazil (A. Hem-
pel), and Sao Paulo, Brazil (Ad. Lutz), labeled “parasitic on Brass-
olis astyra.”

The ventral plates (female) only narrowly showing, overlapped
by edges of corresponding dorsal plates, exposed portion being
wider behind and narrowed anteriorly owing to the posteriorly
rounded-off shape of edges of dorsal plates overlapping them, the
posterior ones showing more widely than anterior ones, all widen-
ing successively from anterior to anal segments.

Family MUSCID/
Subfamily CALlipHORIN 2
Genus Calliphora Robineau-Desvoidy

Girschner and Hough have paved the way for a clearer under-
standing of Calliphora and its allies, and the genera as established
by them are accepted in this paper, with the addition of two new
ones.

Calliphora texensis, sp. nov.

Two males, three females, Paris, Texas. A. A. Girault, Coll.

Length, 9 to 11 mm. Differs from C. coloradensis Hough in the
third posterior intra-alar bristle being absent and without a trace.
The male front at vertex is about one-fifth of head width, and nar-
rows very noticeably in front of vertex in an even curve, widening
at same curve on anterior portion. The male parafrontals and para-
facials are conspicuously pale brassy. The female parafrontals are
obscure brownish, the parafacials light russet and unicolorous with
facialia and facial plate, which are also this color in male. In one
female the anterior reddish portion of bucce (hairy part of cheeks)
looks almost black in some lights, but the reddish tinge can be dis-
tinctly seen, and the specimen should be included with this species.
The color of abdomen varies from metallic green to purplish blue.

Type—Cat. No. 10,883, U. S. N. M.

Calliphora rubrifrons, sp. nov.

Two females, one male, Stickeen River, British Columbia, H. F.

Wickham, Coll.; two females. one male, Kaslo, British Columbia,
FG, Dyar, Coll.

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 117

Length of female, 9.5 to 12.5 mm.; of male, 8.5 to 9.5 mm. Bucce
black, beard black. The two Stickeen River females and one of
those from Kaslo, being the three largest specimens, show the bucce
with a good reddish tinge on anterior half, the two males and the
other Kaslo female not. Third posterior intra-alar bristle absent.
Frontalia bright orange red on anterior portion, in the Stickeen
River male more of a yellowish red, in the Kaslo male a brownish
yellow. Parafacials, facialia, epistoma, palpi, and apex of second
antennal joint with base of third joint nearly the same color as the
frontalia anteriorly, but sometimes a lighter shade of same color.
Female front over one-third of head width, male front about one-
twentieth of head width. ‘Thorax faintly silvery white dusted, most
thickly so on front border. Abdomen metallic green to blue, dis-
tinctly silvery pollinose in certain lights. Wings clear, with more
or less distinct flecks of black on humeral, small, and basal cross-
veins, origin of third vein, and apex of auxiliary. Alulz well tinged
with smoky, appearing quite black if resting against thorax or base
of wing, tegule blackish with narrow white margins.

Type.—Cat. No. 10,884, U. S. N. M. (Stickeen River, British
Columbia).

Calliphora popoffana, sp. nov.

One female, Popoff Island, Alaska, July 16, 1899. Harriman Ex-
pedition. T. Kincaid, Coll.

Length, 10.5 mm. Buccze black, beard black. Front and face
black, with a faint silvery white pollen distinctly to be seen in certain
lights, even on facial plate, and especially on the broad frontalia and
on the parafacials. Palpi light reddish yellow, facialia and epistoma
darker reddish yellow, second antennal joint reddish, rest of an-
tennze black. Front distinctly more than one-third head width. No
trace of third posterior intra-alar bristle. Wings quite clear, even
at base, tegule white. Abdomen metallic green. Legs black. ‘The
plumosity of the arista is much shorter than in the other species.

T ype.—Cat. No. 10,885, U. S. N. M.

A male from Bear Lake, British Columbia, 7,000 feet, R. P.
Currie, Coll., measures 7 mm., and may be this species. The front
is about one-eighth head width. The parafacials and narrow para-
frontals are strongly silvery white; also facial plate. The frontalia
are brownish. Tegule blackish. Wings with two smoky streaks
on costal half. Abdomen metallic blue, silvery white dusted. The
antenne are paler on basal half of third joint. Otherwise it agrees
with the female just described. The plumosity of the arista is quite

118 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

normal, and this, taken with the blackish tegulz and wing streaks,
would point to it as a distinct form.

Calliphora irazuana, sp. nov.

One female, Irazu, Costa Rica, Schild and Burgdorf.

Length, 11.5 mm. Bucce black, beard black. Third posterior
. intra-alar bristle wholly absent. Parafrontals black, with a soft
brassy brown pollen on front half. Parafacials dark dragon’s-
blood red, facial plate blackish. Palpi reddish yellow, antennz
blackish, inner basal portions of third joint paler. Front equilateral,
one-third head width. Thorax and scutellum black, faintly silvery
on front and lateral edges. Tegulz and wing bases blackish. Ab-
domen purplish blue. Legs wholly soft black, as are also the pleure,
with hardly a trace of silvery.

T ype.—Cat. No. 10,886, U. S. N. M.

EUCALLIPHORA, gen. nov.

Proposed for Calliphora latifrons Hough. Differs from Calli-
phora in possessing two strong pairs of ocellar bristles. This is a
character of considerable importance in the Muscoidea, especially
in the higher groups, and may well form a generic distinction here.

Eucalliphora latifrons Hough.—A large series of this interesting
species, consisting of some sixty specimens, was brought from
Kaslo, British Columbia, by Messrs. Dyar, Caudell, and Currie.
The character of the second pair of ocellar bristles is constant in all.

There are also two females in the U. S. N. M., collected by H. S.
Barber, Las Vegas Hot Springs, N. Mex., and Fieldbrook, Cal.,
which both belong to this genus and are apparently this species.

Genus Lucilia Robineau-Desvoidy

There are several species of this genus, notably sericata (Meigen)
Hough and sylvarum (Meigen) Hough, which have a well-devel-
oped second pair of ocellar bristles. The latter are remarkably
strongly developed in these two species, and were it not for the pres-
ence of certain intermediate forms, like pilatet Hough, and especially
oculata, n. sp., they would constitute a well-marked new genus sep-
arable on this character. But in pilatei the second pair in the male
is hardly to be differentiated in strength from some of the other
pairs of divergent ocellar hairs, and in oculata the male shows no
second pair, though the females of both possess the character quite
distinctly. As genera are mere matters of convenience, and these
forms do not otherwise differ in points of generic value, the charac-

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND I19

ter in question can not be used here for the erection of a separate
genus. ‘This is only another illustration of the fact that a character
of value for the separation of certain forms may be valueless for this
purpose in certain other forms closely allied to the first. In all the
species there“are several widely divergent pairs of weak ocellar hairs
behind the first or regular pair of ocellar bristles. In the forms
which have a second pair of ocellar bristles well developed, this sec-
ond pair is always inserted just behind the two posterior ocelli, and
not inside the ocellar triangle. In other words, it is only the pair of
hairs inserted just behind the two posterior ocelli that ever develop
into a second strong pair of bristles. L. cesar is typical of the forms
in which this pair of hairs is not developed in either sex, but it is to
be noted that some of the bristly hairs within the ocellar triangle in
this species often seem strong enough to be considered additional
pairs of ocellar bristles.

Fourteen species of Lucilia are here recognized, occurring in ma-
terial in U.S. N. M. They may be separated as follows:

Table of Lucilia spp.

t. Only one postacrostichal bristle present...%............. morrilli, sp. nov.
MOU pOStacrOStIGMalDTIStIES PRESEMty .)-\-1-heretels se iseejorspcteveie te se ieleteteyersketoe iol 7
MaReewpostacnostGlalll DiIStIES: PTESEME. ..). <1) cise pte elders wlevenes eek 2

2. Palpi-more or less yellowish...........:. Spugdosr nooo eS beep iot 4
Ralpieawintolliva blacketormplackishia.., <7, aaj-cicea cueicheteta ol pekeneteets ers teen creole 3

A SeConGpaimmon ocellan inmsties:deyvelopede se aci ice tae is elt sylvarum
Secondapain notedevelloped: a. s- . «sco sec oeeer des «e nigripalpis, sp. nov.

Am Palate Mollivevell owes acres clo. sche veld sie ekaiatchere er ehser ae te ie ie ayeit na aN 5
Fall iettbtiSCabera te tiple 5.7.2 a(t a:a,0 cis: ave) aeralcnaeclapetoieteter o avobe, shekey tet set telat obae rare 6

iceeoecond pain ocellarpnisties: developed 4-15. - semis sleet stare sericata
Second pam, mot developed. 4. 20. +,s6b oo gee-seoe + angustifrons, sp. nov.
HSE COMEE AE SU CV LOPS, = situa, ste dyad ic disks oi «eye wee eres giraulti, sp. nov.
DECONdepaite MotdevelOMediy: 2s acc.c:s.rsie disje-ave elec =r cheer cnet barberi, sp. nov.
Fey EN DYOLGanareinl Ab aelol KOs ROLLINS 3 SAE ROR REE Ta IMO es oidmin din atts Gbood ooo e oe 8
Basdlusecoment on abdomen ublack tor blackish. sc eee seine een: 9
VROeCONGe maine demelOpedhytorac sie scs oie vcs oe epee scien unicolor, sp. Nov.
Second in atn wate develomeder..\ sais tae statcoversepacinte loi tele retaeltoede ci eieracs cesar
9. Whole body purplish, except basal abdominal segment, second abdom-
inal segment with a marginal row of bristles......... purpurea, sp. nov.
WWE OIE sO diyentn@ tar Olecepaees tye re cic fe elena se ae le ate OE OS IS AE aeons 10

10. Second and third abdominal segments with a purplish or blackish
TTDAT Catan te ee CeN Ee eA crate aac thk oon asthe ePIC ogg ERI ED AE eye AA RC ge II
second and third: sesments: umicolorous:.. ic sacs ods onion eee bat sees 12
Mie buicese yellows: wihollya@m Matthias eersles aoe eee ene. pilatei
ingece black, not at alll yellow... 2. se: suse acl nae eb. australis, sp. nov.
mah yesmnonmalsmtaceunlack-« asec yee ce eee on eee ate. infuscata, sp. nov.

Eyes flattened anteriorly with large front aspect, face brownish yellow.
oculata, sp. nov.

120 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Lucilia morrilli, sp. nov.

Six males, nine females, Texas, New Mexico, Arizona, California,
British Columbia, and Missouri.

Only one postacrostichal bristle. Male front one-seventh of head
width, female front fully two-fifths of head width. Whole of abdo-
men, thorax, parafrontals, and cheeks, including occiput, strongly
metallic green. Face and frontalia black, silvery. Palpi black.
Tegule white. No macrochetz on abdomen. No second pair of

ocellar bristles.
Type.—Cat. No. 10,887, U. S. N. M. (Victoria, Texas—Morrill).

Lucilia sylvarum (Meigen) Hough—One female, Prussia.

Three postacrostichal bristles. Male front very narrow, female
front one-third head width. Palpi black. Two stout marginal
macrochztz on second abdominal segment. Second pair of ocellar
bristles well developed.

Lucilia nigripalpis, sp. nov.

Two females, Cuyahoga County, Ohio. W. V. Warner.

Differs from infuscata only by having three postacrostichal bris-
tles ; palpi quite blackish, faintly paler basally ; antennz, face, bucce,
and front all more deeply black; tegule white. A trace of purplish
on hind margins of second and third abdominal segments, especially
on second. Second segment with a marginal row of weak macro-
chetz. No second pair of ocellar bristles.

Type.—Cat. No. 10,888, U. S. N. M.

Lucilia sericata (Meigen) Hough.—Two males, six females, east-
ern United States, Alabama, Hidalgo (Mexico), Kadiak Island
(Alaska).

Three postacrostichal bristles. Male front one-eighth to one-
sixth head width, female front two-fifths head width. Palpi yellow.
Abdomen unicolorous, tegulae white. A strong second pair of
ocellar bristles in both sexes.

Lucilia angustifrons, sp. nov.

One male, England (Brunetti).

Same as c@sar, but having three postacrostichal bristles. Front
linear, eyes almost contiguous. Palpi yellow. A female, having
front one-third head width, from Kaslo, British Columbia (Cau-
dell), seems to be this form. No second pair of ocellar bristles.

Type.—Cat. No. 10,880, U. S. N. M.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 121

Lucilia giraulti, sp. nov.

One male, Paris, Texas. A. A? Girault, Coll.

Three postacrostichal bristles. Male front one-eighth head width.
Abdomen likepilatei, but no dark hind margins to second and third
segments. Buccz and whole face and front black, palpi yellowish
but infuscate apically. Tegule nearly white. No strong macro-
chetz except marginal row on third segment. Of the three post-
acrostichal bristles, the front one is well behind the front postsutural
bristle, and the middle one is a little behind the middle postsutural.
A second pair of ocellar bristles present.

T ype.—Cat. No. 10,890, U. S. N. M.

Lucilia barberi, sp. nov.

six males, Arizona (H. S. Barber), California (Coquillett),
Guanajuato (Mexico), Alabama, West Virginia, and District of
Columbia.

Three postacrostichal bristles. Differs from giraulti practically
only in the second pair of ocellar bristles not being developed appre-
ciably longer than the ocellar hairs, and the three postacrostichal
bristles being even with the three postsutural bristles. Palpi yellow-
ish, infuscate at tip. Bucce, face, and front blackish, facialia red-
dish, epistoma yellowish. Tegulze white. Basal abdominal seg-
ment black. An even row of ten marginal macrocheete on third
segment above, and three on each side below. No dark margins to
second and third segments. Male front one-eighth head width.

Type.—Cat. No. 10,891, U. 8. N. M. (Williams, Arizona).

Lucilia unicolor, sp. nov.

Five females, New Mexico, Mexico, and British Columbia.

This form corresponds to cesar, differing therefrom in having the
second pair of ocellar bristles distinctly developed. ‘Two postacros-
tichal bristles. Female front a little less than one-third head width.
Palpi yellow. Abdomen unicolorous. Tegule white.

Type—Cat. No. 10,892, U. S. N. M. (Mesilla, N. Mex.—Cock-
erell).

Lucilia cesar Linné——Numerous specimens of both sexes, Eng-
land, eastern United States, and British Columbia.

Two postacrostichal bristles. Male front linear, female front one-
third head width. Abdomen unicolorous. Tegulze white. Palpi
yellow. Second pair of ocellar bristles not developed, or only very
weakly so.

122 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Lucilia purpurea, sp. nov.

One female, Fort Wrangel, Alaska, Wickham; one male, Kadiak,
Alaska, Kincaid (Harriman Expedition).

Two postacrostichal bristles. Male front one-twelfth of head
width, female front one-third head width. Palpi yellow. Basal
abdominal segment blackish. Whole body purplish, strongly violet
tinged, especially in the female. Tegule of female white, of male
smoky. Bucce, face, and front blackish, epistoma paler. Second
abdominal segment with a marginal row of bristles or macrochete,
but not as strong as those of marginal row of third segment. No
second pair of ocellar bristles.

T\pe.—Cat. No. 10,893, U. S. N. M. (Fort Wrangel, Alaska).

Lucilia pilatei Hough.—Two males, two females, Florida, Porto
Rico, Guatemala, and Peru. A neotropical species.

Two postacrostichal bristles. Male front one-eighth head width,
female front one-fourth head width. Palpi yellow. Abdomen as
in australis, only the purplish or black margins of segments often
more marked. Buccz of female yellow, of male gray with yellow
anteriorly. A second pair of ocellar bristles in female more or less
hair-like, but distinctly larger and thicker than the other hairs of
ocellar area; in male very weak, not appreciably stronger than the
other ocellar hairs.

The purplish black hind margins of second and third abdominal
segments are characteristic of this and one or two other species,
added to which is the blackish basal segment. ‘The latter in some
females shows a little metallic green on sides, but the general opaque
black of its dorsum is the distinguishing character. Also the hind
margins of second and third segments are only faintly purplish in
some specimens, but distinct traces are present in all. The white
tegule are characteristic of this species, and serve to separate the
males of pilatei from the males of similar species having a black
basal.abdominal segment.

Lucilia australis, sp. nov.

Two females, Tennessee, Texas (Girault); one male, Popoff
Island, Alaska (Kincaid, Harriman Expedition). The male is pro-
visionally referred here.

Two postacrostichal bristles. Male front one-twelfth head width,
female front one-fourth head width. Palpi infuscate yellow. Basal
abdominal segment black above, conspicuously so, the purplish or
darker hind margins of second and third segments also showing.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 123

Distinguished from pilatei by the bucce being black, silvery gray
pollinose, not at all yellow. Second pair of ocellar bristles present

in female, not developed in male.
T'ype.—Cat. No. 10,894, U. S. N. M. (Tennessee, Coll. Riley).

Lucilia infuscata, sp. nov.

Nine males, six females, Massachusetts, New Hampshire, Ohio,
Missouri, New Mexico, Arizona, and British Columbia.

Two postacrostichal bristles. Male front very narrow, female
front two-sevenths of head width. Basal abdominal segment black
or purplish black in female, but no dark margins to second and third
segments. Male tegule infuscate, female tegule more nearly white.
Palpi yellowish. Buccz, face, and front black. No second pair of
ocellar bristles. The female can be told from female cesar only by
narrower front and darker basal segment.

Type—Cat. No. 10,895, U. S. N. M. (Organ Mountains, New
Mex., on flowers of Lippia wrightti—Townsend).

Lucilia oculata, sp. nov.

Six males, two females, District of Columbia, Kentucky, North
Carolina, Mississippi, Kansas, and Cuba.

Two postacrostichal bristles. Male front linear, eyes nearly con-
tiguous and approximated more anteriorly than in imfuscata, with
larger front aspect than in that species. Female front one-fourth
of head width. Tegule nearly white, only very faintly tinged with
yellowish. Antenne and face brownish yellow instead of black.
Basal abdominal segment quite black. Male shows no second pair
of ocellar bristles, but female has them developed. Otherwise like
infuscata.

Type.—Cat. No. 10,896, U. S. N. M. (Cumberland Gap, Ky.—G.
Dimmock). :

PROTOPHORMIA, gen. nov.

Hough characterizes Phormia as having the mesonotum “some-
what flattened caudad the transverse suture,” as in Protocalliphora.
This is a mistake. P. regina, which is the type of Phormia, does
not show this flattening at all. The species terrenove is not a
Phormia, but differs in possessing the same conspicuous flattening
seen in Protocalliphora. The new genus Protophormia is herewith
proposed for its reception. The characters given by Hough for
Phormia (Ent. News, x, p. 66) all apply to P. regina except the
character of the flattened thorax. This flattening carries with it a
more or less complete abortion of the postacrostichal bristles except
the hindmost one of each row.

124 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Subfamily Muscrn
Tribe Mesembrinini

Two new genera are here proposed in this tribe, and the genus
Mesembrina is restricted as follows:

Genus Mesembrina Meigen

Type of the genus, M. mystacea Linné. Densely pilose flies.
Subalar pile present, representing the pteropleural bristles. Sterno-
pleural bristles 1. 0. 1. Fourth longitudinal vein very deeply and
roundly bent far before reaching margin of wing, which latter point
is same distance behind that termination of third vein is before ex-
treme wing-tip, the portion between bend and margin being fully
three times that in margin. Apical cell much narrowed, its mouth
width not over one-third its greatest width. Small crossvein dis-
tinctly before middle of discal cell.

METAMESEMBRINA, gen. nov.

Proposed for Mes. meridiana Linné. Hairy, not pilose, flies.
Subalar bristly hairs present, representing pteropleural bristles.
Sternopleural bristles 0. 0. 1. Fourth longitudinal vein reaching
front margin of wing before tip, arcuate at bend.

EUMESEMBRINA, gen. nov.

Proposed for Mes. latreillei Robineau-Desvoidy. Hairy, not pi-
lose, flies. Pteropleural hairs present. Sternopleural bristles
1. 0. 2. Fourth vein very slightly and roundly bent a little before
reaching hind margin of wing, the portion between bend and margin
about equal to the portion in margin. Apical cell very widely open,
its mouth width equal to about three-fourths its greatest width.
Small crossvein distinctly beyond middle of discal cell.

Eumesembrina latreillei Robineau-Desvoidy.—Two_ specimens,
White Mountains, New Hampshire, Morrison; one, Colorado; two,
Washington State; two, Kaslo Creek, British Columbia, June 18,
R. P. Currie and A. N. Caudell. All show face and parafacials sil-
very white from above. Antenne reddish yellow to brownish.
Palpi reddish or brownish red.

Eumesembrina alascensis, sp. nov.

Four specimens.—Kukak Bay, July 4; Kadiak, July 20; Saldovia,
July 21; Juneau, July 25. All Alaska. Collected by T. Kincaid
(Harriman Expedition).

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 125

These specimens are more hairy, more bristly on thorax and scu-
tellum, and on peristomalia. They also usually show less silvery
on face and parafacials, and the antennz are quite black. Palpi
black. The Kukak Bay and Kadiak specimens show no silvery on
the soft blackish facial plate, and the parafacials are tan-colored
without a sign of silvery. The other two specimens show some
silvery, not only on facial plate, but also on the more or less tan-
colored parafacials.

T\pe.—Cat. No. 10,897, U. S. N. M. (Kukak Bay, Alaska).

The two Washington State and two British Columbia specimens
mentioned under Jatreillei are certainly distinctly to be referred to
that species, which is the eastern form, and which is thus seen to
tange from the Atlantic to the Pacific. Eumes. alascensis doubtless
represents rather a boreal form.

Family PHASIIDAE

Tribe ANUROGYNINI
Genus Hyalomyodes Townsend

Hyalomyodes weedii ‘Townsend.—This species seems distinct
from Hyalomyia triangulifera H. Loew, but needs further study.
The writer has examined the type of the latter in Cambridge.

Hyalomyodes triangulifera H. Loew.—Ten specimens from the
White Mountains of New Hampshire, one from Massachusetts, and
one from Maryland agree perfectly with the description of H. weedit
Townsend. They also agree with Loew’s description, but an exam-
ination of the type in Cambridge seemed to indicate differences.
The front, frontalia, and parafacials are wider in the male, and the
claws are elongate. Humeri grayish.

Hyalomyodes robusta, sp. nov.

Two males, North Fork of Rio Ruidoso, White Mountains, New
Mexico, about 8,200 feet, on flowers of Solidago trinervata, August
17, Townsend.

Differs from triangulifera in being more robust, and first abdom-
inal segment with pollinose fascia same as second and third. The
thorax is also more conspicuously pollinose. Hind crossvein quite
straight, in one specimen much nearer to small crossvein than to
bend of fourth vein, in both distinctly nearer. The pollen of median
portion of thorax and abdomen has a brassy tinge, that on sides
being silvery-whitish. Macrochetze not so well developed, consid-
erably weaker. Parafacials wide in both specimens. Length, 5 mm.

T ype.—Cat. No. 11,651, U. S. N. M.

126 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 5

Hyalomyodes californica, sp. nov.

Two specimens, male and female, Santa Clara county, California
(C.F. Baker).

Almost like trian gulifera, but distinguished by humeri being more
golden, extending back in a lateral stripe.

T ype-—Cat. No. 11,652, U. S. N. M. (female).

Tribe CLISTOMORPHINI
Genus Clistomorpha Townsend

A synonym of Clistomorpha is Clytiomyia Coquillett (non Roén-
dani). This genus is very distinct from Clytiomyia Rondani
(Clytia Robineau-Desvoidy). C. hyalomoides Townsend is distinct
from C. didyma H. Loew (described as Xysta). The writer recog-
nized the fact of the two being congeneric nearly fifteen years ago,
from drawings of the type furnished by Mr. Samuel Henshaw, and
has since examined the type of did\ma in the Cambridge Museum.

Clistomorpha didyma H. Loew.—The apical cell is very short-
petiolate, and the hind crossvein is curved and in middle between the
small crossvein and bend of fourth vein.

Illinois.

Clistomorpha hyalomoides Townsend.—The apical cell is prac-
tically closed in the margin. The hind crossvein is in middle and
straight.

New York.

Clistomorpha atrata Coquillett—The apical cell is closed in mar-
gin, or almost narrowly open. The hind crossvein is sinuate and
nearer to bend of fourth vein than to small crossvein.

Idaho, Washington State.

Genus Himantostoma H. Loew

Himantostoma sugens H. Loew.—This genus belongs in this
tribe, as shown by an examination of the type in Cambridge.

Subfamily PHAsIIN»
Tribe Alophorini
The following table will serve to separate the genera of this tribe:

1. Front above antenne thickly beset on both sides with small bristles... .. 2
Front above antenne naked, only one row of frontal bristles on each
SCG Pie aalnitade, oem cieja:a as bho eo wt ht Rte tele aa ts ae ee 3

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 127

2. First longitudinal vein elongate, small crossvein placed opposite end of
auxiliary vein, fourth vein very obtusely bowed, apical cell sharp-
ansled atextremity and: short petiolate.,.: .ccc. See. sees eens): Alophora

First longitudinal vein not elongate, small crossvein placed opposite end
of same, fourth vein roundly bowed, apical cell usually long petiolate.

Hyalomyia
3. Second longitudinal vein ending opposite the junction of third and
fourth veins, wings of male usually much widened............ Phorantha

Second longitudinal vein elongated beyond junction of third and fourth
veins, wings of male not widened, apical cell very long petiolate,
LOUEtHEVE Ik HO UNG lyn DOWedasa cetseie eicieikactmioksicts metcioel ters er Paralophora

Genus Alophora Robineau-Desvoidy

Alophora sp.—A large species from Texas. The female shows
ventral plates overlapped by dorsal plates. The male shows ventral
plates free, at least those of second, third, and fourth segments, with
membrane widely exposed on each side.

Genus Phorantha Rondani

The genus Alophora has the front prominent in profile above in-
sertion of antenne. Phorantha has front flattened, and with greater
slope so as to present in profile an almost perfectly straight line
from insertion of antennz to vertex.

Probably all, or nearly all, of the various forms of the Alophorini
that have been described are distinct and entitled to recognition.
We know practically nothing of the early stages or the mating of the
adults, and it is premature to attempt to outline the synonymy in the
absence of such knowledge. |

Tribe Cistogasterini
Genus Gymnoclytia Brauer and von Bergenstamm

The genus Gymnoclytia is distinct from Cistogaster. The pe-
duncle of apical cell is continuous with fourth vein in Gymnoclytia,
but with third vein in Cistogaster.

Gymnoclytia has ventral membrane (female) very widely visible
and ventral plates free, much as in Gymnosoma.

Gymnoclytia occidua Walker—Male.—Thorax brassy or golden
pollinose, with two straight narrow median vitte extending from
front margin to behind suture, and two irregularly widened vittz
obsolete before and interrupted at suture. Abdomen more or less
ferruginous, sometimes entirely so, but usually with a longitudinal
fuscous stripe in connection with a median pollinose vitta, and more
or less brown on third and fourth segments with grayish pollen.

9

128 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Female.—Thorax silvery-whitish pollinose, with two heavy shin-
ing black vittz, sides of front silvery-white pollinose becoming black-
ish posteriorly, abdomen black with silvery pollen in median vitta
and two or three fasciz.

New Hampshire, District of Columbia, North Carolina, Georgia,
and Texas.

Gymnoclytia occidentale, sp. nov.

Male.—Thorax deep brassy to old-gold pollinose, with same vitte
as in occidua. Abdomen like occidua except that pollen is golden,
the ground color bright ferruginous and markings varying from
none to the usual ones strongly marked.

Female.—Colored almost like the male of occidua. Thorax brassy
pollinose, with two broad heavy brown vitte extending from an-
terior margin almost to scutellum, and two very narrow linear vitte
between them. Abdomen the same as in the male, pollen being
golden, but no specimens occur with abdomen entirely ferruginous,
the usual markings being pronounced in all.

Colorado and New Mexico to California.

Type—Cat. No. 11,653, U. S. N. M. (female, Beulah, New Mex-
ico, Cockerell, July, 1902).

Gymnoclytia immaculata Macquart—Male.—Fuscous stripe of
abdomen wanting, median pollinose vitta more or less distinct. Ab-
domen yellowish, the third and fourth segments with lateral polli-
nose reflections.

Female.—Thorax shining black, without pollinose markings ex-
cept the humeri, sides of front shining black, abdomen without
distinct pollinose vitta or crossbands, apical cell quite long petiolate
(as in the males of the preceding species). Abdomen distinctly red
on the sides, especially anteriorly.

This form and Gym. occidua Walker are distinct. See Robert-
son’s and the writer’s notes in T. A. E. S., xxi (1895), pp. 66-67,
and Ann. and Mag. N. H., xx, pp. 283-284.

Gymnoclytia ferruginosa van der Wulp.—Male.—Thorax deep
golden or old-gold pollinose, with the same stripes as occidua more
or less apparent. Abdomen ferruginous, fuscous stripe hardly ap-
parent, but pollinose stripe present, and third and fourth segments
more or less pollinose, pollen being golden.

Female—Sides of front faintly golden-silvery, thorax shining
black, with three faintly golden pollinose vittea. Abdomen shining
black, with median pollinose vitta and third and fourth segments

TAXONOMY OF MUSCOIDEAN FLIES—-TOWNSEND 129

more or less pollinose, pollen being grayish with a hardly brassy
tinge.
Veracruz and Nicaragua.

Tribe Nanthomelanodini
Genus Xanthomelanodes Townsend

Syn. Xanthomelana VAN DER WULP preocc.

The name used by van der Wulp was applied by Bonaparte to a
genus of birds in 1850.

Xanthomelanodes arcuata Say.—Only a single vibrissa on each
side.

Male.—Front and face deeply golden, especially parafrontals.
Abdomen usually with a well-defined black median vitta, last ‘seg-
ment and last half of penultimate segment black.

Female.—Front and face silvery-white. Abdomen all black ex-
cept yellow on sides of second and third segments, only covering
anterior half of third segment, but some specimens show less black.

New Hampshire, Kansas, Veracruz.

Xanthomelanodes atripennis Say.—One vibrissa on each side.

Male.—Front golden. Abdomen golden, with only some brown-
ish shading for the median vitta. Wings quite smoky on inner
border.

Dixie Landing, Virginia (Townsend).

Xanthomelanodes californica, sp. nov.

Two vibrisse on each side.

Male.—Front and face almost silvery, with only a faint suggestion
of golden, in some specimens quite silvery-white. Abdomen ferru-
ginous, more or less dusky, the brown markings not well defined as
a rule, consisting of a broken median stripe and the usual dark
markings of last two segments.

Female.—Face and parafrontals silvery-white. Abdomen nearly
same as in arcuata.

Colorado, Nevada, California.

Type.—Cat. No. 11,654, U. S. N. M. (male, Los Angeles county,
California, Coquillett).

Tribe Trichopodini
The following is a table of the genera of this tribe:

1. Hind tibiz without flattened cilia, with only a row of short appressed
bristles and one or two stronger bristles among them............... 2
Hand tibicee ciliate with the usual! flattened icilia.........-...+-..-.-4- 3

130 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

2. Wings infuscate on less than costal half, gray or hyaline on other

FACEDION os eS me aaa oie sears eae at aPe= Seep pyerenee ode ein np ants Acaulona
Wings almost wholly infuscate, but much more faintly so on inner half,
the infuscation rather graduated into almost hyaline on inner border.

Euacaulona
MS Cy Sea TISC AEE! 4. os aioik a2 scrais, a Ratyh iW acon eye es in eels see neers 4

Wings more or less widely hyaline on inner border,, the hyaline
BSE L GCE en clea /naen'y am x oe otime Selec alam cls Lika Racket ceils lee 6

4. Hind femora ciliate with closely appressed flattened bristles on one or
PPPOSIEECABOS Ae abics © Jin cute bo'aly cored bina b aletpece teense Galactomyia (males)
Hind emora not-ciliatesat:alllv. ).% a ajacletersmevenl tee eran rts 5
Byer ea Ce MOG cio scan wis,ats ogee che hee aaE sa sine ete ae at Homogenia
aie eell CIOSCM.c. Sea a'd . Oma esu ia oo tweoe te lena kate eaten elem emied Euomogenia

6. Wings hyaline on more than inner half, abdomen subcylindrical in both
sexes atid dargely translucent “in both... a.c0s <0 sre-0 tie nlelete ss Pennapoda

Wings with inner hyaline border almost as wide as the infuscate
costal half, abdomen subcylindric in both sexes and wholly opaque
TEPPSPISEES SS igraca ness icin =, oe heas Seana oe TNS, oases OEE Polistomyia

Wings with hyaline border about one-third width of wing. ..Eutrichopoda

Wings with hyaline border very narrow, not over one-fifth of wing

FU LCE IL 5 Mer cat iter Mtcya ayant yor eek cte nas RO ae Late PaTaene EE Pores Macias ae esha ao eee if
7. NVholly hlack, fotin. fs. sah See agree eee Galactomyia lanipes (female)
Partly reddish forts. s. acts rare are emia oh nie te ans vereingese cre etc ean 8

8. Hind femora ciliate distally on inner edge with closely placed bristles;
abdomen cylindrical, reddish or orange with apical half or at least
anal -seeinent: black ....7. Semabasis scene Galactomyia radiata (female)

Hind femora not at all ciliate, smaller forms with abdomen more or
less flattened and almost wholly light reddish or yellowish in both
SOROS: sees xd se ehh yl PR REE es ice rte Ghee ciate Trichopoda

Genus Acaulona van der Wulp

Acaulona costata van der Wulp.—One female, Tehuantepec, Su-
michrast; one male, Frontera, Tabasco, February 9, Townsend. The
Tehuantepec specimen is of much lighter coloration than Veracruz
and Tabasco specimens. Tegul are yellowish in this genus.

Acaulona tehuantepeca, sp. nov.

One female, Tehuantepec, Sumichrast. Labeled “17. Homogenia
sp.” Length, 7 mm.

Differs from A. costata in having the apical cell subfuscous, the
abdomen with a median blackish vitta and more or less wholly
blackish on apical half, and the hind tibize weakly subciliate in a row
of short, closely approximated bristles. The form is intermediate
between Acaulona, Euacaulona, and Homogenia, but nearest to
Acaulona. .

T ype—Cat. No. 10,878, U. S. N. M.

TAXONOMY OF MUSCOIDEAN ILIES—TOWNSEND eel

EUACAULONA, gen. nov.

Differs from Acaulona in having somewhat more than costal half
of wings pronounced fuscous, the rest of wing not being clearly
hyaline, but more or less so, the fuscous rather gradually fading out
on inner border. ‘There are also two distinct grayish or milky vitte
on wings (male), one between the first and second veins, one be-
tween the third and fourth veins, besides a short one in front of the
auxiliary vein. Tegule brownish or fuscous, paler in middle.

The front at vertex is nearly as wide as either eye, and gradually
widens anteriorly to almost width of both eyes as viewed from in
front, the face in same view being fully three-fifths width of head.
The frontalia are very wide, of equal width, as wide as front at
vertex.

Apical cell closed in margin. Hind tibiz not ciliate, bearing only.
a row of short appressed bristles with one or two stronger bristles
among them. Claws of male elongate. Abdomen of male flattened.
Type, the following species:

Euacaulona sumichrasti, sp. nov.

One male, Tehuantepec, Sumichrast. Length, 9.5 mm.

Blackish, the venter and basal half of femora, also base of hind
tibiz, yellow; the usual golden yellow markings on prothorax along
and in front of suture, also extending posteriorly on the sides and
along the scutellar suture. Frontalia black, the narrow parafrontals
and all of face and cheeks golden yellow. Thorax, scutellum, and
abdomen above brown or blackish.

Type.—Cat. No. 10,879, U. S. N. M.

Genus Homogenia van der Wulp
Syn. Trichopododes 'TowNSEND.

This genus has the wings wholly infuscate, those of male with
considerable luteous and more or less of a milky bloom (/atipennis
and nigroscutellata) ; female not known. Hind femora not ciliate
at all, hind tibie only weakly ciliate. Apical cell open. Tegulz
yellowish. Type, H. latipennis van der Wulp. The species rufipes
van der Wulp evidently does not belong with the other two described
under the genus, and will have to be separated generically.

Hi. latipennis van der Wulp.—One male, Tehuantepec, Sumichrast.
Labeled “Trichopoda luteipennis Wd.” ‘This specimen agrees with
van der Wulp’s description except that there is no trace of a black

132 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

median abdominal vitta, and abdomen is only a little dusky on anal
segment as seen through the golden silvery bloom.

H. nigroscutellata van der Wulp—One male, Cacao, Trece
Aguas, Alta Vera Paz, Guatemala, April 18. Barber and Schwarz,
collectors. This specimen agrees well with van der Wulp’s de-
scription except that abdomen is widely blackish on median portion,
with only narrow lateral borders yellow. The scutellum has golden
pollen on dorsum.

EUOMOGENIA, gen. nov.

Differs from Euacaulona in the wings (male) being wholly in-
fuscate, uniformly so, the same milky vitte being present; and in the
hind tibiz being ciliate with moderately developed cilia. Front like
Homogenia, very broad. Apical cell closed in border. Tegulz
blackish. Type, the following species:

Euomogenia lacteata, sp. nov.

One male, Frontera, Tabasco, March 3, Townsend.

Length, 9.5 mm. Blackish, the usual silvery golden markings on
mesoscutum, including the sides back to scutellar suture and along
latter. Scutellum somewhat silvery golden on dorsum. Abdomen
wholly fuscous, with a reddish tinge showing through the fuscous.
The broad frontalia velvety blackish, narrow parafrontals and whole
of face and cheeks golden. Antenne brownish. Palpi yellow, dark
on tips. Basal half of femora yellow, least extensive on front pair,
most extensive on hind pair, base of hind tibiz yellow, rest of legs
black, claws and pulvilli yellow, tips of claws black. Wings black-
ish, with the milky or golden grayish vitte described for Euacaulona.

Type—Cat. No. 10,880, U. S. N. M.

Genus Pennapoda Townsend

This was described as a subgenus, in Ann. and Mag. N. H., xx, p.
282. It is here raised to generic rank. Type, Trich. phasiana
Townsend, loc. cit., male and female. The species Phania simillima
Wiedemann and Trich. subalipes Townsend may belong to this
genus. There are no specimens in U. S. N. M. for examination.

POLISTOMYIA, gen. nov.

This genus is proposed for the Trich. trifasciata H. Loew group.
The abdomen is subcylindrical in both sexes, slightly more widened
on apical portion in male. Apical cell closed and quite long petiolate.
Wings with but little more than costal half colored, the inner por-

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 133

tion clear. Abdomen in both sexes wholly opaque, brown or black
in ground color, more or less golden pollinose, never with translu-
cent portions. Scutellum always yellow. Both sexes have yellow
on the wingsys Hind femora not at all ciliate. Tegule white or
yellowish. Parasitic in Acridiide (Dissosteira), so far as known.

The male has frontalia suddenly narrowed, presenting a curved
outline on each side, closely followed by the frontal row of bristles,
the width on posterior half being only one-half the width at base of
antennz. Claws strongly elongate in male, hypopygium exserted
and tucked up under the end of abdomen.

The female has the frontalia but little narrowed behind, being
evenly narrowed from anterior to posterior end, the sides and frontal
row ‘of bristles being quite straight. Claws somewhat elongate in
female, even slightly longer than last tarsal joint, but very markedly
less elongate than in male. Anal end of abdomen truncate, the ovi-
positor more or less withdrawn within anal segments, its apex
usually showing.

Type, 7. trifasciata H. Loew.

The other species belonging here are /istrio Walker, indivisa
Townsend, probably wmbra Walker and plumipes J. C. Fabricius ;
also the following new species. The writer formerly suggested
these (except plumipes) as varieties of one species, but now con-
siders them valid forms differing in marked characters. They form
a group apart by themselves, distinctly contrasted with the other
members of the Trichopodini.

Polistomyia subdivisa, sp. nov.

One female, St. Helena, Napa County, Cal., bred by A. Koebele
from a locust (Dissosteira venusta Stal) ; issued August 30, 1887.

Length, 6.33 mm. Segments three and four of abdomen golden
pollinose, segment three with a median vitta and median hind mar-
gin brown, segment four wholly pollinose with a trace of vitta, seg-
ment two with a large yellow spot on each side, and segment one
with a similar smaller spot on each side.

Type.—Cat. No. 10,881, U. S. N. M.

Two female specimens from Las Cruces, New Mexico, collected by
the writer, August 25 and September 2, on flowers of Solidago ari-
zonica, are larger, measuring 7 to 8 mm., show no median vitta on
third and fourth segments, and only a faint vitta on second segment,
which bears a fascia rather than separated spots. They very likely
represent another form, but more material is needed from California
and New Mexico before separating them as distinct. They occupy
an intermediate position between trifasciata and subdivisa.

134 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

T. plumipes (J.C. Fabricius) Wiedemann is probably a Polis-
tomyia, as indicated by the yellow scutellum, broad, clear inner mar-
gin of wings, and the cylindrical abdomen. ‘The latter is described
as black, which would indicate a form without fasciz or pollinose
markings, since it is hardly possible that such could have been so far
lost as to leave no trace. We thus have the following forms of this
genus, to be separated as below:

Polistomyia plumipes—No pollinose fascize on abdomen. Continuous

black surface.

histrio—Two pollinose fasciz, interrupted.

trifasciata—Three fasciz, broadly interrupted.

subdivisa—Four fascie, two broadly interrupted and two
faintly so.

umbra—Continuous pollinose surface, interrupted by median
vitta.

indivisa—Continuous pollinose surface.

EUTRICHOPODA, gen. nov.

Differs from Trichopoda in the apical cell being moderately long
petiolate, and the wings with inner border broadly hyaline, the latter
being nearly or about one-third of wing breadth. Hind tibiz cil-
iate, hind femora without cilia. Abdomen cylindrical in female,
probably flattened in male. Tegule pale or whitish yellow. Type,
the following species :

Eutrichopoda nigra, sp. nov.

Syn. Trich. lanipes VAN DER Wutp (non J. C. Fabricius, Wiedemann),
Biol. C. A. Dipt., 1, pp. 434-5.

One female, Tehuantepec, Sumichrast.

Length, 9 mm.; of wing, 8 mm. Black. Parafrontals silvery
white, with only a faint tinge of golden, which tinge is lost in view
from above and behind. Face wholly silvery white, including para-
facials. ‘Transverse suture of mesoscutum marked by a golden yel-
low linear fascia, with two golden lines running to front border of
thorax, humeri broadly golden. Scutellum is of the same dull black
as the abdomen, with hardly a brownish tinge. Tegule saturated
with a faint yellow tinge. Femora almost as black as rest of legs,
with a faint brownish tinge. The mesoscutum behind suture is
faintly purplish or bluish shining. The wings have no yellowish
tinge in the black, and the inner hyaline border is hardly one-half as
wide as the black portion.

T ype-—Cat. No. 10,882, U. S. N. M.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 135

This form comes nearer agreeing with Wiedemann’s description
of plumipes than anything that has turned up since Bosc’s time. It
differs therefrom only as above described, and principally in the
black scutellum.

Mr. van der Wulp (1. c.) has described this species from what he
records as one male and four females, but says nothing as to whether
the apical cell is petiolate or closed in the margin, nor does he men-
tion the shape of the abdomen in the sexes. It seems quite certain
that his specimens are this species, and it is likely that all five of
them have the apical cell moderately long petiolate.

Genus Trichopoda Latreille

This genus, as here restricted, has the wings with inner margin
narrowly hyaline, hind femora not ciliate at all; only male with yel-
low in wings, no milky radiations, apical cell very short petiolate,
and tegule yellowish. Type, T. pennipes J. C. Fabricius. Parasitic
in Heteroptera (Anasa, Leptoglossus), so far as known.

GALACTOMYIA, gen. nov.

This genus is proposed for Trich. radiata H. Loew. Trich.
lanipes J. C. Fabricius (description is of female; 7. formosa Wiede-
‘mann is the male) also belongs in this genus.

The males have the abdomen flattened; the wings infuscate to
inner margin, milky radiate on a yellow or fuscous background, the
milky radiations conspicuous and the yellow less pronounced. Hind
femora strongly ciliate on posterior half, with flattened bristles.

The females have the abdomen cylindrical; the wings wholly black
except narrow inner border, without yellow coloring, the internal
border abruptly limpid. Hind femora at least short-ciliate distally,
though bristles may not be flattened. G. radiata female has the
abdomen reddish, with at most the apical half black. G. lanipes
female is to be distinguished by its wholly black coloration, aside
from the usual yellow of head, thorax, claws, and pulvilli.

It is yet uncertain what species can be referred to this genus be-
sides radiata and lanipes (syn. formosa Wiedemann). As to the dis-
tinctness of these two species, Loew pointed out in his description of
radiata (male) that it has the palpi reddish yellow, abdomen purple
black, and bases of femora yellow. G. lanipes (male) has palpi
black, abdomen obscure rufous, and femora wholly black.

The males of Galactomyia have ventral membrane widely visible,
and all the ventral plates free. There are six abdominal segments,
the first extremely short and not visible above unless abdomen is

136 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

detached, but visible on sides below; the second to sixth segments
visible above, and a seventh wedged between the sides of ventral
aspect of sixth, rounded in outline and forming the base of the
hypopygium. This seventh segment occupies the position of a ven-
tral plate to sixth segment and belongs to dorsum, being a dorsal
plate. Five ventral plates, corresponding to first to fifth segments ;
first plate rather crescent shaped, much shorter (antero-posteriorly )
and wider than second to fourth; second plate long-oval, third and
fourth long-elliptical; fifth subquadrate and widened behind, about
as wide as first. Immediately behind the fifth plate is the hypo-
pygium, and behind latter is the seventh segment, with the lateral
ends of sixth dorsal plate enclosing it on the sides.

In the female of G. lanipes there are seven ventral plates visible,
the first three free, with ventral membrane showing on each side,
fourth plate showing ventral membrane only around anterior edge
and corners, fourth and fifth plates overlapped on sides by lateral
edges of corresponding dorsal plates, sixth and seventh plates over-
lapping the corresponding dorsal plates, but sixth overlapped basally
by fifth, and seventh by sixth, as is to a less extent fifth by fourth.
Seven segments visible on sides and below, the first shortened, the
sixth and seventh retracted with only their narrow posterior edges
showing, the sixth being retracted within fifth and seventh within
sixth. The seventh segment does not show at all dorsally, though
the sixth shows equally widely dorsally and ventrally, and sixth and
seventh show equally widely ventrally.

Galactomyta lanipes J. C. Fabricius——As the description of lanipes
is earlier than that of formosa, the species must be known by the
former name. Mr. C. W. Johnson, of the Boston Society of Nat-
ural History, has a pair of this species taken in copula by Mr. P.
Laurent, at Miami, Florida, March 26, 1901. This pair is men-
tioned in Ent. News, November, 1901, page 294. The capture of
these specimens in copula confirms Brauer and von Bergenstamm’s
statement as to the sexes of this species. Both specimens have the
palpi black, and the femora wholly black. The male has the abdo-
men obscure rufous, the female wholly black. The hind femora are
conspicuously flattened-ciliate distally in the male, but only short-
bristly-ciliate in the female. Apical cell closed practically in margin,
tegule blackish. The female is the form described by Fabricius and
Wiedemann as lanipes. The male is the form described by Wiede-
mann as formosa.

Carolina, Florida, Texas.

TAXONOMY OF MUSCOIDEAN FLIES—TOWNSEND 137,

A small female from Costa Rica (Schild and Burgdorf) differs
only in its smaller size and in having the apical cell rather more than
short-petiolate. More material is needed to demonstrate its dis-
tinctness.

Galactomyia tropicalis female-—This is a large robust form, with
hind femora distinctly ciliate near tip. Body wholly black. Palpi
lighter colored, bases of femora reddish. Apical cell closed in mar-
gin. Male not known. Closely allied to lanipes. (Mexico, Costa
Rica. )

Galactomyia radiata H. Loew.—Mr. C. W. Johnson has males
from New Jersey, Pennsylvania, and New York. He also has a
female specimen collected by him at Delaware Water Gap, New
Jersey, July 10, 1898, which is doubtless the female of this species.
It has the palpi yellow and bases of femora yellow. The hind
femora are short-bristly-ciliate distally. The abdomen is reddish
yellow, except anal segment, which is wholly shining black including
narrow posterior border of preanal segment.. A female specimen in
the U. S. N. M., and others that the writer has collected in the Dis-
trict of Columbia, agree with this specimen in Mr. Johnson’s collec-
tion and are no doubt females of radiata.

The writer wishes to especially thank Mr. Johnson for kindly
placing his private collection at his disposal, and for many other
favors.

Subfamily AMENIINA

Genus Amenia Robineau-Desvoidy

Amenia leonina J. C. Fabricius (det. Coquillett) —Australia.
Both sexes show broad ventral plates overlapped by sides of dorsal
plates.

Subfamily AMPHIBOLIIN 2

Genus Amphibolia Macquart

Amplubohia fulvipes Guérin (det. Coquillett).—Australian genus.
This species shows in both sexes posterior triangular views of ven-
tral plates where the rounded-off posterior corners of dorsal plates
fail to cover them from view. ‘The male shows a very large paired
plate-like hypopygial process similar to that of Rutilia.

Subfamily Rutm1n&
Genus Rutilia Robineau-Desvoidy

Rutilia spp.—The species are all Australian. An examination of
specimens of both sexes of several species in U. S. N. M. reveals

138 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the following characters: Neither sex shows any ventral plates, but
the males show a paired plate-like process widened on apex, occupy-
ing the position of a ventral plate to the hypopygial segment, and the
long fifth or anal segment is shortened to a mere margin on venter
by reason of the hypopygial cavity being pushed strongly forward.
There are five abdominal segments, the first being rudimentary and
greatly shortened.

SMITHSONIAN MISCELLANEOUS COLLECTIONS

PART OF VOLUME LI

SMITHSONIAN EXPLORATION IN ALASKA
IN 1907 IN SEARCH OF PLEISTOCENE
FOSSIL VERTEBRATES

WITH THIRTEEN PLATES

BY

CHARLES W. GILMORE

Of the United States National Museum

No. 1807

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1908

1

\

WASHINGTON, D. C.
PRESS OF JUDD & DETWEILER, INC.
1908

SMITHSONIAN EXPLORATION IN ALASKA IN 1907 IN
SEARGH OF PLEISTOCENE FOSSIL VERTE-

BRATES. SECOND EXPEDITION

By CHARLES W. GILMORE

TABLE OF CONTENTS

Page

me EEO GCE Oe ere atrsiscee etek e suet Tc ret earner eg ann eee ura en inl ana aas Pk Sia 3
Pole libtivercitcy.s sawee oicistere cox clee sols adel otaver Peale stated oatenapee ai aoe stare tera wee ieee tet 5
MI Ge curnencesOlrtOSsilSieen.: ocx sist Lites into teint ee Ae eens 14
Teabonanzan Creel ocalities:. .;ay-locnaca a ato anes oe Aero kee eee 15
2rbithle: Munooks Creek: Junior... acts so aise ees hee eles ieee y/
salto Mimoolke Creeks. i'.<d 4. saceccaneeenines Se OR ae hats varniae 17

FA ERNE SEL Gia aed cat Seve ow Nhe Sassi con nsehepatucre rae ete fe tast erent ge ea eters ole 17

ee NO Witte IRN VOI; ct ch tem ce cca sc Scape eee ete cree Channa ce wera 22

Ose Waikalkalkeat Rivers oe cece weal) s ia os coders euetta ueted ste ehe oho) sust arereeeneeauers 2
Gemlaliciiica eat Heuvelen crete kt or < Soak wtara apse ha hee lays atatene eerie eres 2
SMIISCHSSTO LSA feet Mcrae Cele ace te (3 Scene ee eee UE CRE Re Rear 24
IWVemieleistocene fatinanon Alaska ao..: cece sci mcs ee eer un ocrienerg cheno 26
Ta LO PNAS: PFUIMAZEMIUS). 2. oe. sc so o8 aes 8) a ae Rag tee ele ae tL Ocoee = 2

Be TADHAS GOUPMION (GE): aiisd & o32'< te a mieeed aa, Regd Neen ee eee te A 30

SE MIG IIE AMOTUC ON WIN Seo, ois aire clos ose ey Oey arses ea ae > Ee aysieioes "ore 30

AEE ITUES fot EVN Node bois ace SG oo aisicke Ais wiotee Oe Sache a eess aR Ste ea ee es aI

MED USOM ICHASSICOUMUSiaeiokn «cue oi ots onsitee Susie Lemay siete cin Sin ce pene eT os 21
OPES ON GULCH at pct aces ct aiadicar sated GUT oe HTS Soe Nea os nee oce moe: SSR EEE 33
TMBUSON OGCLLCITOIIS mh autenroetas aie verte the Dee ei oes ele hetartsie ie 33

But ts0n PEASCUSH2) te ahierad = s . . d wore Gere ee re 34

Oy SOS AV AAAI Ue de oo HMR aoe ou ore CoRotod Sanat bem One 34
TOMRSYVIVOS GAGS FONS fale 38 alancs, 0c da ES ye Be A aay eS eestencas e 35

TED) 24D OS 11 ELIS essed Ls or led is aE Se OT Se tea 35

T2 OUI OS MMOSCHALUS. (08 )imss ofa) -moronc nck ee te oe sera oe STR ne Somes ees 35

IN al OLA IG Ane oa aoe ok en rere cro BE orcs PSPLRCRD, Oro Sabo OF CRONE REC 30
TALL C Cpe es og ate aR TAINS SNE Pact, 55 & cath ve guile SECT on ep OEMS CPR RTO: cee ener e ee 30

LUNs Sele 1 IHN IA Rests or OR, ERE IIIS Ms cr ie. i te Stn © Ohba Bete uenrenaes 30

Otay ERG RS ase od PAN oN |e en rae APR Ag Ae Roeser eae meee 37

1B ley Gee Ly 10) «at Stee ROO RP ogo Se ok eae Oe 37

Eee MOTTE ATE ts Ses aia ala a. Se a) ote «' aps ea eo eee ee es ese 37

I. INTRODUCTION

Since the discovery of extinct vertebrate remains in Alaska by
Otto von Kotzebue, in 1815, while on “A Voyage of Discovery into
the South Sea and Beering Straits,” much interest has been manifest
regarding the occurrence and cause of extinction of the Pleistocene

~
a]

4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

fauna of this northern country; and, although various expeditions
have collected specimens and much has been written concerning
them, it was not until 1904, when the first Smithsonian expedition
was organized, that the subject was taken up in a systematic man-
ner. This expedition was conducted by Mr. A. G. Maddren, whose
report has now been some years before the public.’ It was planned,
at that time, to carry on the exploration for two or more consecutive
seasons, but it was not until 1907 that the present writer was detailed
to continue the work so well begun three years previous. The report
herewith presented gives the results of this second trip, undertaken,
as was the first, under a grant made by the Secretary of the Smith-
sonian Institution at the suggestion of Dr. George P. Merrill, Head
Curator, Department of Geology, U. S. National Museum.
The writer’s instructions were, in part, as follows:

“You are hereby authorized to proceed to Alaska, on or about May
22, 1907, for the purpose of exploring the regions herein described,
with a view to securing remains of large extinct vertebrate animals
and investigating the causes which have led to their extinction.

“While it is expected that you will exercise your best judgment
in carrying out the details of your itinerary, it is suggested that on
leaving the city of Washington you proceed to Seattle, securing at
that point the necessary outfit, excepting provisions, and arranging
for the services of a competent assistant.

“On leaving Seattle you will go by way of Skagway, Alaska, to
White Horse, and thence down the Yukon River to Rampart, where
the first stop will be made and the area explored, from which certain
bison skulls now in the Museum collections have been obtained. You
will then proceed to Fort Gibbon, exploring the territory in the
direction of the Nowi River—the so-called “Bone Yard” region—
and from this point either by steamer or canoe, to Hall Rapids,
investigating the areas on both sides of the Yukon as far as
Andreafski.

“Should the explorations so far outlined not yield results warrant-
ing your delay, it will then be advisable for you to proceed, provided
the season be not too far advanced, by the most expeditious route
to Kotzebue Sound, and make similar investigations in the areas
drained by the Buckland River.

“Should you at any point discover material of such importance as
to justify the making of immediate excavations, you are authorized
to undertake such work, though bearing in mind that it may be
advisable to first make a reconnaissance of the entire field, leaving
the work of actual excavation until the following year. This is a
matter, however, which must be left to your discretion.

“Tt is expected that the explorations herein authorized will prob-
ably consume not more than four months of the present year.”

* Smithsonian Exploration in Alaska in 1904 in Search of Mammoth and
Other Fossil Remains. Smithsonian Misc. Coll., vol xL1x, pp. I-117.

EXPLORATION IN ALASKA IN 19Q07—GILMORE 5

II. ITINERARY

In compliance with the above instructions the writer left Wash-
ington, D. C., May 22, for Seattle, Washington. At this place a
canoe and the necessary camp equipment were purchased and shipped
to Rampart, Alaska, where the first active field work was to be done.
Some time prior to leaving Washington the services of Mr. Benno
Alexander were engaged. His several seasons’ experience with
various scientific expeditions in the different parts of Alaska made
him a very desirable companion and an efficient assistant.

The party consisted of Mr. Alexander and the writer, the plan
being, as explained in the instructions, to employ such help from
time to time as might be necessary.

On May 30 we took passage on.the steamer Jefferson, arriving at
Skagway, Alaska, June 4. It was learned upon our arrival there
that all accommodations on the first boat down the Yukon had been
engaged and that it would be best to remain in Skagway until the
next boat, which was scheduled to sail from White Horse June 12.
On June 10 we left Skagway over the White Pass and Yukon Rail-
road for White Horse, Northwest Territory, Canada, the terminus
of the railway and head of steamboat navigation on the Yukon
River. Here passage was secured on the river boat White Horse,
which sailed June 12 and arrived in Dawson, Yukon Territory,
Canada, June 14. This being a transfer point between the upper and
lower river boats, we were again delayed because of inadequate
accommodations, and it was not until June 22 that we left Dawson
on the steamer Sarah for Rampart.

The delay at Dawson was profitably spent, however, in examining
fossils in the possession of citizens of that place; in making inquiries
concerning the occurrence of the fossils found in the Klondike
region, and in visiting some of the localities on Bonanza Creek from
which many of the specimens examined had been obtained. Scat-
tered remains of Pleistocene mammals are commonly found in the
diggings of this region, but the result of diligent inquiry. regarding
the finding of complete or partial skeletons in the mining operations
conducted here were not encouraging. In only one instance were we
told of the finding of an accumulation of bones such as would lead
one to believe that an entire skeleton or any considerable part of the
skeleton of a single individual had ever been found. ‘The single case
mentioned was that of the remains of a mammoth (Elephas primi-
genius) disinterred while sinking a shaft on Quartz Creek in March,
1904. The skull and tusks were recovered intact (see pl. vir),

6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

but, according to our informant, although surrounded by a mass of
other bones, no attempt had been made to preserve them.

We arrived at Fort Yukon, Alaska, the farthest point north in our
journey, at midnight June 23, and Rampart (see pl. 1, fig. 1), the
limit of steamer travel, was reached the evening of June 24. While
here, the area drained by Little Minook Creek, Junior, where scat-
tered mammal remains had been found, was visited. We were shown
a few specimens taken out by miners, but the character of their
occurrence here did not justify a continued search; so, after over-
hauling our camp outfit and laying in a supply of provisions, we
loaded our canoe, and on the evening of June 28, left Rampart
(see pl. 1, fig. 2) for our trip down the Yukon.’ For thirty or forty
miles below Rampart the Yukon flows between walls of the older
rocks with a current of from five to six miles an hour, accelerating
somewhat as the rapids are reached, near the lower end of what is
known as the Lower Ramparts. The first alluvial deposits en-
countered of any considerable thickness after passing the rapids
were on the right-hand bank some twelve miles above the mouth of
the Tanana River. Imbedded in these were myriads of small land
shells representing the living forms, Euconulus trochiformis Mtg.
and Succinea grosvenori Lea, as determined by Dr. W. H. Dall. No
vertebrate remains were found.

Fort Gibbon, a military post at the junction of the Tanana and
Yukon rivers, was reached the evening of June 30. Here inquiry
was made regarding localities on the lower river points and par-
ticularly relating to the Palisades, better known locally as the
“bone yard,”? some thirty-five miles below. We were informed that
scattered fossil remains were also to be found along the Tanana
River and its tributaries; but, as the information was somewhat
indefinite as to exact localities, it was decided not to investigate the
reports at this time.

The first exposures of the elevated Yukon* silts were observed
twenty miles below Fort Gibbon, where the bluffs are undermined by
the river for a half mile or more, and although a careful examination
was made for the presence of vertebrate fossils, none were found
either in the face of the cliff or in the talus at its base. This point
marks the beginning of the escarpment of which the Palisades, some

*The day we left Rampart a small tusk of the mammoth was brought in by
some miners from Ray River, a locality from which Pleistocene mammals had
not been previously reported.

* So named because of the great number of fossil bones found here.

* Spurr, J. E.: 18th Ann. Rept. U. S. Geological Survey, pt. 111, p. 200.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 GILMORE, PL. |

Fig. 1.--RAMPART, ON YUKON RIVER, WHERE THE CANOE TRIP COMMENCED

Fig. 2.--EXPEDITION ABOUT TO LEAVE RAMPART

gu

wn

es

EXPLORATION IN ALASKA IN I9Q07—-GILMORE vf

fifteen miles farther down, are a part. Covered with a dense vegeta-
tion, this level-topped bluff or ‘“‘plateau terrace,” as called by Russell,*
extends along the left side of the river, only separated from it by a
heavily timbered flood-plain at its base. The Palisades were reached
July 3, and two days were spent in the studying of this historic
locality. Some scattering fossil remains were found, of which a
more detailed account will be given later.

The evening of July 5 camp was pitched some five miles below the
Palisades, at the mouth of “Wasikakat” River, a small tributary
flowing into the Yukon from the south. This stream, which enters
the river through a low alluvial flat, was ascended some distance in
the expectation of reaching a place where it had dissected the higher
silts.of the Palisade escarpment, but we were obliged to turn back
because of its small size and the consequent difficulty in navigating it.

The mouth of the Nowitna River? was reached June 7. Inquiry
concerning the occurrence of bones along this stream elicited the
information from an intelligent Indian, who visited the headwaters
of this stream occasionally on hunting excursions, that he had seen
“big horns and other big bones” on the river bars, and a white
trapper also told us of having picked up the “shank bone” of some
large animal along the stream.

The information was stimulating, for it had been planned before
leaving Washington that this stream should constitute one of the
principal areas of search. Before leaving Fort Gibbon, three weeks
provisions had been purchased in the expectation of the supply being
sufficient for us to reach the headwaters of this stream, the length
of which, as given by Dall,? is one hundred miles. We ascended the
stream for nine days, and at the farthest point reached, estimated
to be at least one hundred and seventy to one hundred and eighty
miles from the Yukon, found it to be a considerable stream still
(see pl. vi, fig. 1). It may be explained, however, that in a straight
line the distance covered might not be half of this estimate. Trap-
pers who have ascended its entire course estimate its total length as
being two hundred and seventy-five to three hundred miles. The
Nowitna enters the Yukon from the southwest, about seventy-five
miles below the mouth of the Tanana. It rises on the eastern flank
of the Kaiyuh Mountains, and we were told its headwaters are con-

* Russell, I. C.: Geological Society of America, vol. 1, 1890, p. 146.

* By a recent decision of the United States Geographic Board, this stream,
which has been successively designated Nowekaket, Nowikakat, and Nowi,
now becomes the Nowitna.

* Dall, W. H.: Alaska and Its Resources, 1870, pp. 87-282.

8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

nected by portages with those of the Innoko and Kuskokwim rivers.
There are no settlers living on this stream, although deserted winter
cabins of the lonely trapper were passed several times on our journey.
The stream flows by a tortuous, meandering course through a low
alluvial valley covered with a dense growth of alder, willow, poplar,
birch, and spruce. Its course forms a series of curves. alternately
sweeping from right to left, the channel being confined between
banks of unconsolidated alluvium and silt from twelve to fifteen feet
in height. It presents the typical effects of meandering erosion so
well described by Maddren’ in his description of the lower reaches
of the Porcupine, 7. e., “cutting away the banks on the concave side
and depositing the material removed lower down on the opposite side
as bars” (see pl. vi, fig. 1). Often the water has cut in under the
bank, which extends out over the stream like a great shelf. The
trees growing on these undermined banks frequently lean far over
and dip their tops in the water before being carried away. Large
blocks of the bank, with its superincumbent vegetation, cave off into
the stream, where they remain standing half submerged for long
periods. Another feature of the undermined banks is the mantle of
moss that hangs down from the top like a curtain (see pl. 11, fig. 2),
as if to hide the destruction the waters have wrought. This blanket
is composed of the tenacious and closely woven moss and rootlets
which everywhere cover the ground throughout these lowlands.

The banks are not sufficiently high to prevent their overflow by
the spring floods, and the quantity of drift materials lodged in the
growth on top of the banks indicates the great volume of water that
flows down during the spring break up. Lanes through the dense
undergrowth indicate recently abandoned watercourses, many of
which hold ponds and sloughs. The erosional effects of ice are also
seen in the scarred and abraded tree trunks and the deep gouges and
gashes along the higher banks.

The bars on the lower part of the stream are low and frequently
covered with stranded trees and other drift materials, but on the
upper reaches where the bends are more abrupt, they are fairly clear
of drift and furnish a good path for the “trackers.’” On some of the
upper river bars the interstratified sands and gravels have been piled
in great heaps nearly as high as the inclosing banks. In ascending
the stream, the first two days good progress was made with the pad-
dle against the clear but sluggish current, but on the third day, to
facilitate our movements against the rapidly increasing current, a

*Maddren, A. G.: Smithsonian Misc. Coll., vol. xnrx, No. 1584, 1905, pp.
Q-IT.

SMITHSONIAN MISCELLANESUS COLLECTIONS, VOL. 51 GILMORE, PL. II

Fig. 1.--CHARACTERISTIC CUT BANKS OF THE LOW FLOOD-PLAINS DEPOSITS OF THE
NOWITNA RIVER

Fig. 2.--CUT BANKS ON THE YUKAKAKAT RIVER, SHOWING THE CHARACTERISTIC CURTAIN
OF MOSS AND TURF

ns
‘cy Fr.

EXPLORATION IN ALASKA IN 1907—GILMORE 9

“cache” was made of all articles in the outfit not absolutely needed.
Many times, in order to get over the swift places, “tracking” was
resorted to, and a little later it was nearly all tracking and wading, as
we alternately crossed from bar to bar at the bends in the river.
Nearly evefy bar searched yielded something—either fragments or
one or more complete elements of skeletons representing the mam-
moth, horse, bison, and other extinct forms.

The first of the older series of rocks encountered was some seventy
to seventy-five miles above the mouth, where the stream has cut the
end of a low-lying ridge on the right bank. This outcrop is com-
posed of a mass of badly shattered schistose rock. Some fifteen
miles farther up, the river again touches the end of a spur of this
same ridge, exposing rocks of a similar nature.

Elevated beds of silt of perhaps fifty feet in height were observed
twice in the ascent, but appeared local in character, and no fossils
were found in them.

The ridge paralleling the right bank extended along the river to
the most distant point reached by us and as far beyond as the eye
could reach. It rises above the level of the stream from three hun-
dred to five hundred feet, and is covered with a dense growth of
trees.

The “Suletna,”! the first important tributary, enters the Nowitna
from the west ninety miles above its mouth.

The ascent of the stream was continued until July 16, when an
inventory of the remaining supplies showed only enough provisions
to last until we should reach the Yukon again. On this account we
were obliged to turn back. While the specimens found at the
farthest point reached were not more abundant or better pre-
served than those collected farther downstream, it was hoped we
could reach the very headwaters, to learn, if possible, the source of all
the scattered bones found along its course, and it was with reluc-
tance that we abandoned the search.

The Yukon was reached on the 19th of July, and “Mouse Point,”
a small trading post, the same day. After a short stop here our
journey was continued to Kokrines, an Indian settlement where the
Northern Commercial Company maintains a trading post. Some
little time was spent here in overhauling our outfit, laving in supplies,
packing fossils for shipment, etc.

An exposure of elevated silts on the right bank of the Yukon,
some three miles above Melozi, a United States telegraph station, was

?’The name by which this tributary is known to the Indians and trappers of
this region.

10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the next area visited. Here members of the Tenth United States
Infantry had unearthed the almost complete jaws of a mammoth
shown the writer while at Fort Gibbon. On our visit, however,
nothing was found.

We had been told by Indians, who are in a position to be best
informed concerning these out-of-the-way places, that large bones
were to be found on the Yukakakat River,’ a tributary entering the
Yukon some seventeen miles above the settlement of Louden.

The mouth of the Yukakakat was reached on July 23. The ex-
ploration of the stream occupied the best part of a week, but was
without especial incident. The farthest point reached was estimated
to be ninety miles from the mouth, and although the current on the
upper reaches was swift, it was free from serious rapids and usually
had along its shores bars sufficiently broad to give good “tracking.”

The sluggish current of the first few miles of its meandering course
flows through a low alluvial flat, heavily wooded and very similar in
character to that part of the Nowitna. Farther up, however, the
course of the stream is flanked by low ranges of hills which grad-
ually converge and thus confine its wanderings to a shorter radius.
On either side of the stream back of the low hills mountains were
observed rising from one to two thousand feet in elevation.

In many places the growth on the banks was very sparse, and
consisted principally of scattering clumps of alders, willow, and birch
interspersed with a few stunted spruce trees. Here and there back
from these low banks were many shallow lakes that furnish splendid
breeding grounds for the geese and ducks which abound there On
the uppermost part of the stream reached by us the shores were
more heavily timbered and there were long straight stretches of
river flowing between banks from ten to twelve feet in height, which
in most cases were covered with undergrowth and a tall luxuriant
growth of grass extending nearly down to the water’s edge. At the
bends the undermining of the concave side presented features similar
to those observed on the Nowitna River.

The first elevated silts of any importance observed were some
sixty miles upstream from the Yukon, where the river makes a
right-angled bend. At a comparatively recent date the river at this
point has changed its course, and at the time of our visit was not
cutting the bluffs (see pl. 111). It could undermine them only at an
extremely high stage of water. These cliffs have almost perpendic-
ular faces and are from eighty to one hundred feet in height, com-

*This stream appears to be known in Alaska as the Yukakakat, although
Dall has indicated it on a map compiled by him in 1875 as the Soonkakat.

GILMORE, PL.

Al

Vol

SMITHSONIAN MISCELLANEOUS COLLECTIONS,

EXPOSURE OF ELEVATED SILTS ON THE YUKAKAKAT RIVER, 60 MILES FROM ITS MOUTH

ce a

oe

4

r i"

{

id

EXPLORATION IN ALASKA IN IQO07—GILMORE IE

posed mostly of fine light-colored, unstratified silts. Some sixty feet
down from the top is a layer of coarse gravel conformable with the
silt, which may represent the Palisade conglomerate of Spurr.?

This terrace at irregular intervals has been dissected somewhat by
the drainage from above (see pl. 111). In many places along the
cut banks of the stream the silt was underlaid by a stratum of rather
fine reddish-colored gravel. <A section of these flood-plain deposits,
when no complications occur, presents the following divisions in
their natural order and approximate thickness:

JERE reg Sa Se Gate ea ts eR ere AN Eee 18 inches to 2 feet
ILANele Chemie, Glia Adana ee eo coe ers ter nnppaae 8 feet to 10 feet
rime LeCuiohtn OhAUEl ae ote, ls cc's aide oS ec ee ee 4 feet to—

Dall? noted the occurrence of a similar fine reddish gravel in the
deposits of Eschscholtz Bay.

A few scattered bones were collected on the bars below the depos-
its of elevated silts just described, but although continued search
was made for two days upstream from this point, no fossils were
found. Even though no indication of vertebrate remains were seen
in the silts, the writer is inclined to the opinion that the few frag-
mentary specimens picked up on the bars below may have been
washed out of these bluffs and carried downstream by the river dur-
ing a flood stage. This idea is strengthened somewhat from the
fact that no mammal remains were found in the lower cut banks or
alluvial deposits of either this stream or the Nowitna, although
persistent and continued search was made, and from our own
experience and that of others we do know they occur in the elevated
lacustral phase of the silts.

The absence of fossil evidence on the last two days of our ascent
and the fact that little had been found previously showed that this
stream did not cut an extensive deposit of Pleistocene mammal
remains, and it appeared to be a waste of time to continue our
search; so we returned by the same route we had ascended, reaching
the Yukon on July 30.

A short distance above Louden we met Mr. R. A. Motschman,
who, being thoroughly familiar with the region, told us of several
localities where fossils had been found. The most important of
these was an exposure on the Klalishkakat River, a locality visited
by Mr. Arthur J. Collier, of the U. S. Geological Survey, some five
years previous. At the time of Mr. Collier’s visit a large tusk was

=

‘Spurr, J. E.: 18th Ann. Rept. U. S. Geological Survey, 1896-97, p. 199.
“17th Ann. Rept. U. S. Geological Survey, pt. 1, 1895-06, p. 852.

12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOR. 51

protruding from the bank, a picture of which is shown on plate 1,
fig. 2, in Mr. Maddren’s account of his trip in 1904.

This small stream enters a branch of the Yukon from the south
three miles below the settlement of Louden. At the time of our
visit there was a high stage of water, and it was with some difficulty
that we made the comparatively short distance upstream to the point
where the river cuts the elevated silts. That portion of the bluff
where Collier had photographed the tusk in place had been under-
mined and washed away. Scattered fragments of fossil ivory found
by us on the bars below probably tell the story of its disappearance.
A few fragmentary bones were found, some imbedded in the undis-
turbed silt and others in the talus at its base.

Eight miles below Louden, on the right bank of the Yukon, occurs
a typical exposure of the Yukon silts. The bluffs extend for a dis-
tance of perhaps two miles and present faces from two hundred to
two hundred fifty feet in height, equal to those of the Palisade
escarpment, which they resemble in all their stratigraphic detail.
Mr. Motschman told us of finding fossils here, but not even a frag-
ment was secured at the time of our visit.

Here, it was observed that the wind is quite a factor in the erosion
of these bluffs. The fine silt dries rapidly, and as it commences to
sift down the precipitous face it is caught by the currents of air and
carried away. From a distance this silt-laden air, as it poured up
over the crest of the bluff, reminded one of an ever-ascending vol-
ume of smoke. In places large drifts had accumulated like so
much wind-drifted snow.

Nulato, an important Indian village, was reached on August 2,
and Kaltag on August 5. Here the Government telegraph line that
extends down the river leaves the bank of the Yukon, ascends Kaltag
River to near its head, crosses the divide to Unalaklik River, and
descends that stream to Norton Sound, a total distance of one hun-
dred miles.

Inquiry here concerning localities on the Kaltag River failed to
elicit information of enough importance to warrant investigation;
so canoe travel was resumed to Anvik, some two hundred miles
below Nulato. Many stops were made to examine silt deposits, but
in only two places were fossils found. Some five or six miles above
Hall’s Rapids, on the right bank, bones of the mammoth and bison
were collected at the foot of the silt bluffs, and again above the old
station of Greyling, some twenty-five miles above Anvik, where the
silts are exposed for two or three miles by the cutting of the river.
Here, during the summer of 1907, a fine pair of lower jaws of
Elephas were picked up by Mr. W. C. Chase, of Anvik, and pre-

EXPLORATION IN ALASKA IN I9Q07—-GILMORE ne

sented by him through the writer to the Smithsonian Institution.
The Rev. J. W. Chapman, of the same place, also had specimens in
his possession from this locality.

It was planned before reaching Anvik to explore the area drained
by the Anivik River, as some years previous, while visiting this
place, Mr. A. H. Brooks, of the U. S. Geological Survey, had been
shown fossils by the Indians said to have been collected along the
banks of this stream. Inquiry here among both the white and
native inhabitants, many of whom are thoroughly familiar with the
river and the country drained by it, developed the fact that, so far
as they knew, no fossils had ever been found in the region. Never-
theless, we ascended this stream some distance to fully satisfy our-
selves as to the conditions prevailing there, but nothing in the nature
of a fossil vertebrate was found. It appears quite probable that
the specimens shown Mr. Brooks came from the deposits near
Greyling.

Upon our return to Anvik we were delayed some few days by
continued rains from resuming our journey down the Yukon. At
Holy Cross, a Catholic mission, fifty miles below Anvik, we were
told of the occurrence of large bones in the banks of one of the
sloughs leading to the portage to the Kuskokwim River. Difficulty
in securing the services of a competent guide deterred us from
making an investigation of this locality, which was some distance off
from the Yukon.

Russian Mission was reached August 25, and Andreafski, where
our canoe trip ended, on August 29. The almost incessant rains,
accompanied by winds, during the last ten days of canoe travel were
the most annoying feature of the whole trip. On several occasions
it became necessary to go ashore and wait for the wind to abate, for
fear of being swamped by the high waves encountered.

In the two months spent upon the Yukon and its tributaries, after
leaving Rampart, we traveled by canoe alone nearly fourteen hun-
dred miles.

At Andreafski passage was secured on the river boat D. R. Camp-
bell, for St. Michael, which was reached September 1.

Here it was learned fossils were occasionally found on the main-
land shore across the bay, and this area was investigated, but no
success was met with.

Nome was reached by the local steamer Yale on September 7.

The autumn season being too far advanced to undertake an ex-
ploration of the Eschscholtz Bay and Buckland River localities, we
took passage on the ocean steamer Northwestern from Nome Sep-
tember 20, and Seattle, Washington, was reached on September 29.

I4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

We were not successful in finding that which was most desired,
a fairly complete skeleton of a mammoth, but the expedition was by
no means barren of results, as will be noted later.

III. OccURRENCE OF FossILs

The scattered remains of Pleistocene animals occur throughout
the unglaciated region of Alaska and adjacent Canadian territory in
three quite distinct deposits: First, in the black muck accumulated
in gulches and the valleys of the smaller streams; second, in the fine
elevated clays of the Yukon silts and Kowak clays; and, third, in the
more recent fluvial and alluvial deposits. The specimens as found
have been disinterred either through the erosive agency of the
streams or by the work of the miner in the operations conducted
in search of gold.

Although so generally distributed, there have been reported, so
far as known to the writer, but two well-authenticated occurrences of
accumulations of bones under such conditions as to suggest an
original entombment. While the writer was shown bones pro-
truding from the face of the undisturbed beds in the Klondike
region (see pl. IV, fig. 1), and in other instances collected specimens
actually imbedded in the elevated silts along the Yukon River, they
were in all cases disarticulated and scattered, and there was no
evidence of an association of any of the parts found.

Diligent inquiry was made among miners, trappers, and other
residents of Alaska, met along the route traveled, concerning what
they knew of the occurrence of fossil specimens. While nearly all
were familiar with the fragmental and scattered parts, very little
information was elicited of an accumulation of bones that would
lead one to believe a skeleton or even a part of a skeleton had ever
been found together in any one place.

While the scattered depositions occur as separate bones, skulls,
teeth, tusks, horns, ete., throughout the formations mentioned, the
condition of the specimens found varies greatly. Some are in such
a good state of preservation they certainly could not have traveled
far from the original place of interment, while on the other hand
many bones are broken, abraded, and water-worn, and show unmis-
takable evidence of having been carried considerable distances.
Bones representing these several phases were often found com-
mingled and occupying relatively the same positions, whether it be
in the muck, on a river bar, or imbedded in the undisturbed silt
deposits.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 GILMORE, PL. IV

Flg. 1.--TUSK OF ELEPHAS PROTRUDING FROM THE FACE OF THE UNDISTURBED
MUCK IN FOX GULCH, BONANZA CREEK

Fig. 2.--SKULLS OF ELEPHAS PRIMIGENIUS AND BISON FROM THE MUCK OF FOX GULCH,
BONANZA CREEK, NEAR DAWSON, YUKON TERRITORY, CANADA

EXPLORATION IN ALASKA IN I9G07—GILMORE 15

The best-preserved specimens coming under the observation of
the writer were those seen at Fox Gulch, on Bonanza Creek, in
Yukon Territory, Canada, somé twelve miles distant from the city
of Dawson. On account of the excellent state of preservation of
many of the»specimens found here and the fact that they occur in
what may be considered as an approach to a primary deposition, a
somewhat detailed, description of this locality will be given.

BoNANZA CREEK LOCALITIES

Bonanza Creek empties into the Klondike River about a mile and
a quarter above Dawson. ‘The valley is trough-like in character and
follows a sinuous line bending from right to left. The present valley,
according to McConnell,’ has been cut down through the floor of an
older valley. At irregular intervals the sides of the valley have been
dissected by gulches. Magnet and Fox Gulches (see pl. 1x (x) ),
on the left-hand side, are the most important from the standpoint of
vertebrate fossils. Gold has been found in both, and at the time of
our visit hydraulic operations were being carried on here by the
Yukon Consolidated Gold Fields Company. In the prosecution of
this work the content of the entire gulch to bed-rock was being
sluiced down (see pl. v1, fig. 2), the talus spreading out fan-like into
the creek bed below.

In the talus from Magnet Gulch representative parts of the mam-
moth, horse, bison, and moose were picked up.

At Fox Gulch we were shown many fine skulls and other skeletal
parts of Elephas, Bison, Equus, and Alce. On the bank near the
working face was a complete skull of the mammoth beside two bison
skulls, recently uncovered (see pl. Iv, fig. 2), and protruding from
the face of the undisturbed muck was a large tusk (see pl. IV, fig. 1)
and the skull of another bison. These had been uncovered the morn-
ing of our visit.

Fox Gulch is a short, deep gulch that has been cut down through
the quartz drift and “White Channel” deposits and deep into the
present bed-rock. The bed-rock is covered with a thin layer of
rather coarse gravel on top of which is a thick layer of muck (see
fig. 1). The gold occurs in the gravel underlying this muck, and in
order to reach it the mass of superincumbent material is washed
down by the powerful streams of water from the nozzles of the
Ee ae

* McConnell, R. G.: Preliminary Report on the Klondike Gold Fields, Yukon
District, Canada. Geol. Surv. Canada, No. 687, 1900, p. 21.

16 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The working face as we saw it varied from twenty to forty feet in
height. It is in the bottom part of the muck that the fossils are
found. Those seen in place were from twelve to eighteen inches
above the layer of gravel, and upon inquiry it was learned that all of
the specimens taken out here had come from approximately the same
horizon.

The muck and gravel, which rest unconformably upon the under-
lying rocks, is solidly frozen, but thaws rapidly under the heat of
the summer sun, and large pieces were continually dropping during
our examination of the face. This thawed material emitted the dis-
agreeable odor of decomposing organic matter, a phenomenon
observed by many others, particularly Dall,’ who attributed it to

Fil :

Fic. 1.—Cross-section of Fox Gulch, Bonanza Creek, Yukon Territory, Canada.
a. “White channel” gravels and quartz drift; b. Muck; c. Bed rock; d. Layer
of logs, limbs, etc.; x. Level where fossils occur.

decaying animal flesh or to dung of the mammoth or other herbiv-
orous animals. The present writer agrees with Mr. Maddren,? who
attributes it to the gases from decaying vegetable matter, of which
the deposits are largely composed.

Interbedded with the muck in Fox Gulch was a layer of wood,
represented by many fair-sized sticks (see (d), fig. 1), their ends in
many instances being much rounded and water-worn.

Many of the fossils found here were beautifully preserved. For
example, several of the bison skulls had the external horn, the entire
dentition, and the frail, delicate bones of the anterior portion of the
face remaining intact. The conditions are unusual, for, as a rule,
only the horn cores and the heavier and stronger parts are found, and’
it is upon such fragmentary specimens that the descriptions of most
of the extinct species of bison of this continent are based. Stranger
still, however, is the fact that here no parts of these animals are
found articulated or even so associated that skeletons might be
assembled. All of the material is dismembered and scattered.

*Dall, W. H.: 17th Ann. Rept. U. S. Geol. Surv., pt. 1, 1895-96, p. 853.
*Maddren, A. G.: Loc. cit., pp. 64-65.

’

EXPLORATION IN ALASKA IN I9Q07—GILMORE LE?

The preservation of the horn sheaths, as in the cases of the bison
skulls, and the completeness of many of the skulls and other elements
show they have not been subje¢ted to the rough usage incident to
their removal from one place to another; nor after death could
they have lomg lain on top of the ground exposed to the vicissitudes
of the elements. The external horn would in such case be the first
to disappear, as all know who have visited our western plains and
have noted the almost total disappearance of the horn sheaths from
the buffalo skulls scattered about. Their destruction, even in a dry
climate, has been accomplished in a comparatively few years.

LittL—e Minook CrEEK JUNIOR

This small stream enters Big Minook Creek from the right some
six “miles distant from the town of Rampart. Here, as in the
Klondike region, the fossils occur in the lower part of the muck,
which covers everything from two to twenty-five feet in depth.
Specimens would be uncovered here only through the agency of
mining, as the volume of water in the creek is not sufficient to cut
away the banks.

While sinking a shaft on claim No. 21, operated by Messrs.
Bowen and Coole, a skull of Bison crassicornis (No. 5727, U. S.
National Museum) associated with bones of Elephas was taken out
twenty feet below the surface.

Some years previous to our visit, we were told, the tusks of a
large “mastodon’’ (mammoth) were found in a shaft sunk on a
claim above No. 21.
LittL—E Mrnook CREEK

This creek is also a tributary of Big Minook Creek, and here, as
in other localities, the fossils found occur in the lower layers of the
muck.

In the vertebrate fossil collection of the U. S. National Museum
is a portion of the skull of Bison alleni (No. 2383, see plate x1)
from this locality having the entire horn sheaths preserved.

Mr. J. B. Duncan, of Rampart, presented to the Smithsonian Insti-
tution, through the writer, a skull of Bison crassicornis (No. 5726,
U. S. National Museum, see plate x) from one of the claims on this
creek, and Mr. C. B. Allen, of the same place, presented the Institu-
tion with the calcaneum of Elephas irom claim No. I.

PALISADES

The Palisades, or “Bone Yard,” on the left bank of the Yukon,
thirty-five miles below Fort Gibbon (see pl. v, fig. 1), has long been

DA

18 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

famous as a locality for vertebrate remains. This escarpment has
been described by Russell,t Spurr,? and later by Collier? and Mad-
dren.*

The bluff region extends for a mile or more down and around an
almost right-angled bend in the left-hand channel of the river (see
fig. 2). The bluffs, from one hundred and fifty to two hundred feet
in height, and solidly frozen, are composed principally of an ex-
tremely fine silt, greenish gray in color and showing no traces of
stratification. ‘Their almost perpendicular faces are being contin-
ually undermined (see pl. v, fig. 2) by the swift current causing
large masses to break off, many times with-a startling report and
subsequent splash, as they fall into the water below. Often during
the two days’ stay here the report sounded so like the firing of a gun
that we were startled by the sharpness of it.

Near the lower end of these exposures the bluffs have been ele-
vated somewhat, exposing the gravels which underlie them. These
last have been called by Spurr the Palisades conglomerate, and it
has been suggested they may be of Pliocene age. The top of the
bluffs extend back from the river as a level, densely wooded table-
land. In several places small watercourses have dissected this
table, forming deep gorges. Near their mouths, where they enter
the Yukon, their levels are but little elevated above its high-water
stage.

At the up-river end of the bluffs we found numerous bones of the
mammoth in the débris from a recent slide, and a short distance
farther down (2 on map fig. 2) the scattered elements of a bison
were found securely imbedded in a huge block of silt not long since
‘ displaced from its original position higher in the face of the cliff.
The sacrum, part of the pelvis, two dorsals, rib, and scapula were
the parts recovered. The scapula (shoulder-blade) was quite com-
plete (see fig. 4), which, on account of its frail nature, appeared
rather remarkable, the heavier and stronger bones being broken and
abraded before their interment here.

The small streams mentioned previously as dissecting the bluffs
were followed inland for considerable distances, and although their
banks in many places presented very clean-cut exposures of the silt,
no evidence of the presence of fossil remains was found. However,

* Russell, I. C.: Notes on Surface Geology of Alaska. Bull. Geol. Soc. Am.,
vol. 1, 1890, p. 122.

* Spurr, J. E.: Geology of the Yukon Gold District. 18th Ann. Rept. U. S.
Geol. Surv., pt. 3, 1898, pp. 200-221.

* Collier, A. J.: Bull. No. 218, U. S. Geol. Surv., 1903, pp. 18 and 43.

*Maddren, A. G.: Loc. cit., pp. 17-18.

SMITHSONIAN MISCELLANEOUS CO

LLECTIONS, VO 51

Fig. 1.—PALISADES ON THE YUKON RIVER, 35 MIL BELOW FORT GIBBON, VIEWED FROM
R

ES O
A DISTANCE UP THE RIVER

Fig. 2.--ELEVATED SILT BLUFFS AT THE PALISADES, SHOWING BLOCKS OF FROZEN SILTS
AS THEY ARE UNDERMINED AND SUBSIDE INTO THE RIVER

EXPLORATION IN ALASKA IN IQO7—-GILMORE 19

among the débris of driftwood and other vegetable material accumu-
lated at their mouths many disassociated bones were recovered (see
(+), fig. 2). The concentrating action of the water in carrying
away the fine silt and leaving the heavier objects behind would
account for their abundance here.

In drifting down along the base of the cliffs in the canoe, the skull
of an Ovibos sp. nov. (No. 5728, U. S. National Museum) was
found on a narrow shelf just above the point (3 on map, see fig. 2)
where the underlying gravels first appear. That the skull came

+

Silkeudi@llaumun Trac kk. fossils Faalt

Fic. 2.—Sketch Map in Vicinity of “Palisades.”
1. Where section was taken, shown in Fig. 3; 2. Bison bones (Fig. 5) ;
3. Musk ox skull, No. 5728, U. S. National Museum.

down from the cliff above there can be no doubt, for it lay on a pile
of talus accumulated since the last high stage of water. The high-
water marks were still plainly evident on either side and above the
heaps of detritus. Moreover, the cranial and other cavities of the
skull were filled with the fine silt composing the bluff. This skull
was in fairly good condition, having, beside two of the molars, some
of the bones of the anterior part of the face in a good state of preser-
vation. The worn and abraded appearance of most of the fossils
here indicates that they are drift and not in a place of primary
entombment.

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Maddren' makes the observation, “There is a little ice on top of
these bluffs, but nothing like the extensive development exposed in
the Old Crow Basin.” Ice was also observed here by the writer,
which on first sight appeared to represent the typical ice-bed deposits
of many other localities. Upon closer examination, however, it was
found to be a superficial layer on the face of the exposure and not
a continuous ice-sheet interstratified with the muck and humus.
The formation of this layer of superficial ice appears to be of interest
and it may explain the presence of apparent ice-beds in some other
places. Moreover, it does show that caution should be exercised in
pronouncing all ice on the face of a cliff as being a section of a con-
tinuous bed.

At (1) on the map (fig. 2), a deep depression or basin in the top
of the silt has been filled with alluvium and mucky material. The
brow of the escarpment here, three or four hundred feet back from
the edge of the stream, was estimated to be one hundred and fifty to
one hundred and seventy-five feet above the level of the river. The
Yukon, having cut laterally into the center of this basin, has left the
remaining muck resting on a slope of silt inclined toward the river
(see cross-section, fig. 3). By the undermining of the face of the
cliff, one block after another of this frozen muck has broken away
from its original position in the face of the escarpment and moved
riverward. In most instances this movement has been so gradual
that the blocks retain their upright positions and carry with them
the superincumbent turf and vegetation undisturbed. The thawing
of their faces and subsequent wasting away has allowed the turf to
bend down without breaking, thus affording protection against
further disintegration. The final destruction of the blocks, as they
eventually fall into the stream (where several were seen half sub-
merged), has resulted in leaving a basin-like area of an acre or more
in extent devoid of its former covering of from thirty to forty feet of
muck, except that here and there are masses recently detached from
the walls of the basin. The inclosing walls or faces of the basin are
perpendicular and from twenty to thirty feet in height. From three
to four feet below the top of the walls was a layer of ice. Upon first
sight it had every indication of being a section of a continuous bed.
Some of the detached blocks standing in the center of the basin
showed ice on both front and back faces. The top of this ice was
straight, but the lower margins were irregular when not covered by
the detritus at the foot. The face of the ice was also irregularly
melted, due to the more exposed position of some parts.

*Maddren: Loc. cit., p. 18.

EXPLORATION IN ALASKA IN 1907—cILMORE 21

Upon ascending to the top of the escarpment at the point most
remote from the river, it was found that a mass of frozen muck,
estimated to be two hundred feet*long and fifteen to twenty feet in
thickness, with a vertical face of twenty to thirty feet, had moved
outward at its center for fully fifty feet, but had not yet become
detached at its ends. The crevasse formed by this displacement was
filled by water to such a depth that the bottom could not be found
with a long pole. Back of the crevasse, in the surface of the bluff,
were numerous parallel cracks varying from six to eighteen inches
in width and many feet in length. These had water standing in
them nearly to the top of the ground. The conditions observed
here appeared to the writer to explain the presence of the ice on the

Fic. 3.—Cross-section of “Palisades” Escarpment, showing Formation of
Superficial Ice.

1-2-3. Blocks of frozen silt; 4-5. Water level of the Yukon; 4-6. 150-170
feet; 7. Crevasse filled with water; 8. Ice on faces; 9. Overhanging turf;
to. Lacustrian silts; 11. Detritus (thawed muck).

faces below. With the advent of winter, assisted by the already
frozen ground, the water in the crevasses becomes frozen solid. A
subsequent outward movement of the blocks would leave the ice
clinging to the face of either the cliff, or the block, or both, and
under the influence of the rays of the summer sun would rapidly
smooth the broken and ragged edges. On the faces of blocks 1 and
2 (see fig. 3) such layers of ice were observed, and where protected
by the wet mantle of overhanging turf and moss were thawing very
slowly. In places the ice was so thin the writer with a few strokes
of his pick was able to penetrate it and into the frozen muck wall
behind. Sections of the ice, protected by curtains of turf and falling
débris, would persist for considerable periods. In places it had
melted away, leaving its mould in the face of the cliff.

22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Under the influence of the summer sun the blocks were gradually
disintegrating. Large pieces were continually falling as thawing
progressed, and all along the bases of the face and around the blocks
were small piles of talus of the mucky material.

The same pungent, disagreeable odor of decaying organic matter
was noticed here as in the deposits of Bonanza and Minook creeks.
The stench was so strong it could be easily detected on the river a
considerable distance away. In many places on the wet muck banks
a rusty red fungus-like plant grew in extensive patches.

The writer does not wish to be understood that the observations
recorded here apply to all ice deposits, but as a local phase it may
explain the occurrence of many so-called “ice-beds.” It may also
help to explain the position of the mammoth found frozen in the
cliff along the Berezovka River in Siberia in 1901. From the posi-
tion in which the carcass was found it would appear as though he
had fallen into a crevasse from which there was no escape. The
description’ of the locality is not so unlike the conditions observed
here.

Nowitna RIVER

The exploration of this stream added but little information con-
cerning the occurrence or derivation of the fossils found along its
course.

After the first day of our ascent of this stream nearly every bar
yielded some fossil evidence, either in the shape of a tooth, limb
bone, vertebra, or scattered fragments. The specimens found were
in various stages of preservation; many broken, others entire, some
badly water-worn, and a few as perfect as the day they performed
their functions in the skeleton itself. Some elements, which on ac-
count of their frail nature should by the very character of their
structure have been broken and abraded, were found complete.

In examining the bars we soon came to know that the up-river
ends, where the materials composing them were coarsest, was the
most favorable part for finding the scattered bones. The remains
without exception were all found below the high-water level of the
flood stages of the river, and were without question brought down
from some source or sources of deposition, either by the water itself
or by floating ice.

A close examination was made of the low-cut banks and elevated
silts, but not in a single instance were fossils actually found in place.

The conditions on this stream differed somewhat from those found

*Herz, O. F.: Frozen Mammoth in Siberia. Ann. Rept. Smithsonian Inst.,
1903, pp. 611-625.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 GILMORE, PL. VI

Fig. 1.--TYPICAL SANDBAR ON THE NOWITNA RIVER, 180 MILES FROM ITS MOUTH

Fig.2 .--LOOKING UP FOX GULCH, BONANZA CREEK, NEAR DAWSON, CANADA

Sluice box in the center, and the muck filling of the gulch not yet sluiced out may be
seen in the background on the right

EXPLORATION IN ALASKA IN I9Q07—GILMORE 23

by Mr. Maddren on the Porcupine and Old Crow rivers, from the
fact the fossils did not become more abundant on the bars as we
went upstream. On some bars many fossils would be found, while
others would yield only a single specimen. The varying degrees of
preservation exhibited by the specimens points to the conclusion that
the source of supply is diverse and not one large deposit. The
writer is inclined to the opinion that the fossils found on the bars
have been washed out of the silt banks along the stream and trans-
ported to their present resting places largely by the action of the
water.

The finding of abundant remains on the bars of a stream that is
cutting elevated silts does not necessarily lead to the conclusion that
all of the specimens found there have come from the headwaters of
that stream, for we know that scattered bones occur in the silt depos-
its, and it appears that the bones brought down from far upstream
may be augmented in numbers by those washed out of the silts along
its course.

The following list gives the fauna of this area as represented by
the scattered bones collected :

Elephas primigenius.
Bison.

Equus.

Ursus.

Alce.

Castor.

YUKAKAKAT RIVER

Although fewer fossils were collected along this stream, the pre-
vailing conditions as to their occurrence were found to be similar
in most respects to those observed on the Nowitna River.

The following forms were recognized:

Elephas primigenius.
Bison.

KLALISHKAKAT RIVER

A locality on this stream some three miles inland from the Yukon
was visited. Here the bluffs present nearly perpendicular faces from
sixty to eighty feet in height, the lower parts of which are com-
posed of reddish cross-bedded gravels, varying from fine to very
coarse and unconformable with the overlying silt. The silt shows no
traces of stratification and is solidly frozen. Back from the bluff
is a level tableland, bordered on all sides, except that adjacent to the
river, by low hills. It was at this locality that Mr. Collier in 1902

24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

photographed a tusk protruding from the face a few feet below the
top of the escarpment.

The bases of the bluffs are washed by the stream, and during
stages of high water are undermined, causing large masses to break
off. ‘The tusk seen by Collier five years previous had disappeared,
but a recent slide had exposed the distal end of a femur of Elephas
in place about three feet above the underlying stratum of gravel.
Other broken fragments were found in the loose clay of the talus
along the foot of the bluffs. The silt varies in thickness from thirty
to thirty-five feet, and broken and abraded fossil remains occur, scat-
tered throughout. The conditions here are not favorable for the
securing of good specimens. Bones of Elephas and Bison were col-

lected.
DISCUSSION

After a review of the conditions prevailing in localities where fos-
sils have been found in Alaska and contiguous territory, the writer
feels inclined to dissent somewhat from the views expressed by
Maddren regarding the most promising collecting grounds.

Mr. Maddren* has advanced the opinion in the following state-
ment that the old lake shores offer the greatest inducements:

“That the fluvio-glacial Pleistocene lakes of Alaska were subject
to annual winter freezing, at least at various stages of their existence,
there appears no doubt, because scattered apparently indiscriminately
through the clays, at varying depths and considerable distances from
the former shore lines of these basins, are some mammal remains.
Their positions can only be accounted for by supposing they were
carried out on the waters of the lakes from the adjacent shores or
tributary streams by ice during spring breakups and freshets, there
to be dropped by its melting to their present positions interbedded in
the silts. There appears no other logical way of i eos the
presence of these bones in the lacustrine areas.’ :

“The main point is that the remains occur in the silts < as scattered
depositions.

“The animals from which they were derived probably died about
the shores of these lakes, and it is these Pleistocene lake shores we
must examine carefully if we are to obtain anything like complete
remains of the mammals inhabiting the region at that time.”

There appears to be one objection to this hypothesis as applied to
these fine-silt deposits. If the great number of isolated mammalian
bones scattered through it were carried out from the shores and
tributary streams by ice, it is hard to understand how they could be

1 Maddren, A. G.: Smithsonian Misc. Coll., vol. xix, No. 1584, 1905, p. 26.

EXPLORATION IN ALASKA IN IQO07——-GILMORE 25

selected for distribution in deposits from which all other large frag-
ments of detrital materials are absent.

It might be explained, however, on the supposition that the bones
have been carried out from muck deposits in which there is no heavy
detrital material. In that event many of these deposits might be
considered older than are the silts; or, the presence of interbedded
layers of lignite at the “Palisades” and in the silts of Cooleen basin
(which would indicate a local drainage or elevation of these beds at
one time) might furnish the necessary conditions for the accumu-
lation of animal remains, followed by subsidence and further depo-
sition.

Up to this time the best-preserved remains have been found in
the deposits of muck accumulated in gulches and the valleys of the
smaller streams. Typical examples of the occurrence of this muck
may be seen on Little Minook Creek, near Rampart, Alaska, and
Bonanza and other creeks, near Dawson, in Canadian territory.
Only a single skull of bison with the horn sheaths preserved is
recorded as coming from the silt, while they are of common occur-
rence in the muck. ‘Their presence here may be accounted for on
the supposition that the animals became mired in the bogs before
they became solidly frozen as they are now. This naturally raises the
question: If mired down in such a place, why is it that the remains
should be so universally scattered? The writer suggests that they
may have been separated by the creeping of the muck or peat—a
phenomenon familiar to all students of deposits of this nature. By
such creeping the muck may have moved considerable distances,
particularly where the floor is inclined, as in many of the gulches.
From the fact that most of the bones occur in the lower layers of
the muck, no matter what the depth of the deposits may be, it is
apparent that their specific gravity has caused them to sink to their
present resting places. Thus it would not be necessary for the
extermination of the fauna to have taken place at one time, as might
be inferred by their occurrence at one level.

It was from the muck forty-two feet below the surface that the
skull and tusks, surrounded by other bones of the skeleton of Elephas
primigenius shown in plate vil, was obtained. Mr. A. H. Brooks,
of the U. S. Geological Survey, tells me of seeing a portion of a
skeleton of Elephas from Woodchopper Creek, Alaska, probably
taken from a similar deposit.

The two instances just cited undoubtedly represent places of
primary entombment, and the manner of their occurrence appears to
approximate the conditions found in the bogs and swamps in the

26 SMITHSONIAN. MISCELLANEOUS COLLECTIONS. VOL. 51

Eastern States, from which many of the best skeletons of the
Mastodon have been obtained.

From the evidence reviewed the writer believes that the deposits
of muck represent the most likely places from which to secure
remains of this extinct fauna.

The writer takes this opportunity to express his appreciation for
the assistance given him by Mr. A. H. Brooks and Mr. A. G.
Maddren, of the U. S. Geological Survey. Many services were
rendered by residents of Alaska along the route traveled, and favors
were extended by agents and officials of the Northern Commercial
Company. Mr. J. B. Duncan, of Rampart; Mr. Frank Haslund, of
Kokrines, and Mr. Frederick, of Andreafski, were especially kind
in many ways. My thanks are also due Mr. J. W. Gidley of the
National Museum, for help in the identification of specimens.

IV. THe PLEIsStocENE FAUNA OF ALASKA.

Although a number of species have been described from the Pleis-
tocene deposits of Alaska, they have for the most part been based
on fragmentary, and therefore rather unsatisfactory, specimens. In
many cases the principal osteological and dental characters are not
known, and on that account it is not always possible to compare them
intelligently with related forms.

Only a few of the large number of localities where fossils have
been found furnish well-defined specimens, capable of specific
determination, and while these vertebrates are interesting from the
standpoint of their general geographical distribution, they are of
comparatively little aid in the interpretation of the local deposits. The
forms have been entombed under such exceptional conditions as to
raise some question regarding the exact age of the deposits in which
they are many times found, although they could not have antedated
Pleistocene time. A glance at the list of determinable species is
sufficient to show at once that they represent a typical Pleistocene
fauna, some of which, as the moose, caribou, musk-ox, sheep, bear,
and beaver, have persisted down to the present day.

To aid the student, there is given here a list of the various genera
and species thus far reported as occurring in Alaska, followed by
a brief review of each, with a reference to the original description ;
the condition and present location of the type specimen (if known,
and when based upon fossil remains) upon which these were
founded, and in some cases figures of representative specimens from
Alaska. Some additional information has been derived from a
study of specimens in the vertebrate paleontological collection of the

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EXPLORATION IN ALASKA IN 1907—GIL MORE 27

U. S. National Museum, collected in Alaska by Lieutenant Hooper,
Dr. W. H. Dall, E. W. Nelson, L. M. Turner, A. G. Maddren, and
others. .

ELEPHAS PRIMIGENIUS Blumenbach

7 Tue NortHEeRN MAMMOTH

Elephas primigenius BLUMENBACH, Handb. Naturg., Ist French ed., vol. 11,
1803, p. 407.

DESCRIPTION.—‘Jaw broad and rounded; profile in front of tooth
row almost vertical; enamel folds narrow and compressed; rather
more than two folds to the inch, or twenty-four in ten inches ; enamel
itself thin.”*

ReMARKS.—This species is, geographically, the most widely dis-
tributed of extinct elephants. It has been reported as ranging from
Florida, Texas, and Mexico on the south and northward into Can-
ada and Alaska. It is also found in Great Britain and nearly all
Europe and northern Asia.

Its remains are particularly abundant in parts of Alaska and
Siberia. As yet no complete specimens have been found in Alaska,
although several good skulls and nearly all parts of the skeleton
are known from scattered but well preserved bones. Neither have
specimens been found in the flesh, as is so often reported through
the columns of the newspapers and even by some of the magazines.

The size of the mammoth has been so grossly overestimated by
the general public that a few comparisons may help to correct some
of these false impressions. The largest mounted specimen known is
the skeleton in the collection of the Chicago Academy of Sciences,
obtained in 1878 from Spokane County, in the State of Washington.
The height of this animal when alive has been estimated to be thir-
teen feet. The African elephant “Jumbo” was eleven feet high,
and there have been other elephants recorded as measuring twelve
feet in height; so, as this would indicate, there is not so much differ-
ence in size between the mammoth and living elephants as is often
supposed.

Mr. Lucas says:

“Tusks offer convenient terms of comparison, and those of a fully
grown mammoth are from eight to ten feet in length, those of the
famous St. Petersburg specimen and those of the huge specimen in

*Lucas, F. A.: Systematic Paleontology of the Pleistocene Deposits of
Maryland. Maryland Geol. Surv., December, 1906, p. 163.

The above characters are given by Mr. F. A. Lucas as distinguishing this
species from all other elephants.

28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Chicago measuring respectively nine feet three inches and nine feet
eight inches. . . . Compared with these we have the big tusk
that used to stand on Fulton Street, New York, just an inch under
nine feet long and weighing one hundred eighty-four pounds.”

In a footnote’ he gives the measurement of the left tusk of an
African elephant that is ten feet three and one-half inches in length
along the outer curve, twenty-four and one-quarter inches in cir-
cumference, and weighing two hundred and thirty-nine pounds.

The longest tusk reported from Alaska is twelve feet ten inches
in length. During the summer of 1907 the writer measured a tusk
at Fort Gibbon that was ten feet seven inches long and the greatest
circumference was twenty-one inches. This specimen was broken at
both ends.

The tusks belonging to the skull shown in plate vir are seven feet
six inches in length.

The tusks of the mammoth, as a rule, were more curved and of
greater length than of the living forms, although there is a great
variety of shapes and sizes.

Economic ImMporTANCE OF MAM™MoTH Ivory.—lIt appears that
the mammoth remains found in Alaska are not in as fresh a state
of preservation as those found in Siberia, where for a good many
years their tusks have constituted an important article of export.
Dr. Middendorf, who visited Siberia about the year 1840, estimated
the annual output of this fossil ivory to be one hundred and ten
thousand pounds and representing at least one hundred individuals.”
From their great abundance, Dr. R. Lydekker® has suggested that
tusks were probably developed in both sexes.

It is seldom, if at all, that tusks are found in Alaska sufficiently
well preserved to compete on the market with those of the African
and Indian elephant, as is the case with the Siberian ivory; usually
they are found to be discolored and either badly checked or exfoli-
ated. A curio dealer in Nome, however, told the writer, “A few
years ago a man would not take a tusk as a gift, but of late the best
ones had acquired a commercial value, being cut into curios for the
tourist trade.”

In the “curio” stores at Skagway we were shown some of the
articles manufactured for the trade from this ivory, consisting of

*Lucas, F. A.: Annual Report Smithsonian Institution, 1899, p. 355.

* This estimate appears rather low, as the average tusk would hardly weigh
two hundred and fifty pounds, or five hundred pounds for the pair, which
would give over two hundred individuals.

* Lydekker, R.: Annual Report Smithsonian Institution, 1899 (pp. 361-366).
p. 362.

EXPLORATION IN ALASKA IN I90/7—GILMORE 29

sawed sections polished for paper-weights, on which were etched
representative scenes and animals of Alaska. The life restoration
of the mammoth with its long hair and curved tusks appeared to be
a favorite subject. In one instance a miniature of the mammoth
had been carved from it. This carving and etching is done by the
Indians and Eskimo, many of whom become quite adept at this line
of work. Similar objects were observed in the curio stores at
Nome. The Skagway dealers obtain most of their tusks from the
Klondike region, while the Nome dealers procure the ivory used by
them from the Eschscholtz Bay, Buckland, and Kobuk River local-
ities.
In 1854 Sir John Richardson said:

“Eskimos are in the habit of employing the soundest tusks for the
formation of various utensils ; and the American fossil ivory has for
at least a century, and for a longer period of unknown duration, been
an article of traffic with the Tchutche of the opposite shores of
Beering Straits; so that we can venture upon no calculation of the
multitudes of mammoths which have found graves in several icy
cemeteries of the American coast of Beering Sea.”

Dr. W. H. Dall? tells of obtaining “in 1880 a deep ladle as large
as a child’s head, carved, handle and all, out of a solid tusk of mam-
moth ivory by those people,” referring here to the Eskimo.

The writer also saw pieces of tusks fashioned into sled runners,
having holes at intervals by which they were lashed to the wooden
framework above. On the Yukon it was observed the Indians some-
times used sections of tusks as weights for sinking their salmon nets.

An account of this fossil ivory would not be complete without a
mention of the blue phosphate of iron sometimes formed by the
decomposition of the tusks and used by the Alaskan Eskimo as a
pigment.

Sir John Richardson was the first to make note, in 1854, of this
phosphate? (Vivianite) occurring between the plates, of the exfoli-
ated tusks. The writer saw this blue stain on many of the tusks
examined by him, and it was particularly noticeable on those just
recently removed from the ground. The same iron phosphate was
found in the metacarpal bones of the bison collected on the Nowitna
River.

* Dall, W. H.: Seventeenth Annual Report, U. S. Geol. Surv., pt. 1, p. 857.

*In this connection it is interesting to quote from Warren’s report on
Mastodon giganteus: “On burning the bone, the ash which remains is of a
beautiful blue color, owing to the presence of phosphate of iron, which appears
to have been formed from the iron which had penetrated into the bone from
the marl surrounding the skeleton.”

30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

ELEPHAS COLUMBI Falconer

Elephas columbi Faiconer, H., 1857, Quart. Jour. Geol. Soc. of London,
XI, p. G10:

The only reported occurrence of E. columbi is given by Dall,’ who
mentions that tusks, teeth, and bones of E. primigenius and E. co-
lumbi were collected by Wossnessenski near Topanika Creek, Norton
Sound. We quite agree with Maddren? that “the identification needs
verification before it is assigned to Alaska.”

MAMMUT AMERICANUM (Kerr)
Tur AMERICAN MAstTopON
Elephas americanum, Kerr, R., 1792 Anim. Kingdom, p. 116.

Drscription.—It may be readily ‘distinguished from Hlephas
primigenius by the character of the teeth, which bear simple tent-
like ridges (see plate vit). By its low massive build and shape of
the skull and the tooth characters just reviewed, it may be told apart
from the mammoth by the most casual observer.

ReMARKS.—This animal also has a wide distribution. Its re-
mains have been found from New York to Florida and west to
Texas and Washington. It extended north into Canada, and re-
cently two teeth have been found in the Klondike region near Daw-
son. ‘The writer refers here to a Mastodon molar secured by Dr.
T. W. Tyrrell on Gold Run Creek in 1902, and through him pre-
sented to Mr. W. H. Osgood,’ of the U. §. Biological Survey, and
now in the vertebrate paleontological collection of the U. 5. National
Museum (see pl. vii, fig. 1). A second occurrence of this species
in this region was noted by the writer in the summer of I1907—a
tooth collected during the spring of 1906 on Sulphur Creek, near
Dawson (see map, plate 1x), and now in the possession of Mr.
Joseph Nichlas, of that city. This specimen is reproduced here from
a photograph (pl. vim, fig. 2). It is of interest to note the occur-
rence of the mastodon in this region and in both places associated
with remains of the mammoth.

In 1904 Mr. M. T.. Obalski* mentions the occurrence of the mas-

*Dall, W. H.: Seventeenth Annual Report U. S. Geological Survey, 1896,
p. 856.

*Maddren, A. G.: Smith. Misc. Coll., vol. xnix, No. 1584, 1905, p. 7.

* Osgood, W. H.: Proc. Biol. Soc. of Washington, November, 1905, vol.
XVIII.

* Obalski, M. T.: Les grandes Fossiles dans le Yukon et l’Alaska. Bull. de
la Musée d’Hist. Nat., Paris, 1904, No. 5, pp. 214-217.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 GILMoRE, PL. vill

Fig. 1.--UPPER MOLAR OF MASTODON (No. 5102, U. S. National Museum) FOUND ON GOLD
RUN CREEK, NEAR DAWSON, YUKON TERRITORY, CANADA, IN 1902

About 2/5 natural size

Fig. 2.--MOLAR OF MASTODON FOUND ON SULPHUR CREEK, NEAR DAWSON, YUKON
TERRITORY, CANADA, IN 1906
In the possession of Mr. Joseph Nichlas, of the city of Dawson. About % natural size

75

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GILMORE, PL. |
SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51 REx be

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MAP OF

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YUKON DISTRICT

Scale, 2 miles to 1 inch.

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Pee eres on various creeks shown thus = e@ Sym b os tyrrelli
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EXPLORATION IN ALASKA IN 1907—GILMORE 31

todon in the placer gravels of the Klondike region. Maddren*
attributes this to an error. While tt may have been an error in this
particular instance, it is likely to be a very common one, for through-
out this entire region all of the tusks, teeth, and big bones are usually
referred to by the people as those of the mastodon.

So far as*the writer knows, there have been no authentic cases
recorded of the occurrence of mastodon in Alaska. From the fact
that its remains do occur in the Klondike region, there appears no
logical reason why it should not be found in Alaskan territory as
well. It is on that account that the brief review is appended here.

Through the kindness of Mr. R. G. McConnell, of the Canadian
Geological Survey, the writer is enabled to present a map (see plate
1x) of the Klondike district on which has been indicated the local-
ities where mastodon and mammoth remains have been found. With
three exceptions, the localities indicated are based upon specimens

seen by the writer.
EQUUS sp. undet.

Scattered remains of Equus are commonly associated with the
other Pleistocene fossils found in Alaska. These bones have been
considered by various authorities as representing the extinct species
Equus fossilis and E. fraternus, and by some referred to the living
form &. caballus. On account of the very fragmentary nature of
the specimens upon which these determinations have been made, in
all cases the identifications are open to question, and until better
material is found the species should be considered undeterminable.

Remains of horses have been found in the following localities:

Eschscholtz Bay, Seward Peninsula, on the Kobuk and Buckland
Rivers; “Palisades,” on the Yukon; Nowitna River, Old Crow
River, and in many places in the Klondike district.

BISON CRASSICORNIS Richardson
Bison crassicornis RicHarpson, Zool. Voy. of H. M. S. Herald, 1852-54,
pp. 40-60, pls. 1x, x1, fig. 6; pl. xu, figs. 1-4; pl. x1, figs. I-2, pl. xv,
figs. I-4.
Typr.—Poorly preserved skull in the British Museum, from
Eschscholtz Bay, Alaska.
' Description.—“‘Horns long; length of horn core along upper
curve very much. greater than circumference at base; horn cores
slightly flattened on superior face; transverse diameter much greater
than vertical; curve of horn regular, the tip not abruptly reflected
nor pointing decidedly backward; horn cores raking decidedly back-
ward.”

*Maddren, A. G.: Smithsonian Misc. Coll., vol. xnrx, No. 1584, 1905, p. 7-

Rae ey SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

RemarkKs.—This species heretofore has not been known outside
of Alaska, but, as might have been anticipated, skulls of this species
were observed at Fox Gulch, Bonanza Creek, Yukon Territory, Can-
ada, by the writer during the summer of 1907. In the foreground
of plate rv, fig. 1, may be seen a portion of the skull and horn cores |

Fic. 4.—Scapula of Bison crassicornis (?)

(Cat. No. 5941) from “Palisades,” on the Yukon River. (See 2, Fig. 2.)
Greatest length, 22% inches.

- of this species. Remains of B. crassicornis have been collected from
the following localities: On the tundra back of Point Barrow, Ele-
phant Point, Eschscholtz Bay, Little Minook Creek, Little Minook
Creek Junior, and Bonanza Creek, Yukon Territory, Canada.

q "—' oe ¥ |
: fou . ; i? ey *— rh

sayour SP YJpIM 4sa}BI1H
ByseLY “aeduey ivau ‘Ya015 Yoour 2]IWVI woy ‘poasssaid syjvays Woy YIM ‘UNIUBID JO MATA 1OL19}sOqd (‘Winesn] [BUONEN “SO ‘Egez “ON “38D)

ysueW INA1T1V NOSIS

LG ‘1OA ‘SNOILO31109 SNOANVIISO0SIN NVINOSHLIWS

IX ‘Id “SHYOWTI9

EXPLORATION IN ALASKA IN I9Q07—GILMORE 33

This is the largest of the extinct bisons found in the deposits of
this region, and a scapula (see fig. 4) collected by the writer at the
“Palisades” on the Yukon River may, on account of its size, pertain
to this species. Plate x represents a typical skull of this form col-
lected on Little Minook Creek and presented to the Smithsonian
Institution through the writer by Mr. J. B. Duncan, of Rampart,
Alaska.

BISON ALLENI Marsh

Bison alleni Marsu, Amer. Jour. of Science, vol. xiv, 1877, p. 252.

Typr.—Horn core, No. 911, Museum of Yale College, New
Haven, Connecticut, from Blue River, near Manhattan, Kansas.

Descriprion.‘—‘‘Horn cores long, slender, much curved, slightly
flattened above at base; transverse diameter considerably greater
than vertical; length along upper curve much greater. than circum-
ference at base. Bison alleni is distinguished from B. crassicornis
by the much greater curvature of the horn cores, these being also
more flattened and more elliptical in section in crassicornis.

REMARKS.—This species is represented in the U. S. National.
Museum paleontological collection, by a skull, No. 2383, from Little
Minook Creek, near Rampart, Alaska.* It (see pl. x1) was found in
the frozen muck twenty-five feet below the surface, and is of more
than usual interest on account of the excellent state of preservation
of the horn sheaths and from its being the first of this species found
in Alaska. This species is also reported as occurring in Idaho.

A skull of B. alleni from the Porcupine River is now in the Grand
‘Rapids Museum, of Grand Rapids, Michigan.

BISON OCCIDENTALIS Lucas
Bison occidentalis Lucas, Science, November 11, 1898, p. 678.

Typr.—Portion of skull with horn cores, No. 4157, U. S. National
Museum, from Fort Yukon, Alaska, collected by Sir John Richard-
son. ;
- Description.—“Horn cores moderate; circumference at base
equal to or slightly greater than length along upper curve; sub-
circular in section, regularly curved upward and backward.”

*The descriptions of the Bison from Alaska is taken from Mr. F. A. Lucas’
article, “The Fossil Bison of North America.” Proc. U. S. National Museum,
vol. xx, 1899, pp. 755-771.

* This specimen was presented to the Museum by Messrs. McLain and Bal-
lou, of Rampart, through the efforts of Gen. Timothy Wilcox, U. S. A., of
Washington, D. C.

3A

34 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

REMARKS.—A second specimen, No. 2643 (see pl. x11), in the U. S.
National Museum collections, was collected by Mr. A. G. Maddren
on the Old Crow River in 1904. A fairly complete skeleton’ of this
species from Gove County, Kansas, is now in the University of Kan-
sas Museum. This species has also been reported as occurring on
the Tatlo River and St. Michaels, Alaska. The writer doubts very
much the authenticity of this last locality. Mr. Lucas says: “It is
the species most nearly resembling the existing bison, with which it
was probably for a time contemporaneous.” In that event B. crassi-
cornis was also a contemporary, as the writer recognized skulls of
B. occidentalis and B. crassicornis at Fox Gulch, on Bonanza Creek,
coming from the same layers in the deposits there.

BISON PRISCUS (?)

A skull collected at Eschscholtz Bay, Alaska, was provisionally
referred” to this species by Sir John Richardson. In a more recent
paper,*® however, Mr. F. A. Lucas has considered this specimen (No.
24,580, British Museum) as representing an immature individual or
“spike horn” of B. crassicornis.

Horn cores collected by Maddren on the Old Crow River and by
the writer at the “Palisades” on the Yukon River appear to resemble
the figure (see pl. x11, fig. 3) given by Richardson in his report.

SYMBOS TYRRELLI Osgood
Scaphoceros tyrrelli Oscoop, Smithsonian Miscellaneous Collections, vol.
xvi, No. 1585, 1005, pp. 173-183, pl. xxxvu, fig. 2; pl. xxxvumt, fig.
2: pl, XXx1x; fig. 1 ppl..34, ‘fig, 2.
Symbos tyrrelli Oscoon,

Type.—Fairly complete skull, No. 2555, U. S. National Museum,
from Lovett Guich, Bonanza Creek, Klondike District, Yukon Terri-
tory, Canada (see map, plate 1x).

DEscRIPTION—Generic characters.~—‘“‘Similar to Ovibos, but horn
cores much smaller, less compressed at base, and more divergent at
tips; crown of skull between bases of horn cores surmounted by a
prominent exostosis with an anterior bounding rim and a deep
median excavation; orbits much less produced laterally than in

* Stewart, Alban: Kansas University Quart., July, 1897, Sec. A, pp. 127-135.
Described as B. antiquus, but referred later by Lucas to B. occidentalis.

* Richardson, Sir John: Zodlogy of Voyage of H. M. S. Herald, 1852-54, pl.
vu, fig. I, p. 34.

* Lucas, F. A.: The Fossil Bison of North America. Proc. U. S. Nat. Mus.,
vol. xx, 1890, p. 762.

“Generic and specific characters as given by Osgood.

soyour + fF yApIM jsa}zeaIyH
PpRURD ‘ISATY MOID Plo TMHO1F WNLUEID JO MSTA IOII39}sOq (‘UInasn] [BPUOTJEN 'S "QQ ‘Ehgz ‘oN JED)

seon] SIIVLN3GIO00 NOSIg

IX “Id *3YOWTI9

1S “10A ‘SNOIL037100 SNOSNV171390SIN NVINOSHLIWS

EXPLORATION IN ALASKA IN 1907—GILMORE 35

Ovibos; facial part of skull nearly as wide as cranial; basioccipital
without a high median ridge; teeth very large and relatively broad ;
m?! and m? quadrate in transverse view.”

SPECIFIC CHARACTERS.—‘‘Size smaller than in SS. cavifrons
(Leidy) ; horn cores much smaller and shorter; exostosis less exten-
sive, but more deeply excavated ; depth of brain case and surmount-
ing bony mass decidedly less.”

ReMARKS.—The only reported occurrence of this species in Alaska
is a horn core, No. 2378, U. S. National Museum, presented by Rev.
J. W. Chapman through Dr. Arthur Hollick. The label with the
horn gives the locality as Anvik, on the Yukon River, but it is un-
likely the specimen was collected in the immediate vicinity of that
place. It is more probable that it comes from some of the silt de-
posits along the Yukon twenty-five or thirty miles above Anvik.

SYMBOS CAVIFRONS (Leidy)

Hay? cites the occurrence of O.? cavifrons in Alaska, due to the
fact that he includes Richardson’s indeterminate species, Ovibos
maximus, under this head.

This species, therefore, is not known to occur in Alaska.

OVIBOS MAXIMUS Richardson

Ovibos maximus RicHarpson, Zool. Voy. of H. M. S$. Herald, 1852-54,
pp. 25-28, pl. x1, figs. 2, 3, and 4.

.

Typre.—An imperfect cervical vertebra, the axis or dentata (No.
99, Haslar Museum), from Eschscholtz Bay, Alaska.

REMARKS.—From the very fragmentary nature of the type this
species appears indeterminable.

OVIBOS MOSCHATUS (?) Zimmerman

This is a recent species found at present in northern North Amer-
ica and Greenland. At present this animal is not known to range
west of the McKenzie River, but Pleistocene remains which have not
been distinguished from this species are found in Alaska. Ass in the
case of other remains referred to living species, more complete ma-
terial may show an extinct species separable from the living form.

This appears more probable since a skull, collected by the writer
at the Palisades, on the Yukon, in 1907, is being described by Mr.
J. W. Gidley as the type of a new species, and it may be that all the
remains formerly considered O. moschatus should be referred to this
species.

* Hay, O. P.: Bulletin No. 179, U. S. Geological Survey, p. 688.
* Osgood now includes Ovtbos cavifrons under Symbos.

36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Buckland, because of the preservation of a horn sheath on a skull
of Ovibos submitted to him from Eschscholtz Bay, considered it of
recent origin, but now that Bison (see pl. x) skulls are known dis-
tinct from living species having the horn thus preserved, this argu-
ment would apply equally to the case in question.

OVIS, sp. undet.

A list of species occurring in the Eschscholtz Bay deposits is
given by Seeman in his “Narrative of the Voyage of H. M. S.
Herald in 1853, in which Ovis montana is mentioned as being found
there.

This list was compiled from a report? made by Sir John Richard-
son, but a careful perusal of his report failed to reveal any mention
of fossil remains, although he does describe the recent skeleton of
Ovis montana,

It is probably by mistake that this species was included in
Seeman’s list, although sheep remains will undoubtedly be found,
as Mr. W. H. Osgood, of the U. S. Biological Survey, has frag-
mentary remains of Ovis in his possession from the Klondike district,
Yukon Territory, Canada. At present, however, the writer does not
know of an authentic record of their occurrence in Alaska.

ALCE, sp. undet.

Like Rangifer, scattered remains of the moosé are known from
several widely separated localities in Alaska and adjacent territory.
These bones have usually been referred to as representing the living
form Alce americanus, but it appears the identifications have been
based upon such scanty material that the assignment to this species is
open to question. When better specimens are known, characters of
sufficient importance to distinguish it from the living species will
probably be found.

Remains of Alce are known from the deposits of Eschscholtz
Bay, on the Old Crow and Nowitna rivers, and fragmentary antlers
were found in the muck of Magnet and Fox gulches on Bonanza
Creek near Dawson.

RANGIFER, sp. undet.

Fragmentary remains representative of this genus are commonly
found with the bones of other Pleistocene animals in Alaska. These
scattered and fragmentary parts have been referred by various
writers to the living species, R. caribou and R. tarandus. It appears

* Zoological Voyage of H. M. S. Heraid, 1852-54.

EXPLORATION IN ALASKA IN 1907—GILMORE 37

more likely, however, if referable at all to a living form, it would
be FR. articos, the barren-ground caribou and now living in these
regions.

As mentioned by Richardson, Zodlogy of the Voyage of H. M. S.
Herald, 1854% p. 20, fragmentary remains have been found at Esch-
scholtz Bay, and the writer collected fragments of antlers on Little
Minook Creek Junior and on the Nowitna River.

So far, remains have not been found sufficiently complete upon
which an accurate specific determination could be based.

URSUS, sp. undet.

The finding of a scapula and astragulus of Ursus associated with
the remains of other Pleistocene animals on the Nowitna River
during the summer of 1907 verifies a former record of the occurrence
of the bear in the Pleistocene of Alaska.

The scapula, although incomplete, indicates an animal about the
size of the black bear (Ursus americanus), an inhabitant of these
regions at the present time.

Bonest of Ursus have also been found associated with mammoth
remains in a cave on St. Paul Island of the Pribilof group.

CASTOR, sp. undet.

Among the vertebrate remains collected on the Nowitna River in
1907 were the left pelvic bones (No. 5942, U. S. National Museum)
of a beaver. This appears to be the first occurrence recorded of the
finding of bones of Castor, although Mr. E. W. Nelson,” who visited
Eschscholtz Bay in 1881 with the U. S. S. Corwin, observed a
beaver’s nest imbedded in the cliffs at that place, and noted that
many of the sticks composing it had been gnawed and others still
retained the tooth-marks made by that animal.

The remains found, however, are too fragmentary to admit of
‘specific determination.

SUMMARY

From the preceding review of the extinct vertebrates reported
as occurring in the Pleistocene deposits of Alaska, it will be seen
that the identification of several of the forms has been based upon
such scanty and fragmentary material that their determination is

*These remains, collected by the party with Dr. D. S. Jordan in 1897, are
now in the paleontological collection of the U. S. National Museum.

*Maddren, A. G.: Smithsonian Misc. Coll., vol. xtrx, No. 1584, 1905, pp.
112-113.

38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

open to question. This observation is particularly applicable to those
so long regarded as being identical with living species. The writer
believes that when more perfect material is available it will be found,
probably in all instances, to be quite distinct from the living forms.
That this is in some instances the case is shown by the discovery
this past summer of a skull of Ovibos sufficiently complete to show
characters of enough importance to warrant its separation from the
living form O. moschatus, to which nearly all musk-ox material
found in this region previously had been referred.

More persistent collecting, aided by improved methods, will un-
doubtedly increase the faunal list and widen the geographical dis-
tribution of the known forms.

Now that Mastodon and Ovis remains have been found in Cana-
dian territory and at a comparatively short distance from the inter-
national boundary, there appears no logical reason why both of these
animals should not have lived in Alaska at one time.

While in some cases we are unable to adequately define many of
the species, still a very good idea of the fauna as a whole is obtained.
Its close relationships in many instances with living animals fur-
nishes an interesting link in the development of mammalian life of
this continent.

The following list, based upon material sufficiently complete for
fairly accurate determinations, represents the Pleistocene fauna of
Alaska as we know it today:

Elephas primigenius BLU MENBACH.
Equus, sp. undet.

Alce, sp. undet.

Rangifer, sp. undet.

Ovibos, sp. nov.

Symbos tyrrelli Oscoop.

Bison crassicornis RICHARDSON.
Bison occidentalis Lucas.

Bison allenit Mars. : :
Ursus, sp. undet.

Castor, sp. undet.

sMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51
GILMORE, PL. XIII

MAP OF ALASKA.
From U.S.Geological Survey.

X Deposits ofPleistocene Mammals.
A Mastodon Remains.
---- Route Travelled in 1907.

Part of Route travelled by Maddren
in 1904.

wustelias >
——$_1. =

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SMITHSONIAN MISCELLANEOUS COLLECTIONS
VOLUME 51, NUMBER 4

Horgkins Fund

THE MECHANICS OF THE EARTH’S
ATMOSPHERE

A COLLECTION OF TRANSLATIONS
BY

CLEVELAND ABBE

THIRD COLLECTION

~eeeetena,

(Pusucation 1869)

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
IgI0

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+ 25)
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hy daa
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, eS AS oe Es

ERT.
. Braschmann and Erman, 1859-1862. The influence of the

XVI.
XVII.
XVIII.
XIX.

XX.

; CONTENTS

. Poisson, 1837. On the motion of projectiles in the air, tak-

ing into consideration the rotation of the earth.........
Tracy, 1843. Onthe rotary action of storms........-......

diurnal rotation of the earth on constrained horizontal
Motions elLher wniLorm Or Vatiables ce. ce e-em se

. Erman, 1868. On the steady motions or the average con-

dition of the earth’ siatmospmere sa %)2ia2.c'1 alsin w 2 wera ois 'e 2 =

. Kerber, 1881. The limit of the atmosphere of the earth.....
. Sprung, 1881. On the paths of particles moving freely on the

rotating surface of the earth and their significance in
MANOR OD Gap odumeona ee Uuaeo eu Oo dua cco Cduocmpo aT

. Pockels, 1901. The theory of the formation of precipitation

Gia fanloybiayehtal SN Oyolssao spb one eso OUe ons odeduED Oda

. Gorodensky, 1904. Researches relative to the influence of

the diurnal rotation of the earth on atmospheric disturb-

. Gold, 1908. The relation between wind velocity at 1000

meters altitude and the surface pressure distribution. ...

. Guldberg and Mohn, 1876-1883. Studies on the movements

GE CHE SE MOS PNG ic s\./,'s:4<! es atone cle m cielo a etera meme alare

. von Bezold, 1892-1906. Onthe thermodynamics of the atmos-

PHCLG-TOUEEN MeOICIT «fc ale sale amen em Miele miavel a ase tae

. von Bezold, 1900-1906. On the thermodynamics of the

atmosphere: fitth communication 522. cielo wei 4 <

. von Bezold, 1900-1906. Theoretical considerations relative

to the results of the scientific balloon ascensions of the
German Association at Berlin for the promotion of
ACTOMATIGL CS ich ten re a ohe 4 eee AUR hae chee a kar ane eI Roatan

. von Bezold, 1884-1906. On the reduction of the humidity

data obtained in balloon ascensions...............+..
von Bezold, 1898-1906. On the changes of temperature in
ascending and descending currents of air...........-+-.
von Bezold, 1890-1906. Onthe theory of cyclones.........
von Bezold, r901-1906. On the representation of the distri-
bution of atmospheric pressure by surfaces of equal pres-
SORE ATC NE ESO DAES 1 1~ seed ales ci alot cue autaens mabe eaeetlal hel nile) oar
von Bezold, 1892-1906. The interchange of heat at the
surface of the earth and in the atmosphere..............
von Bezold, t901-1906. Onclimatological averages for com-
plete small circles.of latitudes... sno. 2 ise 2 ev hs ides

57

80

105

eRe

I22

249

iv

XXI.

XXII.

XXIII.

XXIV.
XXV.

CONTENTS

Neuhoff, r900. Adiabatic changes of condition of moist air
and their determination by numerical and graphical
SHCthGGS oo oi. as Sis Fag, tise otk dw ek one win ts ome

Bauer, 1908. Therelation between ‘‘potential temperature”’
atid “enbrspy 6s i .ss ow acto boo ica ate nips pla vow eee

Margules, 1901. The mechanical equivalent of any given dis-
tribution of atmospheric pressure and the mainte-
nance of a given difference in pressure..............-+.

Margules, 1904. Onthe energy of storms................--

Pockels, 1893. The theory of the movement of the air in
stationary anticyclones with concentric circular isobars.

430
495
501
533

596

THE MECHANICS OF THE EARTH’S ATMOSPHERE
A THIRD COLLECTION OF TRANSLATIONS

BY CLEVELAND ABBE

INTRODUCTION

In order to introduce English-speaking students of meteorology
to the rapidly increasing literature bearing on the fundamental
mechanical problems of that science, I have been encouraged to
publish numerous translations either in the ‘‘Monthly Weather
Review”’ of the U. S. Weather Bureau or in the technical journals.
Others are collected in the ‘‘Short Memoirs on Meteorological Sub-
jects,’’ Smithsonian Report for 1877, pp. 376-478, and in ‘The
Mechanics of the Earth’s Atmosphere,’ Smithsonian Miscella-
neous Collections, 1891. As our knowledge of the subject pro-
gresses and we perceive new difficulties arising, so also we learn
to conquer those older ones that were the ultima thule of the
past generation. Step by step man is penetrating the complex
maze of forces that push our atmosphere hither and thither. Its
internal mechanism is so complex that superficial students content
themselves with empirical rules or search for cosmical relations
of minor importance: the very ablest investigators have as yet
solved only the simpler problems relating to idealized conditions
that rarely occur in nature.

In this third collection of translations bearing on the mechan-
ics of the earth’s atmosphere I have ventured to begin with that
elementary but classic memoir by Hadley which gave occasion to
the Berlin Academy in 1746 to offer a prize for a mathematical
discussion of the motions of the atmosphere. The prize was
awarded to d’Alembert ; subsequently Musschenbroek, deLuc, Euler,
Bernoulli, Lambert, von Lindenau (in 1806) and Brandes (in 1822)
successively contributed to the elucidation of this subject. But
it was Poisson who, in 1837, first deduced correctly the influence
of the earth’s rotation on moving solids, and Tracy who in 1843,
applied similar views to the rotation of storms. Poisson’s works
and ideas were generally known to the scholars of France as shown
by the prolonged discussion, 1850-1860, of the Foucault pendulum

I

2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL-s5m

and gyroscope phenomena. There are indications that Babinet
and others at that time applied his results to the mechanics of
the atmosphere. But the modern study of this subject is properly
traceable to the influence of Prof. William Ferrel in America and
Prof. William Thomson in England, both of whom codéperated to
put our knowledge of the subject on a firmer basis than was
before possible. Meanwhile a profound Russian scholar, Brasch-
mann, and the equally profound German scholar, Erman, were
independently working over the same ground, though their publi-
cations have been scarcely noticed by technical meteorologists.
The neglect of Erman’s work in dynamic meteorology seems
remarkable, but has been atoned for by the enthusiastic activity
of Sprung and his successors at Hamburg and at Berlin.

The works of Espy, 1840, on the Philosophy of Storms; Thom-
son, 1862, on the Convectional Equilibrium in the Atmosphere;
Peslin, 1868, on the Thermodynamics of Moist Air; Ferrel, 1857, on
The Motions of Solids and Fluids, and his subsequent important
memoirs; together with Sprung’s Lehrbuch, 1885, mark the tran-
sition from ancient to modern meteorology.

The modern sounding balloon has assured us of the intimate
connection between the lowest stratum of air and that which is
20 miles above us; but the conditions above this latter level are
doubtless of equally great importance to our surface climatology
and these can be made known to us only by the study of meteors,
auroras, spectrum lines,and refractions. I have, therefore, included
a memoir by Kerber on the limit of the earth’s atmosphere, that
avoids some of the difficulties attending every application to the
outer atmosphere of our knowledge of the kinetic theory of gases.

All students will gladly welcome the translation by Waldo of
the memoir by Guldberg and Mohn, first published in two parts,
1876 and 1880; it was revised by the authors in 1883 at the per-
sonal request of Prof. Frank Waldo who expected its prompt
publication, and to him we owe the privilege of including in the
present collection this new edition of that classic paper.

The series of papers by Von Bezold were revised by himself in
1906, for publication in his collected memoirs and as thus revised
they are now reproduced by permission of his heirs and publishers.

The study of strictly adiabatic changes that was so greatly
facilitated by the Hertzian diagram published in the preceding
collection of translations is now advantageously replaced by the dia-
grams of Neuhoff, rg00, which adapt themselves to any atmospher-
ical condition.

MECHANICS OF THE EARTH’S ATMOSPHERE—ABBE 3

In conclusion, the two memoirs* by Margules (xxi, 1901, and
XXIV, 1904) introduce us to the great problems of the future,
that is, the thermal transformations of energy persistently going
on in the atmosphere. Margules has been the first to find methods
of studying and solving these problems. It only remains for
future students to combine the equations of thermodynamics
with those of hydrodynamics so as to further elucidate the details
of the phenomena as to time and place—a result that we may
hope will eventually be attained by the analysis of fields of force
that is now being perfected by Bjerknes of Christiania.

CLEVELAND ABBE.

Washington, D. C.
November, 1908.

CONCERNING THE CAUSE OF THE GENERAL TRADE
WINDS

BY GEO. HADLEY, ESQ., F. R. S.
[Phil. Trans. Vol. XX XIX, London, 1735-36, p. 58]

I think the causes of the General Trade Winds have not been
fully explained by any of those who have wrote on that subject,
for want of more particularly and distinctly considering the share
the diurnal motion of the earth has in the production of them.
For although this has been mentioned by some amongst the causes
of those winds, yet they have not proceeded to show how it
contributes to their production; or else have applied it to the
explication of these phenomena, upon such principles as will appear
upon examination not to be sufficient.

That the action of the sun is the original cause of these winds,
I think all are agreed; and that it does it by causing a greater
rarefaction of the air in those parts upon which its rays falling
perpendicularly, or nearly so, produce a greater degree of heat
there than in other places; by which means the air there becoming
specifically lighter than the rest round about, the cooler air will
by its greater density and gravity, remove it out of its place to
succeed into it itself, and make it rise upward. But it seems,
this rarefaction will have no other effect than to cause air to rush
in from all parts into the part where ’tis most rarefied, especially
from the north and south, where the air is coolest, and not more
from the east than the west, as is commonly supposed: so that,
setting aside the diurnal motion of the earth, the tendency of
the air would be from every side towards that part where the
sun’s action is most intense at the time, and so a NW. wind be
produced in the morning, and a NE. in the afternoon, by turns,
on this side of the parallel of the sun’s declination, and a SW.
and SE. on the other.

That the perpetual motion of the air towards the west, cannot
be derived merely from the action of the sun upon it, appears
more evidently from this: If the earth be supposed at rest, that

5

6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. jt

motion of the air will be communicated to the superficial parts,
and by little and little produce a revolution of the whole the same
way, except there be the same quantity of motion given the air
in a contrary direction in other parts at the same time, which
is hard to suppose. But if the globe of the earth had before a
revolution towards the east, this by the same means must be con-
tinually retarded. And if this motion of the air be supposed to
arise from any action of the parts of it on one another, the con-
sequence will be the same. For this reason it seems necessary to
show how these phenomena of the Trade Winds may be caused,
without the production of any real general motion of the air
westwards. This will readily be done by taking in the considera-
tion of the diurnal motion of the earth. For, let us suppose the
air in every part to keep an equal pace with the earth in its
diurnal motion; in which case there will be no relative motion of
the surface of the earth and air, and consequently no wind, then
by the action of the sun on the parts about the equator, and the
rarefaction of the air proceeding therefrom, let the air be drawn
down thither from the N. and S. parts. The parallels are each
of them bigger than the other, as they approach to the equator
and the equator is bigger than the tropics, nearly in the propor-
tion of tooo to g17, and consequently their difference in circuit
about 2083 miles, and the surface of the earth at the equator
moves so much faster than the surface of the earth with its air
at the tropics. From which it follows, that the air, as it moves
from the tropics towards the equator, having a less velocity than
the parts of the earth it arrives at, will have a relative motion
contrary to that of the diurnal motion of the earth in those parts,
which being combined with the motion towards the equator, a
NE. wind will be produced on this side of the equator and a SE.
on the other. These, as the air comes nearer to the equator, will
become stronger, and more easterly, and be due east at the equator
itself, according to experience, by reason of the concourse of
both currents from the N. and S. where its velocity will be at the
rate of 2083 miles in the space of one revolution of the earth or
natural day, and above one mile and one-third in a minute of
time; which is greater than the velocity of the wind is supposed
to be in the greatest storm, which according to Doctor Derham’s
observations, is not above one mile in a minute. But it is to be
considered, that before the air from the tropics can arrive at the
equator, it must have gained some motion eastward from the
surface of the earth or sea, whereby its relative motion will be

CAUSE OF GENERAL TRADE WINDS——-HADLEY 7

diminished, and in several successive circulations, may be supposed
to be reduced to the strength it is found to be of.

Thus I think the NE. winds on this side of the equator, and
the SE. on the other side, are fully accounted for. The same
principle as *hecessarily extends to the production of the west
trade-winds without the tropics; the air rarefied by the heat of
the sun about the equatorial parts, being removed to make room
for the air from the cooler parts, must rise upwards from the earth,
and as it is a fluid, will then spread itself abroad over the other
air, and so its motion in the upper regions must be to the N. and
S. from the equator. Being got up at a distance from the surface
of the earth, it will soon lose great part of its heat, and thereby
acquire density and gravity sufficient to make it approach its
surface again, which may be supposed to be by that time ’tis
arrived at those parts beyond the tropics where the westerly
winds are found. Being supposed at first to have the velocity
of the surface of the earth at the equator, it will have a greater
velocity than the parts it now arrives at; and thereby become
a westerly wind, with strength proportionable to the difference of
velocity, which in several revolutions will be reduced to a certain
degree, as is said before, of the easterly winds, at the equator.
And thus the air will continue to circulate, and gain and lose
velocity by turns from the surface of the earth or sea, as it ap-
proaches to or recedes from the equator. I do not think it neces-
sary to apply these principles to solve the phenomena of the
variations of these winds at different times of the year, and differ-
ent parts of the earth; and to do it would draw this paper into
greater length than I propose.

From whatever has been said it follows:

First, That without the assistance of the diurnal motion of the
earth, navigation, especially easterly and westerly, would be very
tedious, and to make the whole circuit of the earth perhaps imprac-
ticable.

Secondly, That the NE. and SE. winds within the tropics must
be compensated by as much NW. and SW. in other parts, and
generally all winds from any one quarter must be compensated
by a contrary wind somewhere or other; otherwise some change
must be produced in the motion of the earth round its axis.

II

ON THE MOTION OF PROJECTILES IN THE AIR, TAKING
INTO CONSIDERATION THE ROTATION OF
THE EARTH

BY M. [S. D.] POISSON!

In this memoir the projectile will be considered as an isolated
and material point, that is to say, as a body whose mass is col-
lected at the center of gravity, and the problem will be to ascer-
tain the influence of the rotation of the earth on its motion. I
shall present shortly another memoir to the Academy, in which
we shall take into consideration the form and the dimensions of
the moving body, and the object of that will be to determine,
principally in what relates to the projectiles used in artillery, the
influence that their own rotation can produce on their motion of
translation.

Up to the present time the theory of the resistance which fluids
in general, and the air in particular, offer to the motion of the
bodies that traverse them, has received only a very imperfect
development. We compare this force to a continual succession
of shocks of the moving body against the particles of the fluid,
which disappear and are annihilated, so to speak, when they have
been struck by the body and have carried away small quantities
of motion, proportional to their own masses and its velocity.
Newton, to whom we owe this theory, had concluded that, ignor-
ing the rotation of the moving body, the resistance of the air for
a sphere, for example, is equal to the weight of a cylinder of this
fluid having for its base the great circle of the sphere and for
height the “‘full-height”’ due to its velocity. But the experiments
made on the fall of bodies in the air soon showed him the inac-
curacy of this result, and led him to reduce by one-half this
measure of resistance; subsequently, it has been found that this

1Memoire sur le mouvement des projectiles dans l’air en ayant égard
la rotations de la terre. By [S. D.] Poisson. Read before the Academy
of Sciences, Paris, November, 1837. Published in the Journal de 1’Ecole
Royale Polytechnique, Vol. XVI, Cahier 26, Paris 1838, pp. 1-68. Trans:
jated by Profs. Frank Waldo and Cleveland Abbe.

8

MOTION OF PROJECTILES—POISSON 9

reduction is too great, and Borda has concluded from his own
observations that the measure of the resistance must be only
diminished to three-fifths of its theoretical value. From the theory
of Newton as modified by experiment, the retarding force relative
to the unit of mass for a sphere moving through the air has for
its expression the square of the velocity of the sphere divided by
its diameter and by the ratio of its density to that of the fluid,
and multiplied by a numerical coefficient concerning which the
writers on ballistics do not agree. According to Lombard,? and
relying on the experiments of Borda, this coefficient should be
equal to about nine-fortieths. But the true law of the resistance
as a function of the velocity is far more complex; for motions
which are either very rapid or very slow the coefficient seems
to deviate considerably from being proportional to the square of
the velocity; in the case of very great velocities it increases at
a much greater ratio, and on the contrary when it is a question
of small velocities, such as the very small vibrations of the seconds
pendulum?’ this coefficient is proportional to the simple velocity.

In order to determine directly and without any hypothesis the
law of the resistance that a body meets with in moving through
a fluid, it will be necessary to consider at the same time both the
motion of the body and that which the moving body communi-
cates to the fluid; as the result of this double motion the fluid
exerts at each instant a certain pressure at each point of the
moving body and normal to its surface; this pressure is different
from that which occurs in the state of rest and produces the resist-
ance, properly so-called, that the moving body experiences, and
to which it will be necessary also to add the force tangential to
the surface of the body arising from the friction of this body against
the layer of fluid in contact with it. In fact, this is what I have
been able to do in my Memoir on the simultaneous Motions of
the Pendulum and of the surrounding Air, and which has led
me to deduce from theory the new correction which M. Bessel
has confirmed by experiment on the length of the seconds pendu-
lum. Hereafter I shall try to extend that analysis to the case of
the progressive motion of projectiles in the air and to determine,
if it is possible for me to do so, the pressure that the fluid dis-
placed by them exerts on their surfaces by its compression on one
side and expansion on the other, or the resistance that they

* Treatise on the motion of projectiles, p. 99.
’ Additions to the Connaissance des Temps for the year 1834, p. 18.
* Memoirs of the Academy of Sciences, Vol. XI [Paris].

se) SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

meet with considered from the point of view that I shall indicate.
I do not need to say that the exact and general knowledge of
this law will be important in many questions, for example, in the
problem of ballistics. But for the object which I have in view in
this present memoir I can admit the ordinary law of the resistance
proportional to the square of the velocity as being sufficiently
accurate.

It is Newton, also, who has given the first example of the deter-
mination of the motion of a heavy body in a resisting medium.
He solved the problem when the motion is vertical by assuming
the resistance proportional either to the velocity or to its square,
but when the projectile is projected into the atmosphere in any
direction whatever he confined himself to considering the case
of a resisting force proportional to the simple velocity, observing
nevertheless that this case is not that of nature. The two equa-
tions that Newton was obliged to integrate in order to determine
the horizontal and vertical components of the velocity at any
instant, are linear of the first order and with constant coefficients;
and the two unknown quantities are so separated in them that
these two equations are solved independently of each other, and
their solution really implies only a simple direct integration. This
is no longer true in the case of a resistance proportional to the
square of the velocity; the two unknown quantities enter at the
same time into each of the equations of motion, which are no
longer linear, and it is only by a special combination that we
succeed in separating the variables therein and in reducing them
to quadratures, which we consider as the complete solution of
the problem.

This was done by John Bernoulli, who published it in the Acta
Eruditorum, Leipzig, May 1719, pp. 216-226, more than thirty
years after the solution by Newton, and at an epoch when the
integral calculus had already made great progress. However, Euler,
at the beginning of his memoir on this subject,*> expresses his sur-
prise at seeing that Newton, ‘‘who has well solved other problems
more difficult,” should stop with the case of the resistance pro-
portional to the simple velocity, and not consider the case of
nature. We know, however, that the question of the trajectory
in a medium resisting in proportion to the square of the velocity
was proposed as a challenge to the geometers of the continent
by an Englishman named Keil, who believed the problem insol-

* Memoirs of the Academy of Berlin; year 1753.

MOTION OF PROJECTILES—POISSON Ii

uble because his illustrious countrymen had not solved it. Now
the numerical calculation of the integrals which express the time
and the two codrdinates of the moving body, in functions of a
fourth variable, is effected as simply as the question allows, and
enables the approximations to be carried as far as we wish. We
can see an example in the “Exercises du calcul Integral’ of Legen-
dre® in which these codrdinates are calculated to within less than
a hundred-thousandth part of their values.

Independently of the centrifugal force arising from the rotation
of the earth (which influences the motions of heavy bodies by
diminishing the force of gravity by a quantity that varies with
the latitude), this rotation also produces in these motions certain
deviations that it is interesting to understand, either in themselves
or in order to know to what extent they can influence the trajec-
tory of the projectiles, and whether it is necessary to consider them
in the practice of artillery.

Many physicists have measured, with as much precision as has
been possible, the small distances by which bodies that fall trom
a considerable height deviate from the foot of the vertical. La-
place and Gauss submitted this question to the calculus, but in
integrating the equations of this almost exactly vertical motion
they have left out of consideration the resistance of the air, which
can, however, sometimes have a very great influence on the result.
I have therefore thought it would be useful to go over this problem
entirely and to extend the solution to the general case in which
the projectile is projected into the atmosphere with any velocity
and in any direction whatever.

To this end I have in the first place formed the differential
equations of the absolute motion in space by referring the coérdi-
nates of the moving body to fixed axes; then I have deduced from
these the equations of apparent motion such as we observe near
the surface of the earth, referred to fixed axes at the surface which
participates as well as we ourselves in the rotation of the earth.
These differential equations are very complicated, but by taking
the second of time for the unit of time, the angular velocity of
the diurnal motion becomes a very small fraction, which permits
(us) to reduce them to a more simple form. From these we deduce
some general consequences, enumerated as follows:

(1) The motion of the earth prevents a liquid contained in a
vase and turning with a constant velocity about a vertical axis

nv Og Ts. p.. 336.

1 i SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

from assuming the rigorously permanent figure of a paraboloid of
revolution as it would do if the earth were immovable.

(2) If the body moves along a given curve that is attached
firmly to the surface of the earth, the differential equation of its
motion does not contain the velocity of the rotation of the earth
and consequently this motion is the same as if the,earth were at
rest. Thus, for any given value of gravity resulting from the
figure and the rotation of the terrestrial spheroid, the oscillations
of the pendulum are the same in all azimuths around the vertical;
a result that was important to demonstrate, considering the
degree of precision that we now attain in the determination of the
length of the seconds pendulum at different places on the earth.
But the diurnal rotation and the direction of the plane of oscillation
have a slight influence on the variable tension that the wire expe-
riences during the oscillations and which is not rigorously the
same in all azimuths.

(3) Finally, when a projectile is sent into the air in any direction
whatever the rotation of the earth neither increases nor dimin-
ishes the distance that it attains at any instant from a plane
through the point of departure and parallel to the equator.

Before seeking the integrals of the equations of apparent motion
in the general case of an initial velocity having any magnitude and
any direction whatever, I have considered the simpler special cases.

The first case is that where the moving body starts from a point
situated at a given height above the ground without imparting
to it any initial velocity whatever and is left to the action of
gravity, so that it commences to fall vertically. The velocity [of
the eastward motion] at the point of departure, due to the rota-
tion of the earth in which it participates, being greater than that
which belongs to the foot of the vertical, we perceive that the
moving body when it has reached the earth must have departed
from the foot of the vertical line, to the eastward or in the direc-
tion of the true motion of the earth, but mathematics alone can
give the measure of this distance, especially when we consider the
resistance of the air; one can see that the deviation takes place
toward the east and that it is nothing in the direction of the
meridian. In order to compare with experience the formula which
expresses the amount of deviation, I have chosen the observations
of this phenomenon which were made in 1833 by Professor Reich
in the mines of Saxony. The height of the fall was 158.5 meters
and M. Reich concluded for the mean of 106 experiments
that there was a deviation to the east of 28.33". He also

MOTION OF PROJECTILES—POISSON 13

found very nearly six seconds for the duration of the fall.
By means of this latter datum I have been able to calculate with-
out any hypothesis the coefficient of resistance of the air which
the moving body must have experienced, and the formula gives
ya eee for the deviation; which ‘differs from the experiments
by less than a millimeter. In a vacuum this deviation would
not have exceeded by a tenth of a millimeter that which
occurred in the air; so that in this case the resistance of the air
has had only an inappreciable influence.

When the projectile starts from the surface of the earth and 1s
thrown vertically from below upwards with a given velocity, we
conceive that during the time of its ascent it must be departing
from the vertical toward the west, or in a direction contrary to
the rotation of the earth. It would seem that afterwards during
its fall it should approach this line and return again very nearly
to its point of departure, but this is in fact not the case. When
it has arrived at the highest point of its trajectory and has lost all
its vertical velocity, the projectile by deviating towards the west
has also acquired a horizontal velocity in the same direction, by
virtue of which it continues to deviate in this direction, at least
during part of its fall. The analytical difficulty which this second
case presents is to reconcile, so to speak, the two successive motions,
ascending and descending, of the projectile, which are expressed
by very different formule when we take account of the resistance
of the air. In order to apply to an example the formula expressing
the total deviation of the moving body when it has fallen back to
the earth, I have assumed that this body is a spherical ball fired
vertically from an infantry gun, with a velocity of about 400
meters per second. The amount of this deviation varies much
with the resistance of the air; by giving successively to the coeffi-
cient of this resistance different values which have to each other
the ratio of four to three, we find deviation toward the west in
both cases but of about one and three decimeters respectively.
In a vacuum this deviation would be about fifty-five meters, so
that by the greater of these two resistances it is reduced to the
fifteenth part of this value.

I have also examined in particular the case where the initial
velocity of the projectile is nearly horizontal, which corresponds
to firing at a target. In my present memoir will be found the for-
mule that relate to this and which express all the circumstances
according as the firing is directed toward any given point of tle
horizon. Here I shall only stop to say that the initial velocity

[4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

being always about 400 meters and the distance of the target,
placed point blank, being equal to 200 meters, then the horizontal
and vertical deviations of the ball, due to the motion of the earth,
would amount to scarcely half a centimeter, that is to say, they
have no sensible influence on the precision of this shooting and
it is unnecessary to consider them in practice. These deviations
are equally unimportant in firinga cannon, and in all motions
which take place in a nearly horizontal direction.

In general the effects that the motion of the earth produces on
the motion of a projectile are: first, to increase, either positively
or negatively, the interval of time that the moving body takes to
go from its point of departure to the point where it falls onthe
earth; second, to increase the distance of this latter point from the
former, which we call the horizontal range. The signs of these
increments depend on the direction of the vertical plane in which
the projectile is thrown; there is augmentation in one direction
and diminution in another; their values are expressed by double
integrals, whose numerical calculation would be very laborious.

In addition to this the diurnal motion causes the moving body
to leave the vertical plane in which it was initially projected.
This gives place to a horizontal deviation, whose value is composed
of two distinct parts, expressed also by double integrals. One
of these partial deviations is independent of the direction of the
vertical plane; it is always toward the right of an observer stationed
at the point of departure and facing the trajectory. In our lati-
tude we can consider it as being the principal effect of the rotation
of the globe, and happily we can obtain for it limiting values that
are easier to calculate than its own value, and which may, if we
wish, be deduced numerically by means of the length of the range
and the duration of the movement as given by observation, with
an accuracy sufficient to appreciate the amount of the deviation.
Applying, for example, these limits to such firing of shells as
takes place in actual artillery practice, that is to say, at an angle
of elevation of 45°, with an initial velocity of 120 meters per second,
which gives a range of about 1200 meters, for a projectile of 27
centimeters in diameter, and 51 kilograms in weight (the shell
of ro inches and roq4 pounds old French measure); we find that
the deviation of the point of impact will be between 90 and 120
centimeters when we aim in a vertical plane, tangent to the parallel
of latitude at the point of departure. The deviation will be toward
the south if we fire toward the east, and toward the north if we
fire toward the west. Calling it a meter and observing that such

MOTION OF PROJECTILES—POISSON 15

a deviation in a distance of 1200 meters corresponds to an angle
of about three minutes of arc, it follows that in order to be more
sure of hitting the mark it will be necessary to aim in a vertical
plane to the left of the given plane, and making with that an angle
of three minutes. The consideration of this result may influence
the accuracy of the aim and the chance of striking the target in
exercises where the gunner must seek great precision. The hori-
zontal deviation will be a little less and will be toward the east
when we fire toward the north; it will be a little more and toward
the west when we fire toward the south. In the firing of a shell
at long range, for example, at a distance of about 4,000 meters
from the mark, which supposes an initial velocity of a little more
than one-third of 800 meters, at the elevation angle of 45°, and
for a projectile weighing 90 kilograms and a third of a meter
in diameter, the limits of deviation, firing either to the east or to
the west, will be very nearly 5 meters and to meters, respectively.
Estimating then its average amount at 7 or 8 meters, we see that
in sieges some buildings and persons have been reached because of
the deviation of a shell by the motion of the earth and others
have not been from the same reason.

These numbers, and those that we have before given, relate to
a mean latitude; they vary with the latitude of the place ofthe
experiment. At the equator when the firing takes place in its
plane, the horizontal deviation vanishes while the increase in the
duration of the trajectory and in the length of the range attain
their maximum values. In high latitudes, on the contrary, it is
the deviation which approaches its maximum and the increase
of duration which diminishes. At the pole, the horizontal devi-
ation, which is the same at this point for all vertical planes of
firing, would exceed by very nearly one-half that which takes
place in our latitude. Everywhere the increments of the range
and of the time are nothing when the initial velocity is directed
in the plane of the meridian.

[The preceding text is followed by a detailed mathematical
analysis that need not be reproduced here].

III

ON THE ROTARY ACTION OF STORMS
BY CHARLES TRACY!

The investigations of Mr. Redfield and Colonel Reid have accumu-
lated a vast amount of evidence in favor of the propositions they
maintain. ~The tendency of this evidence is to demonstrate,
that in the large storms which affect extensive districts, and also
in the violent tornadoes which devastate a brief path, there are
two motions, the rotary and the progressive; and that the rotary
is by far the most violent, and has an uniform direction of revolu-
tion, being from right to left if the storm is in the northern hemi-
sphere, and the reverse if it is in the southern hemisphere. That
is to say, on our side of the equator the rotation is about the cen-
ter through the points of the compass, in the order of N. W.S.E.,
or contrary to the movement of the hands of a watch lying on —
its back; and south of the equator the rotation is through the
points in the order of N. E.S. W., or conformable to that of the
hands of a watch.

These propositions, although authorized by induction, have en-
countered doubts or gained a feeble faith in many minds, for the
want of a good cause to assign for the production of the alleged
phenomena. Hence the occurrence of rotary storms, and the uni-
formity of direction of revolution, have been too readily attributed
to mere accident; and the notion that a whirlwind, once started
by mere chance, contains the elements of growth and stability of
motion, has been too easily admitted. An active whirlwind,
great or small, undergoes a constant change of substance. As the
central portions waste into the ascending column, supplies from
the adjacent tranquil air must be drawn into the vortex and set
in motion; and if the fresh air is neutral to the circular movement
and must acquire velocity from the whirling mass itself, then
since ‘‘action and reaction are equal and in opposite directions,”

‘Reprinted from the American Journal of Science and Arts, Vol. XLV,
October, 1843, pp. 65-72. Read before the Utica Natural History Society.
(Dated Utica, N. Y., February 27, 1843.)

16

ROTARY ACTION OF STORMS—TRACY 7

the whirling mass itself must lose just so much velocity as the
fresh supply gains. By such a process the forces of the whirl-
wind would be rapidly exhausted, and its existence must speedily
cease. A stable source of momentum, adapted to originate and
sustain the uniform rotary movement, is still required; and it is
now proposed to develop such a source of momentum in the
forces generated by the earth’s diurnal revolution.

The velocity of the earth’s surface in the daily revolution being
at the equator more than one thousand miles an hour, in latitude
60° half as much, at the pole nothing, and varying in intermediate
places as their perpendicular distances from the earth’s axis, and
the atmosphere near the ground everywhere taking in part or
wholly the motion of the surface it rests on, important conse-
quences upon aerial currents must follow. A body of air set in
motion from the equator northward maintains the equatorial east-
ward velocity, and when it passes over regions of slower rotation
deviates eastward from the meridian, and ultimately describes
over the earth’s surface a curved line bearing towards the east.
A current of air from latitude 45° north, having a due south
direction, soon reaches regions moving faster to the east, falls
‘behind them and describes a curve to the west. Winds oblique
to the meridian are similarly affected. These familiar matters are
referred to here, and illustrated by fig. 1, to elucidate what follows.

FIG. I.

The influence of the figure and revolution of the earth upon
east and west winds, must also be considered. A parallel of lati-
tude, being a lesser circle of the globe, and at all points equally
distant from the pole, necessarily describes upon the earth’s surface
a curved line. But a direct course, due east at the commencement
follows a great circle and parting from the parallel reaches a lower
latitude. The due east course continued in a right line describes
a tangent to the curve of the latitude. The velocity of the earth’s
surface at any place, by virtue of the diurnal revolution, has for
its direction the line of that tangent; and when the airreposing
over any spot is transferred to a region of diverse motion, the

18 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

direction, as well as the degree, of its previous force is to be taken
from that of the soil on which it previously rested. Hence a wind
from the west, if in our hemisphere, will soon be found pursuing
a southeasterly course, and crossing successive parallels of latitude.

The labors of Mr. Espy have been directed to the hypothesis
of a central ascending column of rarefied air, and centripetal
currents from every side rushing towards its base. Without pur-
suing his reasoning, it will be safe to assume that his collection
of facts established the existence of a qualified central tendency
of the air, in both the general storms and the smaller tornadoes.
He presents a theory to account for such motion, which it is not
necessary now to examine. Dr. Hare has proposed another method
of accounting for tornadoes—a truly brilliant suggestion—of which
it is only to be remarked, at present, that it proceeds on the assump-
tion of a rush of air from all quarters to a central point. It has
been attested also, that at large clearing fires in calm weather,
creating centripetal currents, the whirlwind and mimic tornado
have been produced. In accounting for the whirlwind motion,
therefore, the central tendency of the air will be presupposed.

In the case of a large fire kindled in an open plain on a calm
day, a small circle about the fire is first acted on by the abate-
ment of pressure on the side next the fire, and thus receives an
impulse toward the common center. As this moves in, the next
outer circle loses support and begins to move. Each particle of
air is moved at first by an impulse towards the center, and during
its approach to the central region it receives fresh impulses of the
same direction; and if it comes from some distance its velocity
is in this way accelerated, until it reaches the space where the hori-
zontal is broken by the upward motion. It is obvious that par-
ticles propelled by such impulses would seek the common center
in the lines of its radii, and their horizontal forces would be neu-
tralized by impact, if no cause for deviation was at hand. But
the great law of deflection which affects the course of the winds
applies to the movements of these particles. The particles which
seek the center from the northern points are deflected west, while
those from southern points are deflected east. The whole rush of
air from the northern side of the center, coming like a breeze
bears west of the center, while an equal breeze from the southern
side bears east of the center. The consequence is that the central
body of air, including the fire, is acted upon by two forces which
combine to make it turn round to the left. These forces are aided
by the deviation of the currents from the easterly and westerly

ROTARY ACTION OF STORMS—TRACY ime)

parts of the circle. The breeze from the west extreme inclines to
the tangent of the parallel of latitude at its original place of repose,
and therefore strikes south of the center into which the impulse
it receives would otherwise carry it. The air from the east side
also inclines toward the tangent of the parallel of latitude there,
which is, obliquely to the north from the radius, and therefore is
deflected northwards and strikes north of the center. The breezes
from all quarters thus codperate to produce the result; and all
their forces are constant; and act with precision and at great advan-
tage to cause and maintain a whirlwind. A diagram presenting
the lines of approach of the particles or streams of air, will explain
this result. The black lines in fig. 2 show the deviating currents,
from+the cardinal points alone, when the area affected by the fire
is so small as to require no perceptible curve in those lines.

FIG. 2.

Upon the same principle, the tornado, the typhoon, and the
widespread storm of the Atlantic, if their currents move toward
a central spot, must have a rotary character. The circular motion
in the outer portions may be slight, but it is stronger near the
center. In every such case the incoming air may be regarded as
a succession of rings taken off the surrounding atmosphere and
moving slowly at first, but swifter as they proceed towards the
center. Each such ring is affected by the law of deviation during
its passage. The particles are veering from the radii, in its northern
quarter westward, in its southern quarter eastward, in its eastern
quarter northward, and in its western quarter southward, and
hence the ring begins to revolve when far from the center, turns

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

more and more as it draws near it, and finally as it gathers about
the central spot all its forces are resolved into a simple whirl.
Ring after ring succeeds, and the whirling action is permanent.

The deflecting power thus applied.is not small. The rotary
motion of the earth varies as the cosine of the latitude, and the
differences of velocity for any differences of latitude are easily
computed. The following are samples; being differences of velocity
for 1° or 694 miles of latitude.

Miles

per hour.
Between lat: 2° and “3° dit. of velocity -( onc... 2 verte 0.79
Between lat.) 3° and ‘4° difivof velocity. <s 0.2.0. -6.ssesacn | SE
Between lat; 1o° and 1z° diff. of velocity. ......c.5...28-0 58 9.8%
Between lat. 23° and 24° diff. of velocity... 2.2.2.0. vin. 7.25
Between lat. 42° and 43° diff. of velocity.......0.+ sas. 000s. 12.28

The differences of velocity for one mile, or 51.84” of latitude

are as follows:

Difference of velocity
for1 mile north.

Latitude. Feet per minute.
10° 4
23° 9
42° 15.4
43° 15-7
45° 16.3

The deflection of easterly and westerly breezes by reason of
the spherical form of the earth, also, can be computed; and it is
obviously no less important than the deflection produced in merid-
ional winds. The angle between the courses north and east, at
any point, is a right angle; and if two points in the same latitude
are taken, it is evident that the obliquity of the north courses
from the two points equals the obliquity of the east courses from
the same points. :

These results show that in the northern states a fire large enough
to affect the atmosphere over a few acres may possess the essential
force for generating a whirlwind, and may produce it in fact if
the day be calm. A large storm, covering the whole country with
its centripetal currents, must produce a vortex about the center,
which will combine the principal energies of the storm. The tor-
nado and water-spout must revolve with terrific violence.

The necessary condition, centripetal motion, may arise when-
ever a central spot subjected to intense heat is surrounded by a
cool atmosphere. Tunis state of things, on a small scale, may occur
on a summer day, upon a ploughed field surrounded by extensive

ROTARY ACTION OF STORMS—TRACY 21

pastures; upon a black and charred clearing in the midst of a cool
forest; or at a large clearing fire. Upon a great scale—if an island
beneath a tropical sun received tipon rocks and sands the intense
radiance of a succession of clear, calm, and hot days, and conse-
quent sea breezes from the deep and cool ocean pressed in upon
all its shores with the violence of a high wind, it should not cause
surprise if these various breezes combined to generate a vast
whirlwind; nor if the lofty revolving column should at last leave
the place of its origin and traverse the sea, as a hurricane. The
cause which first excited the centripetal tendencies of the storm,
might be renewed as the upper currents of the atmosphere bore
it over other heated spots; and the law of deflection will inevitably
transform the central into circular motion. The destructive
storms of our sea-coast may have such an origin among the islands
of the West Indies, from which they appear to proceed.

FIG. 3.

In the southern hemisphere the same law of deflection produces
contrary results. There the wind which first moves north bends
to the west,and the wind which moves south at first turns towards
the east, that from the east turns south, and that from the west
turns north. Fig. 3 represents these effects. Hence south of
the equator storms revolve from left to right, or conformably to
the movement of watch hands. Fig. 4 exhibits the rotary action
of a storm in the northern hemisphere; fig. 5 the samein the south-
ern hemisphere.

22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLS 5

The relative motions of the parts of a small circular space on
the earth’s surface, by reason of the diurnal revolution, are pre-
cisely what they would be if the same circular space revolved
upon an axis passing through its center parallel to the axis of the
globe. If such space be regarded as a plane revolving about such
supposed axis, then the relative motions of its parts are the same
as if the plane revolved about its center upon an axis perpendic-
ular to the plane itself; with§ this modification, that an entire
revolution on the axis perpendicular to the plane would not be
accomplished in twenty-four hours. Such plane daily performs
such part of a full revolution about such perpendicular axis, as
the sine of the latitude of its center is of radius. The plane itself—
the field over which a storm or tornado or a water-spout is form-
ing—is in the condition of a whirling table. Hence the tendency
to rotary action in every quarter of the storm is equal and all
the forces which propel the air towards the center codperate in
harmony to cause the revolution.

———————_—

Re

FIG. 4. FIG. 5.

Be ey Ie

Water discharging from a broad basin through a central orifice,
is subject to the same law. It forms a vortex which in our hemi-
sphere turns to the left, or against the sun, and in the southern
hemisphere must turn to the right or contrary to the sun there.

These rotations of the atmosphere and of water, being from
west to east about lines inclined to parallelism with the earth’s
axis, are singularly coincident in direction with the rotation of
the globe, and harmonize with the general mechanism of the
heavens.

7 IV

THE INFLUENCE OF THE DIURNAL ROTATION OF THE
EARTH ON CONSTRAINED HORIZONTAL MOTIONS,
EITHER UNIFORM OR VARIABLE

AN ABSTRACT BY PROFESSOR A. ERMAN OF A MEMOIR BY PROFESSOR
N. BRASCHMANN, WITH ERMAN’S NOTES THEREON

[Translated from Archiv fur Wissenschaftliche Kunde von Russland

Vol. XXI, 1862, pp. 52-96 and 325-332']

The first volume of Braschmann’s Theoretical Mechanics, Mos-
cow, 1859, combines to such a high degree condensed and precise
presentation with abundance and variety of problems that the
best interests of the mathematical study of motion demands its
broadest possible dissemination.

As an example of the treatment of the problems enumerated
above, we choose first the theory of relative motion of a free or
restricted mass point and then the application of this theory to
the so-called Foucault experiment and to other physical prob-
lems arising from the rotation of the earth, which first began to
be considered and empirically studied in recent years.

The second practical application that Braschmann makes? of
his general formule for relative motion consists (1) in the remark
that every mass moving on the earth’s surface along a restricted
path exerts a horizontal pressure on the boundary of its path

*The early publications of William Ferrel relative to the motions of
the atmosphere, beginning with 1856, were made accessible by reprints in
Professional Papers, Nos. VIII and XII, of the U. S. Signal Service. In
these, as in most other memoirs on the subject, the motions of the atmos-
phere were assumed to be uniform in velocity, but in 1854-1862 Braschmann
and Erman gave a notable enlargement of our ideas. Since that date two
elaborate memoirs by Dr. Joseph Finger of Vienna (I, 1877; II, 1880) have
given further details of the motions of bodies on a rotating spheroid.

Day:

2 See his article in Bull. Imp. Acad. Sci. St. Petersburg, Feb. 3, 1860.

23

24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

which tends toward the right-hand side in northern latitudes but
to the left-hand in southern latitudes:

(2) In the determination of the amount of this pressure.

The following is Braschmann’s treatment of this problem as
given in his Memoir of Feb. 3, 1860.

Equations (1) [general equations of motion, here omitted] de-
termine also the accelerating force that the current of a river
exerts on its right-hand bank.

FIG. I,

Let M N, fig. 1, be a section of the river, b any point in this sec-
tion at which the average velocity of the steady stream of water
is v, that is to say, the uniform or steady velocity is the result of
all other influences combined with that of the acceleration due
to the rotation of the earth. Designate by x positive towards the
east and y positive towards the north the rectangular coédrdinates
of a point in the horizontal plane through b, neglecting the very
small fraction w’, we then obtain from equation (1) the following:

oe ae iene

dt? dt

: (2)
eigee —2w sind. ae

df? dt

Let a be the angle between the direction of the current and the
positive axes of y, then we have the following integrals’

3 For « =o and y = 0 or at the origin of codrdinates, the steady velocity —
v and therefore its projections on the x and y axes are

dx : dy
yd = vsina de = vcosa

ROTATION AND HORIZONTAL MOTIONS—BRASCHMANN AS

= =A+2wsindy=vsin a+2 wo sin 1.4.
t

dy ‘ :
-=65 —2o0 sn ijax —v cos ad — 2H sin_/.x.
dt »

By substituting these values in equations (2) and neglecting w*
we have

2
eae +2wucosasinAa
dt?
EV —2wvsinasinA
d#?

These equations determine the accelerative force

2 2.
F= (az) + (G2) =2 09 sin
df? dt? :

This shows that the amount of this force is independent of th
direction of the current of the stream and moreover that it is
directed steadily toward the right-hand bank.

If uw is the angle made by this accelerative force with the axis

of y or the north line counting it positively around to the right,
then

2
a = F sin u
at?
2.
¢ ae F cos u
dt?
but
F=+2wevsina
hence

sin u = +cosa
cos 4 = — Sin a
u =a + 90°

that is to say, when A is positive the direction of F is go° farther
toward the right than the direction of the current.
When AJ is negative we have
sin “= — cosa
cos u = + sin a

u =a + 270°

26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL: 51

that is to say, in southern latitudes the pressure F will be against
the left hand and will be zero at the equator itself.

In order to determine the pressure mF exerted upon the right
bank by the whole section MN of the river, let A be the area of
this section and a the density of the water, then

mF = Avo.2wu.sin A

This mf relates of course to the pressure exerted by the mass
of water that flows through the section MN in a unit time or by
the mass Avp.

In the preceding paragraphs we have assumed a constant or
steady and uniform velocity. It seems unnecessary to say that this
condition is rarely fulfilled in practical cases, or that the demon-
strated result does not hold good in such cases. But since there
is a distinction to be made between a theorem that is not yet demon-
strated and one that is clearly shown to be erroneous it will be of
interest to see from the following modifications of Braschmann’s
analysis as suminarized in the Comptes Rendus, Paris 1861, how
in the case of non-uniform motions along paths restricted to the
earth’s surface, the direction of the horizontal pressure depends
on the variations of the respective components of its velocity.

[The original memoir in the Paris Comptes Rendus contains
numerous typographical errors that are corrected by Erman in his
Archiv Wiss. Kunde Russland.]}

Let X, Y, Z, be the projections (or rectangular components) of
the accelerating force and P,, P,, P, the projections of the pres-
sure exerted on a unit surface, at a point whose codrdinates relative
to a fixed system of rectangular axes are x, , 2,; we have then

x FH

dt? 7

d
vee x (1)
| epee AS

de

If both the axes and the origin of codrdinates are all assumed to be
in motion then we have to substitute herein the values of the accei-
eration at the point x, y, 2,. Let x, y, 2 be the coérdinates of this

ROTATION AND HORIZONTAL MOTIONS—-BRASCHMANN 27

point referred to the moving axes at the timet. Let w, w, w, be the
angular velocities of this point about these axes at the same instant.
Let w be the resultant of these angular velocities and let a, f, 7 be
the codrdinates of the origin of the movable system of axes with
reference to the fixed system; we have then the following expres-
sion for the accelerations:

et Ged) + da;

de dt ah ce

+ a, (W,% + ay + w,2) — w x ee

dt?
ay, dy ( dx dz dw, dw
ee ee =,— ) +x = — 2
dé dP ae a) oe
\ = 9
+ w, (@,% + any + Wz) — w yon ss
2 (Wy, - 2 39 ¥y de |
9 ‘ !
a2, a2 2( ay — a) + du, _ y Mr
af. dé dt dt dt dt
2
+ w, (w, % + wy + w,2) — w2 + a

[The detailed demonstration of these expressions was given by
Braschmann in the Bulletin of the St. Petersburg Academy for
1851 and is repeated in Vol. I, Chap. IV of his Treatise on Theoret-
ical Mechanics and at pp. 74-88 of Erman’s Archiv X XI, 1862;
its equivalent is found in many recent treatises on mechanics under
“constrained motion.’’]

If the last named initial point or origin of the movable system
of coérdinates be at the point O on the earth’s surface and movable
with it about the earth’s axis then it has a constant velocity of rota-
tion about this axis. Hence the accelerations of its motion are
zero and therefore we have

Pa _ 9 |

dé

dp

pee. ef) erm ph nee as Ys he
= (3)
Pry |

28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOR Sa

_ Imagine the three codrdinate axes movable with the earth to be
so drawn through this point that the xy plane is horizontal, x being
positive eastward along the tangent to the small circle of latitude
and y positive northward along the tangent to the meridian but 2
positive downward toward the center of the earth considered as a
sphere. Let Ol be the direction of the positive half of the momen-
tary axis of rotation or in our case a line drawn through O parallel
to that half of the earth’s axis that extends from its center to the
south pole; then in general

W, = w, cos (lx) w, = — w cos (ly) Wz = w COS (/z)
and in our special case
w= @, = —wcosa w, =w sind
where A is the latitude of the place of observation (QO) and-a is the

angular velocity corresponding to the diurnal rotation of the earth.
Since in this case of steady rotation

and considering the conditions expressed in equation (3), therefore
in the present problem the general equations (2) become

2 2
Phy FH 2 o( cos a2 + sin 2%) — w’.Xx
dt? dt? dt dt

Py day

2
ies | gy Sid = — w’ cos 4 ( —cosd.y+sin A.2) — wy (2,)

@ d@ d < 2
a as? w cos A — w’ sin A ( — cosd.y + sin 4.2) — wz

The terms in w* may be omitted because they are very small; but

Z
for the same reason the term 2 w cos 4 —-must be omitted in all those

dt

cases in which the gradient of the surface (the rails or the river),

ee
and hence also 5 is small or zero.

Let a be the angle between the direction of the motion of the point
x, y, 2 and the direction of the positive axis of y and let v be the

ROTATION AND HORIZONTAL MOTIONS—-BRASCHMANN 29

velocity of this point, then

dx ;
__ =% sin a
at

? psa
dt

Let v, v, ¥, be the components of the momentary velocity along
the axes x y z and hence their differential quotients with respect
to t will be the momentary accelerations in these directions and
identical with

as d*y dz

dt? dt dt?

Equation (2,) now becomes

2

agp ee ini Cbs a

dt’

ay, du, : :

—-!— ¥Y¥42 yw sin A.v.sin a Uy sect ee
dt? dt ©
2

Oe Dies cos )-4. saa

dt’ dt

Now gravity and friction are the accelerative forces acting on a
point in contact with the sides of the track or path of constraint.
The projections of gravity on the horizontal plane are equal to
zero and equally so the projections of the lateral friction on the
direction of the lateral pressure disappear. Hence if we designate
the acceleration of gravity by g we have the forces

xX =0
Y=0
Z=g
and equation (4) gives the pressure
P= er aa
dt
Py = Eb oh aa aie Sia ON oa yeaa a)
dt
Be Pasar ee ger ASO: Sina

‘ dt

30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

If the horizontal motion is uniform then

EO BN ee
dt dt
whence
PZ = -— 2-@ sar Ay cos ¢
(6)
P,= —2wsindvsin a

whence
; P=2wvsinA

where P is the whole pressure exerted in a horizontal direction.

If wesubstitute in equation (6) successively all values of a between
a=0 and a@=2 x we soon perceive that the pressure P is
always perpendicular to the path of the moving mass and if A is
positive the pressure is always directed to the quadrant on the
right-hand side of the direction of motion.

If the motion is uniform along the axis of x only, then for positive 4
the direction of the pressure P will still be always toward the right-
hand of the direction of progress of the mass so long as the value
of a lies between 0 and z, 1. e., so long as the progress is in a direc-
‘tion between east and south and west.

But if the motion is uniform along the axis of y only, then for posi-
tive A the pressure of P will be directed toward the right of the direc-
tion of progress for any value of this latter direction that lies be-
tween a = z and @ = az.

If the motion is not uniform along the axis of x or the axis of y
then the direction of the pressure P may be either toward the left
or the right of the direction of motion depending on the current
values of = and = toan extent and manner easily determined from
equation (5).

Vv

ON THE STEADY MOTIONS OR THE AVERAGE CONDI-
TION OF THE EARTH’S ATMOSPHERE

BY PROF. DR. ADOLPH ERMAN!

In the third book of his Mécanique Céleste, Laplace has demon-
strated that the atmosphere of a rotating planet is at rest relative
to any point of the solid nucleus of this planet and that at the same
time any pressure and any density can occur within any level sur-
face of such an elastic fluid, i. e., within any surface that at any
point is normal to the resultant of gravity and centrifugal force.
In this he assumes that a uniform temperature prevails throughout
the elastic fluid.

The surface of the sea is such a level surface and apparently on
the strength of the above demonstration by Laplace most physicists
assume that the product of gravity by the height of the barometric
column? which measures the pressure of the air must recessarily
be the same everywhere at sea level. They grant that temporary
disturbances of the atmospheric equilibrium are accompanied
by temporary interruptions of this uniformity of atmospheric
pressure, but imagine that these two exceptions are only periodical
(viz: variations about a mean condition) which mean must be
primarily a condition of rest relative to the earth, and secondarily
must be that uniform mean reduced barometric height that one
should find from measurements taken during one or many whole
years at different points on the earth’s surface.

The falsity of every portion of these assumptions was shown
many years ago and should have been evident a priori still earlier.

I have found the mean reduced barometric readings for different
localities at sea level extremely different. Among others, for in-
stance, the pressure at the polar limits of the two trade wind belts
is from two to three Paris lines (0.18 to 0.27 English inches) greater

‘Translated from the Astronomische Nachrichten, No. 1680, February,
1868, Vol. LXX, cols. 369-378.
* For brevity I will call this product the reduced barometric height or
the pressure of the air.
an

32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

than at the equator; again, on the Sea of Okhotsk and at Cape Horn
it is six Paris lines (0.53 inch) smaller than at latitude 23.5°. At
any point in the interior of a continent whose altitude above sea
level is known by geometrical measurements (e. g., railroad level-
lings), the observed mean air pressure can be reduced to the value
appropriate to the sea level vertically below it and thus gradually
an empirical expression can be found for the pressure at sea level
and, therefore, for the atmospheric pressure in general, as a func-
tion of the longitude, latitude, and altitude above sea level, or the
distance from the center of the earth. Individual contributions that
I have made to this subject leave no doubt that above the solid
land, as also above the ocean, the mean air pressure at any lev

layer differs very much according to the latitude and longitude. “

The first of the above stated two fundamental assumptions (v:
that the atmosphere is in a state of rest relative to the globe’
also decidedly negatived by ordinary observation. In one p
tion of the atmosphere, lying between the parallels of +25° an
—25° the air is at every minute and, therefore, on the average
of all time, in that state of strong steady flow that we call the irade
wind; in other words, therefore, the average or permanent condition
of 0.4225 of the total mass of the atmosphere is a regular flow that
is certainly not to be ignored. In the remaining portions of ‘th
atmosphere, however, the movements are less steady as to time.
But when the successive motions of the air, during one or mn»
whole years at any place are combined into one resultant, the ©
general this resultant differs from zero and in such a way tha”
direction and velocity depend upon the codrdinates of the loc&
and are independent of the years or number of years for which’ ~
computation was made.

Therefore, after eliminating the influence of periodic and accid+
tal circumstances and in direct opposition to the above-giv
assumptions of the physicists, we find that the earth’s atmospher
shows the following phenomena:

(x) A current whose direction and velocity are iienen dete of
the time and which, therefore, at every place depend only on the
coérdinates of locality.

(2) At any level surface (or one that is perpendicular to the result-
ant of the explicit forces) the atmosphere is under a pressure that
varies with the coérdinates of the points of this surface, but is con-
stant as regards the time.

These two observed facts contradict the results of the an@ ‘ysis

of Laplace only because in place of a certain assumption 4 ‘ais
Ig°*

STEADY MOTIONS OF EARTH’S ATMOSPHERE—ERMAN 33

analysis precisely the opposite holds good in the earth’s atmos-
phere. The temperature which Laplace assumed to be uniform
throughout the fluid is in the earth's atmosphere extremely unequal
and, indeed, not only so in respect to the periodical portion of its
expression depending on the time, but also as to the other perma-
nent portion, which we ordinarily call the mean temperature of the
place. These mean temperatures, which are invariable as to time,
are, as is well known, a function of the coérdinates of the location
to which they belong and, not only the analytical form of this
function, but also the constants that enter it are already known
with considerable approximation.’ In accordance with these re-
alts of experience, it is certainly worth while to investigate the
ollowing problem:

What ts the nature of the movement and how great is the pressure

reduced barometric reading at any point of an atmosphere for which
voth the resultant of gravity and centrifugal force and, also, the tem-
perature are expressed as functions of the coérdinates of locality and
are independent of the time?

Tae remarks that follow seem to me to prove that this problem
can be solved.

If at any point of a liquid, or an elastic fluid or gas, at the time
t and with reference tc three rectangular axes, we have the co6rdi-

tes x, y, 2; the explicit forces X, Y, Z; the velocities of motion u,

w; and if at this same point x, y, z, we have the density o, the

‘ssure p and the temperature t, then by combining the conditions

equilibrium of this fluid with the general theorem for the move-

nt of any system, remembering‘ that

Ox . Oy 02
Ob) SSS 5
ot ot ot

p dx at 0x ay 0z
d
at Pk OU OO ey re eee ee
p ay at ax ay dz
Pe ery ot Sa Mee
p dz ot ax ay dz

yee for example Erman’s Memoirs in the Archiv Wiss. Kunde, Russland.
he translator has taken the liberty of substituting @ for partial differ-
and d for total differential instead of Erman’s notation.—C. A.

34 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLF5 5

and, as the condition that the mass of each particle of fluid shall
remain invariable, we have

sp SAR ONPE) OME Oe ae re

0 ‘
0x oy 0z ot

In these equations the variations with the time, when x, y, z re-
main constant, are expressed by the differential with regard to t.

Since now in our present case of the earth’s atmosphere, we
assume that at every point the pressure, temperature, motion and,
therefore, the density are invariable as to time, therefore, we may
in equation (II) substitute :

Ou Ov Ow

Furthermore, we have

Pe oar 2

Seats ,

where Pis that value of the pressure (or the reduced barometric
reading that measures the pressure) for which the atmospheric
air at the temperature o° C. is 0 times heavier than the mercury
of the barometric column and k is the coefficient of expansion of
the air for one unit of the thermometric scale that is used to measure
the temperature or tT.

Since t is assumed to be independent of the time it can be ex-
pressed as

hor ij (x, y; 2)

where f indicates a known function, which, as above stated, is now

approximately known; therefore we may also write
‘

Ps Pe
ML Nee eC
0 a 7)
where F (x, y, ) again indicates a known function which for brevity
we indicate by Fs

STEADY MOTIONS OF EARTH’S ATMOSPHERE—ERMAN 35

Therefore, we now have
62 P tt
FG 4.2). Ff.

or

1 :
ae

t

and the left-hand portions of the equations (1) become respectively

Be EPR rs TOE ok
p ox p 0x Ox

1 op _F op_ , dlogp _y

o ay =p ay ay
2d an OG as Rie Lg
oO 02 p 02 0z

where log indicates the natural logarithm.

Since it is known that the components x, y, 2, of the resultant
of gravity and centrifugal force, as also the components u, v, w
of the velocity of a fluid particle, depend only on x, y, zor on the
variable coérdinates by which we express the location of any point:
on the sphere, therefore, as is well known, there are two functions
of x, y, 2, which I will designate by V and ¢ respectively® which are
determined by the relations

OV. Weare ed
ax” ay ” 02
and
est ae poems gave
Ox Oy Oz

If these values are substituted in equation (I) and the sum is
taken after multiplying the first,second, and third respectively by
dx, dy, dz, and if we recall that

° These functions are now generally called the force potential, V, and
the velocity potential, Y, or the potential function for the external forces and
the potential function for the resulting velocity. If such functions actually
exist there can be no discontinuous whirls, and if the whirls exist then there
can be no such functions,—C, A,

36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

16)
Ae to Mee |e a Sd
Ox Ox

ai . ore) “()

ee eae
oy 0
a ee es
Ox OX |

and recall that
ag rata) HBR s
ov oy 0z

result in a similar manner from the six remaining terms of the right-
hand side of the summation, then there results

- ag \? ag \?
~dp = F .dlogp=dV ya} (2) + (2) +(2) hw

=F .dlogo+dF.

Again, from equation (II), after substituting the values of u, v, w
and dividing by o, there results®

_ J Aloge a9 , dlogp. dy , dlogp sar
ax 0x oy.” oy @z = az

Pp Pp Hyp }
_ { ant f ay? + og? (B)

The equation (A) can be more perspicaciously replaced by the
following

log ¢

0
* Because p is assumed not to vary with #, therefore por i = 0, and this

term drops out.—C. ABBE.

STEADY MOTIONS OF EARTH’S ATMOSPHERE—ERMAN 37

dp\? /ay\? 2
(2) By}
Glagp 91 8V dlogF- 1 @ \\ax ay az/ J

Ox F ax Ox QF Ox
2 a0\2 d0\2
04 (2) +) +(%)
motogp 1 aV dlogP 1 ax \dy/ OB)
ay F ay ay oF ay
2 a 2 a 2
Teles
d log p nt Vi -dlog Ff - 1 Lex] ay) ear!
0z F ide dz PAN 0z

and we can, therefore, by simple substitution of A¥ in B construct
an equation in which, in addition to the partial differential quotients
of the first and second order of the function g=¢g(x y 2) there enter
only the known functions F = F (x, y, 2) and V = V (x, y, 2) and
their first differential coefficients.

If x, y and z are replaced by the angular coérdinates of any point
of the atmosphere so that

* =rcosdV1— p2 =rcos Bcosd
y =rsindA V1 — p? =rcosPsind
2=Tp =F Sim 2

where r is the distance from the center of the earth to any point
in the atmosphere; J is the longitude of this point; # is the latitude
and mw is the sine of the latitude, then, as is well known, we have’

1 q Gp. 9) ix 2
V =(7 R? t4(4).0- 2 —4)r
(7 R*) z 3R ont 5)

where for the surface of the earth and at the equator, we have

a— ie
y = acceleration due to the attraction of the earth
q= acceleration due to centrifugal force = =

7 This expression assumes that gravity and centrifugal force are the only
external forces and thus ignores viscosity or internal friction and the resist-
ance of the earth’s surface and the attractions of sun and moon.

38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLS i

This expression for V, as well as those that must obtain for F,
for g and for o respectively, when we write these out as functions
of w, A and 7, all possess the properties that Laplace has demon-
strated for all functions of this kind that have definite real values
for constant 7 and for all values of A, from 0° to 360° and of wx from
—1to+41. That is to say, since this latter condition (the having
a definite real value) is evidently fulfilled in the earth’s atmosphere
as to temperature t, density o,and the function g whose differential
coefficients are the component velocities, therefore, in accordance
with the Laplacian theorem just referred to, we may similarly assume
for V, for F, for gy, and for p, respectively such expressions as the
function

Ge + RPO boy Pe eee

in which, as we pass from one to another of these four functions,
V, F, ¢ and op, there occur:

(1) Those coefficients a, 8, y . . . uv which only vary with r
(2) the constant numbers that enter into P®, P1, P?, P”,as defined
in the next following paragraph.

In general P” is defined by the partial differential equation

ap™ azp™

ei ae eS
a ; ie see ee (n)
0 i pe ye =e ek) Pe

and from this it follows explicitly that

— 42)4 (n)
P™ —Be X 4 (A, sind + B’,cosi)x POH) OA
n

Oye
(1 ae: ye at xX)
Gi. cite ae

+....(Af sina A+B cos7 A)
n

where B,°, A,’ , B,’ are constant numbers and

XM = ym n(m —1) ao , w(m—1) (n—2) (n-- 3) eases

: es tc.
2 (2n —1) 2.4. (Qn —1) (2% —38) ;

Since the development of each function, V, F, ¢, o, in the form |

aP° + BP’ + etc.,

STEADY MOTIONS OF EARTH'S ATMOSPHERE—ERMAN 30

is only possible in one manner and since it always gives a converg-
ing series, therefore, each of the functions occurring in equation (B)
consists of a limited and, in facet, probably a small number of terms,

, aP®, BP’, +P" ,etc.,

which altogether constitute a series progressing according to the
whole powers of
wand (1— 4”)?

whose terms are multiplied into the sines and cosines of multiples
of A. Furthermore, since the terms of this nature, in equation (B),
resulting from the development of V and F contain respectively only
a well-known function of r, while, on the other hand, the terms aris-
ing from the differential quotients of g contain the functions a, f, 7
of this same form and the constants A, B, C—which are the only
unknown quantities of the problem—therefore, these latter must
be determined by equating to zero each of the sums of known and
unknown terms that in equation (6) are multiplied by

ut. —p?)? sin zd or wl — p?)?cosza.

In order to practically execute the determination of the velocity
function ¢, for a given temperature function F, we can easily con-
vert that form of the latter equation which results from the combi-
nation of equations (A*) and (B) into the equivalent differential
equation inr, w, and 4 whose specialization then leads directly to
the desired end.

The two following relations between any two functions, ¢ and
¢’, of the codrdinates x, y, z are easily demonstrated

Op ag’ | ap Og | db a’ _ ap Ay’, Ob a 1—
dx dx dy dy 2 Og Or Or Oe a Yr
dp af’ 1

ee a
dA OA (1 — p?)r?

and

Od ah
sfa-08} (B) wy
2 42 2 772 2(y
arg " ae * Op n Om J n OA 0 (rp)

Oe dy? — oz? a Sey: eee
y z yu u ?

waence it follows that equation (B) may be written thus:

40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 352
0 -( - oe (sr - ae we ag ao 1 dy
dr ar du On/ vr dp A ABA/(1—p?)rP ad

ae Ne: ie tats Gaia lenee

9 ie . Or
1 Hea + (Sy os aah a ; ‘ya 4 1-2 a
q ls —# ag
as eb Ret by ee erg (C)

leila
1 Nar) Nene} PF Naas GPS =) dy

2 ay Oa
ae ( ? #) (=) # (r
i = ar a ee oe

where, finally, V, F, and g are each to be replaced by a converging
series of the form

oP? + BP’... . + Po

and where the series for V and F will contain known functions of
ry and known constants, but the series for g will contain similar
terms whose functions and constants are to be determined.

In order to obtain an approximate idea of the practical solution
we may take the above given value of V,

V=(R) s+ (fh )e-(4)e — 4),

which agrees with the form of the converging series when we put

1 q-
= R?)_— + aS r.
a= (7B?) cS

and further take for the function of F the following.

Fe= @ br ee 4)

STEADY MOTIONS OF EARTH'S ATMOSPHERE—ERMAN 4l

which agrees with the form of the converging series by putting

a = (a + br)
B=d0=e=... =0
f= re

In agreement with these assumptions determine the functions of
r that I will in general indicate by

(n)
i (m)

A™ B™ etc.

(m) ’ (m) ’

and the constants

that enter into the following general expression for g,
eg =f. + fi (u) + fi’ (Ai sind + B,’ cosa) (1 — p’)?
+ f.P(—4 +7,(1—)*. 2. (A, sind + B, cosa) (1 — 2’)
+ f,? (A,? sin 24 + B,? cos 2 2)

0 3 2 F Py ale ae
+ fs (w - oa) + fs (1-7) (« = =) x
x (A,’ sind + B,’ cosa) +

From equation (C) it is evident that in this special case the terms
in g that are multiplied by functions of A must disappear and that
therefore also the direction and velocity of the steady wind must
be as independent of the longitude of the place as is the assumed
distribution of temperature.

‘If we have thus carried out the determination of y, then, from
equation (A) there follows

gp = ff a C0 ee Gd — @)rs

2b
+ Constant.

and since the quantities under the integration sign can also be devel-
oped in series of the kind above considered, then, for all points of the
atmosphere, we shall know

ver iads the (1) «(Y(2Y

42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5i

where b designates the mean barometric pressure, as soon as we
have determined the constant of integration by observation of the
barometer at only one point, for which also the force of gravity,

ie) pee
i Ox oy 0z
shall have been given.

If the mean barometric pressures computed in this manner be
compared with the observed pressures, we get a sharp control over
the theory. ;

It is only when in this way it shall have been shown that the
observed steady components of the motions of the atmosphere and
of the barometric pressures are not properly represented, that we
shall be justified in assuming that the friction of the particles of air
against each other and against the earth’s surface exert a sensible
influence on the phenomena. In this case, and in so far as the
friction is assumed to be proportional to the square of the velocity
and uniform throughout the atmosphere, we shall have to replace
equation (A) by the following:

do \? do \? do \?
Fdl ae ee | ee ee (#) (2
oe ya) (2 z ay aaa
0 2 0 2 2
-2((zy+(aye(2)},
Ox oy 0z J

By the introduction of the fourth term in the right-hand side of this
equation and of the undetermined constant, C, nothing of a a
is changed in the development above considered.

, VI

THE LIMIT OF THE ATMOSPHERE OF THE EARTH

BY DR. A. KERBER
(Dated Chemnitz, February, 1881)

[Annalen der Physik und Chemie, New series XIV, whole series 250. Leipzig,
1881, pp. 117-128]

I. THE CARDINAL POINTS OF THE ATMOSPHERE

For small zenith distances the atmosphere constitutes an optical
system of refracting media separated by centered spherical sur-
faces of small aperture, so that the theory of such optical systems
developed by Gauss and Mobius! can be applied to it. The impor-
tant matter is the determination of the ‘‘Cardinal points’? by this
theory. It is well known that the cardinal points are:

(1) The principal foci f and j’ in the first medium A and the last
medium A’ (fig. 1). At either of these points are united the rays
that come through the opposite medium parallel to the optical axis

if’.

FIG. I.

(2) The nodal points k and k’ having the property that every
ray (ab) passing through the first medium in such a direction as
would pass through k, when it reaches the second medium goes on-
ward in a direction ¢ a’ passing through k’ parallel to its initial
direction ab.

1Gauss: Dioptrische Untersuchungen, Goettingen, 1840. Compare also
Helmholtz, Physikalische Optik. Braunschweig, 1861. In the present arti-
cle I refer to the Physik of Mousson, which is widely used.

43

44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

(3) The principal points h and h’ for which object and image are
identical.

As in all complicated systems whose constitution is not known,
so here, the location of these cardinal points can only be found
experimentally? based on the astronomical determinations of the
refraction of light by the atmosphere.

Let m in fig. 2 be the center of the earth, c the location of the
observer; cc’ a small are of a great circle of the earth; bb’ the inter-
section of the circle with the boundary of the atmosphere; a a fixed
star; abe a pencil of rays from a toward ¢ which is refracted at c
toward the direction cf’ so that the apparent zenith distance
¢ determines the astronomical refraction 0; am the axis of this
optical system whose first medium is the vacuum for which the
refractive index is ~ = 1, and whose last medium is the lowest
stratum of air whose refractive index is ’, and which is assumed
to have no limit.

The nodal points of the atmosphere coincide at the center of the
earth. For, because of the concentric boundaries of the refracting
media a pencil of light passes through the atmosphere in a curve
whose tangents are never parallel to each other, so that only one
ray, moving in the medium n’ toward m, can proceed farther in the
same direction.

The location of the second focal point f’ is easily found when we
consider the ray starting from a as originally parallel to the axis,
It is deflected from its initial direction by the amount of astronom-
ical refraction o and in the last medium finally proceeds toward
the second focus of the system or 7’. The corresponding focal dis-
tance F’ is found from the triangle c. m. 7’; in this triangle we have
cm = R, y=¢ and since in this case ab is parallel to aj’ there-
fore a’ = p hence

Bree RO ee ee
0

2Mousson: Physik, 2d Edition, section 731; 3d Edition, section 8ro.

LIMIT OF THE ATMOSPHERE—KERBER 45

The ratio of the astronomical refraction to the apparent zenith

p

distance is — = 57.3’’ according to the current tables of refraction

for the average condition of the atmosphere,’ so that we can write
-

a Den Lae Bae (2)

where 57.3’’4 represents any possible error of observation that we
include in our computations in order to show the degree of accuracy
of the results. Hence we have

R
eld)
57.8 3)

| fu

I

about 22 918 400 kilometers for R = 6366 .7 kilometers.

The first focal distance of the atmosphere follows from the relation
according to which the distance of the two focal points from the
respective nodal points is inversely proportional to the ratio of the
refractive indices of the respective media.‘ Hence we have
aes n’ R
ie ee + 4) =about 22 924900 .. . (4)

where we assume the coefficient of refraction for the average condi-
tion of the atmosphere (b = 0.752 meters, ¢ = 9.3° Cent.) to be
n’ = 1.000282 according to Ketteler’s determination.

All celestial bodies except the moon are farther removed from
us than the focal distance F. Hence the atmosphere produces
as a whole and at the focus inverted real images of these. The
convergent pencil of rays coming through the atmosphere enters the
eye so that it also unites the pencil into an inverted image within
the focus ¢ of the whole eye (or it falls short of the retina) and thus
there forms on the retina under all circumstances for a perfect far-
sighted eye a circle of diffuse light, no sharp image, and thus the
spread of the stellar image over the retina finds its physiological
explanation.

On the other hand, the atmosphere produces a correct upright
virtual image of the moon because she is within the front focal dis-

* Bruhns: Astronomische Strahlen-brechung, p. 19.
‘Mousson: 2d Edition, section 731; 3d Edition, section 809 (4).

46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

tance and the eye receives a diverging pencil of rays. Thus the -
inverted image produced by the two optical systems combined,
the eye and the atmosphere, lies inside gy counting from the retina
forward; but on account of the great distance of the objects, always
so far from the retina that it requires an extraordinary power of
accommodation to produce a sharply defined image,on the retina.
The muscular tension thus excited explains the apparent floating
of the moon in the atmosphere. But even with this extraordinary
accommodation the image of the moon will only just attain the
nerves of the retina, and since this partial touching also occurs in
ordinary vision for objects that are at a definite terrestrial distance
that we may call D, therefore the eye locates the moon also at the
same distance D because it produces the same sensation or excite-
ment on the retina, whereby is explained the apparent floating of the
moon at a relatively nearby point in the atmosphere.®

In relation to the location of the principal point, h, its distance
from the corresponding focus is equal to the distance of the opposite
focus from its nodal point.®
Therefore we get from fig. 2

jh = F’ and fl’ =F

whence

mh =jfm—fh =F — F’
and also

mh’ =f'h!' —fim=F — F'
consequently

mh = mh' = F — F’
and thence by substituting from equations (3) and (4)

mh = mh!’ = oe (1 — 4) = about 6463 kilometers . (5)

Therefore the two principal points, like the nodal points, coincide
in one point h, that is 6463 km. distant from the center of the earth
or 96.3 = 6463 — 6366.7 above the surface of the earth at c (fig.
2 or fig. 3). Therefore according to the definition of the principal
points the object and the image coincide at the point h, that is to

’ We determine D experimentally by measuring the distance at which an
intense flame is sharply seen.
® Mousson: 2d Edition, section 731 (2); 3d Edition, section 809 (2).

LIMIT OF THE ATMOSPHERE——KERBER 47

say, all rays that in vacuo are directed towards h, diverge after their
passage through the atmosphere from this same point h. If, for
instance we imagine a planetary nebtila between any fixed star
and the earth and the star-like image of the nebula located at the
point h (see fig. 3), which is now to be considered as the luminous

Cc

FIG: 3.

object seen through our atmosphere, then will the rays ab converg-
ing toward h be so refracted by the atmosphere, that on their
entrance into the last medium n’ they will appear to diverge from
h in the direction cd, and hence an identical virtual image should be
seen at that same point () at which a real star-like image must
have existed if there had been no atmosphere.

II. FIRST APPROXIMATION TO THE HEIGHT OF THE ATMOSPHERE

By reason of the nature of the curve of the beam of light abcd,
which has its concave side toward the center of the earth, it is evi-
dent that the principal point must lie within the atmosphere.
For if e, fig. 3, were the principal point, then a pencil of rays that in
vacuum may have the direction ef must necessarily on its entrance
into the medium m’ go on farther in the direction egk, if an identical
image of the object is to be formed at e; but this is impossible be-
cause ef and gk cannot be tangents to the same curve at f and g.
Hence therefore it follows that H > ch, that is to say, according to
the note on equation (5s),

Hii SS n9une: KiOmMebers.yack sity Y. (6)

But a more accurate determination results at once from the fol-

48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

lowing consideration. Since for small zenith distances the curved
path of a yencil of light is very nearly an arc of a circle of very large
radius of curvature’ therefore the tangents (to these curves) bh
and ch, fig. 3, can be considered as equal and because for small
zenith distances the tangents can be exchanged for the distances
of the principal points from the limits of the atmosphere, therefore
we have approximately

H =2 ch
or from equation (5)
H =2R a=. (1 — 4) — | = about 192.6 kilometers . (7)

Hence the determination of H from the observations of the twi-
light arc as given by Alhazen (leading to the value of 79 kilometers)
is far too small, and in fact it follows from Fresnel’s formula for the
intensity of reflected unpolarized light that the argumentation by
Alhazen by no means excludes the existence of still higher strata
of air.

According to Fresnel’s formula, if the incident light has the inten-
sity unity, and e and b indicate the angles of incidence and refrac-
tion, then the intensity of the reflected light is

qe, eae Os E pee fe)
2 sin? (e+ b) |. cos? (e — b)
Since in one case the reflection takes place at the thinner layer

therefore the refractive index is -__-- and _ we have
n+ on

sin b = (1 + 6n) sin e
cos b=cose—sineige . dn

and by substituting these values we obtain

2
y= 3 we | x [1+ (int & cost |

2 cos? e— don
or approximately, since e is not far from go°

On 3
Ae ah ips ae Pe arcane a ee |)
J « cos’ e ) )

7 Bruhns: Astronomische Strahlen-brechung, p. 66.

LIMIT OF THE ATMOSPHERE—KERBER 49

Now let me in fig. 4 be the radius of the earth and ac the horizon
of the place c, and s the sun. If the sunlight is reflected from the
layer of the air at a whose radius is R + h toward the horizon at ¢
then

h

sin e = 1 — —

cos? ¢ = ah

R

and the intensity of the beam of light seen at ¢ will according to

equation (8) be
pine ( OOK N*
: ( |

.
.
.
Ds,
.

N
\
‘

\

\

'

\

I

'

\

I

\

'

I

t

¢

v
Mt

FIG. 4.

If now the twilight ends, or the stars of the feeblest intensity J,
become visible to the naked eye, when the sunlight is reflected from
the layer of air at an altitude of 79 kilometers, then the only con-
clusion that should be drawn is that at this altitude the intensity
of the reflection

( on R )

4x 79

50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL: 52

has become less than J,. But whether there are still higher re-
flecting layers of air and a still further diminution of the intensity
of the twilight is beyond our power of direct observation; however,
the possibility cannot be gainsaid so long as J, > 0.

The fact that the limit of the atmosphere really is considerably

higher than 79 kilometers, assuming that By 57.3’’ is correct, is
i

shown by the well-known differential equation for astronomical
refractions,

f iW) Sik 5a!
R+h . dn

R Hn
"| n? — ( ai) an sin*
© od

which for small zenith distances reduces to the expression

x R we On
R+h n

(9)

If for h we substitute its maximum value H so that the right-hand
side of this expression becomes still smaller, then
On

a,
id

hon ae n :
4 R+H >

and after integration between the limits m = 1 for the highest layer
and ” = n’ at the earth’s surface we have

R
> n’ — 1
eae i 5, | Ve
whence
H> [E(w -1)-1]R
p
in which
pom ft n’ — 1 = 00002820, R = 6366.7 kilometers
pone”
whence
Hf > 96:.a lalometers” ..- 2 3) 2 eee

which may be compared with the value in (6) above given,

LIMIT OF THE ATMOSPHERE—KERBER 5

III. SYMMETRIC POINTS OF THE ATMOSPHERE AND THE ZENITH POINT
OF THE RAYS

For brevity I speak of the two conjugate points a and a’ in fig. 5
as symmetrical when the angles of divergence of the rays from the
axis are equal to each other so that

Cee RN ete ee te auc

Let the distances of these points from the center of the earth be
DandD’. According to the theory of Gauss the ratio of the dimen-

sions of the object and its image, or D/D’, multiplied by the ratio of

4 : t .
the tangents of the respective angles of divergence ced is equal to the
: iga
inverse ratio of the indices of refraction of the first and last media®
whence

D tga ?
St
D’ tga’
or by equation (11)
D ae ry)
Di
and by equation (4)
De a Dy PF

A second equation between D and D’ results from the relation devel-
oped by Gauss between two pairs of conjugate points® for instance,
the nodal point m and the symmetrical points a and a’ of fig. s.
If we divide the distances F and F’ of any pair of conjugate points

®Mousson: 2d Edition, section 730 (7); 3d Edition, section 808 (19).
*Mousson: .2d Edition, section 730 (4); 3d Edition, section 808 (16).

52 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

m, from the focal points, by the distances D and D’ of the two pairs
from each other (see fig. 5), then the sum of the quotients is unity
and we have therefore

S ee soln SEE oh ee
1h tae 8 i
hence from equation (12)
2F

Sb Pa aP pe ow
D

t

From these we at once find the distances of the points of symmetry
from the (upper or lower) boundaries of the atmosphere, namely,

alWl=2F —R-H
ae a2 +R
and substituting
F = 22 924 900 km. R = 6366 .7 km.
F’ = 22 918 400 km. H = 200 km,
there results
ab) = 453819 233 ems Oh eee
a’ c’ = 45 843 167 km.
Hence the points of symmetry are at approximately equal distances

from the boundaries of the atmosphere, and since a = a’ the points
of entrance and exit, b and c, of the corresponding pencil of rays

are at equal distances from the axis so that bc is parallel to am. By
the zenith point of the pencil I understand the point of intersection
d (fig. 6) of its initial direction with the prolonged radius of the place
of observation.

LIMIT OF THE ATMOSPHERE—KERBER 53

Let a and a’ be the conjugate points; D and D’ their distances
from the center of the earth; a and.a’ the angles of divergence of
the corresponding pencils; then in the neighborhood of the zenith

and according to the theorem just stated we have
-

D «a
ee . (16
Ae (16)
But from the triangle mca’ since y = ¢ there results
Desa or D'a’ = R¢
KO -a@
substituting this in equation (16) gives us
D
ra a Pee ae tee we LE)
R¢

Furthermore from the triangle mad, designating the altitude of the
zenith point by h we have

fs RS eal!
¢t+e D
or
Da (Bah) (6 +p)

so that equation (17) becomes

(145) (1+2)=¥ ot ee (ES)

Ifin this we substitute for 7 its value from equation (2) we get
le

h =[(n! — 1) — 57.3" nw’ (1 + A)] R = about 0.027 kilometers... (19)

For zenith distances up to 1° the altitude of the zenith point is
independent of o and ¢; or, for the same locality, R, and the same
condition of the atmosphere, u’, the zenith point has an invariable
position.

54 SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 51

IV. SECOND APPROXIMATE VALUE OF H; ACCURACY OF THE RESULT

By reason of equation (15) the triangles bcd and amd, fig. 5,
are similar to each other, wherefore for the point of symmetry a
we have

be =” cd or eee
dm R+h

and substituting the values from equations (4) and (19) we get

n’' —1

He2k x
57.3”

(l — 4) -— n'| = about 189.0 km. ... 5 420)

as compared with 192.6 in equation (7).

The agreement of these two values shows that the error made
by equating the distances in equation (14) is without important
influence on the result of the computations; that therefore in
fact the distances of the points of symmetry from the boundaries

of the atmosphere are nearly equal to each other when c= UE.

and n’ — 1 = 0.000282.

But of the two formule (7) and (20) for H the first is more exact
because the curvature of the beam of light through the zenith de-
parts but infinitesimally from a circular arc.

As to the numerical determination, H = 192.6, the assumption
that the ratio of the refraction to the zenith distance (57.3’’) is cor-
rect to within o.0oo1 part of itself makes 4 < o.oo1 and this would
lead to an error of a few kilometers in the determination of the
height of the atmosphere.”

Vv. CONCLUSIONS

On the basis of the preceding determinations it seems natural to
attempt a new development of the differential equation (9) for
astronomical refraction.

The law of diminution of refractive power with altitude may with
great probability be

107 have recently found that the numerical determinations of ,n=1,

and H really do need important corrections.

LIMIT OF THE ATMOSPHERE—KERBER 55

which is deduced in a manner similar to that of Bunsen’s law of
absorption. After substituting this value then the solution of the
differential equation offers no difficulty and the equation of the
curve of the pencil of light is easy to find.

As to the constant exponent m, that is best found from one
accurate determination of the refraction. I will hereafter check
the value of m thus found against the diminution of temperature
with the altitude, since I hope to be put in possession of the neces-
sary observational material through the kindness of a physicist,
a relative, who expects to remain several years in the tropics.

In accord with my previous efforts I also believe that I shall suc-
ceed in obtaining from the observation of the twilight colors material
for the direct demonstration of the diminution of the refracting
power and the determination of the constants.

Let cm in fig. 7 be the earth’s radius and ca the horizon of the
observer at c. At ?¢’/ and #”’ hours after sunset the sun is at s’ and

ees [el

Sx

FIG. 7.

s’; the altitudes of the reflecting strata of air are a’ c’ = h’ and
a!’ c!’ = h’’; the corresponding angles of incidence and reflection
aree’ande’’. We easily find

¢=(--—)a er = (

a vos

Wo = (= sine’) K hi? ("sine 27) i

56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

and according to equation (8) the intensity of the reflections from
these layers h’ and h’’ whose indices of refraction are n’ and n’”’
will be given by

/ = ee ty i, and ” = ( é ite i
J € cos? e’ J 2 cos? e”

If by means of a good photometer we measure the intensities /’
and J’’,then the diminution of the refracting power between the
two neighboring layers at the altitudes h,’ h,”” h’” can be computed
from the equations

dn’ = 2 cos’ e’ V J’,
on” 2 cos @ vy j#,

CLG

; VII

ON THE PATHS OF PARTICLES MOVING FREELY ON THE
ROTATING SURFACE OF THE EARTH AND THEIR
SIGNIFICANCE IN METEOROLOGY

BY DR. A. SPRUNG

(Dated Hamburg, June, 1881)

[Published (August 1881) in Wiedemann’s Annalen der Physik und Chemie
New series, Vol. XIV, 1881, pp. 128-149.

Translated by Thomas Russell and C. Abbe}

Although the view expressed by Hadley in the year 1735 as to
the influence of the rotation of the earth on the currents of the
atmosphere has become very well known, especially through Dove’s
writings, and has been treated of in all manuals of meteorology and
physics, still the actual construction of the path of a particle of air
has in general only seldom been carried out according to Hadley’s
principle. There are, however, in this very ‘“‘Annalen”’ three art-
icles! in which the problem of rigorously calculating the paths of
the winds is proposed either under the definitely expressed or readily
recognized assumption that the particles of air are to be considered
as freely moving points or elementary particles of mass. The ques-
tion treated in these articles is therefore a mechanical problem that
can be formulated exactly, namely, the free motion (motion due to
its inertia) of a material particle which is constrained to remain on
arotating surface. Since the year 1858 a number of mathematicians
have busied themselves with this problem, and about the year 1861
a general theorem was enunciated by Coriolis? by which every prob-
lem of relative motion can be reduced to one of absolute motion.
From these analytical investigations it evidently follows that the
Hadlerian principle gives only very imperfect expression to the
influence of the rotation of the earth on motions parallel to its sur-

1°Von Baeyer: Pogg. Ann., 104, p. 377, 1858.

Ohlert: Pogg. Ann., 110, p. 234, 1860.

Mousson: Pogg. Ann., 129, 652, 1866.
2 Coriolis: Journ. de 1’Ecole Polytechnique, XV, p. 142.

57

58 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

face, so that the calculations based thereon in the above-mentioned
three articles must necessarily lead to incorrect results.

The oldest of these, however (by von Baeyer), appears of special
interest as in it reflections are made which betray a tendency to
abandon the Hadlerian motion. On p. 380 von Baeyer says: “‘a
particle of air put in motion at a definite angle to the meridian on
the surface of our spheroid of rotation at rest and continuing its
way in the direction given to it without any hindrance or disturb-
ance under the general influence of gravity would describe a short-
est line. . . . Let us now imagine the terrestrial spheroid put
in motion from its condition of rest, then the particle of air when set
in motion in the direction @ will already have this motion of rotation,
it can therefore no longer describe a shortest line but its path will
be the development of the shortest line on the spheroidal surface
according to the circumstances of the rotation pertaining to it.”
It is to be regretted that these fruitful ideas were completely set
aside in the course of the mathematical discussion in favor of the
Hadlerian theory. When I first became acquainted, this year, with
von Baeyer’s article the above lines reminded me forcibly of a pro-
cess I had made use of in the year 1879 to set forth the origin of the
relative paths in simpler cases of a rotating system such as the earth
presents and to base on it also a derivation of the equations of rela-
tive motion.’

My treatment was simply. as follows: If a plane disk revolves
uniformly, then will a body or material particle influenced by no
forces whatever or by those whose direction is perpendicular to the
disk, progress uniformly in a right line (that is when considered
absolutely) and the relative path on the disk will be the continuous
series of points which come in contact successively with the body.
This conception, which evidently agrees essentially with that of
General von Baeyer, can be extended to the rotating system of the
spheroid which is under discussion, but at the same time it is evi-
dent at a glance that the first part of the above quotation from von
Baeyer’s article contains an inaccuracy. The course of the point
on the surface of a spheroid at rest can be a shortest or geodetic
line described with constant velocity, only when the attractive force
of the earth is everywhere perpendicular to the surface; in reality,
however, it is the force of apparent gravity, that is to say, the result-

8’ Sprung: Studies concerning the wind and its relations to air pressure,
Part I; On the mechanics of the motions of the air. From the archives of
the Deutschen Seewarte (German Marine Observatory), No. 1, 1879. Zeit-
schrift der Oesterreichisches Gesellschaft fiir Meteorologie, XV, 1880.

PATHS OF MOVING PARTICLES—-SPRUNG 59

ant of the attractive force of the earth and the centrifugal force
that is perpendicular to the earth’s surface; the latter is moreover
a level surface only by virtue of its rotation. If the earth should
come to rest without a change of form, then the body would move
parallel to the surface under the influence of a horizontal force
directed towards the pole, which force is a component of the force
of attraction and whose magnitude can be easily given. If we
denote by ¢ the latitude of a point on the earth’s surface (which
here and in what follows will be considered in an entirely general
manner as a body of revolution) by r the distance from the axis,
and by w, the angular velocity of rotation of the earth, then the
acceleration! of the horizontal poleward directed component of the
force of attraction is equal to the expression

Se
rw sin 9

which represents the horizontal component of the centrifugal force
directed toward the equator in the case of a point at relative rest
on the rotating surface of the earth; for in fact the condition that
these two horizontal forces are in equilibrium determines the form
of the surface of the rotating earth.

At the pole and at the equator this force has the value zero, it
reaches its maximum at » = 45°; over the zone from the pole to
45° latitude it acts in a manner similar to the action of the com-
ponent of the force of gravity in the case of the spherical pendulum
under the influence of which for angles of elevation between o° and
go° the pendulum makes its vibrations. Hence in general the free
absolute motion of a body which does not take part in the rotation
of the earth’s surface, but glides on it without friction will consist
of uninterrupted oscillations around the pole as a center; if the
original motion began in the direction of a meridian, then the body
would never leave it; if the body be started in the direction of a
specific parallel of latitude (dependent on its velocity), then it would
forever keep moving along this parallel with constant velocity, etc.

It cannot be doubted that it is allowable in our consideration of
the relative motion due to inertia on the rotating surface of the
earth to begin in the above indicated manner with the consideration
of the absolute motion; for since we do not consider thé influence
of the rotating surface as any other than that of a rigid opposing
shell it can therefore be considered as infinitely thin and as closely

*In what follows, the expression ‘‘force’’ will for brevity always be used
for the accelerating force.

60 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5a

enclosing the similarly formed body of the earth at rest within it,
while the physical forces at work (force of attraction) are perfectly
independent of the condition of motion of the mass of the earth
It therefore appears profitable to approach the above stated prob-
lem of the absolute motion under the influence of the force r w’
sin g directed towards the pole and to treat it at least approximately
just as the problem of the oscillations of a pendulum is solved par-
ticularly in the case of infinitely small amplitudes.

In the vicinity of the pole sin g changes only very slowly, but r
very rapidly; no great error will then be committed if we give to
sin g the limiting value 1 at the pole and neglect the corresponding
component of the motion parallel to the earth’s axis, that is to say,
the motion is to be considered as taking place in a plane; the error
is thus purely geometrical and easily estimated inasmuch as the
forces arising from the special form of the surface are already taken
into account. Adopting the codrdinates x and y in a tangent plane
and the origin at the pole the differential equations of motion are
therefore as follows:

2
Mx y 2%

= — ry’_ = — xu

dt? Yr

(1)
aw, re) = — vw

dt? t

(Strictly speaking these equations apply to the absolute motion of
a liquid particle parallel to the level bottom of a circular vessel
revolving with the velocity w, in which the liquid is subjected to a
force perpendicular to the bottom surface—in so far as this abso-
lute motion can be considered as entirely unimpeded.)

Equations (1) agree perfectly with those on which is founded the
theory of oscillations in an elastic medium; they can (for example
by the substitution of x or y = e®) be integrated separately and
lead to the final equations?

(2)

ee

y = bcos wt

U,, = aw cos wt
(3)

U, = — bw sin wt

5’ Compare, for example, the following treatises on physics: Willner: 3d
Edition, I, pp. 443 and 450; Mousson: 2d Edition, II, p. 531; Miller: 7th
Edition, I, pp. 278 and 281. There will also be found given in these places
the geometrical representation to be spoken of presently.

PATHS OF MOVING PARTICLES—SPRUNG 61

from which it is apparent that the point moves in an ellipse whose
semi-axes are a and b; for from (2) we get the equation of the ellipse

x \2 ey
sd) ed aie) eel
pret A)

(7 og ee |g ie Au ela en (9

If we put

then 7 denotes the entire time of revolution of the point in the
ellipse, for when ¢ = T then both the codrdinates and the com-
ponents of the velocity U, and U, attain the same values they had
at the time ¢ = 0. Since w denotes the angular velocity of the
rotating surface, equation (4) shows ‘that for the absolute motion
(elliptical) the time of revolution agrees with that of the rotating
surface.

The absolute motion of the point can now be easily constructed.
Let us choose for example the time of revolution of the surface (and
of the material particle) as T = 24 seconds (compare fig. 1, page
62) and divide the circumference of a circle constructed on the di-
ameter 2a into 24 equal parts and from the points of division Jet fall
perpendiculars on the diameter, which in this case can be done by
joining the points in pairs by straight linesas the points of division
are symmetrically distributed with respect to 2a. The 12 diameters
which join the 24 points of division divide at the same time into 24
equal parts a circle constructed on the small axis 2b; from the points
of division of this small circumference let fall normals to the di-
ameter 2b, which is perpendicular to 2a, and prolong them on both
sides to the larger circle. If the time ¢is reckoned from the moment
at which the body is at the extremity of the radius b, then the
points of intersection of the twosystems of normals which are marked
On 02,3 . . . lie on the elliptical path characterized by
equations (2), (3) and (4) for T = 24, from which the correspond-
ing relative motion is derived in the following manner.

A rotation of the surface about an angle w, 2w,3w . . . cor-
responds to the absolute motion of the body up to the points 1, 2, 3,
: ; evidently therefore we can find the positions at the mo-
ment —o Of those points 1, II, III .°... of the rotating sur-
face which will come in contact with the body after 1, 2, 3 cae
seconds, by going toward them in a direction contrary to the mo-
tion of rotation of the surface along the concentric circles through

62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

t 23)... 40. by the ares ¢ bl at, eae eG. onespettivelss
From this follows in a striking manner the important result that
the relative “inertia path” consists of a circle which will be de-
scribed twice in the absolute time of revolution T and in such a way
that the direction of the rotation is opposite to that of the rotation
of the surface.

4.665 S55 5e5cei
ATT RSE
II. WUT ZA SEIN IN|
Zee

eRe eA Se ea
: Nvecumn
Sa ee Oe ee ae ee

Sauni 7a,

ON Pic ahah Oo a
ana oi

Introducing® different modifications regarding the form of the
elliptical path and the direction in which the body traverses t,
we can exhibit clearly in a direct geometrical manner the mutual
dependence of the absolute and relative motions and also, for exam-

° Fig. 1, for example, differs from fig. 2 only in the circumstance that
the ellipse is traversed in the opposite direction; the relative velocity and
circle of inertia are in consequence about 2} times as great as in fig.r,

“a

J

PATHS OF MOVING PARTICLES—-SPRUNG 63

ple, convince ourselves that for the same relative velocity v the
circle has always the same magnitude whether it passes through the
point of rotation M or at a greater distance from it.7. There is no
tendency on the part of the moving body to remain in a circle of
latitude or to move parallel to the latitude circles as assumed in the
theories of Hadley and Dove; for every azimuth of the motion the

Sn

FIG. 2

tendency is precisely the same, that is, to deviate toward the right
from the momentary current direction of motion.
Let us now try to follow the above construction analytically.

’ By the aid of a ball of chalk rolling about on a rotating parabolic-shaped
blackboard an autographic representation of these inertia paths can be
reproduced; the unavoidable friction will only be manifest in this, that
the curves (approximately circular) become gradually narrower and _ nar-
rower. I recommend the following as suitable dimensions for this appa-
ratus: diameter of the parabolic shell, 120 cm.; depth in the middle, to cm.
In this case the time of revolution, 7, must be 2.7 seconds.

64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. §1

The relative motion will be referred to the coérdinates (¢, n), moving
with the rotating system and which at the instant t = o (as the
figure shows) coincide with x, y. Denote by B the angular distance
from the y-axis at the time ¢ in the case of the absolute motion, and
by @ the corresponding difference from the y-axis in the case of
relative motion, evidently then

BSB nt ee 5s bo ee
Further if ry denotes the radius vector at the time ?:

x=rsinB

(6)
y=rcosB |
Fi aia c)
(7)
n =rcos B
From (5) we derive
rsin 8 = rsin Bcos wt — rcos B sin wt (8)
rcos 8 = rcos B cos wt + rsin B sin wt

By substituting x, y from (2) in (6); 7 sin B and r cos B from (6)
in (8); and finally r sin 8 and r cos @ from (8) in (7); we get

E€ = (a — b) sin wit cos wt

n = bcos? wt + asin? wt = a — (a — 5) cos? wt,
But for this can be written, by application of known goniometrical
formule:

a gles sin 2 wt,
2

‘ : - (9)
7 tes Qut + as
2 2

4 (a — b) is the radius of the desired circle; and 4(a + b) is the dis-
tance of its center m from the center of rotation M on the 7-axis.
Instead now of starting with the construction of the absolute
motion, as here done, we can also follow the reverse process, assum-
ing the arbitrary relative velocity v, in an arbitrary direction as
being given for any distance b of the body from the center of revo-
Jution M@. For simplicity it will however be for the present assumed

PATHS OF MOVING PARTICLES—-SPRUNG 65

that vy is perpendicular to the radius vector b, and that v, is reck-
oned positive in the direction of rotation of the system (from west
to east). Hence v, + bw is the absolute west-easterly velocity of
the body at the time ¢ = o, for which according to (3) we have the
expression (U,)) = aw; we have therefore the relation:

v

aw =v, + bw or i Di oe sz, (LO)
w

by using which relations the equations (9) finally pass into the fol-
lowing form:

— "0 sin 2 wt,
2w
etd)
r= Yo cos 2 wt + (2 + fa
2 20
Therefore we have:
op = 52 the radius of the circle of inertia,
7)
eles
Nm =O+ = the n-codrdinate of its center
w

These equations give us all desired information concerning the
relative motion due to the inertia of the body. We first derive
d
ve = vu, cos 2 wt;
dt

But from these we have

| (dé \? a
° V(G) +9 a
that is to say, the relative motion due to inertia is a uniform one
and only distinguishable from the absolute motion due to inertia
in free space, by this, that its path is not a straight line but curved.
For the direction of rotation of the system assumed in our figure,
which agrees with that of the northern hemisphere, the center of

curvature always lies on the right-hand side of the path, since the
coérdinate 7,, of the center of the circle will be < b as soon as vp

66 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

becomes negative, that is to say, when the original relative velocity

is directed from east to west.

For vu) = 0, we have 7,, = 6, op = o and a = b, that is to say,
the point remains at rest relatively while its absolute path is a circle.

For vu = —bw, we have 7,, = + $b and a =o; the absolute
path consists of a pendulous oscillation in a straight line. When
a changes sign, that is to say, for still smaller values of the
velocity vy, the ellipses are described in the opposite direction.

For vy) = —2bw, we have 7,, = 0, oe = b,anda = —b; thecenter
m of the relative inertia circle coincides with the center of rotation
M, the absolute path is again a circle as for v) = o, but the direction
of the rotation is opposite to what it was before.

The angular velocity 2w of the relative inertia motion ts twice as
great as that of the rotation of the system, the relative path will
therefore be traversed twice during the time T of one revolution
of the system. The figures 1 and 2 also show directly, as bas
already been indicated above, a time of rotation of 12 seconds, when
24 seconds is assumed for the whole system. As now our investi-
gation may be applied with a high degree of approximation to the
region surrounding the north pole we attain at once the interesting
result that a body confined to the earth’s surface, but otherwise free
to move, will deviate from its original direction twice as much as
does the plane of the Foucault pendulum.

The value of w is 0.00007992 m, so that the length of the radius
o becomes about 69 km. when the velocity is v = 10 m. or that of a
fresh breeze; at this velocity therefore the body only passes a little
way beyond the space between two successive parallels of latitude.’

Now on a plane that is not in rotation a path can be produced,
similar to the path of inertia found for the relative motion, by intro-

ducing a physical force A = if always acting from left to right, per-
0

‘
pendicular to the momentary direction of motion, But if the value

of o given by (11’) is substituted in this expression, then we have

The motion on the rotating region near the pole can therefore be
treated as an absolute one, if in addition to all the forces customarily
taken into consideration there is introduced this other force A, which
in modern meteorology is called the ‘‘deflecting force of the earth’s
rotation.”

5’ Namely, the difference between 138 and 111 km.

a

.

4

PATHS OF MOVING PARTICLES—SPRUNG 67

A current of air in the neighborhood of the north pole can only
flow in a straight line no matter in what direction, when a force
to the amount of 2vw in the opposite direction to this deflecting
force or directed from right to left renders this departure from the
path of inertia possible; in this case therefore the barometric or
elastic pressure in the current of air must increase from the left
towards the right. In the same manner in a straight channel, no
matter in what direction it trends, the moving liquid should stand a
little higher on the right than on the left, and in fact independently
of the nature of the liquid it results that we must have®

EH , 2u0
L g

where H — H, denotes the difference of height between the two
shores of the stream, and L the width of the stream assumed to
flow everywhere with uniform velocity.

The special case of motion due to inertia in the region of the pole
has been treated so fully in the foregoing text because the construc-
tion of the paths in that region can be made on the basis of certain

*It will be proven presently that the above expression corresponds to
the following equation for any latitude 9:

g(H — A) = 2vw sin g.L

For example, if for = 50°, 2w sin Y has the value 0.0001117; for a width
of river L = roo meters and a velocity v = 10 meters there results H — H, =
0.0114 meter. Hence in every horizontal layer the pressure of the water
is by about 1.14 cm. of a column of water, greater toward the right than
toward the left. This amount certainly appears to be inconsiderable, but
geologists are accustomed to see very insignificant but constant causes
produce great results. Hence it has been attempted by the axial rotation
of the earth to account for such gradual displacement of river beds as is
seen in the frequently recurring and notable phenomenon that the right
side of a river is frequently closely bordered by a range of hills while on the

left side a tolerably broad strip of entirely flat land stretches along the

course of the river, as, for example, on the lower part of the courses of the
Elbe, Weser, Thames, Seine and Gironde and also on the Danube, Volga,
and other rivers of southern Russia where this is especially noticeable.
But recently this explanation, proposed by von Baer, has been freely con-
tradicted.

The relation between the direction of the wind and its force and the dis-
tribution of atmospheric pressure which has found empirical expression in
Buys-Ballot’s law can be easily derived from the above text. Further
details on this subject can be found in the works of Guldberg and Mohn
in the Zeitschrift der dsterreichisches Gesellschaft fiir Meteorologie, 1877,
Vol. XII, pp. 49, 177, 257 and 273; also Sprung. Ann. d. Hydr. u. maritime
Meteorol., VIII, Jahrg. 1880, p. 603, and Beiblatter, V, 1881, p. 237.

68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

well-known theorems of physics. For other geographical latitudes
the problem becomes considerably more difficult; however, even
here with the aid of our conception of the process we are enabled
to directly attain some results.

The condition of relative rest of a body on a horizontal plane in
any latitude ¢, consists, absolutely considered, of a circular oscilla-
tion (diurnal rotation about the axis of the earth) under the influ-
ence of a poleward-directed component rw? sin g of the force of
attraction of the earth which neutralizes the local equatorial tend-
ency. The forces required in the absolute motion are evidently the
same whether the circle of latitude is traversed from west to east or
east to west with the velocity rw. Inthe latter case, however, the
relative motion of the body is an east-west one with the relative
velocity v = 2rw; the latter motion is therefore, just as in the case
of relative rest, a special case of the relative inertia motion. Only
in. two very special cases of the relative velocity is it possible for a
free body to remain on a circle of latitude, whilst it was formerly
assumed that the final results of every deviation due to the rotation
of the earth consists in a motion parallel to the circle of latitude.

It can easily be seen that the horizontal radius of curvature of
the small circle of latitude (whose curvature must always be deter-
mined by comparison with the geodetic line which is a great circle

r Ak.
on the sphere) is equal to the slope ane of that cone which is tangent

to the earth’s surface at the latitude gy. The ‘deflecting force of

the earth’s rotation” is therefore in this case (2rw)? ( a 2 and
r

by using the above relation v = 2rw this can be written A = 2vw
sin g. The “‘deflecting force” at the latitude ¢@ (at least for the
velocity v = 27w) is then smaller than at the pole, where the value
is 2uw, its direction is the same as there, perpendicular to the path,
towards the right in the northern, towards the left in the southern
hemisphere, and the influence of the earth’s rotation is thus repre-
sented perfectly, because the relative motion due to inertia here
under consideration is a uniform one.

For the completion and generalization of this result the general
problem of absolute motion under the influence of the force rw’ sin ¢
directed poleward will be here treated briefly.

Denote by V the absolute velocity parallel to the surface of the
rotating body, by @ the azimuth of the absolute motion (counted
positive from the north around by the east towards the south) and

~~.
bi

PATHS OF MOVING PARTICLES—-SPRUNG — 69

by ds the differential of the path, then will the principle of living
force, vis viva or mechanical energy be represented by the following

equation:
d (4 V*) = rw? sin ¢ ds cos 0
ee. r ;
But since, as is evident at once geometrically, — FAR Mas sin 9,
then the same equation can be written:
d(4V?) = — rw? dr

from the integration of which results

| Geert TG a9) Pear et Nera en eRa By Gls")

' where Dis a constant. Again the principle of the conservation of
areas gives

GUE pom toa la roma Cara
r

In these two equations the general problem is contained, and toa
certain extent already solved. From (14) there is first derived

2
V?cos?6@ = V? — ¢
id

and by introducing the value of V? from (13)

V cos @ = peer ye eioierae tebe 1 (la)
id

The expressions (14) and (15) contain the west-easterly and south-
northerly components of the absolute velocity as functions of the
distance r from the axis; we have only to subtract from these the
velocity of the surface of the earth at the place in question to obtain
the corresponding components v sin @ and v cos @ of the relative
velocity; in this way we obtain

v sin 0 = ¢ — rw
r
. (16)

vcos 0 = 4] D — rue — &

r
By squaring and adding these equations the following is obtained:

Say Got ue time et

7° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLE. 52

Hence the velocity of the relative motion due to inertia is con-
stant at any latitude whatever on the earth’s surface, just as found
before for the region of the pole.

By a general theorem applicable to all rotating bodies, the radius
o of the geodetic curvature of a curve running in any direction what-
ever on the surface of a rotating body can be expressed by

_ rcos @ds
° d(rsin6)
If in
d(r sin 0) =rcos 0d 6+sin 6 dr

we substitute the two values derived from the first of equations (16),
having regard to (17):

cos 6d6@ = are (S+0)ar

ur
and
sind =" (©— nw)
v\r
then we have
_ _ ucos dds
~ 1 Bwar
or, since
cos@ds_ 1
--dr sing
tf gee er
2w sin g

This value of the radius of curvature p of the relative path due
to inertia corresponds perfectly to the value po = = = found above
2

(compare equation (11’). for the region of the pole, and shows that
the path is less slightly curved the more nearly the equator is
approached. For the equator itself (g = o) the path becomes the
geodetic line or great circle itself. In the southern hemisphere ¢
is negative and therefore the radius of curvature has the opposite
sign from that in the northern hemisphere. The center of curva-
ture in the one case lies on the right side and in the other on the
left side of the “inertia path.” The proof of this statement is

PATHS OF MOVING PARTICLES-——SPRUNG Fal

easily deduced by a closer consideration of the expression for sin 0
in the first of equations (16); if, for example, we introduce the con-
dition that sin 0 = o for r = 7, and write

If now we consider two places on the earth’s surface at the same
distance r, from the axis, one of which is in the northern hemisphere,
the other in the southern, then sin @ is in both cases = o, that is to
say, the motion is to be a purely south-northerly one. In the far-
ther course of these motions, however, r becomes smaller in the
northern hemisphere and therefore sin 0>0; on the contrary in the
southern hemisphere r will become greater and therefore sin 0<o;
the body therefore deviates from the meridian towards the right
in the northern hemisphere but towards the left in the southern
hemisphere.

If the motion is followed still farther (in the northern hemisphere
for example) then we have

- for the value 6 = 90° the distance r,

I

|
bo
mal
-—
a=.
pac |
a
a
DO |
e |
—

I

R 2
1AM RET; “« 9 = 279° “« “ Ts au = + . ioe a8 =

the value of 0 becomes 360° again for 7, = r and therefore in the
same geographical latitude in which 6 = 0. But it can be easily
seen that in this case the body has not returned to the meridian of
the starting place but to one lying farther west; for since the curva-
ture of the path continually diminishes while @ passes through its
values from go° to 270°, therefore the southernmost point of the
_ path must lie farther westward than the preceding northernmost
point. The motion is therefore enclosed between two definite par-
allels of latitude and carries the body in many nearly circular con-
volutions gradually toward the west. Presumably this progression
is connected with a peculiarity of the corresponding absolute motion
which the latter has in common with a peculiarity of the spherical
pendulum; in this latter case it is known that the successive tempo-
rary highest positions show a regular advance in a determinate direc-
tion on a horizontal circle.

The correct representation of the relative (or absolute) path in
the form of an equation between the geographical co6érdinates gy and

72 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5a

A presupposes that the form of the rotating body is known [i. e. the
slope of the surface of revolution] therefore that r is given as a
definite function of the latitude or y = F. (yg): for example, in the
case of a sphere r = RK cos ¢: in the case of a spheroid

= R cos @
V1l—ésin?o
Since v sin 8 =r ey ,andvcos@ = —- a (=) ee therefore
dt sin g \dg/ \ dt

equations (16) would become

dA C—?rw
dt r
2 ria) eG
ee ee es ies
dt dr r
do

and from this by the elimination of dt is derived the definite inte-

gral:
: (c -- ro)
ean ae : dg dy ~. a= (20)

Pa A sin ¢ V Dr — rw? — CP

in which the constants D and C from (16) can -be expressed by the
values of v, 6, and r orfrom (14) and (15) by the values of V, 0
and r for the initial circumstances of the motion as follows:

D =v? + 27,0? + 2urw sin 6, (= V,? + 1,°w") uf
C =rZw + ur, sin 0, (= Vor, sin 8,) ue

The solution of this problem leading to elliptic integrals does
not seem to be worth the while, because in the first place the func-
tion r = F. (g) for the earth can not be given with entire certainty,
and in the second place the careful determination of the path has
only a subordinate interest in meteorology, since the notion, for-
merly entertained, that the particles of air actually follow the ‘‘inertia
path” has been completely refuted by the synoptic weather charts
that show the simultaneous conditions of the atmosphere over large
regions. It may even be asserted that in fact the direction of curv-
ature that pertains to the inertia path is not even the more frequent:

PATHS OF MOVING PARTICLES—-SPRUNG 73

in fact there are many more curved wind paths that are cyclonal
than anticyclonal.

On the contrary it is of the greatest interest to know that the
tendency towards change of direction by the rotation of the earth
is far greater and more general than was formerly supposed. The
“deflecting force” acting from left to right, corresponding to equa-
tion (12) can by substituting the value of p from (18) be written

Ay 2a) Sie tm ce oe Ge)

in which ¢ is to be taken positive for the northern hemisphere and
negative for the southern. Therefore, for horizontal motions on
the rotating surface of the earth the dynamical differential equations
in a rectangular system of codrdinates, for which the positive 4-
axis extends from the positive direction of the x-axis towards the
left, are as follows:

GS Say
= Oe a) Sine = ,
df! corse
(23)
st ARs | See Siocniee
dt? dt

In fluid motions the given forces generally consist of pressures,
so that X and Y are to be replaced respectively by

mee SS and — = 24 (where o is the density).
o \ dx o \dy

With reference to the application of these equations and their
necessary extension to motion in any direction, reference may be
made to the theoretical investigations in the domain of meteorology”
whose number has lately increased to a most encouraging extent.
Since, however, the vertical forces can be readily ascertained a short
_ discussion of these may properly follow here as a conclusion to the
preceding presentation.

For motions parallel to the earth’s surface the vertical pressure
N directed downwards, evidently has the value

2 2 2 D eqere
Fey i et eg Gov sin? 0
R 1S R,

10W. Ferrel: Meteorological researches; Reports of the Superintendent
ot the U. S. Coast and Geodetic Survey for 1875 and 1878.

C. M. Guldberg et H. Mohn: Etudes sur les mouvements de l’atmos-
phére; programme de 1’ Université de Christiania pour 1876 et 1880.

J. Finger: Wien, Sitzungsberichte, Jahrg. 1877, 1880.

74 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

in which G is the vertical component of the accelerating force of
attraction and R the radius of curvature of that normal section
which is tangent to the direction of the absolute motion; Rk, and R,,
however, denote the radii of curvature of the principal normal
sections of the rotating body, respectively parallel to the meridian
and to the circle of latitude for which we have in fact:

wena sin ae
R, ? ar
1 cosg

jee r

For 86 must be introduced the azimuth @ of the relative motion;
from (14), (15) and (16) we have

V cos 8 =vcos@

V sin@ =vsin@ + rw

From all this we obtain

R; R,

Ky K,

v'cos?@ v® sin? é rw 2rvw sind
G - ( += ) Sipe ie ey
or, by introducing in the last two terms the preceding expression
for ik,;

N =G — ru? cos ¢ — 2 ww cos y sin 8 — sin chm igre (24)
in which R’ denotes the radius of curvature of the normal-section
parallel to the direction of the relative motion. The first two terms
represent the local acceleration g of the force of gravity™

G' =F’ 008 @. = 2s sO, ep ee

If the motion of the body has a vertical component, then the
same equation (24) will apply if the v therein is made to denote the
velocity of the horizontal projection of the motion, and @ its azi-
muth. The magnitude of the force N will be changed slightly by
the vertical component of the motion only when this latter motion

dah mee
is not uniform and in fact the change corresponds to a which is

The apparent force of gravity or the vertical component of the attrac-
tion of the earth minus the vertical component of the centrifugal force.
CsAs

PATHS OF MOVING PARTICLES—-SPRUNG 5

the expression for the vertical acceleration, ‘The entire system
of vertical forces must be considered as a modified force of gravity
g, and therefore it must be introduced, instead of g alone, in the
differential equation dp = —o g dhof the barohypsometric formula
if it is desired to take the state of motion of the atmosphere into
account in the derivation of the hypsometric formula. According
to the equation for the gaseous condition the density o is dependent
on the pressure p and the absolute temperature T in the following
manner:

pP=akKT

where K is the gas constant for atmospheric air.

If the change with altitude in the composition of the air is left
out of “account and the decrease of the temperature upwards, in
accordance with the usual custom, is assumed to be constant so
that T = T, — eh then there results finally the following equation

Kk? se Mati € — 2uw cos ¢ sin? — eee hae) (26)
p T, — ch R’ dt

(Strictly speaking g is also a function of the height h and the
geographical latitude gy.) This equation is of great importance in
meteorology inasmuch as it gives us the means of determining the
horizontal distribution of pressure at any altitude h, in case this
distribution is known for any other altitude (for example, at the
mean level of the ocean where # = 0), and provided sufficient
initial points are given for the estimation of the condition of the
atmosphere as to temperature,and motion.

For the purpose of illustration and investigating briefly the mag-
nitude of the influence of the horizontal motion of the air on the

vertical distribution of pressure, it will be assumed that the tem-
d? S.
perature everywhere = 7), therefore « = 0; since also se worthere-

fore by integration there results:

Po ( . ae
Lf Klee ht — 2 vwcosesin 0 — — }.
0 p ( :] 2 J) @ R’

For an atmosphere at rest we should have

DTG ROS (Ups ew ae el Fo eT
Pp

76 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. §1

If now it is assumed that p (the atmospheric pressure at the upper
level) has the same value in both equations, then by subtraction
there results:

7 2
(ga a: =(4 -- I.) (200 008 ¢ sind + F).
Pp KR’

If in this we replace h — h, by its value from (27) and the ratio

Po

re!

ae 6} : :
etc., by the ratio = etc., from the recorded barometric readings

we have finally:

Bo -(%)? (2.0 cos g sin 0 + @) eer)
i, B

For example, let B = 620™™ denote the reading of the barom-
eter on the Schneekopfe, B, = 748™™ the corresponding reading
of the barometer at Breslau, the difference of level being about
1450™); also let v = 30™, (the velocity of a violent wind storm),
and » = 51°; then by computation the exponent on the right of
equation (28) is found to be

0.000 280 8 sin@ + 0.000 of4 4.

The extreme values of this exponent and the corresponding values
of B, at the level of Breslau are as follows:

nm
Exponent. Bo

for 6 = 90° (west wind); 0.0002952 747.958
for @ = 270° (east wind); —0.000 2664 748.037

From this it follows that under the same circumstances in other
respects, the pressure on the lower side of a stratum of air 1450”
thick, moving with a horizontal velocity of 30 m. p. s. and having
an equal pressure at the upper side in the two cases will with an
east wind be about 0.079™™ higher than with a west wind. If

the term 7 had been neglected then for the west wind there would

have resulted B, = 747.960 and the difference between the west and
east wind would have been 0o.080™™. The influence of this term
is therefore very inconsiderable.

Moreover the whole effect of the horizontal movements of the
air must be called very insignificant because a change of pressure
of o.0o8™™ can scarcely be observed with our barometers.

|
‘
i

PATHS OF MOVING PARTICLES—-SPRUNG ‘ilall

Since the horizontal forces conditioned on the axial rotation of the
earth are of the same order as the vertical ones just considered
(equation 22) and become equal to them at the latitude 45°, there-
fore the question arises, how comes it that the first are of such great
importance in naeteorology; the reason lies simply in this that much
greater dimensions come into play in horizontal directions. It
frequently happens indeed that the whole region between the Alps
and southern Scandinavia is occupied by one and the same current
of air, in which the difference of pressure on the two sides of the cur-
rent (measured in a horizontal direction perpendicular to the iso-
bars) amounts to 30 or 4o™™. From this there results a “‘Gra-
dient” of 2.5 to 3.3™™ (for the unit length of one equatorial degree
or 111 km.), whereas for a distance of 14 km. (corresponding to the
vertical distance above considered between Breslau and Schnee-
kopfe) there.results a proportional difference of pressure of 0.039™™,
a quantity that is no longer measurable with our barometers.
Therefore if at about latitude 50° a parallelopiped of air extending
from west to east of 1.5 km. height and breadth and previously at
rest were set into a condition of stormy motion then the simul-
taneous difference of pressure for the surfaces lying opposite each other
in a horizontal as well as a vertical direction, must change by about
o.o4™™. Inversely the production and maintenance of such an
insignificant difference of pressure would suffice to gradually bring
about these same stormy motions; but the fundamental fact is that
the horizontal difference of pressure suffices for this purpose and
we should conceive the processes as going on toward completion in
the following order:

At the start the motion of the air takes place in the direction of
the gradient, but this is departed from more and more with increas-
ing velocity and diminishing acceleration of the wind, until the
direction of its motion when it has become uniform finally stands
perpendicular to the direction of the gradient or at least approaches
this perpendicular direction to a certain degree, because of the
action of frictional resistances which render necessary the introduc-
tion of a component of the gradient parallel to the motion of the air
and directed forward with it. The change of the vertical differ-
ence of pressure is to be considered as primarily a consequence of
the circumstances of the motion since the effect of the latter can here
be conceived of as a mere diminution of the force of gravity.”

12 See the exponent of equation (28) where the influence of velocity opposes
that of gravity.— ABBE.

78 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. Si

Another important question is that of the relation between the
vertical distribution of pressure and the motion of the air in the
vertical direction. If there are no motive forces present except
the difference of pressure, then equation (26) is to be applied in this
case and for v = o it becomes:

dp dah
fe: pee a | nS Pe ee ee
jones (e+ 52) (29)

2
It will be assumed that ae = bisaconstant quantity. Proceeding

in a method entirely similar to the preceding we finally get

= =f oe
Be Bo g
ee oni a es ares Ee

where B, is the value of the barometer-reading B at the lower level
under the condition of uniform motion throughout the whole mass.
If, for example, it is asked how great b will become in the case of the
values used above for B, and B when the relation B, X 748.1 =
By, X 748.0 exists (when therefore the difference of pressure is about
0.1" greater in the condition of accelerated motion than in that
of rest or uniform motion), the result is, there will be an upward
directed acceleration of b = 0.007 meter per second.

If the air has simultaneously an east-west component of velocity
to the amount of 25 to 30 m.p.s., then the diminution of the pres-
sure from below upwards will become about 0.10 + 0.04 = o.14™™
greater than in the condition of rest.

If in any manner whatever an increase of the vertical difference
of pressure of o.1™" should be brought about and maintained,
for example, by an upward directed removal of air at any altitude,

then an ascension of the air must take place and by integration of
th ; ;

the above equation =o = b for uniformly accelerated motion, the

velocity which a particle of air attains in passing over a distance

h — h, of 14 km., can be deduced. As bis assumed to be con-

stant there results:

dh | 200
—=4/2b(h-h
7 ( 0)
For the above value of b = 0.007 and for h—h, = 1500™ we obtain

dh = 4.58™ per second. In this vertical motion, as is known,
there appears again a horizontal component of motion in conse-

PATHS OF MOVING PARTICLES—-SPRUNG 79

quence of the rotation of the earth, in case such motion is not pre-
vented by differences of pressure. In an ascending motion the
tendency to deviate toward the west is represented by the expres-

sion (Gr) w COs ¢ as can be very readily proved by the aid of the
a

principle of the preservation of areas.

Vial

THE THEORY OF THE FORMATION OF PRECIPITATION
ON MOUNTAIN SLOPES

BY PROBES P. POCKELS
School of Technology, Dresden, Germany
[Translated from Ann. d. Physik, (4) Vol. IV, pp. 459-480. 1901]
Reprinted from the Monthly Weather Review for April, 1901

It is a well known principle of climatology that the side of a
mountain range which is turned toward the prevailing wind has in
general a greater precipitation than the plain on the windward
side, and a still greater in comparison with the leeward side of the
mountain range. There has been no doubt as to the explanation
of this phenomenon since it has been recognized that the principal
cause of the condensation of the aqueous vapor is the adiabatic
cooling of the rising mass of air; for a current of air impinging against
rising ground must, in order to pass over it, necessarily rise. So
far as the author knows, however, no attempt has yet been made to
investigate this process quantitatively, except perhaps, for the
stratum of air immediately contiguous to the earth, whose ascension
being equal to that of the surface itself, is thereby known directly.
Such a quantitative treatment will be attempted in the following
article. Even although this is only possible under special assump-
tions which represent nature with the closest approximation, it will,
however, always offer a practical basis for estimating the purely
mechanical influence exerted by the configuration of the surface
of the earth on the formation of rain.

I

In order to find the standard vertical components of the velocity
of the air currents that determine the condensation, we must, first
of all, solve the hydrodynamic problem of the movement of the air
over a rigid surface of a given shape. In this connection we must
make a series of simplifying assumptions, as follows:

1. The current must be steady; 2, it must be continuous and
free from whirls; 3, it must flow everywhere parallel to a definite

80

PRECIPITATION ON MOUNTAIN SLOPES——POCKELS 81

vertical plane, and consequently depend only on the vertical co-
Ordinate (y), and one horizontal codrdinate (x); 4, the internal fric-
tion, as well as the external (or that due to the earth’s surface),
may be neglected; 5, at great heights there must prevail a purely
horizontal current of constant velocity (a). As to the configura-
tion of the ground, we must, corresponding to proposition 3, assume
that the profile curves are identical in all vertical planes that are
parallel to the plane of x; 6, and further, we assume the surface
profile to be periodic, that is to say, the surface of the earth is formed
of similar parallel waves of mountains without, however, deter-
mining in advance the special equation of the profile curves.

If we designate by uw and v the horizontal and vertical components
of velocity and by ¢ the density, then, in consequence of assumptions
t and 3) there follows the condition

OE #) d (ev) Lay
Ox oy

and in consequence of 2 there must exist a velocity potential, ¢,
which, according to 3, can only depend upon x and y, so that

u ete ee end eee) +- ie) = 0.
Ox oy Ox Ox oy \ oy

If we consider that the density of the air (excluding large differ-
ences of temperature at the same level) changes much more slowly
in a horizontal than in a vertical direction, then we can regard ¢ as
a function of y only, and obtain for ¢ the differential equation—

_ 08 09

e4o = ae
fe oy dy

(1)

The law of the diminution of density with altitude will, strictly
speaking, be different for each particular case, because the vertical
diminution of temperature in a rising current of air, which deter-
mines the rate of diminution of density, depends upon the conden-
sation. But it is allowable, as a close approximation and as is
usually done in barometric hypsometry, to assume the law of dimi-
nution of pressure which obtains, strictly speaking, for a constant
temperature only, and which, as is well known, reads as follows:

82 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

where q is a constant and has very nearly the value of 1/8000 if
y, the difference in altitude, be expressed inmeters. Inthis casethe
following also holds good:

log =qy,
€
and, consequently,
hee =a
Be oy

0
ae =p ae ae ee
A solution of this differential equation that satisfies the assump-
tions 5 and 6, is given by the expression
Gg =a (eS loos nt ea eee (3)

in which the following relation exists between the constants m and
n,

mM? —n? = qn; !
n= — 3 +r, where r = V m+ q?/ 4. AS)

In order to ascertain what profile or configuration of the ground
corresponds to the current determined by this velocity potential,
we must look for the lines of flow; for one of these must certainly
agree with the profilecurve. The differential equation of the stream
lines reads as follows:

dy:dx = ae Lie abncosmx.e-™:a (1+ bmsin mx .e~"").
Oy Ox

The integration of this equation gives

got ein ieee = Ber ew hae en
bqu

wherein B represents the parameter of the stream lines.
If we assume that the curve of the profile of the surface passes
through the points x = o and y = o, then for these values B =

PRECIPITATION ON MOUNTAIN SLOPES—POCKELS 83

m/b qn,and if its ordinates are designated by 7, its equation becomes

b2" sin mx eT =e) — 1
m

or -

n ae ae
b—sin mx.e 7” = -
m

As long as 7 remains so small that for both the highest and lowest
points of the profile of the surface of the earth (q n/2)? is negligible
in comparison with unity—which is practically always the case
for the mountains that come under our consideration—we-can
write

5, ead
7 = b "sin mre; rr, sage babe yas feet (5)

r=Vm> + q/4

In these expressions b and m appear as parameters that can be
chosen at will, the first of which determines the altitudes and the
second the horizontal distances between the mountain ridges; we
have, namely, m = 27/A, if A denotes the wave length, that is to
say the distance between two corresponding points, as for example
the summits of neighboring mountain ranges.

It is easy to show that the stream line determined by the velocity
potential (3) for the configuration of the ground given by the trans-
cendental equation (5’) is the only one compatible with the general
conditions 1 to 5. Moreover, since a potential current is determined

6
single valued, for the interior, by the value of oe along the bound-

An

ary of a closed region, therefore, our solution in case it gives hori-
zontal velocities that are constant, or slowly diminish with the
altitude above the center of the valley, is also applicable to the
specially interesting practical case in which only one single moun-
tain range rises above an extended plain and is struck perpendicu-
larly by a uniform horizontal current of air. To what extent this
holds good must be established in each special case.

The horizontal and the vertically upward velocity components
corresponding to our solution are:

‘ia (li DIN SIN MR En) os is oe, a)

DME TE COSMER Ga 1 URE a eae 8 071)

84 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

It would now be desirable, in order to be able to handle the cases
actually occurring in nature, to adapt our solution to some form
of the earth’s surface arbitrarily chosen. The first thought would
be to attempt this by the superposition of a series of velocity poten-
tials of the form of equation (3) having different constants m and
b, or in other words to write

7) = >) oy =a {x — > 4b, cos m,x.e-"nY} Perera,

but we find that this solution only corresponds to a superposition
of the profile curves, that is to say, it gives

Te ms
=> n=>, iy ai a RS ae es

only when we can put the exponential functions e~"”¥ and ch” both
equal to unity. In this case y is at once transformed into the
simple trigonometrical series

7 = by 2 sin mee Ue ae
™,

and therefore, by putting m, = h m, we can develop any arbitrary
function, 7 =f (x), into a series, proceeding for any value of x
greater than zero and less than A/2. But thecondition that e+"
is equal to unity for any large value of the quantity h will not be
fulfilled for any arbitrary form of the profile curve if its maximum
altitude is assumed to be very small in comparison with the wave
length 4. Therefore, we must limit ourselves to an approximate
representation of the desired profile curve by a definite number of
terms of the series that enters equations (9) or (9’). Especially can
we in this way never attain the rigid solution for a ground profile
that has sharp angles. However, the neglected higher terms of the
series have a proportionately smaller influence on the vertical vel-
ocity at great altitudes and, therefore, on the resulting precipitation,
in proportion as their serial number h is larger.

it

As a first example, we choose a form of profile to correspond as
closely as possible to a plane, broad, valley and a plateau-like moun-
tain range, because, in this case, we may expect nearly the same
conditions on the slope of the mountain as if it were struck by a

PRECIPITATION ON MOUNTAIN SLOPES—POCKELS 85

uniform horizontal current of air. A profile curve of this kind,

A
which rises steadily between the values x greater than — 12 land

|
less than + 12 and falls also with uniform gradient between the
limits x = 5/12A and x= 7/12A, and in the intermediate region
describes a horizontal straight line at the distance + H from the
axis of xy is obtained by means of the Fourier series

24 H 1. hz .. 2hz
=¥conie sin = sine
0 oe A

where h has all positive uneven numbers. In order to represent a
profile curve of the given form approximately, we take the first
three terms of the series, and therefore have

7 =C {hsinm,x + $sin3 mx + g¢ysind5m,x}.. . (10)

The numerical values of the parameters are:

A =60000 meters, hence m, = = = 0. 1047 10

and
C = 1100 meters.

The coefficients b,, in the expressions (8) and (9) therefore, have
the following values:

b, = 881, b, = 148.3, }, = 24.8

The profile given by equation (10) is shown in fig. 1, where the
vertical scale is magnified five times. We perceive that the ascend-
ing gradient is nearly all confined to the interval between

x greater than — fe and less than + ue
12 12

where, moreover, it is quite uniform, and further that the surface
of the valley is raised a little in the center, and the surface of the
plateau mountain is depressed by the same amount. The differ-
ence in altitude between the center of the valley and the center of
the mountain, which according to the adopted numerical values
should be goo meters, is, therefore, not the absolute maximum
difference but is about 18 meters less. The profile curve here con-

86 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL.o$a

sidered corresponds indeed, according to what has been above said
only approximately to the velocity potential.

g =a {x — b, cos mx.e" — bg cos 8m, x.e7-74 (11)
— b, cos 5m, x.e-"4},

as determined by the above coefficients, b,, but we can easily
demonstrate that in the present example the differences could
scarcely be observed in fig. 1.

From the preceding value of ¢ we derive the following values for
the components of the velocities of the current:

u ~a4 1+ Sy mye "sin my, x |

J

= ‘ 1+ = (be "" sin mx + 3b,e "” sin3 m, x . (12)

|
+ 5b,e "sind m, x) i]
v=axX ey b,n,e "*” cos m, x
=a X 0.1152 : he" cosm, x + 46 "8" cos 3 m, x . (18)

—n
+ py e-"s” cos 5 m, x \.

Ns

PRECIPITATION ON MOUNTAIN SLOPES——POCKELS © 87

These equations show that when x = 0, that is to say above the
center of the slope of the mountain, uw is a constant = a at all alti-
tudes; above the valley where x is'less than 0, wis smaller than a;
and above the mountain, or plateau, where x is greater than o,
uw is larger thama; the constant a can also be considered the mean
horizontal velocity at any given altitude.

For different altitudes H above the center of the valley we have
the following values:

| | a)
H =450+ y: | ° 450 2000 | 5000

—— =|
wk —0.068 |—0.0676 | — 0.0675 |

—0.0646

Thefefore, up to the altitude of 5000 meters, the horizontal
velocity is sensibly constant and the vertical velocity 0; and, accord-
ing to what is said in reference to equation (5’) our solution holds
good for the case when the profile is continued as a horizontal
straight line indefinitely toward the negative side from the point
x% = — A/4, and above this there flows a truly horizontal current of
air whose velocity is sensibly constant, namely, 0.93 a up to an alti-
tude of 5000 meters and increases in the strata above that until
it attains the value a.

Above the mountain, as at the point where x = + A/4, the velo-
cities, u, are greater than a by nearly as much as they are smaller
above the valley.

The distribution of the vertical velocity component which deter-
mines the condensation of aqueous vapor is a more complicated
matter. In order to represent it, let the values of v/a for different
values of the codrdinates x and y be as given in the following table:

z
» :
ea | ee ee +4 | +4
| I SUas| 6 4
500 0.099 | 0.0406 | 0.0129 | —0.00r2 °
1,530 0.0842 | 0.04075) 0.0149 | +0.00226 °
2,440 0.0740 0.0400 0.0182 | 0.0064 °
3,460 0.0651 0.0387 0.0206 0.0093 °
4,530 0.0575 0.0370 0.0217 0.0108 °

Therefore, whereas there is a steady decrease of v with altitude
above the center of the slope of the mountain, on the other hand
these vertical velocities increase with the altitude in the neighbor-
hood of the foot of the mountain as well as on the plateau at the

88 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

point x = + 2/8 up to a maximum at some very great altitude.
(The isolated negative value that occurs for x = 4/6 and y = 500
is explained by the above-mentioned slight depression of the sum-
mit of the plateau mountain.)

In order now, to investigate the condensation of aqueous vapor
that occurs in consequence of the ascending currents of air forced
upward by the upward slope of the ground, we first make the assump-
tion that the ascending mass of air experiences an adiabatic change
of condition and that adiabatic equilibrium prevailed already in
the horizontal current of air advancing toward the slope of the
mountain. In this case the air will be everywhere saturated at a
certain altitude that can be computed from the temperature and
humidity of the air at the surface of the valley. In a unit of time
the quantity of air, ve, flows in a vertical direction through a space
having a unit of horizontal surface and an altitude dy. If this
element of space lies above the lower limit of the clouds, then in
this quantity of air there will be as much aqueous vapor condensed
as the difference between what it can contain in the state of satur-
ation at the altitude y + dy and what it can contain at thealtitude
y. Therefore this quantity is

VE.

F
dy,
oy

where F (y) is the specific humidity of saturated air at the altitude

y.
Still assuming a stationary condition, we have—

vy’
ae foer (y) dy, (14)

Yo

as representing the total quantity of aqueous vapor condensed in a
unit of time in a stratum of cloud above the unit of basal area be-
tween the altitudes » and y’.

This would also be equal to the quantity of precipitation falling
from that layer of cloud on to the unit of horizontal basein case the
products of condensation simply fell vertically without being car-
ried along by the horizontal current of air. We will make this
assumption, since as yet we have no clue by which to frame a com-
putation of the horizontal transportation of the falling particles of
precipitation. It is, however, easy to foresee that the horizontal
transportation would be of importance, especially for the slowly-
falling particles of water or ice in the upper strata of clouds, and

PRECIPITATION ON MOUNTAIN SLOPES-——POCKELS 89

that on the other hand, the larger drops that carry down with them-
selves the water condensed in the lower strata of clouds will fall
at a relatively slight horizontal distance. But now, as the numer-
ical computation shows, the lower cloud strata contribute relatively
far more to the condensation than the upper clouds; therefore, the
influence of the horizontal transport will not be so very large, at
least with moderate winds. Moreover, this influence does not affect
the total quantity of precipitation caused by the flow up the moun-
tain side, but only its distribution on the mountain slope and it
consists essentially in a transfer of the location of maximum pre-
cipitation toward the mountain. In this sense, therefore, we have
to expect_a departure of the actual distribution of precipitation
from that which is theoretically given by the computation of W
as a function of x, according to equation (14). This departure will,
under otherwise similar circumstances, be considerably larger in the
case of snowfall than in the case of rain.

As concerns the upper limit y’, which is to be assumed in the
integration of equation (14) in order to obtain the total quantity
of precipitation falling upon a unit of surface, we have to substitute
for y’ that altitude at which condensation actually ceases in the
ascending current of air. Theoretically, if from the beginning
adiabatic equilibrium prevails up to any given altitude, then the
condensation brought about by the rising of the earth’s surface
must also extend indefinitely high, even to the limit of the atmos-
phere, since the vertical component of velocity diminishes asymptot-
ically toward zero. But practically, our solution of the problem
of flow probably no longer holds good for very high strata, and cer-
tainly the assumption of adiabatic equilibrium does not hold good;
but even if the latter were the case, if therefore, the ascending cur-
rent carried masses of air from the surface of the earth up to any
given altitude, still, in consequence of the increasing weight of the
particles of precipitation carried up by the ascending current on the
one hand, and the increasing insolation on the other hand, an upper
limit of cloud must be formed ?

We will therefore assume as given some such upper limit of clouds
at a definite altitude, and for simplicity will assume this to be the
same everywhere. The value of this altitude, y’, is the upper limit
of the integral (14). However, the altitude assumed for y’ if it is
large, namely, many thousands of meters, can have only a slight

?'W. von Bezold: Sitzb. Ber. Akad. Wiss., Berlin, p. 518, 1888, and p. 303,
1891.

go SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

influence on the value of W, since both—F’(y) and ve rapidly
diminish with the altitude.

For the numerical computation of W, it is advantageous to first
bring the expression (14) by partial integration into the following
form:

,

y
Yo Oev ¥ Fe
W (x) -|veFo | + [Foy Sedy.. . siohidas
y edt

Yo

In this expression v is given by equation (13) as a function of y
and x. f(y), or the saturation value of the specific moisture at the
altitude y, as well as the corresponding values of the pressure and
temperature necessary for the computation of e are most easily

obtained with the help of the graphic diagram for the adiabatic - .

changes of condition of moist air first given by H. Hertz, since
a simple analytical expression for these quantities cannot be given.
In using the Hertzian table* we have to remember that y is not the
absolute altitude but the altitude above the axis of x in our system
of codrdinates, therefore, in order to obtain the altitude above sea
level, it is still to be increased by the quantity ~1( x =— ) and
also by the altitude of the valley above the sea. The integral in
equation (14a) can be evaluated with sufficient accuracy by divid-
ing the integral from y, to y’ into parts Vpo..-Vy, Vy----Var Var += Va
(where y, = y’), and for each of these introducing an average
value F,,,, whereby we obtain equation(15).

Uh h
fFo no ay = Dhan | oe - Go). | _. (15)
Yo 0

In order to execute the complete computation of W for a special
example, we will assume that the current of air which strikes the
mountain having the profile shown in fig. 1 has a pressure of 760
millimeters, temperature 20°, and specific humidity, 9.0,* at the
bottom of the valley. Hence, according to our assumption of adia-
batic equilibrium it follows that the lower limit of the clouds will
lie at an altitude of 950 meters above the bottom of the valley, and,
therefore, 50 meters above the center of the mountain, if yy = 500;

3H. Hertz: Met. Zeit., Vol. I, pp. 421-431, 1884, or the preceding collec-
tion of translations, 1891, p. 198.
* That is, 9.0 grams of water per kilogram of air.

a

—"

PRECIPITATION ON MOUNTAIN SLOPES——-POCKELS Ol

the specific humidity is at this cloud level, F (y)’ = 9.0, and the
temperature is 11° C. We will further assume that the upper limit
of the clouds is at an altitude of about 5000 meters, or y’ = 4530
meters, where the temperature has sunk to —13.6° and the specific
humidity to M(y) = 2.5. At the altitude of 3000 meters the tem-
perature o° C. is attained. The application of the Hertzian tables
assumes that for temperatures below o° C.the product of condensa-
tion is ice; whether this is really true is at least questionable for
moderately low temperatures, but the assumption that water below
the freezing point is precipitated will not change the results very
much. Since corresponding to the assumed stationary condition,
we have to assume that all condensed water immediately falls from
the clouds; therefore, in our computation we have to omit the hail
stage of Hertz, in which the water that is carried along with the
cloud is frozen.°

For the computation of the integral according to equation (15)
the cloud is divided into four layers whose mutual boundaries or
limits occur at y, = 1530, again y, = 2440, and y, = 3460 meters;
for these altitudes we have ¢ = 1.00 and o.g12 and 0.816, and cor-
responding to these F(y) = 6.9 and 5.35 and 3.8.

We thus find the following values for W/a:

A A A
Po eee + Hebe
12 8 6
W
ter 0.475 0.241 0.0985 0.0081 grams per second per

square meter.

From this table we obtain the depth of the precipitation in milli-

meters per hour by multiplying by 3.6; the result is shown in the

lower curve of fig. 1. The values of the precipitation for a mean

horizontal velocity of the current of 1 meter per second are as fol-
lows:

A A A A A

Beet eee OS ue oe = + dee ys 4

; 24 12 8 6 4
W= 171 1.47 0.867 0.355 0.029 0

Hence, the precipitation is heaviest above the middle of this slope
of the mountain, where for the very moderate wind velocity of 7
meters per second, it attains the very considerable rate of 12 milli-

5 The influence upon the adiabatics of condensation, whether we assume,
as in the Hertzian table, all condensed water to be carried withit or to imme-
diately fall away, is of no importance in the present problem.

Q2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

meters per hour. In this connection it is, indeed, to be remembered
that we have assumed exceptionally favorable conditions for the
precipitation in that we have assumed the onflowing air to have been
already fully saturated throughout the whole 4000 meters in depth
of the layer between y and ¥.’

The comparison of the curve of precipitation with the curve of
profile in fig. 1 shows that although the maximum of precipitation
coincides with the maximum gradient of the slope of the mountain,
yet the depth of precipitation diminishes more slowly toward the
plane of the valley and the plateau of the mountain than does the
slope of the earth’s surface; thus, for instance, the latter slope at
the point where + = + A/12, and which is given by 07/0 x, amounts
only to 1/20 of the maximum slope, while the precipitation at this
point is more than 1/5 of its maximum value. Therefore, under the
conditions here assumed, the effect of a mountain slope in producing
precipitation makes itself felt in the plain lying in front of the foot
of the slope. All of which agrees with actual experience.* The
fact that in reality the maximum precipitation appears to be pushed
more toward the ridge of the mountain is certainly partly explained,
as well as suggested, by the horizontal transportation of the pro-
ducts of condensation in the clouds, but also in part by the departure
of the real distribution of temperature and moisture from that here
assumed. (See Section IV, page 95.)

The determination of the total quantity of precipitation caused
by the mountain slope will be attained if we integrate the value
of W as determined by equation (14) as a function of x between the

limits « = — 4/4 and x = +A/4. The result is, therefore,
+ = y’ +
G =| woadr~- [ery id tye
Ba Yo Pinok
z

In this equation, according to equation (13) we have:

»|>

+

2 1
vd x =a X 1100 f e-"4¥ — _¢g *Y 4 eo ™Y \.
it 9 25

wl
cS

6 Hann: Climatology, 2d Edition, Vol. I, p. 295; also Assmann, Einfluss
der Gebirge auf das Klimat von Mittel Deutschland, p. 373, 1886.

PRECIPITATION ON MOUNTAIN SLOPES—-POCKELS 93

For our present example we find G = 51o00a grams per second
over a strip 1 meter wide and about 22 kilometers long. Hence,
there follows for the average precipitation for the whole mountain
slope

W,,,’ = 9.833a millimeters per hour.

Dis

In the example we have just discussed the lower limit of the clouds
was higher than the summit of the mountain. If the reverse is the
case, then, for that portion of the mountain slope that is immersed
in the clouds we must take 7 instead of vy) as the lower limit of the
integral in the formule (14) to (16): therefore, the theoretical dis-
tribution of precipitation would no longer be symmetrical with
respect to the zero point on the axis of abscissas. As an example
of this case we will consider the flow of air above the ground profile
that is represented by the simple equation

7 =C sin m x.e7
As to the constants we will adopt the following:

C = 1000 meters, A = 24000 meters;
hence m = 0.262 1073, f= (200 x 10>",

and for the vertical coérdinate n we find from equation (5)

se ee ani uf ies pes ey un
4 6 12 12 6 4
n = — 1495 — 1194 — 585 0+ 444 + 715 + 805 meters.

The resulting curve is shown in fig. 2. The altitude of the sum-
mit of the mountain above the plain of the valley amounts to 2300
meters. The valley may be 100 meters above sea level; the atmos-
pheric pressure in the valley is assumed at 750 millimeters, the tem-
perature 23°, and the specific humidity 10 grams of water per kilo-
gram of air. From the Hertzian table we find the lower cloud limit
at the altitude of 1220 meters, that is to say at y = — 375. ‘The
upper limit of the clouds is assumed at y’ = 2400 and, therefore, at
4000 meters above sea level. Therefore, for that portion of the
clouds lying below the summit of the mountain, which is limited
to the negative values of the abscissas up to x = — 1.35 kilometers
approximately, since according to equation (7)

v = Camcosm x.e—™

94 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

we have:

, ,

y
W=- fevrdy = —aCmcos ms fe P" (vy)e“ dy
Yo Yo

=acosmx X 1.09.

Therefore, the depth of the precipitation will here be represented
by a simple cosine curve and, in general, corresponds to the slope
of the mountain, which is computed from equation (5’) by the
expression :

dn Cmcosmx.e™

ied 4+ Crsin mx.e7*

For the region lying above the lower cloud limit ), the value of
W(x) cannot be represented by a simple function of x. We find

FIG. 2

the precipitation in millimeters per hour for a horizontal velocity
a =1, as follows:

bona =) —6" = 9 | A
Whiet = 0 01/106 yay RaOl et aae
Pore: sssy<7 0 he ar8 ee

W' =3,50 2.94 1.95 0.88 _ G, (17 te cloud:

The distribution of precipitation, as given by these figures is
shown in fig. 2 by the curve of dashes. The curve of dots repre-
sents the symmetrical line that would obtain if the mountain were
not immersed in the clouds. The location of maximum precipita-
tion is 3.93 for x = o and is 3.68 for x = — 1.3.

PRECIPITATION ON MOUNTAIN SLOPES——POCKELS 95

The total quantity of precipitation is computed by the formula:

,

y
G = — aCsin ma |e Peper n Sag
+ Yo
and is approximately equal to 22730; this is distributed over a hor-
izontal strip 12000 meters in length, and therefore, for a uniform
distribution for a = 1 the precipitation averages 1.9 millimeters.
From the preceding expression for G, it is plain that for any given
altitude of the mountain summit G will be smaller the shorter and
steeper the slope becomes, that is to say, the smaller the value of A
is, since the exponent my increases with diminishing values of 2.
In the present case the horizontal velocity of the wind is given hy
the expression:

2
U ag =a(1 4- Gut sin m.e-*” )
Ox nN

=a(1 + 0.332 sin mx.e"");

which attains its minimum, = 0.547a, at the bottom of the valley,
and its maximum, 1.283 a, at the summit of the mountain, and has
a for the mean value of all the horizontal planes. Above the center
of the valley, it increases gradually with altitude, asymptotically
approaching its limiting value, a; for example, at the level y = 0, it
is equal to 0.668a, and at the level y = 2400 it is already equal
to o.80a. Therefore, if the stream under consideration proceeds
from a point x = —J/4, as a purely horizontal current of air flow-
ing over a plain, then its velocity must diminish with the altitude
in the ratio e-™. This would, of itself, be a plausible assumption,
but there would then be a vortex motion for each horizontal cur-
rent of air, which cannot, strictly speaking, continue steadily in
the above assumed potential motion.

IV

The assumptions hitherto made by us, namely, that the distribu-
tion of temperature in the current of air that impinges upon the
mountain side already corresponds to the condition of indifferent
equilibrium, that is to say that it is the same as would occur in an
ascending current of air under adiabatic changes of condition, is in
general not actually fulfilled. The scientific balloon ascensions at
Berlin have recently given us reliable conclusions as to the real con-
ditions of temperature and moisture in the free atmosphere up to

96 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

altitudes of 8000 meters. The mean values of the temperature
and moisture at successive levels, 500 meters apart, which von
Bezold has deduced’ from the observations of Berson and String
show that the mean vertical diminution of temperature is slower
than the adiabatic, and that, in general, the moisture does not attain
the saturation value. Ina horizontal current of air, in which these
average conditions prevail, the air will, therefore, never be satu-
rated, and, consequently, our assumption of the existence of a con-
stant lower limit to the clouds is not allowable. Moreover, it is no
longer the vertical component alone that controls the condensation
that shall occur at any given point in the current of air ascending
above the mountain slope, as was assumed in the derivation of
formula (14). We must rather, in the computation of W, consider
that the quantity of water condensed in a unit of space under steady
stationary conditions is equal to the excess of the quantity of water
vapor flowing into the space above that simultaneously flowing out.
For one cubic meter and one second this excess is:

z oe i a —
0x oy
or since because of the equation of continuity we have approxi-

mately
Oeu dev

eg ee aah,
Ox oy
therefore,’
( oF =
=—€é uUu — + 5 ie ’
Ox oy
and hence,
y’
oF OF
w= — fe(uge +oo%) ay. vy ne
OS oy
y

where y° and y’ indicate the altitudes of the limits of the clouds
above the point under consideration. The evaluation of the inte-
gral still demands not only a complete knowledge of the stream, but

7W. von Bezold: Theoretische Betrachtungen, etc. Theoretical consid-
erations relative to the results of the scientific balloon ascensions of the
German Association for the Promotionof Aeronautics at Berlin. Brunswick,
1900, pp. 18-21. (See No. XIV of this present collection).

®In so far, namely, as the quantity of the aqueous vapor condensed in a
unit of volume is inappreciably small in comparison with the total quantity
of moist air flowing through this space.

-

also the determination of the cloudy region, that is to say, that
region in which the atmosphere is saturated and the distribution of
temperature therein, since the latter first gives us the value of F.
To this end we have to follow the adiabatic change of condition of
the air along each curve of flow, starting with the given tempera-
ture and humidity, in the vertical above the center of the valley
where x = —A/4, where the current is truly horizontal.

By connecting together those points in the individual stream lines
at which saturation is just attained we find, first, the contour of the
cloudy region.

Since the form of the cloud is also of interest in and of itself®
therefore its determination will be carried through as a part of our
second example, in that above the center of the valley, where
x = —Y/4 first for the summer, then for the winter, we make some
assumption as to the mean distribution of temperature in accord-
ance with von Bezold’s collected data, on page 21 of his memoir
above quoted. In accordance with this, we have:

For y = —1500 —600 +400 +1400 +2400 meters.

PRECIPITATION ON MOUNTAIN SLOPES——-POCKELS Q7

Valley above sea Height above sea

level 100 m. level, 4000 m.
meee e711 0” 5.38°, 60.0% 80
i =) 8.25. 70209 — 4259 3.03 2.60*
Fr kee f= 0.2? ~.07,6° =—5.1°. —10.8° —14.6°
(E> 208 2.17 1-64 °° 1.19 0.86

In place of the value of F’, designated by a star, we will take that
value (2.2) that results from the smoothing out of the protuberant
corners which the curve for F (see von Bezold, fig. 11,) shows at
the altitude of 4000 meters.

According to equation 5 the lines of flow have for their expression

Se m
e"’ sin mx = — —__ + Be 2,
bqn
or if y, is the value of y when x = o, and y — y = 7, there results,
: m
en e7” Yo hn yh oe == oe (e2” a 1):
bqn
bn : 1 ay ee a
meson loi se Rin Mh 0G) =e (eine Pe He
m q\

®9Tt seems, for example, quite possible to argue from the observed bound-
ary of the clouds inversely to the percentage of moisture in the current of
air flowing toward the mountain slope.

98 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

With the same degree of approximation as before the right-hand
side of this equation can be put equal to 7; therefore the equation
takes the following form:

7 => sin mx.er" e-™™ 5 capil eo 5 orem

which differs from equation (5’) of the profile curve of the ground.
only through the factor which is constant for each line of flow, which
factor causes the amplitude of the waves to steadily diminish up-
ward.

FIG. 3

If, now, the lines of flow are made through a definite point 7’,
for the vertical and x = —A/4, then for this point we determine the
appropriate value 7’ from the transcendental equation:

i eee BO i een ee ee
m

and then substitute 7, = y’,— 7’ in equation 18.

In this way we have computed the four lines of flow whose initial
and lowest points are at the altitude above sea level of rooo, 2000,
3000, and 4oo0o meters, and which are drawn as curves I, II, III,
IV, in fig. 3. The highest points of these curves are at the altitudes
2940, 3610, 4333, 5100 meters, respectively.

4

PRECIPITATION ON MOUNTAIN SLOPES——-POCKELS 99

If now, by means of the Hertzian table, we determine the altitudes
at which condensation begins at the base curve o and for the curves
I, II, III, IV, then assuming the above given values” of ¢ and F we

find the following results:
,

0 I II EET IV
Mor the summer... ......... 930 1570 2730 4060 (5125)
Porthe winter ............ 600 2070 3100 41380 5100

In the summer, according to this table, condensation will not
take place on the stream line IV, since its summit lies at the alti-
tude of 5100 meters; the summit of the clouds will, therefore, lie
a little below this. Inthe winter, the summit of line IV accidentally
agrees with the summit of the cloud. In the construction of the
cloud limit, introduced as a dotted line in fig. 3, and indicated by
S for summer and W for winter, we have also used the lines of flow
midway between o and I, and I and II, respectively."

We can now, with the help of the Hertzian table, easily find the
quantity of water condensed in every kilogram of moist air as it
progresses along any one of the lines of flow that we have constructed,
either in its totality or as it passes successive vertical lines: we thus
attain the following values of the total condensation:

RENE Knee ibis a sis Ste e's bh 0 i i Ii
Por the summer. ..\...... 2.85 2.42 1.22 0.26 grams.
Por the winter... (6c. 4.. eo 0.74 0.34 0.14grams.

Let g,(z) be the quantity condensed up to the abscissa « when
moving along that line of flow whose initial point is at the altitude
h, and let H be the initial altitude of that line of flow which at the
given abscissa x intersects the upper cloud limit; moreover, let u’

10 From the above numbers it follows that an elevation of any kind of

less than 500 meters will not give occasion for condensation under average

atmospheric conditions, neither in summer nor in winter. In the summer,
for a mountain altitude of between 600 and 800 meters, a cloud will form
between the altitudes 1000 and 3000 meters, but will not touch the moun-
tain; it is only for greater mountain heights that the cloud will rest on the
mountain.

Tn an analogous way for the first example, where we have assumed a
plateau-like mountain of 900 meters altitude, we find a region of cloud which
for the average summer conditions begins at 40 meters below the summit of
the plateau and reaches up to over 3000 meters; but in winter, on the other
hand, it begins at 500 meters above the valley and rises up only about 700
meters above the mountain top; therefore, in this season it covers the moun-
tain like a flat cap.

Too SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLE gL

be the horizontal velocity of flow and ¢’ the density of the air at the
altitude h above the bottom of the valley, therefore, for the point
whose abscissa = —A/4; then will the total quantity condensed
per second above the base area one meter broad from the beginning
of the clouds to the point x, expressed in grams, be as follows:

H

G,= flue, Wah. ch 40 plage ane ae

0

The quantity of air, e u kilograms, flows in one second through a
strip of the vertical plane at x = —A/4, havingaunit width and the
height dh; but an equal quantity must flow out per second through
the vertical whose abscissa is x, and since the condition is steady,
it therefore behaves as though the quantity of air, e u, had moved
in one second along the line of flow from — 4/4 up to x; but in this
the quantity of water eu g,(h) is separated from the air according
to our definition of g.

If we have computed G as a function of x, according to formula
(20), then, finally, we have

WS SO a eS See ee

as the quantity of water, expressed in grams, per horizontal square
meter per second, that falls at the place x. In this way the deter-
mination of Wis executed more conveniently than through the
direct formula (17). By assuming the average conditions for the
summer in the above example for a = 1, we find that the integral
(20), if we compute it as approximately equal to the sum of the
intervals between the individual current curves of flow as con-
structed, gives the following:

G,-9 = 1352, Gyo y= 2680, Gee yy4= 3460 grams.

This last number indicates the total precipitation falling on a strip
one meter wide in one second on the side of the slope that faces the
wind. According to the course of the curve SS, as shown in fig. 3,
the precipitation begins, first, in the neighborhood of x = —o.108A
and therefore is distributed along a strip of the ground surface,
whose length is 0.3584, or 8600 meters; from this we compute the
average precipitation per hour, as follows:

3.6 X 3460 _ 1.45 mm. depth

8600

ll

1.45 kg. mass

ee

a

PRECIPITATION ON MOUNTAIN SLOPES——POCKELS Io!

Similarly, we find for winter:
Gu, = 380, Ge =e 2/70, G. == 1264;

the total precipitation is distributed over a strip 9400 meters long,
so that the avefage precipitation is 0.485 millimeters per hour.

From the above three values of G (*) wecan graphically construct
the course of this function approximately by considering that the
tangent to the curve for G is horizontal at its initial point and when
x= + A/4.

The tangent to the slope of the curve is found by considering its
measure W’. Thus we recognize in our case that the maximum
of the precipitation in summer is attained between x =o and
eT, but in winter between x = 0 and x = + 2 kilometers
and amounts to a X 2.2 millimeters, or a X 0.7 5 millimeters per
hour, respectively, for a wind velocity of a meters at some very
great altitude; furthermore, after passing the summit of the moun-
tain the precipitation diminishes more slowly than was found under
our previous assumption of a constant thickness of clouds. In
reality, on account of the conveyance of the water or ice with the
cloud, which we still neelect as before, the maximum of precipita-
tion is pushed still more toward the summit of the mountain. More-
over, since one part of the cloud floats over the summit and is there
dissipated in the sinking or descending currents of air, the precipi-
tation will stretch a little beyond the summit, but its total quantity
will be less than the computed.

The results of the preceding analysis, namely, (1) that there exists
a zone of maximum precipitation on the windward slope of a moun-
tain and (2) that the inclination of the surface of the earth is more
important than its absolute elevation, in determining the quantity
of precipitation, are confirmed by observations, at least for the
higher mountains.”

12 See Hann: ‘‘ Klimatologie,” Vol. I, p. 298.

I02 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

SUPPLEMENTARY REMARKS BY PROFESSOR POCKELS
ON THE THEORY OF THE FORMATION OF RAIN ON
MOUNTAIN SLOPES

(Reprinted from Monthly Weather Review jor July, 1901)

(1) Assuming the average vertical distribution of temperature
and moisture for each of the four seasons of the year as it is deduced
by von Bezold from the scientific balloon ascensions published by
Berson and Assmann in their ‘‘Ergebnissen.”’ ‘The results of
scientific balloon voyages,’’ there result the following minimum
elevations required in order that condensation may begin in a mass
of air that was originally at the absolute altitude H above sea level.

SPRING-

lake TIME. SUMMER. | AUTUMN. | WINTER.
meters. meters. | meters. | meters. | meters.
° 725 850 | 405 | 400

500 485 | 710 6x57 | 760
1,000 855 |" 570 600 | 1,070
1,500 890 680 | 835 1,140
2,000 920 730 | 1,180 | I,100
3,000 830 1,060 | 1,208 | 1,130
4,000 700 | 1,125 | 1,240 | x’r00

The smallest number in each column is also the smallest altitude
that a mountain ridge must possess in order to cause the formation
of clouds under the assumed conditions, but it is only in the case of
a very broad mountain ridge that such small altitude will suffice.
We see that in the autumn and winter a mountain of about 400
meters in height will suffice to produce a formation of cloud in con-
tact with the summit of the mountain whereas, in spring and summer
the mountain must be higher (namely about 500 or 570 meters
respectively), and when the air passes over this mountain the forma-
tion of cloud will begin in the layer lying at 500 or 1000 meters above
itssummit. These numbers at present serve only as examples; in
practice, however, they suggest that as soon as we observe the for-
mation of cloud above a mountain of less altitude than the above
given tabular minimum altitude, we may conclude somewhat as to
the average moisture at that altitude at that time. We may also
remark that on account of the increasing flatness of the lines of flow
as the altitude increases, the above given minimum altitudes must be
exceeded by so much the more in proption as the width of the sum-
mit ridge is smaller, and the altitude of the layer in which the con-
densation begins is higher.

PRECIPITATION ON MOUNTAIN SLOPES—POCKELS 103

(2) The method developed by me for computing the condensa-
tion that occurs on any given mountain slope cannot be applied to
computing the mean value of the precipitation for any given interval
of time, by introducing into the computation the mean values of
the temperaturerand moisture for this interval. We should in this
way find too small a precipitation. Thus, for example, the altitude
of the mountains might not suffice to cause any condensation at all
for the average condition of the air, but could cause it on those
occasions when the moisture exceeds its average value, wherefore
the average value of the rainfall for the interval of time under con-
sideration would be different from zero. As the variation of the
moisture from its average value may cause rainfalls where otherwise
there would be none, so also, with the currents of air mechanically
forced to ascend mountain ranges, and whose effect is superposed
upon that of the general circulation of the air in cyclonic areas; for
it can happen that neither one of these two causes may alone suffice
to form rain, but that both together do. This explains why eleva-
tions of the surface of the earth of from 100 to 200 meters increase
the annual mean value of the total precipitation, as for instance, as
shown by the charts in Assmann’s memoir of 1886, “‘ Einfluss, etc.,”’
“On the influence of mountains on the climate of central Germany.”

(3) The examples given in my article show that in so far as con-
densation in general takes place on the slopes of mountains, its
intensity (therefore also, the density of the precipitation when fall-
ing vertically) is in general greatest where the slope of the moun-
tain is steepest. If now we consider that in the course of all the
various conditions of the atmosphere that may occur in a long
interval of time, the first condensation occurs most frequently above
the upper portion of the slope, then it follows that the average den-
sity of precipitation computed for a long interval of time, must
increase, not only with the inclination of the slope, but also with
the absolute altitude of the locality under consideration. To this
case corresponds the formula for the annual quantity of precipita-
tion expressed in millimeters deduced by Dr. R. Huber in his
“Untersuchungen,etc. Investigation of the distribution of precipi-
tation in the canton of Basle,’ namely:

N = 793 + 0.414h + 381.6 tana

where his the altitude in meters, and a indicates the gradient angle.
(See A. Riggenbach, Verhandlungen der Naturforschenden Gesell-
Senet, Basel, 1895. Vol. X, p. 425).

104 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

(4) From a comparison of the effects of different broad moun-
tain ranges of the same altitude, it results (see page 474 of my
article, or page 95 of this translation from the Monthly Weather Re-
view) that the smaller, and therefore steeper, mountains always
cause a smaller total condensation than the broader and narrower
mountain summits. Notwithstanding this, the density of precipi-
tation on the slope of the smaller is generally larger than on the
slope of the larger mountains because the smaller total precipitation
is distributed over a ground surface that is relatively much smaller
yet. In reality, however, this only obtains so long as the quantity
of water remaining suspended in the cloud is only a small fraction of
the total condensation; in the case of very narrow mountain ridges
it will be more apt to happen that a considerable fraction passes on
over and beyond the summit and is subsequently again evaporated
[and therefore does not appear as rainfall].

(5) Iregret to notice that in the first two figures of my original
memoir, as also in the translation, the legend inscribed on the curves
representing the distribution of precipitation reads “precipitation
in millimeters per second,’ instead of “‘per hour,”’ as is correctly
stated in the text; the necessary correction should be made.
[Corrections have been made in the present volume. ] .

(6) Aprecise test of this theory cannot at present be carried out
because we have not sufficient observations of the condition of the
upper strata and of ground along the slope ofa given mountain range.

IX

7
RESEARCHES RELATIVE TO THE INFLUENCE OF THE
DIURNAL ROTATION OF THE EARTH ON ATMOS-
PHERIC DISTURBANCES

BY M. GORODENSKY

Memoirs of the Imperial Academy of Sciences of Saint Petersburg, 1904,
Volume XV, section g]

[The original memoir above quoted is published in the Russian language’
the brief abstract, in French, communicated by the author to the ‘‘ Annales”’
of the Met. Soc. of France, Vol. LIII,*pp. 113-120, May 1904, has been fol-
owed in the present translation]

In order to study in detail the causes of the origin of atmospheric
disturbances and their more important properties it is first necessary
to resolve the fundamental problem: given a certain system of me-
chanical forces, how will it act on the air in the different strata of the
terrestrial atmosphere? Ve propose to seek the possible solution for
the special case of the strata situated in the immediate neighbor-
hood of the ground.

It is easy to determine the action of any force in the midst of
an ideal gas, whose particles move among themselves without fric-
tion, as in a vacuum and according to the law of gravitation only.
In order to pass from such a gas to the atmosphere it is necessary
to know not only the special properties of the air itself but also
the value of the friction. The influence of this friction is appre-
ciable in two ways: (1) it diminishes the velocity of the progressive

- movement of the air, (2) it enfeebles the action of the force per-

pendicular to this current of air, and to the same extent diminishes
the angular velocity of the atmospheric particles. The evaluation
of this normal friction, that-is to say, the effect directed along the
line normal to the direction of motion is the subject that we propose
to study in this memoir. |

Fortunately there is at our disposition a very convenient agent
that one can utilize to this end. This is a well-known constant
force and one which is always perpendicular to the trajectory of
any mass that is moving on a horizontal plane: it is the action of
the diurnal rotation of the earth.

105

106 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Let us imagine an elementary small mass projected horizontally
on a perfectly polished plane surface with an initial velocity vp.
It continues along its route with this same velocity tracing a curved
line whose radius of curvature, as is well known, is given by the
equation

4n.
MOUGIT nOh = - oddé kes ws fe ee eee
7 (1)

where T is the duration of a complete day, i. e., one rotation of the
earth and a the latitude of any place on the earth traversed by
the center of the mass. The center of curvature of the path is
always on the left-hand of the direction of motion where the mass
is in the southern hemisphere and on the right-hand in tHe north-
ern hemisphere.
Assume the notation
4x

K = 7 sina

which expresses the angular velocity of the moving point. lis
value can be calculated from observation of the wind between two
stations in the following manner:

At the station A take an observation of the velocity of the wind
blowing towards the station B. The distance between the stations
and the velocity of the wind being known we obtain by simple divi-
sion the interval of time required by the particle of airtoreach the
station B. By observing at this moment the direction of the wind
(at B) we find a difference between the two observed directions,
which difference should give us the required value K. This value
generally differs greatly from that calculated by the theoretical
formula because of the many accidental conditions, among which
there is however one force that constantly and continuously influ-
ences the movements of the atmosphere. This is the internal fric-
tion (or viscosity) of the air and also the friction between the air
and the surface of the terrestrial globe. If the number of observa-
tions employed by us is sufficiently large, as well as the length of
the period of time and the number of stations collated, then all
anomalies neutralize each other and one obtains a resulting mean
value for K as diminished by friction only, ork =pK
Now it is the coefficient » that is the desired characteristic of the
air near the ground.

ROTATION AND ATMOSPHERIC DISTURBANCES—GORODENSKY 107

The preceding expresses only the general scheme of the proposed
method, for in fact we still have to surmount numerous difficulties,
the more important of which are the following:

(1) The terrestrial surfaces separating the stations A and B
should be as flataand smooth as possible, not having any high obstruc-
tions, in order that the air may pass freely from one station to the
other. For this reason we have not utilized observations of refined
anemometers and anemographs which are located frequently in
large cities and have felt obliged to rely on the observations of
stations of the second class in the meteorological system of Russia.

(2) We do not generally find at station A a current of air flow-
ing exactly towards station B but inclined to that direction by the
angle # so that for the length of the path described by the wind
between the two stations it suffices to take the distance

ye tor a. al) One tee eee

In fact this can only be an approximation since the trajectories of
the atmospheric particles are curves and not straight lines and the
value of S is larger rather than smaller than that indicated by the
equation (3).

(3) The instrument by which at Russian stations we ordinarily

raeasure the direction and the velocity of the wind is a wind vane
placed at the summit of a mast and furnished with a suspended plate
of steel which by its departure from a vertical position indicates
the velocity of the wind. Now the iron cross-piece of this mast
showing the cardinal points, N., S., E., W., is often oriented inac-
curately and the wooden mast that carries it often acquires after
awhile a twist introducing an angular error amounting to many
degrees. The observations made by such a primitive apparatus
cannot be very exact, so that one must utilize very many of them
in order to eliminate these errors.
(4) At stations of the second class the observations are made
at 7 a.m., 1 p.m. and g p.m., and consequently we do not generally
find at the station B any observations for the moment of time that
we have found by our calculation. It remains then only to make
a proportional interpolation between the two observations that
come nearest to this moment.

As the detailed exposition of the method now proposed cannot
be given within the limit of this abstract we must here confne our-
selves to giving the results of our calculation:

The mean value of yu for 3762 cases is found to be

ie OF WP Gjiarai er mee we. el Le

108 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

But this value has neither practical nor scientific interest because
it corresponds to the whole scale of different velocities of the wind
from 5 meters per second up to 20. This itself explains the impor-
tance of the so-called mean error.

By grouping the numbers in such a way that each group corre-
sponds to a certain velocity we have formed the following table:

v py! n

Meters Number
per second. of cases.

5 18.0 1461

6 51.9 1232

7 ey 800

8 17.4 698

9 4.9 386

10 age2 444

II 0.3 24
12 20.4 296
13 —3.9 14

14 17.5 194

15 3.3 18

16 5.9 39

a 3-7 52
18 6.4 24
19 — °

20 E77 185

The negative values show the cases where the wind deviated to
the left, in spite of the theory, and not to the right of the rectilinear
direction.

After having submitted this table to a detailed examination,
which I need not repeat here, we have obtained the following values
of the coefficient » corresponding to four different values of v.

U Lt
5.8 0.022
8.8 0.031

12.0 0.051
15.9 0.092

Representing these figures graphically by orthogonal coérdinates
we obtain a very regular curve, a sort of parabola, whose natural
prolongation crosses the axis of y at some distance from the origin.
The equation of such a parabola, as we well know, is

S16 UF EC ice ou os dah eal ee

where ¢ and c’ are constant parameters. The introduction of
the parameter c’ is explained by the law of Dove, according to
which the weather vane at any meteorological station in Europe

a oo

ROTATION AND ATMOSPHERIC DISTURBANCES—-GORODENSKY 109

generally turns in a direction contrary to the motion of the hands
of a watch when an area of low pressure is passing by the station.
In fact by employing the observations of stations for which Dove’s
law holds good we obtain a coefficient greater than it ought to be
by a quantity independent of the velocity of the wind. This inter-
esting phenomenon is shown with perfect clearness in the graphical
representation.

As the function yp v characterizes the friction of the air in a direc-
tion perpendicular to the current, one ought to be able to determine
this function theoretically, if we knew a similar function for the
direction parallel to the current, since the two coefficients ought to
depend directly on each other.

During the progressive motion.of masses of air a certain friction
is developed whose reaction, tending to reduce the linear velocity
of the movement, is perpendicular to this velocity, according to
the simple law of Guldberg and Mohn f = 7 v where fis the reaction
of the friction, v is the velocity of this wind and y is a coefficient
that depends only on the pysical state of the air and the surface of
the earth.

This being recognized, we have studied a regular stationary
cyclone of large extent and without any progressive movement,
from a purely mechanical point of view. After having examined a
portion of this whirlwind somewhat distant from its axis we have
obtained the following expression for the function (vp) viz:

1 1
where
sin a cosa
omy CS eels aan each ace

The letters introduced into these formule have the followin®
signification: a is the angle formed by the direction of the current
of air with the radius vector R drawn to the axis of the whirlwind
and is counted positively starting in the direction of the motion of
the hands of a watch from some initial radius vector; J indicates
the product v R which I have called the expression of the intensity
of any atmospheric disturbance; K is given, as already stated, by

eo == singey er eaten es ore te! ED)

110 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The values of K and 7 being absolutely independent of v, as also
are the values of J and a, for the given disturbance, as has been
demonstrated in our study, therefore the coefficient ¢ is also inde-
pendent of v. But equation (7) expresses a certain property of the
atmosphere, whatever may be the special phenomena by means
of which it has been determined. It results from this that the value
¢ in formula (8) is absolutely constant for any physical state of the
atmosphere and that it cannot vary with a nor with J, but only
with the coefficient ; the values of ¢ and 7 characterize the friction,
both of them, but in different directions only.

This argumentation may seem to be erroneous, as I have already
had occasion to convince myself on hearing the opinions of several
experts to the effect that any such process of investigation seems
to them doubtful and untrustworthy.

In place of defending my logic or my honesty against the incredu-
lous, I allow myself here to show in brief some properties of equation
(8) which result from the assumption as to the invariability of the
coefficient e.

We can consider equation (8) as the expression of the connection
that must exist between the angle a on the one hand and the values
J K and 7 on the other. Let us examine each of these connections
separately by means of the special partial derivatives:

a considered as a function of J.—This function has two different
branches:

(1) At the moment when a disturbance originates J = o, the |

air is put into gyratory motion in the direction of the hands of a

on
watch in the southern hemisphere, for which a = 2 and in the

inverse direction in the northern hemisphere for whicha = 4z. In
proportion as the velocity of rotation increases the current of air
deviates towards the center, that is to say, to the right hand in the
southern hemisphere (and J also increases as a increases), but to
the left-hand in the northern hemisphere, where J increases as a
decreases. We thus have a cyclone properly so-called, and par-
ticularly so far as regards its lower portion.

(2) At the commencement of the phenomenon the air expands
outward from the center along the radius for which ag = z. Then
as the disturbance develops the currents of air commence to deflect
in the direction of the movement of the hands of a watch in the
northern hemisphere, where a increases, and in the inverse direc-
tion in the southern hemisphere, where a decreases. This is the
lower portion of the anticyclone.

ROTATION AND ATMOSPHERIC DISTURBANCES—GORODENSKY III

For these two cases there is a certain limit that the angle a can
only attain when J becomes infinitely large, which is determined
by the equation (10), '

K

GEOG Ce NG ss Wi, eel)
/ 7

K as a function of a.—This function also has two branches.

When a disturbance takes place in the equatorial regions the air
flows along the gradients, that is to say, towards the center (for
which a =o or away from the center in the opposite direction
(for which a =z). The first case corresponds to an area of low
pressure and the second to an area of high pressure. If the center
of the disturbance moves towards the north, the currents of air will
deflect to the right (or a willincrease with K). If the center moves
towards the south, the current will deviate towards the left and a
decreases with K.

n as a function of a.—It may be remarked that theanalysis of this
function can only be of a general character because in the form
of equation (8) it occurs as a function of e of unknown form. If we
rely upon equations (1), (2) and (7) we find without difficulty that
e is infinitely large when 7 = 0; is zero when 7 is infinitely large;
finally the derivative of e with regard to 7 is always very small or
nearly equal to zero. Moreover it is evident that if 7 has positive
values, different from zero, then ¢ also has values greater than zero.

A discussion of equation (8) shows moreover that the product
en is positive for 7 = o and for n = infinity. These peculiarities

n
lead us to adopt ¢ = 7 as the value of the function ¢, in which 7 is

a constant. :

The vitality or duration of any atmospheric disturbance depends
directly on the magnitude of the angle a between the wind and the
gradient; in proportion as a increases the duration increases also;
in proportion as the wind deviates from the gradient it is more and
more difficult to reestablish static equilibrium.

This being understood, let us examine some interesting me-
chanical phenomena that we may draw from the preceding analysis.

(1) When an anticyclone continues to develop its vitality:
(a) increases steadily, whence it results that disturbances of this
character ought to have a very considerable stability not requiring
help from outside.

(2) On the contrary, when a cyclone is developing, its vitality
is decreasing so that a fully formed cyclone carries within itself
the beginnings of its destruction, hence the extreme instability

12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

of cyclonic formations, which can only persist by the aid of such
exterior sources as furnish the necessary energy.

(3) The movement of a disturbance towards the pole increases

its vitality, and vice versa.

(4) As the friction increases, the vitality of a disturbance
diminishes. Since friction [internal friction or viscosity] is greater
in moist air than in dry air it follows that a disturbance should
lose vitality when approaching moist vapors, and vice versa.

Ordinarily barometric maxima follow this rule quite closely, but
the minima seems to behave contrariwise and very persistently
so. This fact shows again that the cyclone of the temperate zone
is essentially a thermodynamic disturbance while the anticyclone
is a mechanical disturbance. Thus we explain the profound dif-
ference that exists in all respects between these two kinds of whirl-
winds which are so similar in appearance.

(5) The intensity of any disturbance, or the product v R, cer-
tainly increases in proportion to the distance from its center, for
the atmospheric currents become more and more nearly horizontal:
hence follows the following very interesting theorem:

The vitality of a cyclone diminishes in passing from its center
towards its boundary which causes an excessive sensitiveness at
the latter; when the cyclone is extensive with a very deep depression
its exterior isobars vary incessantly. On the contrary the anti-
cyclone has permanent and firm contours and its center of high
pressure moves hither and thither without exerting any influence
whatever on the boundaries of the whirl.

Because of this difference the collision between these two classes
of disturbances acts destructively upon only one of the two, that is,
the cyclone, which eventually is destroyed or modified.

From the preceding we see that equation (8) gives us a fairly
probable as well as generalrepresentation of the characteristics and
motions that belong to atmospheric disturbances, excepting only
one of the most important of the movements, that is, the progressive
motion of the whirlwind itself. The direction and velocity of this
movement are determined principally by the diurnal rotation of the
earth, which action becomes stronger in proportion as the height
of the whirlis greater. Now we are not yet able to study this action
because the law according to which the friction of the air varies with
altitude is at present wholly unknown. However, we hope that the
current exploration of the atmosphere with kites and sounding bal-
loons will not fail to clear up this question, which is as interesting
from a purely scientific point of view as it is important for the
practical forecasting of the weather.

“7

"ae

ae

x

Sf

THE RELATION BETWEEN WIND VELOCITY AT ONE
THOUSAND METERS ALTITUDE AND THE SURFACE
PRESSURE DISTRIBUTION

BY E. GOLD, M.A.
Fellow of St. John’s College, Cambridge

[Communicated to the Royal Society, London, by Dr. W. N. Shaw, F.R.S %
February 25, and Read March 5, 1908. Printed in Proc. Roy.
Soc. Vol., 80, May 25, 1908]

For the steady horizontal motion of air along a path whose radius
of curvature is r, we may write directly the equation

(wrsindA+v)’? 1 dp fa (wr sin A)?
Yr o or th

expressing the fact that the part of the centrifugal force arising from
the motion of the wind is balanced by the effective gradient of pres-
sure.

In the equation p is atmospheric pressure, p density, v velocity
of moving air, A is latitude, and w is the angular velocity of the
earth about its axis.

If dp/dr be negative, it is clear that v and wr sin 4 must have
opposite signs: or, for motion in a path concave towards the higher
pressure, the air must rotate in a clockwise direction, the well-
known result for anticyclonic motion. Further, the maximum nu-
merical value of

10p . (wr sin A)?
por 2

and the corresponding maximum value for viswrsind. Therefore,
in anticyclonic regions there are limiting values which the gradient
and the velocity cannot exceed. This limiting value of v for lati-
tude 50° and r = 100 miles is approximately 20 miles per hour.

At the surface of the earth, owing to friction and eddies, the mean
direction of the motion of the air is nearly always inclined to the
isobars; but over the sea the inclination is very much less, and it
seemed probable that in the upper regions of the atmosphere, if

113

I1I4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the motion were steady, the air would in general move tangentially
to the isobars, and its velocity would agree with that calculated from
the equation given above.

The question, however, arises as to whether the pressure is likely
to continue steady long enough for a condition to supervene in which
the equation is applicable. We can get an idea of the time that
would elapse before air, starting from rest, would reach a state of
steady motion, by considering the motion of a particle on the earth’s
surface (1) under a constant force in a constant direction, corre-
sponding to straight isobars; (2) under a constant radialforce corre-
sponding to cyclonic and anticyclonic conditions. The particle
would begin to move at right angles to the isobars in the direction
of the force, but as its velocity increased it would be deflected by the
effect of the earth’s rotation until it moved perpendicularly to the
force.

The equations of motion of a particle, referred to axes fixed rela-
tively to the earth and having an origin on the surface in latitude
A, are

PE ie Oe ee
dt? dt dt
2
SUS ace ta
dt? dt
2
on 4+ 20 Por ud =~,
dt? dt

where the axis of z is vertical and the axes of x and y are west and
south respectively.
If there is no vertical motion we may write the first two equations

2
d’x aw x d*y ao

and the form of the equations and the value of a are unaltered by
changing to other axes in the same plane. Let us take the y axis
to be in the direction of the constant force b. Then

whence

: b
pees (at — sinat), y=-——(1-— cos at),
a a

,

if the particle start from rest. The motion is therefore oscillatory,
and the particle moves in a series of cycloidal-like curves, fig. 1.
The times to the successive interseetions with y = b/a® are z/2a,
3x/2a, etc. For latitude 50° these are about 4and 12 hours. They
are independent of b. If there is damping the motion will be as in
fig 2. If the motion is resisted by a force k v proportional to the
velocity, the path will be inclined to the x-axis. Fig. 3 gives the
path for the particular case k = a and for a period of time equal to
axz/a or 16 hours.

WIND VELOCITY AND SURFACE PRESSURE—_GOLD I15

ey
vv
Rl
ro a
FIG. I
y
TP
ze
FIG. 2
y
ZX
FIG. 3

In the case of a constant radial force we have for the motion

d’r ean dé
=r we One
dt dt
2 y
ge dé dr

— eS en
dt? dt dt pt

116 SMITHSONIAN MISCELLANEOUS COLLECTIONS WOL. 51
whence
dé
P+ har = 5,
dt

If the particle start from the center,
dé

B =0 and — = — ja,
dt

and we obtain

r Hiss dW or cc — cos @).
a? a

The particle therefore describes a cardioid, but if there is damping
the motion will come to be along the circle r = 4R/a’.

The time to reach the circle is z/a, or about 8 hours for latitude
50°.

These times are not large meteorologically, and we may there-
fore expect the relation between air velocity and pressure gradient
to be that corresponding to steady motion so long as there are no
irregularities to produce turbulent motion.

For application to wind velocities in the upper air we require to
know the upper-air isobars. If we have air in which the horizontal
layers are isothermal, then from the equations

dp = — godz, p= gkoT,
it follows that

We have, therefore, if p, and p, + dp, are surface isobars and
p, and p, + dp, the corresponding upper isobars,
GPs _ Po on that 2Ps_ Wate

LP Po Pz YP Ty

Therefore the velocity calculated from the surface isobars will
apply to the upper air, except for the factor, T,/T,). For z =1000
meters the effect of this factor is to diminish the velocity by about
2 per. cent.

If the conditions are not isothermal, but such that the isotherms
and isobars intersect at an angle ¢, the upper isobars will have a
different direction from the surface isobars, and the value of the
upper gradient will also be changed (see fig. 4).

WIND VELOCITY AND SURFACE PRESSURE—GOLD EL?

The pressure at a height z above B the point of intersection of fp,
To, is pye~ */* 7m, and above A, the point of intersection of py + dp,
i; — aT ,, is!

(Do + dp,e*/* CTs ate?

If we assume the vertical temperature gradient to be the same

over all the region considered, d T will be the same for every element

of the above integral, and wecan putdT,, = dT>.
If these two pressures at height z are equal, we must have

pe ?/* mm = (Py + dp) ad (Pm — 47),

or

dp, z2dT, a apy _ & ies ae

Po k do, Po de

In this case A B is the direction of the upper isobar and its incli-
nation ¢ to the lower isobar is given by

tan ¢ a : gdp, +
xd T, cosec f + ydy, cot d

where x dT, and y dp, are the distances between the isotherms and
isobars.
Substituting for dT, and dividing out by dp, we get
2
cot ¢ =cot¢ + a Em cosec W.
Y 021g

Taking y and x for millimeter isobars and 1° C. isotherms and
putting zg = 1000 meters and T,,*/T, = 2T,, — Ty = 270° C. say,
we find

cot ¢ =cot¢ + 2°8 * cosec ¢y.
Bf

In this and subsequent formulas the reader will understand that the
erms following the / belong to the exponents of e.

118 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5a

To obtain the upper pressure gradient, we consider the upper
isobars over B and N. The difference of temperature between B
and N is assumed y/x .dp,cos ¥ = dt.

Therefore the upper pressure difference is

———EE—E—E——

(Po + bpp) e*/k (Ty, + dt) — poe */kT », =e */kT 9, Ez + Le

ie PEPE
=P [RI E 38 “kT.,2 |

The distance between these isobars is ydp, cos ¢ and the upper
gradient is consequently

sl er E 4. Poe cos ¢ |
y cos ¢ * cd 20

2 WANS paper ; " = y cos Y |

y COs Pe, x

and the ratio

2 fs | E OPeis soc # | Ped |

Pp; Or | py Or I pete x cP
which is
g oz cosec ¢. was sit
x
taking T,/T, to be unity, namely,
1 sin

cosec ¢.

Pa Gite ees
cot ¢ — cot¢d sin (f — ¢)
In the special cases, / = o or 180°, the ratios are

(1 4.2) or (1 se , for z = 1000 meters.
1 2.8%

If x = 2y, which would represent a possible case, the increase or
decrease would be about 18 fer cent.

For ¢ = $z the rotation would in the same circumstances be
about 10°. .

During the year 1905 aseries of observations in theupper air was
made at Berlin and Lindenberg, near the time of the general 8 a.m.

WIND VELOCITY AND SURFACE PRESSURE—GOLD 119
morning observations. It was therefore possible to compare the
wind velocities observed with those calculated from measurements
of the gradient by the use of the*formula at the beginning of this
paper, the motion being assumed tangential to the isobars.

For purposes of calculation the formula may be written

409'cosec 1 7 5,

v (1 + 0.00108 ucot ¢ cosec A) = ==
% eae Es

where ¢ is the angular radius of the small circle, on the earth’s sur-
face, osculating the path, v is in meters per second, xis thedistance
in kilometers between millimeter isobars, T, B are the temperature
and pressure, and Ty, B, the corresponding values for air at 0° C.
and 7@0™™.

If the motion is along straight lines, cot ¢ = o, and the valuesof
v for B = B,, T = T,, are as follows if x = 50 kilometers:

ieatifude... .>.). 36° 40° 50° 60° 70°
De ocho & iaale. ahs 28.4 22.1 18.5 16.4 15.1

If vy represent the velocity when cot ¢ = o, wecan most easily
express the solutions of the equation for different values of ¢, x,
4, by taking as independent variables, ¢, vp, A.

Taking, as an example of the dependence on ¢, A = 50°, vy = 40
meters per second, we obtain the following values for v in meters
per second in the case of cyclonic motion:

heey easy ant it Tae) os ke Wh OE AO Mh POs Ow kOe
Bee ee he Wy 21 «624. 26° 28 29° 30 | 6S1l 6381 682

For anticyclonic motion the gradient corresponding to vy = 40
meters per second is above the maximum, and we take for two ex-
amples vy = 12, and y= 30 meters per second.

The values of v are then as follows for the two cases:

p Po 2) 93° A hea eee Go 108

= 120) AG Th 4 eld, 14 1S mip. s:
“a = aS eS es ee ae 50 sé

|
t
3
I
I
|

For uv, =
For zu,

I
wo
S
2

I

|

|

Where no value is inserted for v, the gradient corresponding to
the given value of v, is above the maximum for the corresponding
value of ¢.

To show the dependence on J, we take ¢= 3° and put v, = 40
meters per second for cyclonic motion, and vy = 10.5 meters per

120 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

second for anticyclonic motion. The following table gives the

values of v for different latitudes in the three cases:
4

A ao? 40° 50° 60" “705
Forv, = 40 ...... p= 2 23: 24 25. 26.” mp
-— — — 17 15 °
Web 6.3664) 8.89 B24

ko} by
© ©
Sy
ee
oc so
a

—_
ao
ea
li

By the use of tables giving values of v, for different values of x,
T, B, and of v for different values of A, vg, ¢, each wind observation
at 1000 meters altitude was compared with the value deduced from
the surface isobars. The temperature correction was not applied.

The following table gives the result of the comparisons:

|
|
|
|
|
|

SURFACE WIND = vW |

BETWEEN
MEAN DEVIATION IN

v. M.P.S.

M.P.S.
DEVIATION
POINTS OF WIND v, |

COMPONENT AT.

METERS, M.P.S.
+ Vv, COSINE (DEVIA- |
1000 METERS.

POINTS OF 0; FROM v
(+ WHEN 2 VEERS |
FROM SURFACE WIND.
COSINE (DEVIATION).
TION).

ISOBARS AT SURFACE

AND 2.

WIND AT 1000 METERS

PERCENTAGE DIFFER-
MEAN SURFACE WIND. |
COMPONENT WIND+TO.

THEORETICAL VELOCITY
VELOCITY 2, AT 1000

—————

Berlin:
[ety ata Bie ees £527) | x5.2.| ao | —o+6 ||, Sic 3-3 | 0.45 | 0.97
Webruary..s.s.<..¢-5) Tas0|)0i<.6)) 3.0) | —o.67) “40 |
MatGhe Ao utie ewe sear Sat 6.6 | 23.0 | —0.4 2.6 oy a)

oo
wo >
OH
oo
ow
& 00
fs A oe |
on

September. s\.5..00¢0 5. Io.
Octaber. sites ates oe 12.
IN OV-GENDOE pre crainaisycsena fo Io.
December. ...cckesscs rs

wWwronon fue
-

Lol
oooo of 00 0
|
°
womowwonond oOo
UanaAunnbkw -
MOWPh HMO MNS
WO HWS AW Hw
Oo Oo 0 © 0 Go 0 Oo
a
Ps
ooow Or 0 0 0

ow

Ww nv
wb NS HH HK HH HW
[eh Scie Orica Oe ats

>

i=

09

—]

n

co

~ .
OD WO Ff DW DN
wWwdS ND HH HH WD OH

eae
H
uo
|
°
co
Bee
~
-
|
°
‘o
w&
|

=
E
oo
©
“I
La)

Lal
Ww DQ
Lal
°

no
©
wn
|
°
>
“uw
>
bd
won
°
Ne)
wn

wn
|
°
| oO
>
0

|

Sas
| ©

>

at the surface, and the wind velocity observed agrees well with that
calculated from the pressure distribution. The differences are not
greater than possible errors of observation, except in spring.

It is known that the upper wind always veers from the surface
wind, and the numbers in Column 7 show that in 1905 the veering
was considerably greater in winter than in summer.

GRD S coin eaccila utes cies TO.) 19 [a
The upper wind coincides in direction very nearly with the isobars
If the effect of the earth’s surface were the same as if a frictional
force opposed the motion, the relation between the wind and grad-

7

WIND VELOCITY AND SURFACE PRESSURE—GOLD 121

ient of pressure would be as above, except that the effective gradient
would be the maximum gradient multiplied by the cosine of a, the
angle between the path andtheisobars. Thecorresponding velocity
would be approximately v cos a, except in cases of considerable
curvature. In,the majority of the observations the curvature was
small, and we should therefore expect the surface wind to benearly

_vcos a, so that the numbers in Column 8 would be nearly unity.

This is far from being the case; but the change of the station of
observation from Berlin to Lindenberg is accompanied by a cor
responding change in the ratio of the surface wind velocity to vcos a.

This suggests that the effect of the surface, apart from the purely
frictional effect, is to reduce the velocity in a given direction in a
constant ratio depending on the locality, and that departures in the
observed velocities from those corresponding to this ratio are to
be associated with unsteady meteorological conditions.

The last column! gives approximately the ratio of the volume of
air crossing the isobars at the surface to the volume crossing at
Iooo meters.

The ratio appears to be nearly constant; the change in December
is probably due to the exceptional conditions which prevailed during
part of the month, when the air was considerably warmer at 1000
meters altitude than at the surface.

10Or, the wind component, perpendicular to the isobars at sea level divided
by the analogous component at rooo meters.

XI

STUDIES ON THE MOVEMENTS OF THE ATMOSPHERE

BY C. M. GULDBERG AND H. MOHN!

PART I

(Christiania, 1876, revised 1883)?

PREFACE

Meteorological phenomena being very complicated, we shall
attain final success in their mathematical study only by treating
simple cases which are analogous to those of nature. The equi-
librium and the movement of the air form a part of the mechanics of
fluids that is as yet very little developed because there exists too
few observations for the verification of the numerical calculations.
Encouraged by the fine results obtained by M. M. Peslin, Reye,
Colding, Ferrel and Hann in this new application of analysis to
meteorology, we have applied the principles of mechanics to the
movements of the atmosphere, and have arrived at some results
which we think are not without importance for the development of
meteorological science. In the first place we have found that one
of the first things to do in order to insure the success of meteorology
is the creation of meteorological stations at high altitudes; either
on mountains or in balloons, and supplied if possible with self-
registering instruments.

The winds or the horizontal currents of air at the surface of the
earth are intimately connected with the vertical currents; but the
origin and the displacement of these latter depend not only on tke
physical state of the air at the surface of the earth, but also on the

1Etudes sur les Mouvements de L’Atmosphére. Par C. M. Guldberg
et H. Mohn. Premiére Partie, Christiania, 1876. Deuxiéme Partie, Christi-
ania, 1880. [Revised by the Authors in 1883-’85.]

2? By personal interview with the authors, and correspondence during
the years 1883 to 1886, Prof. Frank Waldo secured from Professors Guld-
berg and Mohn a revision of the original French edition of this Memoir
with permission to publish a translation for the use of American students.
The delay in publication has given me opportunity for a slight revision of
Prof. Waldo’s translation.—C. ABBE.

122

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN N23
physical state of the air of the upper strata. Moreover the velocity
of the wind and its direction are both eminently under the influence
of the surface of the earth, while'their values at a certain height would
probably present the regularity that must obtain in order to be
able to prediet the progress of meteorological phenomena.

In studying horizontal currents under simple hypotheses, we have
introduced the friction due to the surface of the earth, and we have
applied our theory to the winds crossing over the equator, and to
whirlwinds.’

The numerical calculations accord with the phenomena of nature
within such limits as correspond to the established hypotheses.
It follows that the exact observation of the velocity of the wind
will be of great importance to meteorology. We hope that these
results drawn from the mechanics of the atmosphere will show the
necessity of more extended meteorological observations especially
in the tropical regions and in the higher strata of the atmosphere,
and that true progress in meteorology is founded on the develop-
ment of the mechanics of the atmosphere.

CHAPTER I

THE ATMOSPHERE
§1. Pressure, virtual temperature

In studying the equilibrium and the movements of the atmos-
phere, it suffices to consider the air as a mixture of dry air and of
aqueous vapor. The other gases forming the elements of the atmos-
phere, of which carbonic acid gas is the most important, are found

only in such small quantities that their action may be neglected.

The quantity of aqueous vapor in the atmosphere is so small that
we can accept the law of Mariotte and Gay-Lussac for moist air
within the range of temperatures that occur on the earth. It is
necessary, however, to consider the cases in which the vapor con-
denses and passes into the liquid state or the solid state.

We use the notation

p the pressure in kilograms on a square meter.
o the density or mass of a cubic meter.‘
t the temperature in degrees centigrade.

3M. C. M. Guldberg had already, in 1872, developed a part of this theory
in the Norwegian Polytechnic Journal (Polyteknisk Tideskrift), p. 73, 1872.
—EpIror.

‘In the absolute system here used this ‘mass is the weight divided by
gravity.—EDIrTor.

L224 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The law of Mariotte and Gay-Lussac as applied to a kilogram of
gas is written
Peeples Aer): Wao! ee)
where 273° + 7 is the absolute temperature.
Here a designates a constant which depends on the nature of the
gas; for dry air we have

a = 287.09

In applying this law to a mixture containing 1 — q kilograms of
dry air and g kilograms of the vapor of water, expressing the tension
of the vapor of water by 7 and its relative density by 1/e we find

p—f=a(l—q)p (273 + 2).
fj =e aqo (278 + 7).

p=a(l+C—1qgp@7+r) ..... &)
ij eq
ore hy Ese me ee (3)
fp ia
Ley
q= Se iP sap a bedintt ci coh ees ee (4)
1—e-l iy
ey Sup
By substituting this value of g in equation (2) and putting
273 +7
TRE et Pepe UN (5)
PR)

we have for moist air

I
S
>
m
,
=
S
——

a

We call the quantity T the virtual temperature; for dry air the
virtual temperature is the same as the absolute temperature.

If we consider a mixture which contains 1 kilogram of dry air
and x kilograms of vapor of water, we shall have

q ey |

popes ee ae xe ee |
] ex
Pere ave hose

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 125

If we have

e— 1
= 0.623 cn: = 0.377

>| —

Then for air at 760" we have the values in the following table:

| TENSION OF |
TEMPERATURE | THE VAPOR Tr x

OF WATER

ses |
—30°C 0.386 243.05 0.000317
-—20 0.927 253.12 | 0.000761
—-10 | 2.093 263.27 0.001720
° 4.600 273.62 | 0.003794
bce) 9.165 284.30 0.007605
20 17.391 295.55 0.014590
30 31.548 307.81 0.026981

§2. Height of the atmosphere—mean pressure

We can adopt either one of two hypotheses concerning the height
of the atmosphere. Wecan suppose that the atmosphere is limited;
in this case the temperature of the exterior stratum must neces-
sarily be absolute zero, for at this temperature the tension of a gas
is equal to zero. The other hypothesis is that the atmosphere ex-
tends indefinitely into space and that space is filled with a gas whose
tension is extremely feeble. For meteorology it matters little which
hypothesis is chosen, because in both cases the tension of the air
at very great heights will be insensible. Suppose 760™™ be the
pressure at the surface of the earth and suppose the temperature of
the atmosphere constant and equal to zero centigrade, we shall find
the pressure at the height of 200 coo meters equal to 0.000 o00 o1™™,

If the atmosphere does not contain the vapor of water its mass
will be invariable; if we suppose, moreover, that gravity does not
vary with elevation, the weight of this mass will be constant and
by calculating the mean pressure on the entire surface of the earth
it will be found to remain always the same. Considering* the pres-
ence of the vapor of water whose quantity varies from time to
time, we shall see that the mass of the atmosphere does not remain
constant and that, consequently, the mean pressure varies with the
seasons.

We have assumed that gravity is constant. In truth it varies
with the altitude and consequently the pressure of the atmosphere
depends on the law of the distribution of the mass in a vertical direc-

126 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 5"

tion. This distribution is a function of the temperature, and con-
sequently even the pressure of a dry atmosphere will vary with
the temperature in such manner that the pressure will diminish in
proportion as the temperature increases. However, the variation
of gravity for atmospheric strata at slight elevations is so slight that
its action can be neglected in meteorology.

$3. Temperature of the atmosphere

Temperature depends on many considerations and there has
not yet been found any function that expresses the temperature
in terms of the coérdinates of position and the time.

The heat of the sun and of space, the absorption of the earth and
of space, the radiation, the conductibility and the movement of the
air, all affect the temperature. Hitherto we have sought to deter-
mine the temperature at the surface of the earth as a function of the
time. We shall see that the variation of the temperature with the
height is of the greatest importance in meteorology. The observa-
tions of this phenomenon are not numerous and it seems not to
follow simple laws. But one can at least recognize that at slight
elevations where the action of the sun is most energetic the layers
of air experience equal variations of temperature, while it is very
probable that in somewhat elevated strata the variation is slight,
and that whatever may be the temperature at the surface of the earth,
we shall always arrive at the same temperature at a certain height
which will however oscillate slightly.

We shall apply some approximate formulas. The most simple
hypothesis is that the temperature decreases proportionally to the
height; then we have

T =T) — a2;

where z is the height; a, a constant and t, the temperature at
the surface of the earth. In some problems it will be more con-
venient to introduce the above described virtual temperature and
write

ET SPN a

These two formule apply only to small heights; if we wish to cal-
culate the variation of temperature for the greatest height, we can
divide the whole elevation into layers and apply the formula to
each stratum with different values of a.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 127

§ 4. Variation of pressure with altitude

According to the theory of the equilibrium of fluids the increase
of pressure per unit of length is equal to the force which acts on
the unit of volume. Let g designate the force of gravity per unit
of mass and g the height, we shall have:

dp
EE Bes val, Waco)

Introducing the value of o given by equation (6) of §1 we shall
have
dp gdz
yee . (2)
Pp a

(1) The virtual temperature remains constant.

In this case designating by p, the pressure at the surface of the
earth we shall find by integration.

. (3)

g2

Poe oe
in which e is the base of the system of Napierian logarithms.
(2) The virtual temperature decreases proportionally to the height.

By introducing T = T, — azin equation (2) we shall find, by

writing m = 8
an
gz
Bots am a
a
Pe ae AN Arend 8 WS)
r= (Fy
ESS Se er an ger enee <a) 20. HC)
Po Tl 6)
ff ay
ia eatrey «i ate Cre (7)

As to the variation of the pressure of the vapor of water we can
adopt various hypotheses. We shall consider only the following

formula:
Tica i :
a a hy

128 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

In which P# is a constant whose value depends on circumstances.
Knowing » and f we shall find the temperature t by formula (5)
of §1, namely

ee)
hd aha eam

Applications
Hive i Sa hee 3.441 4.0 5 10

Variation of temperature | 0°.994 0°.854 0°.683 0°. 342
per 100™ ea

Height for a variation of |

= aU i 146m 293m
poets pio 4000™ 10000" 20000™
T, = 273 aes
: = 0.880388 0.58259 ~—« 0.21250 0.01233
0
T, = 273 m= 5
os 0.88094 0.59013 0.23681 0.03106
0
T, = 273 ee 10
a — 0.88166 0.59841 0.26266 0.05609
0

Dr. Julius Hann has published a series of observations on the
tension of aqueous vapor at different altitudes (see the Zeitschrift
der Oesterreichischen Gesellschaft fur Meteorologie, 1874, page 195).
In this case applying formula (8) we shall assume

tT) = 20°, f, = 10™, m= 10 and f =3

The values of i calculated for these constants are found in the

0
third line of the following table.
Assuming T = constant = 273° and ~@ = 3 we find the values
written in the fourth line. The observed values are found in the
second horizontal line.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 129

|

1000 | 4000 | 8000 | 12000 | 16000 | 20000 | 24000 | 28000
Observed t/fo Ne ecoyere wore el MOL Sy eee 0.87 | 0.64 | 0,42 Osa7 | 0128) | org | — —_
Computed t/fo rekstak Sh gndy oeraetarehere 0.90 | 0.65 | 0.42 0.27 | o.17 0.11 | 0.07 0.04
Computed t/fo moyepevarstovetersic orators | 0.89 | 0.63 | 0.40 0.25 | 016 | O10 | 0.06 0.04

Altitude, English feet.........

§ 5. Expansion and contraction of the air

The pressure and temperature of a mass of air that experiences
any transformations whatsoever depend on the quantity of heat
which it has gained or lost. We will first consider the case in which
the air experiences a series of transformations without gaining or
losing heat at any moment. The equation between the pressure
and the volume represents a line that has been called the adiabatic
line. |
In the study of meteorology it is also necessary to find the equa-
tion between the pressure and the temperature. It is necessary to
distinguish between several cases. The air can be dry or moist,
and the aqueous vapor water can remain without condensation or
it can pass into the liquid state or into the solid state.

Representing by U the internal energy of a mixture; by V its
volume and by A the mechanical equivalent of heat, we have

Oa Al Dud Vitincp ents Rateinetce a ierens ae (1)
(1) Dry air.
Applying equation (1) to dry air we shall find from the mechan-
ical theory of heat

p & 35 a

py ~ \2738 + fe
es

where ¢ represents the specific heat of dry air at constant pres-
sure, whence we have,
m = 3.441

(2) Motst air without condensation.

Supposing we have one kilogram of dry air and x kilograms of
aqueous vapor we shall find

1 + 2.023 .x
(4)

ee

130 SMITHSONIAN MISCELLANEOUS COLLECTIONS WOOL. 75 1

where 2.023 is the ratio between the specific heat of the vapor of
water and that of dry air. These formulas apply only in so far
as the air is not saturated with the vapor of water. At the moment
when the air becomes saturated, the decrease of temperature is
accompanied by a condensation of vapor and it is necessary to dis-
tinguish between the three cases. We will assume that the con-
densed vapor remains suspended in the mass of air under considera-
-tion.

(3) The vapor of water ts partially transformed into water.

We will consider a mixture consisting of 1 kilogram of dry air,
x kilograms of vapor of water, and 7 kilograms of water. Express-
ing by U’, U’’, and U’” the energies of dry air, of the vapor of water,
and of water respectively we have the total energy of the mixture

ii — U' + xU" + pyitt
The sum of x and y remains constant and writing

ee ad
we shall find

d U = dU’ + E d gym + OE nak Oe

Designating by v’ and v” the specific volumes of the dry air
and of the vapor of water and neglecting the volume of the water,
we have the volume of the mixture

Veav+ a0"
We can then write

padV = (p—jf)dv' + jd (« v")

Expressing the latent heat of vaporization by 7, and the specific
heats of dry air and of water by c and c’ we have approximately,
neglecting the volume of water:

C= bis oe Ce) ay A fu"

(273 + T) il |-aw (UO Uy) + Afd(xv’)

x
273 +t
Aa
cdt =dadU'+ pees
con =aUw"
a
(p—f)u’ ieee ae
l = 606.5 — 0.69 r

Le

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN Ivey

Substituting the values of d U and of pd V in equation (1) and
introducing the values given by the equations mentioned, we shall
find

273 +7

Oe J)
Bat

xl
O= git +icds + e738 +2) d( a)
| Aa
- = G18 ++ (7) aera gore ; (5)

Expressing the initial values by the subscript index o, we shall
by integration and introducing numerical values find

“an eo au eee
tog ( ee = 3.341 [1 + 4210 €] log 734+
sea Ky ls «1 |
3h 7 EE ae Ce - Dae ee
From equation (7) of §1 we have
el

Equations (5) and (6) apply in general, so long as the tempera
ture remains above zero. The temperature being at zero the water
is changed into ice. However, wecan imagine the possibility of the
vapor of water being changed into water at temperatures above
zero. We know this phenomenon in physics; it is not water only,
but several salts which present the phenomenon of super-saturation.
This passage from the state of vapor to the liquid state at tempera-
tures above the point of congealing involves a state of unstable
equilibrium and the introduction of a crystal of ice makes the whole
mass pass suddenly into a solid state. It is probable that this state
of unstable equilibrium is intimately connected with the formation
of hail. In ordinary cases congelation commences at the tempera-
ture zero and we will now consider the passage from the liquid state
to the solid state at zero.

(4) Congelation at 0°.

During this stage the temperature remains constant, the water is
transformed for the most part into ice, but a part of the water is
vaporized because according to equation (7), section (1), any dimi+
nution of the pressure produced by dilatation demands a greater
quantity of vapor of water for the same vapor tension.

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 55

132
Consider a mixture containing 1 kilogram of dry air, x kilograms
of the vapor of water, y kilograms of water and z kilograms of ice.

The sum x + y + 2 remains constant and we put
~+yte=FE

Denoting by U” ” the energy or specific heat of the ice and by L

the heat of fusion of the ice, we have
U = U’ + x Oke + y (Oss + Z UM
Ph Es)

= U'+é&U" ee (U" a Uitr) Se (ue

The temperature remaining constant, we have

Wilds ss (U" a ui") dn (uM Zz OLD dz
We can neglect the volumes of the water and the ice and put
V=xv"
paV=(p—fyv'dx+fu"’dx
From the mechanical theory of heat we have approximately
hee TIE re TO aA oF gy
ahs, = uM via ye
By the aid of equation (1) we find
0=ldx —Ldz+A(p—f)vu"dx
Introducing from equation (7) the value of p — f and observing that
at the temperature of zero we have
ea
ia = — 273
we shall find
Aa ax
0 =Ildx — Ldz+ ate eg A ee

At the commencement we have
X=%V=N,2=0

sates ae a comes
= 606.5 and L = 79.06 we have

15.80 (% — %) or

and when all the water has disappeared (by congelation) we have
~=24; y= 0; 2

By integration and substituting /
x

log — = 1.822
Xo

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 133

Having determined x, we shall find p by equation (7).

When all the water is transformed into ice and vapor, we have
a mixture of vapor of water and of ice and from this moment on-
ward the vapor of waier is transformed directly into ice by the
lowering of the temperature.

(5) The aqueous vapor is partially transformed into 1ce.

For this stage we will apply the formulas given in case (3) sub-
stituting / + L for / and the specific heat of ice (c’’ = 0.5) for the
specific heat of water.

fon . ees)
log (2a ae = 3.441 (1 + 2.105 &) log 734 cate

lash (hee | i
ae Maceee | prem oe

We have supposed that the water and the ice remain suspended
in the air and take part in the thermal phenomena during the three
periods in which the vapors of water are condensed. If we wish to
consider the case in which the water and the ice after their formation
separate from the mass of air, it will be necessary to consider the
term c + €c’ orc + & c’’ as variable, We can in this case give to
€ a mean value and consider it as constant, since its value is very
small. In this case the period of freezing at o° disappears.

M. Peslinthas developed similar formule, but he hasnot considered
the variation with temperature of the latent heat of vaporization.
This causes the difference between his formule and ours.

We shall apply our formule to the case in which a mass of air rises
in the atmosphere with a velocity so small that it can be neglected.
Designating the height by we can write the equation of equilib-
rium from §4,

Vdp=-(1+ 4) dh

Combining this equation with equation (1) we find
=dU+Ad(pv) +AQr+é)dh.... (11)

Applying this formula to moist air we find the formule of section 4.
When we consider the cases in which the vapor is condensed, we
distinguish the following:

1The bulletin hebdomadaire de 1l’association scientifique de France, No.
67.

134 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5a

(6) The vapor of water 1s transformed partially into water.
Approximately we have

a (273 + T)
ay SP EES

OY ee a a Z

x fv"

By the substitution of this equation in equation’(11) and by the
aid of the formulas of case No. 3. we find

O=(¢+lc)dtt+d(e)+A(l+&dh |

O=c+ic)(e —n) +xl—mh+AUAt+hh}
(7) Congelation at 0°
In this case we find
O=ldx—Ldz+A(1 + &)dh \ (13)
O=@+L)@ —«,) —Ly +A + &)h}

(8) The vapor of water is partially transformed into ice.
We find

O= (c+ fc”) (¢ —12,) +x(1 +.L) — x,(l, + L) +A + Oh (14)

All these formulas that we have developed, pertain to the case
in which the air experiences transformations without gaining or
losing heat. Let us suppose that the air receives some heat and
that the heat absorbed is proportional to the variation of the tem-
perature. When the quantity of absorbed heat is small, the tem-
perature decreases during the expansion and in place of equation
(1) we write

~bdeadUe Avpav. ics

Here b expresses a constant which depends on exterior circumstan-
ces. Applying this equation to the dry air we find the law given by
formula (2) and m is given by the equation

b
m=3.4ai(1 +2). memati ce (i l

We see that we can easily apply equation (15) to other cases in
which the vapor is condensed, but we refrain from the development
of the formule because there are no observations wherewith to

MOVEMENTS OF ATMOSPHERE——GULDBERG .AND MOHN 135

check the results. Besides it is more convenient to apply the

formula
p 7
2 -(5) 18 SV er ee)

and to attribute to m suitable values, which vary with the height
of the layer of air. We shall consider then formula (17) as the
general formula, when the air experiences a series of transformations.
By the aid of formula (6) from § 1 we shall find

p ( 0 jen
— =| — |” Fak Gd ston re Sof ey ALLS
Po M ee)
consequently we can write
Once
Sa ee oe a ee eet oe eS
? 2 0 \ P e oy

By integration we find

P d | 1
i! cis ae — Ere te -1| . (20)
p, 0? 0 % Po

0

We shall make use later of formule (19) and (20).

Applications
Let us apply our formula to a mass of air that rises slowly in the
atmosphere.
Assume

aoe os cee
(1) When the air is not saturated.
By the aid of formula (7) of § 1 we find
x= /O0125.

Substituting this value of x in § 5 formula (4) we find
m = 3.46.

So long as the air is not saturated, the value of x remains constant

and consequently the ratio ; becomes constant. We have then

pais (ee
Bi Fo 273 + T,

136 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5!

Attributing to t different values we find the point of saturation by
comparison with the following table, which contains the values of
t corresponding to the maximum tensions of aqueous vapor.

1
We can adopt eae approximately and calculate a table of

the quantity v determined by the formula
273 +7
v= =
z
j™
We shall find
v = 183.6; f = 14.4™™; ¢ = 17°; p = 733.4™™; kh = 306™

Table

T Erase. v T | Fine v
— 30° o. 39mm 319.3 °° 4.60omm 175.4
—25 0.61 286.2 5 6.53 T6154
—20 0.93 259.2 Io 9.17 148.8
—15 I.40 234.0 15 12.70 137.8
—10 2.09 212.4 20 17.39 127.9
— 5 Scr 192.9 25 23.55 119.2

° 4.60 175.4 30 BTo5 III.4

(2) The air is saturated above 0°.

By substituting in equation (6) the value of « from equation (7)
and assuming

€ = 0.0125 = x,; t) = 17°; c = 0°; 7, O= 14.4™2,
Py= 733.4™ and fj = 4.60™™

we shall find

40 .05
log (p — f) = 2.6005 + ia

and
p = 487.2™™; x = 0.00594

Formula (12) gives kh = 3384 meters.

If we had used formula (17) we should have given m the value
6.36.

(3) Water freezing to 1ce at 0°.

By substituting in equation (9) the values
€ = 0.0125, x) = 0.00594, y, = € — x, = 0.00656, f = 7, = 4.6™™
we shall find

x = 0.00607 kg. and from formula (7) p = 476.5™™
Formula (13) gives h = 178 meters.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN may,

(4) The atr is saturated below 0°.
By substituting in formula (10)

t = 0, t= — 20°, fp = 4.6™™, 7 = 0.93"™, p, = 476.5m™
€ = 0.0125, x, = 0.00607

we shall find

log (p — f) = 2.4613 + eens
oO _ == Zi =
BP =) ae,
and

p = 312.5™™, x = 0.00186

Formula (14) gives hk = 3239 meters.
If we had used formula (17) we should have given to m the value
5.30.

Resulting Values

ALTITUDE | PRESSURE TEMPERATURE TENSION | VAPOR

h Pp Tt f ©

om | 760.0om 20° | 15.0 0.01250
306 | 733-4 17 | 14.4 0.01250
3690 487.2 ° 4.6 0.00594
3868 * 476.5 | ° 4.6 0.00607
7107 312.5 —20 0.9 0.00186

(

§6. Causes of the movement of the air

When the air is in equilibrium, the active forces are the attraction
of the earth and the centrifugal force produced by the rotation of
the earth. These two forces have a resultant which we call the
weight, which varies with the latitude and the altitude. In meteor-
ology we consider only the strata of air at a slight elevation and we
generally consider the weight constant and express its value for
the unit of mass by g.

In an atmosphere in equilibrium the weight is normal to the level
surfaces, and the surface of the earth is itself a level surface. At
the same time the density of the air and consequently its tempera-
ture vary only from one level surface to the other; we see then that
in the state of equilibrium the level surfaces are surfaces of equal
pressure and isothermal surfaces. We can consider the earth as ap-
proximately spherical, and the level surfaces as spheres concentric
with the earth. Then the temperature can vary only with the

138 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 52

altitude. In truth the temperature will never be uniform on the
earth and equilibrium has therefore no place in nature.

When the atmosphere is in equilibrium the law of variation of
’ the temperature with the altitude has no influence on the equi-
librium, but the stability of the equilibrium does depend on that
law. It is necessary to distinguish between stability with reference
to an ascending movement and to a descending movement. In
giving to a particle of air an ascending motion the temperature of
the particle of air can change more rapidly or more slowly than the
variation of the temperature of the surrounding air. If the tem-
perature of the ascending particle decreases more rapidly than the
temperature of the atmosphere, the particle will acquire a specific
weight greater than the surrounding air, and consequently it will
descend when the impressed motion is consumed, and we call the
equilibrium stable. Ifthe temperature of the particle of air decreases
more slowly than that of the atmosphere, the particle will attain a
specific weight less than the surrounding air and it will continue its
ascending movement; then the equilibrium is unstable.

By impressing upon a particle of air a descending velocity we see
in the same way that the equilibrium is stable if the temperature
of the particle is increased more rapidly than that of the surround-
ing air and that it is unstable if the temperature of the particle of air
increases more slowly than that of the surrounding air.

The stability of the atmosphere depends consequently on the
law of the variation of the temperature of the atmosphere with
the height.

Let us suppose that in a calm atmosphere the virtual temperature
decreases proportionally to the altitude according to the formule
of $4; by impressing a slight velocity upon a particle of air we can
calculate approximately the variation of its virtual temperature
from formula (17) of §5. Let m be the coefficient of the particle
of air and m’ that of the calm atmosphere, we see® that the equi-
librium is stable for an ascending movement when m < m’.

The general cause of the disturbances of the equilibrium of the
atmosphere is the heat from the sun. The sun communicates heat
to the atmosphere both directly and by the intervention of the
surface of the earth indirectly. This quantity of heat represents

> Let T and T’ be the virtual temperatures of the particle of air and of
the calm atmosphere respectively we have

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 139

an active force which can produce the movements of the particles
of air. The action of the heat of the sun is presented under two
different forms; on the one hand it produces the changes of the
temperature of the atmosphere and on the other hand by the evap-
oration of water it produces changes in the mass of the atmosphere.
The direct action of these phenomena is to produce changes in the
pressure of the air accompanied by movements of the particles of air
which give rise to the currents of air.

The currents of air, which can have any direction whatever, tend
always to destroy the perturbations and to produce a new state of
equilibrium. We can imagine permanent currents in the atmos-
phere; let us suppose that a continuous heating takes place at one
point and that a cooling takes place at another, we see that there
will arise two currents, one carrying warm air and the other cold
air.

The heat set free in the atmosphere in any way whatever, produces
currents of air. We notice the currents of air during a forest fire,
and during the eruption of a volcano. In the last case the vapors
and the shower of ashes set free the heat. We take this occasion to
remark that during the eruptions of volcanoes and during earth-
quakes it is probable that masses in the interior of the earth change
their positions. If the masses are great enough to influence local
gravitation we can explain the formation of the currents of air, by
supposing that the displacement of the masses in the interior of the
earth produces a sudden change in the force of gravity. This
change will be accompanied by a rapid change in the pressure of the
air which will produce currents of air.

CHAPTER II

PERMANENT AND HORIZONTAL CURRENTS OF AIR

$7. Isobars and gradients

During the movement of the air certain new forces come in play
and the level surfaces of § 6 are no longer surfaces of equal pres-
sure. Let us consider a surface of equal pressure, or an isobaric
surface, during such movement; this surface cuts the level surfaces
into lines that are called isobaric. We shall occupy ourselves here
principally with the isobars at the surface of the earth.

In considering the variation per unit of length of the pressure at
any point we perceive that the variation along the isobar is noth-
ing and that the variation has its maximum value along the normal
to the isobar.

140 : SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL» 51

We shall find the variation of the pressure in any other direction
whatever by projecting the maximum variation upon that direction,
which projection is geometrically represented by the chord of a
circle whose diameter is the maximum variation. See the fig. No. 1,
in which J J represents the isobar, O N the maximum variation, and
O P the variation of the pressure in the direction O P.

In meteorology we call the gradient the variation of the pressure
normal to the isobar and expressed in millimeters of mercury per
degree of a great circle.

IV

O

BIG. 5

Let G be the gradient, d p infinitely slight increase of pressure,
dn an infinitely slight increase of the normal, “a constant, we have

10333 90 ( )

as seetranate 2237.
eel. Wem

The direction of the gradient is shown by that point of the com-
pass toward which the pressure is least. From the theory of fluids

it is evident that the quantity ne represents the force produced by

the variation of the pressure acting on the unit of mass. This
force which acts in the direction toward which the pressure dimin-
ishes, must be added to the exterior forces. We shall see later that
the gradient is a small magnitude which even in cyclones does not
exceed. 1o0™™.

Terrestrial gravity g is equivalent at the surface of the earth toa
gradient of 10570 mm.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN r41

§8. Forces which act during the motion

During the motion of the air there are two new forces that come
into action, namely, the action of the rotation of the earth and the
friction between the molecules of air both between themselves and
on the surfacé of the earth. The action of the rotation of the earth
produces properly speaking two forces, the centrifugal force, which
with the attraction of the earth produces the resultant g and the
force called the composite centrifugal. This latter force which we
shall call the deflecting force is perpendicular to the trajectory of
the particle of air, and is directed to the right in thenorthern hemi-
sphere and to the left in the southern hemisphere.

Expressing by v the velocity of the air, by w the angular velocity
of the earth and by 6 the latitude, we have the deflecting force

=n) Ms SIND aansin ha ost oe, PaeES Ck)
The velocity is expressed in meters per second and
22
” = e164 = 0 .00007292

The deflecting force of the rotation of the earth is found by con-
sidering the movement of a point relative to the earth, which is sup-
posed to be at rest. If we do not introduce this force in all the
dynamic problems that introduce movements relative to the earth,
it is because this deflecting force is very feeble and the trajectories
do not extend to considerable distances. On the contrary the
currents of air travel over large parts of the surface of the earth,
and the forces which produce them are very feeble. We may then
anticipate that the deflecting force of the rotation of the earth
plays an important part in the problems of meteorology. Let us
add that this force being perpendicular to the trajectory has no
influence on the velocity of the current, but tends only to change its
direction.

On the contrary, friction is a force that tends to diminish the vel-
ocity. The complete theory of the friction between the molecules
of air is very complicated and will be developed in the second part
of these studies.

For the present we admit that friction is a tangential force and
opposed to the motion. As to its magnitude we will suppose that
it is proportional to the velocity, and expressing by k the coefficient
of the friction, we write

ie jorce-of Fraction =U oe, «st OQ)

142 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLS 5x

The complete theory shows that the value of k depends on the
height of the current. When the height of the current increases,
the value of k diminishes, which conforms with what we know of
the coefficient of friction of water in open channels. For very
broad channels the coefficient of friction is in the inverse ratio of
the height of the current.

In studying the movement of a particle of air it is necessary to
add to the exterior forces the tangential forces and the centrifugal
force produced by the motion. Expressing by s the distance trav-
eled over and by & the radius of curvature of the trajectory, we
have

: vadu .
the tangential force = —— SB ene Oe ee ee)
ds
vy
the centrifugal force = ps) cece Sgr (4)

Let us add tiiat the horizontal currents move along the surface
of the earth which is normal to gravity. Consequently we neglect
the action of the gravity in the following problems and the acting
forces will be (1) the gradient force, (2) the deflective force of the rota-
tion of the earth, (3) the force of friction, (4) the tangential force
of the motion and (5) the centrifugal force of the motion.

§9. Horizontal rectilinear and uniform motion

When the motion is uniform and rectilinear, the tangential force
and the centrifugal force disappear, and equilibrium is established
between the force of the gradient, the force of friction and the deflect-
ing force of the rotation of the earth.

Expressing by a the angle between the gradient and the trajec-
tory and resolving the forces along the trajectory A B, fig. 2, and
perpendicularly to its direction we have

2 pis es ee aed See
0
Seen
= Gy Sia oe 2 SIO on ae een)
p
By division we obtain

2w sin 0

tan oo Se og ee ea ee

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 143

In the northern hemisphere the latitude 0 is positive and in the
southern hemisphere @ is negative. The angle a has the same
sign as 6 and consequently the wind is deflected to the right in the
northern hemisphere and to the left in the southern hemisphere.

a

FIG. 2

FIG. 3

144 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOR. 51

The ratio between the velocity and the gradient is found by equa-
tion (1)

= 4
Bc irsne one ean!

By formule (3) and (4) we can determine the direction and the
velocity of the wind: by graphical construction we find their values
in the following manner.

Let O B, fig. 3, be the direction of the gradient and let two dis-
tances O B and O A be in the ratio.

OB:OA=2w:k

Describe a circle with the radius O B and erect A L perpendicular
to O A : making the arc B D equal to the latitude and draw D N
parallel to B O; we shall have the angle AO N =a. Describe a

semicircle with the diameter O C = a and the chord O M will be

0
equal to the velocity v.

We shall call the angle a,determined by equation (3), the normal
angle of inclination.

Table of the normal angle of inclination a

COEFFICIENT OF FRICTION K =

LATITUDE i r ——— ae ar, —=s

0.00002 0.00004 | 0.00006 | 0.00008 | 0.00010 | 0.00012
| |

°° 0.0° °.0° 0.0? 0.0° | 0,0° | 0.0°

5 32.4 17.6 12.0 9.0 7.3 | 6.0
b de) Sr. 7 32.3 22.9 17.6 14.2 II.9
15 62.1 43-3 32.2 25.3 20.7 17.9
20 68.2 51.3 30.7 32.0 26.5 22.6
30 74-7 61.2 50.6 42.4 | 36.1 | ars
40 78.0 66.9 57.4 49.5 43.2 | 38.0
5o 79.8 70.3 61.8 54.4 | 48.2 43.0
60 81.0 72.4 | 64.6 Si HO 4 | 51.6 | A605
70 81.7 73.7 | 66.4 59.7 53.9 | Sasne
80 82.1 74.4 67.3 60.9 | 55.2 ie Sonm
90 82.2 <7 | 67.6 61.3 | 55.6 | 50.6

The relation between the velocity and the gradient depends on
the density of the air. Supposing the temperature to be o° and the
pressure 760™™ the density op is

d" 1.29805

eet Sere =i aes
Zaz 98089

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 145

and we find the following values for the latitude 45°:

A { v G

e G v
@. 00002 79° 2! 8.84 0.113
0.00004 68 48 8.39 o.119
0.00006 59 49 7.78 0.129
0.00008 52 12 wet o.141
0.00010 45 53 6.46 0.155
0.00012 40 41 5.87 0.170

where

v = velocity in meters per second,
G = gradient in millimeters of mercury per degree of a great
circle on the earth’s surface.

Supposing the temperature to be 20° and the pressure 740™™ the

value of . will be increased in the ratio of 1 to1.102. Supposing the

v
temperature to be — 10° and the pressure 770™™ the value of G

will be diminished in the ratio of 1 to 0.951.

By the aid of the last table we have calculated the following table
for the latitude of 45°, the velocities being always expressed in
meters per second. The scaleof wind forceis that hitherto employed
in several meteorological systems of Europe; the numbers have
the following signification:

o = calm; 1 = feeble; 2 = moderate; 3 = quite strong; 4 =
strong; 5 = very strong or storm; 6 = a hurricane. The values
of the coefficient of friction are the extreme limits which we have
found by preliminary calculations, for the ocean and for the irregu-
lar surface of the earth.

GRADIENT
MM. PER DEGREE G. C.

WIND FORCE lyELOcITY M.P.8.|— =

SCALE o — 6 k = 0.00002 k = 0.00012
O'=3 cAlm:,.\.. 22 6 o— I o—o.1 o—o.2
t = feeble. ..2:..... I— 4 o.I—o.5 0.2—0.7
2 = moderate.... 4— 7 o.5—o.8 0.7—1.2
3 = quite strong — re o.8—1.2 Tt, 21.9
4 = strong....... 77 | BENS t.97-2.9
Sy StORM! Sie. epee 17—28 I.9—3.1 2.9—4.8
6 = hurricane.... 28—5o 3.1—5.5 4.8—8.5

146 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

$10. Horizontal currents of air with rectilinear tsobars—the
latitude 1s supposed to be constant

When a permanent current of air flows over rectilinear isobars
the mass of air that flows perpendicularly to the isobars in the unit
of time must be constant. Expressing by ¢ the angle between the
gradient and the tangent to the trajectory then, the equation of
continuity becomes

U- COB = constant’! vip tuscan ee

Decomposing the five forces (see §8) in the directions of the
tangent and the normal we shall have

fe separ epee 5B Bho See
e ds

| Sage : v

GC sind =20° 0 sin @ = 5. Sense te)
p R

2
20 Sen OF F

FIG 4

Differentiating equation (1) we have,
dv=tangdd¢

and introducing the value of the radius of curvature

| d¢
Ren! es
we shall have
a (e o // / 2 ‘)
ge ee re een, Mt aera ere |
2 G sing =v(2w sino — 0 5*| (5)
: dal ea

MOVEMENTS OF ATMOSPHERE—-GULDBERG AND MOHN 147

These two equations are transformed into the following

Lt 2w sin 0
—G i= Bu Ccosy \ &--—_——-_ tan ¢ =).(6)
p k
7
v d¢
0 =ksin¢ — 2wsin@cos ¢ + (7)

cos ¢ ds
introducing
cos (a S —d %&

where x is the distance along the gradient and s along the trajectory,
equation (7) can be written

vcos¢ d (tan ¢) 2w sind
PMLA Is eae ape ay tenes)

The general integral of this equation is

kx
fae) Ce™ vecos &

where Cis the arbitrary constant. In nature it is necessary to place
C = o because the angle ¢ does not increase to infinity with increas-
ing values of x.

Thus we have (as in §9, eq. 3)

tan: — 2a = tana

Substituting this value of ¢ in equation (1) we see that the velocity
becomes constant and consequently according to equation (2) the
gradient likewise becomes constant, provided that we suppose the
density o constant, and in this case the isobars are equidistant.
If we wish to consider the variation of the density o we introduce

d p= —pGdx

and by the aid of formula (20) from §5 we can calculate the pres-
sure ~. In general we can introduce a mean value of the density
and consider it as constant.

148 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

§11. Influence of the variation of latitude on hertzontal currents
of air with rectilinear itsobars

We consider only the case in which the gradient coincides with a
meridian. The latitude 0 is expressed by the following equation

Oe Ge Pe ee eR ees ee
yee ONE ts es) Se
10®° 180
G
ae y
x
O
FI@. 5

The coefficient A is positive when the gradient is directed toward
the north and negative when it is directed toward the south.

The equations developed in §10 now hold good by considering
6 as variable.

Equation (8) of $10 becomes

d (tang) 2wsin6—ktang

sb 3)
dx v cos ~ \
For the sake of abbreviation we write
h
tau e =A —— 5 ge ae gt ee ee

Placing the arbitrary constant equal to zero, as we have done in
§ro, we find that the integral of (3) is

tan p= = 2 cos ¢ sin (G8) ee ee ae

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 149

Substituting this value of tan ¢ in equation (6) of §10 we shall
have

2
YG =kvcos¢ (1 + ey cos ¢ Sin O@ sin (9 — ) (Oy
p
In order to obtain the equation of the trajectory we introduce
dy=tangdx
Substituting herein the value of tan ¢ and integrating, assuming
y = o for x = o, we get

4 (7) COS € ft 0 a 0, : 0 a 0,
Se eles a hl 9 sin Ser Ae 0)
dp. ; ;
Introducing nG = ae into equation (6) we shall by integration find

the pressure p. Finally by graphically constructing the curve of the
gradient we shall easily determine the curve of the pressure.

According to equation (5) the angle of inclination ¢ depends on
the quantity ¢ :¢ being so small that cos ¢ does not differ sensibly
from unity, we conclude that ¢ approaches the normal angle a,
when the latitude 9 has a large enough numerical value. As for
the winds that cross the equator, 8 has small numerical values, and
the angle ¢ can be very different from the normal angle of inclina-
tion. It is necessary to distinguish two cases:

(1) The gradient ts directed towards the north.

In this case A and ¢ are positive; theangle ¢ isnegative for south-
ern values of @ and for northern values until 9 = «. When @ is
greater than «, the angle ¢ becomes positive and approaches more
and more to the normal value a. We see then that the winds that
come from the south have turned to the left even after crossing the
equator, that the deviation is nothing at the latitude « and that
beyond this point the deviation is to the right.

We recognize this law of deviation in nature in the trade winds of
the Atlantic and of the Indian Oceans during the summer. ©

(2) The gradient 1s directed towards the south.

The value of A and that of « become negative. In this case the
angle ¢ remains positive north of the equator and also south of the
equator to latitude 0 = ¢; then ¢ becomes negative and approaches
more and more nearly the normal value a.

We see then that the winds that come from the north have devi-
ated to the right even after crossing the equator and until 0 = ¢;

150 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

at this latitude the deviation is nothing, then it turns to the left.
In nature, the monsoon called the west monsoon in the Indian
Ocean follows this law during the winter.

We will apply our formule to numerical examples that we can
compare with the charts of general winds. Among these we mention
especially the excellent charts published by the Meteorological
Office at London, under the title ‘‘ Monthly Charts of Meteorological
Data for Square 3: published by authority of the Meteorological
Committee.”’ These are in fact those charts that have led us to
establish the theory of winds crossing the equator presented in this
paragraph. We have developed the preceding formule by sup-
posing that the gradient coincides with the meridian ; approximately
we may apply them to the cases in which the angle between the
meridian and the gradient is small. In the first example that we
shall compute we assume this angle to be 20° as we see it in fig. 6.

Applications
(1) The gradient is northerly (see fig. 6).
Let
0, = 0°,
vcos % = 10",
k = 0.00002,
t = 20°;
we shall find
e = 4° 13/2
and the following values:
) d v G y
° m. mm
— 5° — 50.2 15.6 0.35 AAD
0 — 29.6 nro 0.20
5 Ab 10.0 0.21 —1.3
10 34-9 2.2 0.38 6

Let
a. =";
vcos ¢ = 5™,
k = 0.00002,
t = 20°;

we shall find
e= —2° 15/
and the following values:

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN

a
| m | mm
5 42°5 6.8 0.16 3-0
° 15.9 5.2 } 0.10 oo:
- — 19.2 5.3 0.12 0.2
— 10 — 44.4 | 7.0 0.22 gab

152 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

We shall see that the law of inclination ‘eq. 5) is quite conform-
able to the observations; however the observed velocities and grad-
ients do not follow our formule always, which is very easily ex-
plained when we note that in nature the currents of air near the
equatorial calms have an ascending movement that diminishes the
horizontal velocity and the magnitude of the gradient. We could
easily introduce this influence into the formule, but we shall not
profitably extend our researches any further since we shall treat
the problem in a more general manner in the second part of these
“Studies.”

$12. Horizontal currents of air with circular tsobars around a
barometric minimum

We shall consider the latitude as constant® and the isobars as
concentric circles. The system being symmetrical with respect to
the center of the isobars therefore the quantity of air that enters
per unit of time must remain constant. Designating by ¢ the angle
between the direction of the wind and the radius, which latter
is the direction of the gradient, the component of the velocity in
the direction of the radius will be v cos ¢. Let rbe the radius and
h the altitude of the horizontal current, the section of the current
will be 2x 7 h, and remarking that h remains constant the equation
of continuity will give

ur-cos y..=.0gnstant..— eww eo ED

The acting forces are the same as in §10 and the equations
(2) and (3) hold good by substituting

1 sin
=. he aise dd adr

cos¢dds = —dr

By the aid of equation (1) we shall find

v COS vsin gd ¢
“Geosp =o( e+ : Bes es

v sin v cos ¢d
“Gsin $ = 0(2usino + ast ¢ |
0 r dr

:: we . i . is .
* That is, uniform over the whole barometric depression.—EpITor.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 153

These two equations are transformed into

KG = o( bcos #2 asin 8 sing +”) rae eer)
0 r
: di
* O0=ksing — 2wsin@cos¢— v Set Re . (8)
;
The last equation can be written
D)
SS
rdr urcos ¢ k

By integration making the arbitrary constant equal to zero for
the same reason as in §10 we obtain

tan gs = —2sin 8 tan a te sae

Fic. 8

The angle of inclination has therefore the normal value and the
trajectory is a logarithmic spiral. Designating by g the angle be-
tween the radius and some fixed direction, the equation of the tra-
jectory will be

log nat r == e cotje: Cay. 2 a. a. (0)

Let 7, and wy be the values of r and of uv for any point whatever,
we can transform equations (1) and (2) into the following:

UT Si teh cma noise Sse)
LoL kv Vv?
p cos a ry
‘ (7)
(Si piles ane Ofte ok
were 0 ye de =
0 cosa ft ff

154 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

By introducing a mean value of the density and by expressing
the distance 7 in degrees of the meridian, we can write

a
Ge fd Sais at oye sth ver eae

in which a and a’ are constants. Then the increase d b of the pres-
sure in millimeters is equal to G dr and we shall find

a r aft 1
oh eae ae a te i

patho

The equations that we have developed demand that the altitude
of the current of air remains constant since we assume its horizon-
tality. We can then, therefore, only apply the equations to the
exterior parts of a whirl about a barometric depression, for in the
interior of the whirlwind the currents have an ascending movement
so rapid that we cannot neglect it.

Applications

(1) Whirlwind having a great velocity (see fig. 9).
Let the latitude = 20°,

k = 0.00002,

tT = 20°,

; = 0.001006 (for a mean pressure of 753™™)
Vy= 50™,

ro= 0°.3.

Expressing r in degrees of the meridian we have

G 0.8 2.014 ae eG r est 1.007
~ ¥ T ees LO: °8 ts mi Ee is
To
yg = 328 —; a = 68° 5.8’
:
p=) (U3! 0.°4 0°.5 0°.6 0°.8 1210 PA)
v = 50™ 37 .5™ 30™ 25m 18.75 15™ 7.5m
G =77.3™™ 33.5™™ 17,.77™m 10.6™m 4,9mm 2.8mm 0.6mm
b —b, =0™m 5,]™m 7.6mm 8.9mm 10.4mm Lie 14,.3mm

—yg=0° 41° 73° 99° 140° 172° 340°

a

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN Is

ut
wn

——— al
. r ° . °

2

|

PATH OF THE W/NO.

aoa!

EE SD Oe rene secre Aes
2 i da 7 ep W7 2

FIG. QO. WHIRLWIND AROUND A BAROMETRIC MINIMUM

156 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

(2) Whirlwind having an average velocity (see fig. 10.)
Let the latitude = 60°,

k = 0.00012
Uy= 15",
Tr =7°,

; =0.0009404 (¢ = 0°, b = 750™™).

We shall find

19.43 105.5-
+-

?
aa

a = 46°23 .3'2.G

Vif

r 52.75 5 re
b— b, = 44.73 log me + 1.076 — 2 ;g = 138.5 log. i

= 7° 8° 9° 10° eg 15° 20°

— ee tebe Li St eee BF 120 Osa
aS 02 2. G4 2 oUt 20). 1.682" 1 jo. Oe
SR 2.8. eT ee 1 Ee eae
Se 8° 15° 21° 32° 46° 63°

SS Gy S4~
I

§13. Horizontal currents of air with circular isobars around a
barometric maximum

By making the same hypothesis as in § 12, we shall find the same
equations, but it is necessary to write

= AUR iiss: Go oe Recs eo ee

and to change the sign of the gradient, on the supposition that the
pressure diminishes with distance from the center. We shall then
have

Ur =U1%
ig ee R91 l lt Ve ro (2)
5 gue tele ar
where
a a’
CR ua (3)

et si r ae =) r
o- Sg OS Sates Fae svat we Cay

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 157

FIG. 10. WHIRLWIND AROUNI A BAROMETRIC MINIMUM

158 SMITHSONIAN MISCELLANEOUS COLLECTIONS Vi GL 5 iT

The hypothesis that the pressure diminishes with the distance
from the center requires that

kr

cos a

Vo

In nature the wind about barometric maxima always has a slight
velocity and the pressure diminishes with distance from the center,
However, wecan apply the formule only to the exterior parts of
the whirlwind, because in the interior part the currents are not
horizontal, but have a vertical descending velocity which influences
the horizontal movement.

Applications

Whirlwind about a barometric maximum (see fig. 11).
Let the latitude = 45°,

k = 0.00012,
s ~ 00009281 (r = 0°, b = 760™™), v, =4™, r, =5°
we find
3.406 3.879
a = 40° 35'.9:G = 2:
p
Fh Oy Gat lhe Cen he 118 lee =
50 =7. i ts .O ae ars ir Oe a
pot 4c eel Wn eae g° 10° 15° 20°
v= 4m 3.3m 25m 2.9m 1.3m 1.0m
G = 0.65™™ 0.55™™ 0.42mm (934mm (Q.93mm (17mm
bb —b = 0mm O.57mm 157mm 234mm 3.73mm 4, 72mm
aed! Ota tee 93° = 3342i(isiwASC«@SPP

§14. Currents of air in the interior part of an atmospheric whirl

In §12 and § 13 we have considered currents of air flowing at a
constant elevation approaching the center of the isobars or moving
away fromit. In nature the elevation of the currents does not re-
main invariable; in atmospheric whirls around a barometric mini-
mum the currents have an ascending movement that increases
toward the center, and in whirls about a barometric maximum the
currents have a descending movement that diminishes with the
distance from the center. We shall treat the general problem in
the second part of these studies, but at present we will consider a

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 159

°

=
40

k= 0000/2

PATH OF THE W/NO

FIG. II. WHIRLWIND AROUND A BAROMETRIC MAXIMUM

160 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

special case, namely, the central part of the whirl. For a system of
circular isobars the equation of continuity can be written

2x rhv = constant
Supposing the height to be variable and a function of r, we can write
wT cond =F (r)
Assuming the following hypothesis:
iQ =cr
where ¢ is a constant, then the equation of continuity takes the form
v cos $=cr

Introducing this value of v in equations (2) and (3) of §roand by the
aid of the formule of §12, we shall find

“ Goos $= v(t — vsing 9 —) sD iewrcer GOP ae
p dr

v sin ¢

KGsin gv (2using +7S"¥ + vcos¢ ae
p

Eliminating G we shall have

0 = ksin g —2w sin cos g—2esing— vo . (4)
r

This equation can be written

. d (tang ¢) ry

k — 2c) tang y— 2wsin8
dr

By integration placing the arbitrary constant equal to zero we find
2w sii 6 oa

BS sn Neat 6 ee te

of ~ eo ae (5)

The angle of inclination is therefore constant and the trajectory
is a logarithmic spiral, but the angle of inclination has a value dif-
ferent from the normal value a of § 9, eq. 3. We express this
value by f, and introducing the value

ie.
tana = sin 0

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 161

we shall have

(neti eee (6)
2¢
ie et
k
- -
Equations (1) and (2) may be written
C
= A SET eee ee ee ea |
cos B
Bee (e=ie. : (8)
0 cos? B
Attributing to 9 a mean value, we can write
Ge ee sae ek oa et Nel a ee ten)

in which G, denotes a constant magnitude and r is expressed in
degrees of the meridian.
Then we have
Ob = eh ONG ae =o, eh Pe hee (LO)

in which b, is the pressure in millimeters at the center. Thus the
curve of pressure becomes a parabola.

The preceding formule apply to whirls around a barometric
minimum; by making ¢ negative and substituting (180° + ) for
8 we shall have the following formule which apply toa whirl about
a barometric maximum:

tang a

tang B = ; ee a
a ra
k
iy otpe am dae _. (12)
p cos? 8
Applications

(1) Whirlwind of great velocity about a barometric minimum (see
fig. g).

Consider the central part of the whirlwind No. 1 in §12.
Let

B = 89° 45’;* —0.00103; (¢ = 20°, b = 735™™)
0

162 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

we shall find
v = 2827; G = 566.57; b — b, = 288°

We apply these formule to the central part situated between
the center and r = 0.14° (where the current is one of ascension).
By constructing the curves of v and G we shall also find by graphic
interpolation their values for the region between r = 0.14° andr =
0.3° (where the transition to horizontal motion occurs). The
results are given in the following table:

r = 0° 0.1° 0.2° 0.3°

v= 0™ 25.2m 50.4™ 50.0™

G = 0™™ 56.6mm 113.3™™ 7.3mm
b—b, = 0™™ = 2.8mm 10.Q™™ 18.6™™

(2) Whirlwind of mean velocity about a barometric minimum (see
fife. FO):
Consider the central part of the whirlwind No. 2 in § 12.

Let
B = 55°; » = 0.0009596 (¢ = 0, b = 735™™)

we shall find
v = 3.082 7; G = 0.583 r; b — 6, = 0.2915 7

We apply these formule to the central part (ascension) situated
between the center and r = 5°, but we find by graphic interpolation
the values for the part situated between r= 5° and r = 7°, as fol-
lows:

r=0° 1 2° 3° 4° 5° 6° 7°

yv=0™ 3.1™ G22 972m 12332 15,40 16™ Toe

eS a se Oo Soe
b—b, 9mm (29mm 1.173™ 2.627" 4.667 7.28™™ 10.387™ 13.58"
eh Rookie: 132° 75° 42° 18° OS, bg) cooks ate

(3) Whirlwind about a barometric maximum (see fig. 11).
Consider the central part of the whirlwind of §13.

Let
B= abe.
lt
Oe 0.0009281

we shall find
Y= 1.828776 = Vise t2 0, oe

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 163

Applying these formule to the central (descending) region sit-
uated between the center and r = 1.5° and by graphic interpolation
beyond, we find the following values:

2. 1° 9° 3° 4° 5°

v =0™ 1.8m 3.6™ 4.6™ 4.7m 4.9m

G =0™™ 9.32m™™ 9.62™™ (.68™™ 0.69™m = 0.65™m
b, —b =0™™ 0.16™™ 0.62™™ = 1.25m™m™ —-1,93m™M —- 2. N™™

By these formule and examples we see that for a given latitude
and a given coefficient of friction the whole system of a whirlwind
is determined by the maximum velocity and the distance from the
center of the movement of the point where that velocity is found.

CHAPTER III
THE PERMANENT VERTICAL CURRENTS OF AIR

$15. Rectilinear movement

We consider a particle of air moving in the direction of the vertical
axis of a which we suppose positive upward. We neglect the action
of the rotation of the earth and the viscosity or resistance between
the molecules of air. Then we have three forces, namely: the
force produced by the variation of the pressure

the force of the weight g, and the tangential force
dw
Ode
where w represents the vertical velocity.
The equilibrium between these three forces is given by

La ie eo eae a

Expressing by o, and w, the valuesof o and of w at any point, the
equation of continuity becomes

Oe Moen ns!) troumuatt ron wry aga Ueto is we)

This equation demands that the section of the current be of con-
stant area. The above equations hold good for ascending move-

164 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

ment, but by writing — w in place of w they apply to a descending
movement. To integrate equation (1) it is necessary to know the
density as a function of the pressure. We will assume the relation
given by equation (18) of § 5, and then from equation (20) we shall
have

1
ee eee | ee a
2g g Po:

m — 1

Fe Alig ict else sep ee

Here we have supposed » = p, and w = w, when 2 = o.
Differentiating equation (18) of §5 we have

em Pp

If we differentiate equation (2) and eliminate do and dp by the
aid of equation (1) we shall find

do _m-—1dp

PP fits rca ETc I ot 6 eh TE oe

We conclude from the last equation that the velocity w can never
exceed a certain limit w,, determined by the equation

(ae | (ee eee rere ey Se

Introducing the value of : expressed in terms of w and w, and

noting that 2 is equal to a T, we find
0

m = 1
fe a sg Canna
w m—1 w,”

If we introduce this value into equations (4) and (3) we shall
determine the maximum value of the height z, that a vertical cur-
rent cannot exceed, for a given value of the initial velocity w. We
see by equation (4) that the velocity increases while the pressure
decreases, and equation (3) shows that the pressure p diminishes
for increasing values of w. Ina vertical ascending current the pres-

MOVEMENTS OF ATMOSPHERE

GULDBERG AND MOHN 165

sure is therefore less at the same height than in the surrounding
atmosphere.

If we wish to apply equation (3) to a Vertical current whose sec-
tion varies, it is necessary to employ the following equation of con-
tinuity: ,

eee ere ees ain! ® |. Jacamany

However this formula applies only in case the section of the cur-
rent varies very slowly. It shows that the velocity diminishes as
the section increases, or vice versa, as at the commencement and
at the end of the currents.

Applications
(1) Calculation of the altitude.
Let
m = 9,
eee
we shall find
<> i : | = z
a | W=o | w= 17 | w= 107] wy = 20m Wo = 30 | wo = 50™
Po | |
| ee ee EE
0.80 1874™ | 1874 | 1872™m 1865m 1854™ 1819™
0.60 4169 | 4169 4163 4143 4111 4008
0.40 | 7180 | 7180 7163 7112 7027 6755
0.20 11800 | 11799 11738 11553 11244 10230
0.10 15820 15818 15622 15028 mI KY) — epcoood ac
0.05 19440 | 19434 18807 16908 [ive raystexcie enefovetclcisie aausratarwis
0.01 | 25810 | 25729 ee Ce ee Cece
| |

(2) Maximnm altitude for a given initial velocity.

|
| | Bp | Po a )
Wo | wm | 2m pe | Tm u YMo\ ae Jo
|
ym | L709. | 29530% | 0.001623 81.0 o.r0omm
10 220.3 20620 0.02095 E3520. 10.06
20 238.0 16920 0.04525 157.8 40.35
30 | 248.9 14530 0.07103 172.6 Q1.24
5o 263.4 11180 | 0.1253 193-4 257.4
100 | 284.5 6247 0.2707 | 225.6 Iti.
200 | 307.3 1588 0.5845 | 263.2 6488.
| |

The values of T,, represent the virtual temperatures at the height
2, In the last column we have written numbers that represent

166 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the tangential force at the surface of the earth, expressed in milli-
meters per degree of the meridian. One should compare this force
with the gradients for horizontal movements in order to get a clear
idea of the force that acts in the vertical ascending movements.

§16. Conditions of the existence of ascending and descending
currents of air

If the vertical currents preserve a steady motion, the pressure
within the currents and in the surrounding atmosphere must satisfy
certain conditions which we shall now consider.

Ascending currents

In ascending currents (fig. 12) the air enters along the surface of
the earth and consequently the pressure p’, of the atmosphere must
be greater than pressure p, of the lowest part of the current; this
necessitates the existence of a barometric minimum at the surface of

oe p —? ye

FIG. 12

the earth. Inthe higher strata where the air flows out from the
vertical current, the pressure p in the current must remain greater
than the pressure p’ of the surrounding atmosphere and consequently
we shall find a barometric maximum at a certain elevation.

We remark that great velocities may perhaps modify the phenom-
ena and that the air can flow outward even from a barometric min-
imum’ but it is probable that in nature we shall always find baro-
metric maxima in such cases, because the velocities are slight at the
boundaries of the currents.

7 By substituting 180° + a for a in the equations of $12, we shall have

the formule that belong to currents flowing from the center. This hypo-

; . kr
e ee
thesis requires that v >

os

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 167

In order to study the conditions that obtain on the inside and on
the outside of the current between the pressures p, and p,/ at the
surface of the earth and betweem the pressures p and p’ on the
inside and outside of the current at a given altitude, where the ver-
tical velocity of,the current is equal to zero, we shall assume that
the virtual temperatures 7 in the current and T’-in the surrounding
atmosphere decrease proportionally to the altitude. Let m be the
coefficient that belongs to the current and m’ that belonging to the
atmosphere, we have from $4

£-(£)" =(1- 8? me eh)
Po ive amT,

*-(z) Se eee
a ey am'T,

By writing

(ty
(1 ieee 0 Nee Na (3)
am’ T\
we shall have
a alas Meantime Ore seat (A)

If the movement is ascending it is necessary to have simulta-
neously

pa <dand 2 > 1

0

If the movement is descending it is necessary to have simultane-
ously

ee Vand et
Po P

Differentiating 7 (z) we shall find

dj (2) pe as : rare
“Le =f @) = £5 @—____~ (5)
= To Td (1- g? )Q- 8? )
amT, am tT,

168 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

If 7’(z) is positive, 7(z) increases with the altitude and remains
larger than unity: the condition of an ascending current is then ful-
filled.

We shall distinguish three cases:

(1) T,>T"’,. At the surface of the earth where z = o we shall
have 7’(z) positive. We conclude then that an ascending current
can always exist when the virtual temperature of the current is
greater than that of the surrounding atmosphere.

If m < m’ or m = m’ then f(z) increases continuously with z
and the intensity of the current increases with the altitude.

If m < m’ then f(z) increases at first and reaches a maximum at
an altitude given by

h=*mm' to— to (6)
> ae ,
and at the same time, we have
fae hh

(2) T, =T,’. It is necessary that m> m’ so that f(z) can be
positive. This case includes the unstable equilibrium of the atmos-
phere.

(3) T,< f',. At the. suriace of the earth j(2).1snepative: “Lt
m > m’ then f’(z) = o at an altitude h determined by equation (6)
and f’ (z) becomes positive for greater altitudes. We conclude then
that f(z) at first decreases with the altitude and reaches a minimum
at the altitude h and then decreases with the altitude. It is therefore
possible that an ascending current can occur even when the virtual
temperature of the surrounding atmosphere is higher than that of
the current. The altitude of the current must be greater than h
and the virtual temperature of the current must decrease with the
height more slowly than that of the atmosphere.

Descending currents

In descending currents (fig. 13) the air enters at the height z and
flows outward along the surface of the earth where a barometric
maximum occurs. Therefore the conditions of the descending
motions are p’, > ppand p> p’. We will count the altitude z from
the top downward and write

T ieee aide ee
a WH am

/

MOVEMENTS IN ATMOSPHERE—GULDBERG AND MOHN _ 169
We may write

P = es (1 gs iM 5
am eae Pe Se anenrer tiie:

#- (=) SG ones ) eee ahi
Po Gf. / am’ ee

Assuming

a4 m
148) "
(0 ower (2) ("Pw

we shall have
eae)
| aaa
and the conditions for descending motion are written
4 S 1 and 20 <1
0
and consequently we must have
7) > 1

By differentiating f(z) we shall find
m — wm’
Dis Sai ean EN o g
df (z x 0 0 /
HO _ 9 a 8 § @), “a mm" - 00)
dz a Tae
We shall distinguish three cases:
(1) T, < T’,. For 2 = 0 we have /’(z) positive and we conclude
then that a descending current can always exist since the virtual

170 SMITHSONIAN MISCELLANEOUS COLLECTIONS VGY. 51

temperature of the current is colder than that of the surrounding
atmosphere.

If m > m’ or m = m’, f(z) increases with z and the intensity of
the current increases with the altitude.

If m < m' we have f’(z) =o for a height h determined by the
equation

at! > SS aeeenne

For this value of z, f(z) reaches a maximum and at the same time

we have
Tf = 7

If the altitude of the current is greater than h the virtual temper-
ature of the current at, the surface of the earth is higher than that
of the surrounding calm atmosphere.

(2) T, = T,’. The descending movement requires that m > m’
and this case includes the unstable equilibrium of the atmosphere.

(3) T, > T’,. In this case 7’(z) is negative up to the wpper
stratum where the descending current must begin and consequently
}(z) decreases.

If m > m’ then f’(z) becomes zero for z = h, as given by equa-
tion (11) and f(z) attains a minimum for that value. For values
of z greater than h, /(z) increases and it is then possible that a descend-
ing current can even occur when the virtual temperature of the
current is higher than that of the surrounding upper layers of atmos-
phere. The altitude of the current must be greater than h and the
virtual temperature of the descending current must increase more
slowly than that of the atmosphere.

$17. Horizontal velocity produced by a vertical current

In nature the ascending currents produce horizontal velocities
along the surface of the earth, which can attain very considerable
values and which are dangerous to the obstacles they meet in their
way. As to the descending currents we nearly always find that in
nature the resulting horizontal velocities along the surface of the
earth are slight, but it is probable that the horizontal velocities at
a certain altitude where the air enters the descending current, have
considerable values.

Let us consider an ascending current and let v, be the maximum
horizontal velocity, ~, the minimum pressure in the current at the
surface of the earth; let p,’ be the pressure in the calm atmosphere

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN Te Jal

at a point so distant that we can neglect the velocity, we have ap-
proximately for the equation of the living force or energy, assum-
ing the density of the air to be constant,

Se ae

in which F expresses the energy consumed in overcoming friction
or the work of the friction along the surface of the earth. We shall
find

P, — Py = 0 Uo + F). ey at)

The work of friction [or done in overcoming friction] depends on
the path traversed by the particles of air and on the variation of the
velocity. There are whirlwinds where the work F is very small
and others where it is very great. It is especially the dimension
of the whirlwind that determines the work of friction. In every
case we see that the horizontal velocity depends principally on the
barometric depression p,’ — Py), which we can consider as the meas-
ure of the force of the current. Let us denote by D the barometric
depression at the surface of the earth. For ascending currents by
introducing /(z) we shall have

| p 1
ee ae 22 pf op ee aie, (3)
ee rs ( r FO)

The depression cannot exceed the value given by this equation
after substituting p = p’.

Let us assume the pressure in the calm atmosphere equal to 760™™
and designate by D,, the maximum value of the depression expressed
in millimeters, we have

Dy, = 760(1- 7) Sage anne eres
} (2)
For descending currents, we find in the same way,
, ! Po r
p-p = off -1) fad oy ahi Ec)
Po
=" FO0s Gay aby 4 x ee GG)

Here D denotes the excess of pressure in the center of the whirl-
wind over the pressure of the calm atmosphere and D,, its maxi-
mum value.

172 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

By the aid of these formule and the equations of § 16 we have
calculated the following tables.

TableI. Ascending currents

To Re ™ m’ | Zz h fE J pe Dm
|
293° | 273° 7 6 | BOQOUE | Wrst w sis a 268.6 24475) || 38g
293 | 283 6 oh. val BOOG! Vc aretaa rete s 264.5 248.8 | 22.6
300 | 293 7 7 BQ007 Ti laacet.ake oes | 290.2 285.2 | 3.7
283 | 273 5 7 512 5123 248.0 248.0 9-3
283 | ai sel 5 7 7000 512 235.2 238.8 Chat
300 | 300 | 6 > BOON Mi laictere to, opedeae 288.6 286.3 0.4
300 300 | 6 5 BGO) peti sicteisrerenste cle eseeice| 265.8 4-9
280 | 283 | 6 5 7000 2635 240.2 235.2 atta
Table II. Descending currents
| |
T a m m’ Zz h T dd Dm
——— oo

253 263 | 10 | 2O00m" Ale cre sieveysisiar 259.8° | 272.8° §, 7mm
250 260 | 6 6 | JOOON Wiiarestis mini 267.1 277.1 II.2
253 263 | 5 7 5122 5122 288.0 288.0 10.6
253 | 263 | 5 vp 6000 5122 294.0 292.3 9-9
260 260 | 6 5 DOOM | Nityasis «cle clere 288.5 294.2 4-7
243 240 | 6 5 6000 2635 277.2 281.0 0.4

In whirlwinds of small dimensions we can neglect the action of
the rotation of the earth. Assuming the altitude / of the horizontal
current to be very small it is necessary to attribute to the coefficient
of friction a large value and consequently the air enters into the
current almost radially. In this case denoting by 7 the radius of
the whirl, the equation of continuity gives

at rly =x Ww,

and supposing vy = w, we Shall haver = 21.

In this case the radius of the whirlwind will be equally small, as
is proved by observations of whirls of smoke, the whirls of dust over
roads, and whirls of sand over deserts. In order to calculate the
horizontal velocity we neglect the work of friction, because the dis-
tance traversed is very short, then we shall find

Vy) = | 22¢ ais
0

If we suppose the altitude z to be less than 1000™, we can develop
f(z) as determined by equation (3) of §16 in a series and introduc-

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 173
ing therein this value of 7(z) into equation (4) and placing p = p’
we shall have

We see therefore that for small altitudes the coefficients m and m’
do not appear in the formule, that is to say the latent heat of the
vapor of water plays no part in this case. The formula is identical
with that for the velocity of the air in a chimney (fig. 14) when we
neglect the friction.

FIG. 14

Supposing the air to be dry, the virtual temperature is equal to
the absolute temperature, that is to say T, = 273 +t, and T,’ =
273 +7,’. For this case we have calculated the following table

assuming Tt, = 20.°

Table III. Horizontal velocity in small whirlwinds. 2 = the altitude of the
vertical current

Ga oo | z= 50” z= tool | z= 200"
25° 1.6m 4.1m 5.2m 8.2m
30 2.6 5.8 8.2 DEES)

40 aa, 8.2 11.6 16.4

So ASS 10.0 14.2 20.0
100 Ce} 16.4 23.1 32.7,
200 II.O 24.6 aA 49.1

174 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

When the whirlwinds have great dimensions, we cannot neglect
the work of friction. Assuming that the trajectories of the par-
ticles of air are logarithmic spirals, we can calculate the barometric
depression as we have done in paragraphs 12 and 14 (see figures
9g, 10, 11) where the whirlwind of great velocity shows a baro-
metric depression equal to 32.9™™ for a radius equal to 2 degrees
of a great circle and with a maximum velocity equal to 50 meters
per second. The whirlwind of average velocity shows a barometric
depression equal to 34.9™™ for a radius equal to 20 degrees and with
amaximum velocity equal to16m.p.s. Inthe last case the work
of the friction is much greater than in the first, because the distance
traversed is ten times longer.

Considering table I, we shall see that barometric depressions can
be produced by different states of the atmosphere. The two whirl-
winds, in which the barometric depressions do not sensibly differ, are
distinguished by their maximum velocities, and it is necessary to
seek the explanation of this difference in the lengths of the radii
of the vertical currents that produce the horizontal velocities.
The whirlwind of great velocity belongs to a vertical current whose
radius is probably several tenths of a degree, but whose initial verti-
cal velocity is very great. The other whirlwind of average velocity
belongs to a vertical current whose radius extends over several
degrees and whose initial vertical velocity is not great.

The length of the radius of the vertical current, which we can
assume proportional to the distance from the center to the point
where the velocity attains its maximum value, plays an important
part in the theory of whirlwinds. Comparing two whirlwinds
having the same barometric depression, that which has the shorter
radius has the greater velocity and consequently is the most violent.
Comparing two whirlwinds with the same maximum velocity, that
which has the shorter radius has the greater gradient and the smaller
depression.

The physical cause that determines the length of the radius de-
pends on the difference in the condition of the ascending air and of
the surrounding atmosphere.

“all

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 175
PART II
(Christiania, 1880, revised 1885)
CHAPTER IV
ON MOTION IN GENERAL

§18. TIsobaric surfaces—Vertical gradient

In meteorology we speak of isobaric surfaces as surfaces of equal
pressure or isopiestic surfaces or simply isopiesics. Ifthe airisin equi-
librium we can consider the isobaric surfaces approximately as spheres
concentric with the earth, and, for a small part of the surface of
the earth, we shall treat these surfaces as horizontal planes. If the
air is in motion the isobaric surfaces differ from horizontal planes.
In order to fix our ideas we consider a horizontal current of air
whose isobaric lines at the surface of the earth are concentric circles.
Let the values of the pressure for the different distances from the
center be as follows:

rin degrees of
agreatcircle= 0 4.5 6.5 8 Ors IES 14. alas
bin millimeters
of mercury= 725 730 735 740 745 750 755 760

The diminution of the pressure 4 b for a change of altitude 4 z
can be approximately calculated by the formula (see $4, eq. 2).

ADR ede 7 7 Ale
by ar 8200
Giving successively to 6, the values 725, 730. . .. . we

calculate the values of 4 2 for any value of 4 b, and we can construct
a vertical section of the isobaric surfaces (fig. 15). When the air is
in equilibrium a vertical section of the isobaric surfaces will present.
a series of straight horizontal lines (fig. 16a): supposing that we
have a vertical current, the vertical section of the isobaric surfaces
would also present a series of straight horizontal lines, but different
from those of the series in fig. 16a. We shall call these lines of
intersection vertical tsobars, and if we wish to introduce the term
vertical gradient we should be obliged to establish a definition similar
to that of the term horizontal gradient. Assume the vertical grad-
ient equal to the difference of the pressures shown by two isobars
divided by their distance, we shall always and even in a state of

176 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

equilibrium find a vertical gradient whose value will exceed
10.000™™ provided that we use the millimeter and the degree of
meridian as our units. It is evident that from this definition we do
not get a clear idea of the force that acts during the vertical motion
and which must be represented by the vertical gradient.

777.

6000 W927

7 JOO

6 Lageede

SOOO 400

is 3500

TF Se

ve pei 600
L000 oe 700

0 760 772.7.

FIG. 16a

Let the pressure be p at the height z and q the weight of the column
of air below z and we get

Hite pg tr ee ah ee Cnn

If the air is in equilibrium, the values of IT will be equal to the
pressure p, at the surface of the earth and consequently JI will be
constant and independent of the height z. If the air has a vertical
motion the value of // will be different from p, and will vary with

»

a

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 177

the height z. We shall call JI the pressure reduced to the surface of
the earth. Wecall the horizontal lines that correspond to the values
of II, the reduced vertical isobars.. We call the difference of two
values of JJ expressed in millimeters divided by their distance ex-
pressed in degrees of the meridian the vertical gradient. Denoting
the vertical gradient by H, the coefficient of reduction by yu (see §7)
we have

ae ek ae eae

The sign minus is taken, because we consider the vertical gradient
positive upward in the direction in which the pressure // diminishes.
As regards the rectilinear motion we find from §15

dw
Lo =p... . (3)
dz
Introducing d IT we find by integration
TD =P el (UW ye Oe a cen en ED
If in the formule of §15 we substitute
T = 290°; m = 6;-p, = 760™™; w, = 20™
we shall find the results contained in the following table:
PRESSURE ALTITUDE VELOCITY | VERTICAL REDUCED PRESSURE
Pp z w GRADIENT H
760mm om 20.0 4o.omm 760.00mm
700 | 684 21.4 43-5 759.84
600 1954 24.9 50.8 756.21
500 3413 28.3 61.0 758.48
400 5135 34.2 76.7 757.42
300 7335 43-4 103.1 795.73
200 9992 60.8 158.7 752.55
100 14031 108.4 354.2 743.86

By constructing the curve of JJ as a function of z we shall find the
reduced vertical isobars as we seeinfig.16b. Thedifference between
p, and JI we shall call the vertical depression. Inthe same way that

the horizontal gradient G produces a horizontal force YG (see §7)

so does the vertical gradient H produce a vertical force > H , which

178 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

must be added to the exterior forces. This vertical force includes
also the force of gravity.

FIG. 16)

§19. Equations of motion

In order to study the general motion of the air we take three rect-
angular axes of which the axes O X and O Y are horizontal and the
axis O Z vertical and ascending. Denoting by uw, v and w the com-
ponents of the velocity parallel to the axes and by x, y and gz the
components of the forces referred to the unit of mass and by pe the
density, the equations of hydrodynamics are written

po dx dt

gees Ae ge ee 2 eae
p.ay adi

Zao ee eee

MOVEMENTS OF ATMOSPHERE——-GULDBERG AND MOHN 179

Writing
7, _ du dv dw 2)
dxm@ dy dg
the equation of continuity assumes the form
do
ee Oe tO we os el iad arte (SD)
a

In the preceding equations

du dv dw
ei = ah
at at dt

represent the components of the whole force; the forces produced
by the variation of the pressure are represented by

which are the components of the horizontal force G

and by _ E dp

p dz
which is included in the vertical force is H.

The components X, Y,and Z are the components of the exterior
and interior forces.

The exterior forces are the two following:

Gravity. This is the resultant of the attraction of the globe and
of the centrifugal force produced by the rotation of the earth.
The direction of gravity is normal to the surface of the earth and
is represented by the axis O Z.

Gravity has therefore only one component — g, and by introduc-
ing the vertical gradient H, we have

HIE Sian 9 ma
e : 0 dz

We consider the force of gravity as constant, because the winds that
we are Studying are located in the lower strata of the atmosphere.

The deflecting force of the rotation of the earth. This compound cen-
trifugal force is the force that we must add to the exterior forces

180 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLA5®

in order to be able to treat a problem of relative motion as if one
had to do with absolute motion. Denoting the angle between the
axis O X and the direction north by a and the components of the
deflecting force by Xo, Y, and Z, we have

X, = 2wsin@v — 2wcos 8 sinaw
Y, = 2wsin@u — 2wcos@cosaw |

Z, =2wcos@sinau +2wcosOcosau

Here 6 denotes the latitude considered as positive in the northern
hemisphere and negative in the southern hemisphere and w denotes
the angular velocity of the earth per second of mean time.

2)

os

FIG. 17

The interior forces are the components of the internal friction
or viscosity produced by the difference between the velocities of the
different adjacent strata of air. The surface of the earth offers a
resistance to the currents of air, the effect of which, in diminishing
the velocity of the lower strata, is shown by the variation of velocity
between the different strata. The particles of air having a greater
velocity increase the motion of the particles having a less velocity
and, inversely, the particles having less velocity retard the moticn
of the particles having greater velocity. The resistance of the sur-
face of the earth, therefore, transfers its influence through all the
strata of air and influences both the direction and the velocity of

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 181

the motion. We shall in the following chapter consider some special
cases of interior friction. However, the absence of observations on
the variation of the velocity with the altitude prevents the applica-
tion of the exact theory to the winds in general. We shall consider
friction as an exterior force acting along the surface of the earth.
Denoting the components of the friction by X, and Y,, we write

(see $7):

- (5)

X,=—-—ku
Y,=-—kv .

in which k denotes the coefficient of friction.

By introducing the preceding values of the components of the
exterior and interior forces and noticing that the velocities and the
density are functions of the four variables x, y, z and #, the equations
of motion are written as follows:

po dx dx dy de
LOE go ee Pac cet
ldp_, | dw dw dw__ dw
pee Nr dt de dy

do do do do
eo ge ty Aaa (teen saree 1c Uk
ae dx an. Paes @”)

The trajectory of a particle of air is determined by the equations

ax

Se) UuU

dt

dy

“=49

FT SoMa re ie th a ae ae ae (8)
dz

—_=wWw

dt

§20. Classification of the systems of wind

Each disturbance of the equilibrium of the atmosphere produces
a motion of the air or what we in general call a system of winds.
Considering the forces which act during the motion, we divide the

182 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

systems of wind into two classes. The systems of the first order
are those which extend only over quite a limited part of the surface
of the earth, and which at the sametime exhibit variations of veloc-
ity so great that we can neglect friction and the deflecting force
of the rotation of the earth. For example we mention tornadoes,
waterspouts, whirlwinds of smoke, etc. The systems of wind of the
second order are those in which all the acting forces have some impor-
tance. As examples we mention cyclones, the trade winds, the sea
breezes and land breezes.

Considering the motion of the air in the systems of wind we dis-
tinguish between the permanent systems and the variable systems.
In a permanent system the pressure and the velocity at any place are
independent of time and vary only from one place to another. In

‘

p »—>P m—~ Pe au P

Jil Jil

/
D—> RB <<“ p.. te Pp ymr—> P
POOVDIIVIOTIPIDIOPITIVIVIFIVIVIVIVIF VIVATITTTTIVITTFIFII TIVO OTT IO TOIT:
FIG. 18 FIG. 19

nature we never find a permanent system, but we may consider
the systems of wind which remain nearly invariable for quite a
long time as permanent. As examples we mention the trade winds,
an immovable anticyclone or cyclone, with constant pressure at
the center. The variable systems of wind are divided into movable
systems and zmmovable or fixed systems. In the variable fixed
systems the minimum or the maximum barometer does not change
position with the surface of the earth, but its value varies with the
time.

In our following studies we shall consider four simple systems of
wind.

(1) System of ascending parallel winds.

This system (see fig. 18) has rectilinear isobars, a barometric
minimum at the surface of the earth and a barometric maximum in
the higher strata. The air flows inward along the surface of the

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 183

earth from both sides toward the barometric minimum and the
horizontal current is gradually changed into a vertical ascending
current. At a certain altitude the vertical current is changed into
a horizontal current which flows outward from the barometric
maximum. Denoting by p, the pressure at the lower barometric
minimum and by p the pressure at the upper maximum and by
p, and p’ the corresponding pressures in the exterior atmosphere,
we shall have for the depression D, which belongs to the horizontal
current along the surface of the earth,

| ay LAs ty OS er eh ee hee al ©)

The excess of the pressure D in the upper barometric maximum
is given by the formula

eS eee A oe tcl Geel son ray CA)

Let q and q’ be the weights of the columns of air of the vertical cur-
rent and of the calm atmosphere, respectively, and let /J be the
reduced pressure (see $18) we have

| ue oa eee ee Pee a nape (729)
ea oR Sel 7 ale 7a Ye ea re eh)
EP dn root enc atiia esg (Ol)

in which we call EF the vertical depression of an ascending current
(see §18).
From these equations we obtain

Date 1D} OG ge ee ss eB (6)

This last equation shows us that the difference in weight of the col-
umns of air produces the motion of the three currents.

(2) System of descending parallel winds.

This system (see fig. 19) has rectilinear isobars and a barometric
maximum at the surface of the earth and a barometric minimum in
the upper strata. The air flows in from the two sides toward the
barometric minimum and the horizontal current in the upper strata
changes little by little into a descending vertical current. The ver-
tical current then changes into a horizontal current which flows
out from the barometric maximum at the surface of the earth.

Denoting by p, the pressure at the barometric minimum and by
p the pressure at the maximum and by ?p,’ and p’ the corresponding

184 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLF 51

pressures in the exterior calm atmosphere, we shall have the depres-
sion
2 Si Path th a ER Le

which relates to the horizontal current in the upper stratum. The
excess of the pressure D in the barometric maximum is given by the
formula

| eae, ert ee ee eae eee} et

Let g and q’ be the weights of the columns of air of the vertical cur-
rent and of the calm atmosphere respectively and let /] be the reduced
pressure, we have

LT Bee eT A ee eee
f= Og. Boe Na es See
writing
Be ee, Te Bee ae Soe ree
we shall find
Dy BaD = ge dew tor es bo

The quantity E represents the vertical depression in the descending
current, and this last equation shows us that the difference between
the weights of the columns of air produces the motion of the three
currents.

(3) System of cyclonic winds.

This system has circular isobars around a barometric minimum
at the surface of the earth; in the upper strata it has a barometric
maximum. The air flows in along the surface of the earth from
all sides and the horizontal currents are changed little by little into
vertical ascending currents. Atacertain height the vertical motion
is changed into a horizontal motion and in the upper strata the air
flows out from the barometric maximum. By introducing the same
notation as we have employed in the first system of parallels, equa-
tions (1) to (6) hold good also for cyclones.

(4) System of anti-cyclonic winds.

This system has isobars circular around a barometric maximum
at the surface of the earth: it has a barometric minimum in the
upper strata. The upper air flows inward toward the barometric
minimum and the horizontal currents in the upper strata are changed
little by little into descending vertical currents. ‘The vertical
motion then changes into a horizontal motion and the air flows out
from the barometric maximum at the surface of the earth. Equa-
tions (7) to (12) hold good for anti-cyclones.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 185

Each of these four systems of wind has its calm space at the sur-
face of the earth which represents the interior part where the motion
of the air is nearly vertical and where consequently we do not feel
any wind. Intheupper strata we must also find calmspaces where
the vertical motion changes into the horizontal motion or vice versa.

These four systems which we have called simple systems, trans-
port masses of air, either from the surface of the earth to the upper
strata, or from the upper strata to the surface of the earth. When
we consider the case in which two or several simple systems exist
simultaneously so that their motions encroach upon each other and
the masses of air pass from above to below and inversely, we have
a composite system of winds of which nature offers an infinite
number of examples.

CHAPTER V
INTERNAL FRICTION

§21. Horizontal currents of air of small extent

We shall at first consider horizontal currents so small that we can
neglect the effect of the rotation of the earth; we also assume the den-
sity to be constant. Let A B and C D (fig. 20) be two horizontal
planes that enclose the mass of air; assume that the plane C D is
fixed and that the plane A B moves with a uniform velocity V.
The motion of the air will therefore proceed in horizontal strata of

‘

C DD
ue h
Lo
2 a Ve
FIG. 20

different velocities; along A B the velocity of the air may be my.
and along C D the velocity may be zero. Admitting the hypothe-
sis that the internal friction or the viscosity is proportional to the
difference between the velocities of any two strata, we conclude
that the velocity decreases proportionally to the distance z from
the plane A B. Let h be the distanceof the two planes, the increase

of velocity per unit of length will be = and we shall find the velocity

186 SMITHSONIAN MISCELLANEOUS COLLECTIONS Vola 51

u at the distance z by the formula

ed Cee ee See SEALS ee

The internal friction per unit of surface which we denote by F
will be equal to a coefficient K multiplied by the rate of increase of
velocity and consequently

oe Soon eee Brereton)

The plane A B moves with the velocity V and the air along A B
moves with the velocity 4); the resistance between the air and the
plane A B is proportional to the difference V — u, and to the coeffi-
cient of friction 7 between the air and the plane; consequently we
can write

je cence a eee mer Sl

From these equations we find

Nb, a ATE gy Lite ae At ae etic

In the preceding case the pressure has been supposed to be con-
stant, We shall now consider the case where the horizontal cur-
rent of air has a gradient; the horizontal velocity u depends solely
on the distance z and the vertical velocity is zero. The increase of

du
the horizontal velocity, per unit of vertical distance is =— and the

dz

du
internal friction is equal toK cae Considering a parallelopipedon

whose thickness is dz and whose face is a unit of area, the result of
du
dz
element willbe odz. The force per unit of mass resulting from the inter-
d*u
nal friction will therefore be - de and this force acts in the same
direction as the force of the gradient. The equation of equilibrium
is

the frictions of the two faces will be d(K ——) and the mass of the

Sie ae ER rh ek te ee
e

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 187

The vertical motion being zero, the vertical gradient H will dis-
appear and consequently the pressure is independent of the alti-
tude z. We conclude therefore that the horizontal gradient G is
independent of z and constant. Integrating equation (5) we shall
find

Ri Bara hire 0 (8a hae iG)

°

a

In order to determine the constant C we notice that the internal
friction disappears at a certain value of which we will denote by
uw h; at the same time the velocity has its
maximum value U. It is evident that
Zz the friction is equal to zero in the stra-~
A tum whose velocity is a maximum be-
cause the velocity decreases equally on
each side of this stratum and conse-
quently the difference between the ve-
locities of the two strata located sym-
metrically is equal to zero. By choosing the origin of codrdinates
at this distance h from the surface of the earth (see fig. 21) we
shall have the constant C equal to zero and by integrating equa-
tion (6) we shall find

FIG. 21

Bee Ee es ee LOY

Let the velocity of the air at the surface of theearth be u, then for
z = h we shall have

aide Geog
D arene

ie

. (8)

The upper limit of a free horizontal current is found by placing u =o
and let the corresponding value of z be H, we have

pees aces ha ssl ey ee)

From equation (6) we conclude that the friction at the distance z,
is equal to « G z; at the surface of the earth the internal friction is

188 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

equal to 4 Gh; the friction between the surface of the earth and the
air is equal to f u, and consequently we find

Ce = Po,
or
nee ue Nort a ee eT
e oh

Here k denotes the coefficient of ordinary friction which we have
introduced in our previous problems and we have
/
p Be atl amt tN 6 98 a nirg APR re
ph
This equation shows that the coefficient of friction k is inversely
proportional to the depth of the current measured from the surface
of the earth to the stratum of maximum velocity.
By experiments on the viscosity of the air, Clerk Maxwell found
the value of K at o° C. equal to 0.001878. Introducing this value
in equation (7) we shall have

eS 0. 0038 et. ae Ee

Experiments on the motion of liquids show that inequalities of
depth produce little vortices which play an important part in the
law of velocity. We are led to adopt the following formula:

OP x0 LP OAS ok a ve tre, nuiicg ee

The value 0.04 is taken from experiments on the motion of water
in straight channels.

§22. Horizontal currents of atr of large extent

We shall consider a horizontal current of air that moves over
so large a part of the surface of the earth that we cannot neglect
the effect of the rotation of the earth For horizontal motion the
deflecting force of the rotation of the earth is normal to the trajec-
tory of the wind and its value is expressed by 2 w sin 8 U, where w
denotes the angular velocity of the earth, 0 the latitude and U
the horizontal velocity of the wind.

Assuming that the motion of the current of air is uniform, then
the. velocity and the gradient will be constant; the acting forces
will be the deflecting force of the rotation of the earth, the force of
the gradient and the friction. In the special case where the cur-
rent of air moves along a surface without friction, equilibrium will

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN _ 189
exist between the deflecting force of the rotation of the earth and
the force of the gradient ; consequently the two forces must be oppo-
site and their directions must be alohg the same straight line.

We shall then have

4

5G = 20 U sin 8. Ay Tere ck aki ate oe eC)

The deflecting force of the rotation of the earth being normal to
the path of the wind, we conclude that in the case where the friction
is zero, the current is normal to the gradient, that is to say, the wind
moves along the isobar. The ratio between the velocity of the wind
and the gradient is expressed by

== [ow sind. datte et)

Let the pressure be 760™™, the temperature o° C., and the tension
of the vapor of water o, we shall have

U- 6.304

—

G sin@

whence the following values

@ = 10° 20° 30° 40° 50° 60° 70°
9)

G 36.6 18.6 12.7 ae S:dL. (4:31 6.77

We have supposed that the force of friction, at the surface of the
earth, is opposite to the motion of the particle of air. In this case
its path will form an acute angle with the direction of the gradient.
Since friction has its greatest value at the surface of the earth and
diminishes with altitude, the velocity of the air and at the same time
the angle of inclination ¢ in §11 must increase with the height, which
observations also show to be the case.

In the stratum that separates the lower current from the higher
current, (in the systems of wind that we considered in the preceding
chapter) the gradient must be zero and consequently the velocity
of the air nothing. Thus the velocity of the air increases with the
altitude in the part near the earth while.it diminishes toward zero
in the region near the stratum that is intermediate between the
two currents. The velocity of the air must consequently attain its
maximum at a certain height.

1go SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

As the resultant force of the internal friction does not necessarily
act in the direction opposite to the motion therefore the direction of
the motion of the air in the stratum of maximum velocity remains
uncertain. Probably it does not sensibly deviate from a direction
perpendicular to the gradient.

How are the velocity and the direction of the motion related in
the different strata of acurrent? This is a problem hardly solvable
in the present state of our knowledge of the laws of friction and in
the absence of precise observations of the gradients and the motions
of the upper strata of the atmosphere.

$23. A rotary current of atr

We shall now consider a mass of air revolving about a vertical
axis in consequence of the motion of the surrounding air. The
exterior air moves in circular trajectories and with constant veloc-
ity and by internal friction produces a rotation of the interior mass
of air. We have therefore a mass of a?r within a cylindrical bound-
ary whose velocity is given and which turns about a vertical axis
by reason of internal friction. The tangential velocity U is a
function of the distance r from the axis; the isobars are concentric
circles; the gradient is directed along the radius. The acting
forces are the force of the gradient, the centrifugal force and the
deflecting force of the rotation of the earth, all of which act in the
direction of the radius, and finally the force of the internal friction
which acts in the direction of the tangent. We neglect the friction
at the surface of the earth, so that the velocity is independent of the
altitude. The resultant of the internal frictions acts tangentially
on each element and should be equal to zero, because there exists
no tangential force with which to establish equilibrium; the result
is, that the internal friction along a cylindrical surface must be con-
stant. Let the mass of rotating air be divided into cylindrical por-
tions which rotate with different velocities. The internal friction
is due to the differences of the velocities U, but the radius 7 varies
at the same time and with it the frictional surface; it is necessary
therefore, to make the friction proportional to the variation of the
product of the velocity and the frictional surface, divided by the
increase of the volume, We shall find then

d (r U)
- — = S== COMSbAIE (19 aig et ae

rar

MOVEMENTS OF ATMOSPHERE-——GULDBERG AND MOHN IgI

By integration we find
(gh Uae 0 has A Sic a a Ee |

where a and b denote two constants that we can determine in the
following manner:

Let the given velocity of the exterior air be U, at the distance r,
and assume the velocity of the interior mass equal to zero at the
distance 7,5, we find

and

ye ee El ee (3)

It is quite probable that in nature the radius 7, is equal to zero and
we Shall then have

es i ee omen a

Hence, the current of air rotates with a constant angular velocity (see
§14).

In order to determine the gradient and the pressure, we distingiish
two cases in the northern hemisphere.

(1) Rotation contrary to the sun.

In the cyclones of the northern hemisphere the rotation takes
place contrary to the apparent diurnal motions of the sun, the grad-
ient is directed toward the center, the centrifugal force and the
deflecting force of the rotation of the earth are directed outward.
We have then

le Uy?

Aas Sort SOMOS hosts * fee 18)

dp

By writing 7G = ar and introducing the value of U given in equa-
r

tion (4) we find by integration, p, being the pressure at the center
where U = o,

eee er Gor a ee tadee Un)

(2) Rotation with the sun.
In the anti-cyclones of the northern hemisphere the rotation takes
place with the apparent diurnal motion of the sun; the gradient

1g2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

and the centrifugal force are directed outward and the deflecting
force of the rotation of the earthisdirected toward thecenter. We
shall have then

Le U?
eg Ne Fe AGE)

and

Pe? = 4 Qwsind. Ur — 0») ee ee

Equation (7) demands that the angular velocity ies be less than
r

2 w sin 0 because the gradient must be positive.

CHAPTER VI
PERMANENT SYSTEMS OF WIND

§24. Permanent wind-systems of the first order

In nature tornadoes and waterspouts represent examples of
cyclones of the first order, but meteorological observations of these
phenomena being very scarce do not suffice to show us the changes
of pressure and velocity which take place in them. We cannot as
yet by mathematical analysisconstruct a complete system of wind.
However, we shall consider some simple cases which show analogies
with the systems of nature and from them we shall seek to deduce
applications.

In the general equations of § 19 we may neglect the components
Xo, Yo, Zo, X, and Y, and we shall consider the density as constant

The equations assume the form

1 dp du du du
pve Tn aes gle abe
bevdp dv dv dv ;
tT Tae oa ne Ree
1. ap dw dw dw

SnP Gtedg eee NS Talay ee

0 =— 4-4-7) 5 Le. ea

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 193

Considering the special case, where we have

dw dv du dw dv du

dy dz’dz « dx’dx dy

equations (1) are'reduced to a single one. Denoting the absolute
velocity by V, we have

V2 = uv? 4+ v? + qw?

and
Ue = ee es
and consequently ,
P= Py eo (V ei = V2) eo Gy eee. oe oS StS)
where p, denotes the pressure for V = V, and z = 2).

We designate the distance from the origin of codrdinates by R
and its horizontal projection by 1, the horizontal velocity by U,
and consequently we have

ieee? 72 oe
Ue ey

First example. The trajectories are straight lines directed toward
a fixed center.

O
‘ ; \
4 HL a
FIG. 22

We take the fixed center (see fig. 22) at the origin of codrdinates
and put the equations of the trajectories under the form

a
Re Say tee CG)

Calculation shows that these equations satisfy the conditions which
we have introduced above. For the time ¢ = 0, we have KR = R,,
from which we conclude that all the particles of air are found at first
on the surface of a sphere whose radius is Ry. Differentiating x,

S| 8
|
Sik
|
co)
|
S| oy
|
a

2
0

194 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

y and z with respect to ¢ and introducing u, v and w (see §19) equa-
tion (8) and eliminating the arbitrary constants, we have

oS RES, ENE Oe

For a< o, the air flows in to the center and for a > o the air
flows away from the center.

In any horizontal plane (2 = constant) the gradient G is found
by equation (3), by noticing that

Ve Rartef
ie 5

1 dp pe: Vid» p82 a7 7
Te ae Ske erin dE R: rk at
Let us consider a horizontal plane at the distance z = — h = 2p,

and study the phenomena along this plane, which can represent the
surface of the earth.
Denoting the absolute velocity at the point A by Vo, we shall have

a
; Vo = ip
Writing
r=Eh
we shall find
R=hV1+2
_ e
Ge es
Pe

ee eh eae
P — b= 40 (Vo? — V") 7
Denoting by p,’ the pressure at a point so distant that we can con-
sider the velocity V as zero [V = = from equation (6)] we place

Dy. = Pf) — Po = 40 Ve
and

2644

Pp —Po a (iss g2)2 |

MOVEMENTS OF ATMOSPHERE—-GULDBERG AND MOHN 195

We easily see that all these formule depend on only two con-
stants or parameters, namely the altitude h and the maximum veloc-
ity V,. Wecan change the last parameter and consider the depres-
sion D,as thesecond parameter. Thus the function of U shows that
the horizontal,velocity has a maximum value U, for € = Vi; the
distance r, from point A to the point where U has its maximum
value, is

t= hV/ tand Ui Viv &
The gradient G has its maximum value G,, for

f=VE

whence
G a0 OVE 2Ve

no 26 806k
We shall now choose D,, expressed in millimeters of height of mer-
cury,and7,expressed in degrees of the meridian, as the parameters
of the system and are thus able to establish the following formule,
by introducing a mean value of o (0.1318 at the temperature 0°
and the pressure of 760™™ and for dry air):

The maximum horizontal velocity =U, = V30.6 D,
The maximum horizontal gradient =G,, = 0.715 D,/r,
The distance from G,, to the point A = r,, = 0.63 7,

The height of the absolute centerO =h =1417,

The absolute maximum velocity = V, = 2.6 U,

By the aid of the preceding formule we have calculated the fol-
lowing table, in which D denotes the barometric difference:

gE 0.5 1 2 3 4
(tT Un oere 0.71 1.41 2.83 4.24 5.66
(O beret OD Peer este 2 0.93 0.92 0.46 0.25 0.15

feet Spiel Cos etree rae 0299 0.48 0.06 0.01 0.005
| Ee 5 rae 0.36 0.75 0.96 Q299 0.9965

In fig. 23 we have constructed, from this table, the curve of veloc-
ity, the curve of gradient and the curve of pressure that determines
the system of isobars. Wecan compare our system of wind to the
lower half of a cyclonic system in nature; probably in nature the
maximum gradient occurs at the same point as the maximum veloc-
ity. The depression D, which depends on the physical state of the
air, determines the maximum velocity; the maximum gradient
depends on the depression and the distance 7, which in nature prob-

196 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

ably represents the radius of the vertical current. The radius r,
depends on the height of the verticalcurrent. Finally, it is neces-
sary to remark that in our example the vertical velocity is very great;
the velocity V, at the point A represents the vertical velocity at this
point. But on the other hand, in natural systems of wind the motion
of the air differs much from this motion in our case, because the sur-
face of the earth compels the particles of air to follow trajectories of
a different form.

O

2 ca
4
| { {
I ! '
| ! y
\ ' '

Second example. The trajectories are parallel to a vertical plane
and pass through a horizontal line.

We take the plane X Z (see fig. 22) parallel to the trajectories
and the axis O Y as the horizontal line. The ordinate y disappears
and we write

“n= Ue =rfand =v +e

We write the equations of the trajectories under the form

% Bk Z2at
= = R 1 =f SS ae Nie hinge (8)
Sh eae eg Re

Placing t = o, we have R = R,; consequently the particles of air are
found at first at the surface of a cylinder whose radius is Ry. Differ-
entiating with respect to ¢ and eliminating the constants we shall
have

w V a

Ue eee: aoe (9)

Rls
|

For a < o, the air flows towards the axis and for a>o, the air flows

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 197

away from the axis. The gradient G in a horizontal plane is found
by the formula

besa. VdV x
Pet iy My ee eis teh Se(L0)
P i a % fb. aad Kk
Consider a horizontal plane at the distance z = z, = — h, and study
the phenomena on this plane.
Writing
a x ,
Y= ,andé=7 and D,) = 40 V,
we shall have
e Ve ss
aries zw VoiG bon Ce?
&2

The horizontal velocity has a maximum u, when € = 1 and
uy =4V,. The horizontal gradient has a maximum

G, when € = V4

and

Choosing as the parameters D, expressed in millimeters and the dis-
tance of the axis x, = h, where the horizontal velocity has its
maximum, as expressed in degrees of a great circle, we shall find

The maximum horizontal velocity U, = V 51.5 D,

D
The maximum horizontal gradient G. = 0165, —
0

The distance from G,, to the vertical axis x" = 0.58x,

The height of the horizontal axis = %,
The absolute maximum velocity V,=2U,

By the aid of the preceding formule we have calculated the fol-
lowing table in which D denotes the barometric difference:

gE 0.5 1 2 3 4
0.80 0.60 0.47

re 0.25 0.09 0.04

.00 0.80 0.90 0.94

198 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL si

From this table one can construct the curves of velocity, gradient,
and pressure, and the system of isobars and we shall find a system
of curves analogous to those of fig. 23.

We can compare this last wind system with the lower half of a
system of parallels of the first order in nature and we can make the
same remarks as on the first example.

§25. System of parallel winds of the second order

Mathematically speaking the systems of parallels have an infinite
length. In nature the length is limited, but we can neglect the
disturbances produced by the lateral limits. Along the surface of
the earth the system of parallel as-
cending winds presents two horizontal
currents, which flow from both sides
toward the barometric minimum or
trough situated along a straight line.
We distinguish two halves on each
side of the barometric minimum and
each half has its internal part whose
breadth may be 7,, and its exterior
part. The horizontal current moves

FIG. 24 in the exterior part approximately at

a constant altitude, and in the lower

part at an increasing altitude. Consequently the horizontal veloc-

ity has its maximum value U, at the distance ry from the barom-
etric minimum.

Denoting the height of the external current by h (see fig. 24) and
the angle between the maximum velocity and the gradient by ¢,,
_the quantity of air which enters per unit of length is represented
by U,cos ¢,h. In the interior the current changes little by little
into a vertical current whose velocity we may indicate by wy, and
consequently we have the condition

Wo

Wo! 5p U COS: GgMine ver @ Mal Pee Ox ee

It is probable that in nature the ratioh / 1, is so small that we can
neglect the vertical velocity and the vertical barometric depression
that results from it. We shall therefore consider only the horizon-
tal currents with either constant or variable velocity.

MOVEMENTS OF ATMOSPHERE—-GULDBERG AND MOHN 199

Constant Latitude

We have already in §10 discussed the systems of parallel winds
with rectilinear isobars and constant velocity. We now write

COS OGG ates ae ee Ce)

in which the distance x is measured along the gradient.

Differentiating this equation and introducing the value of U
and of d U in place of v and d v in equations (2) and (3) of $10, we
shall have

KG cos ¢= U(k be+U sin 9 | er ee
0 dx

NG sing = U(2usind — Ueosy ) hy ere (2)
p dx

If we eliminate G from these equations, we shall have the equa-
tion
dy

Sn a ya. sim Oreos US,
%

in place of which we can write
Ber ie ee ot let (onan eu)
cos ¢ dx dx

We see that we can satisfy this equation by placing the last term

equal to zero. Then we have

tang y = 2 w sin 8

The angle of inclination ¢ becomes constant, and the first term of
equation (5) also becomes zero. Equations (3) and (4) become

’Gos¢=(k+o)U
0

(6)

NG sing = 20 sin 6.0 |
pe

200 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The normal angle of inclination being expressed by the formula

we shall have

tang ¢ = —— » | i tza. aa Sa

and

= Se ee, ae ee
G pk+c p2wsiné ®)

From these equations we conclude: That the angle of inclination
_V is constant for a wind of variable velocity and rectilinear isobars,
but that it differs from the normal angle a. The ratio between the
velocity and the gradient remains constant and is expressed by
the same function of the latitude and of the angle of inclination
as for winds of constant velocity.

The gradient increases proportionally to the velocity and con-
sequently to the distance x. It follows that thedepression between
two isobars is found by multiplying the distance by the mean of
the corresponding gradient.

When c > o the wind blows with increasing velocity and the angle
of inclination is less than the normal angle. Whenc < o the wind
blows with decreasing velocity and the angle of inclination is greater
than the normal angle.

If we consider a station situated on the seashore and note that
the coefficient of friction is greater on the land than on the ocean,
we must expect that the ocean winds at such a station will have
an angle of inclination greater than the inclination for the land
winds.

Let us consider a system of par-

ace allels in which we can represent

the curve of velocities approxi-

Jo To mately by two straight lines (see

FIG. 25 fig. 25). The curve of the gradient

will be also represented by two

straight lines and placing the maximum gradient equal to Gy we
shall have

Da Geo en 2 WG eee

—_—

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 201

In nature the velocity is represented by a curve, and at the point
where U = U,, the variation of the velocity is zero. Consequently
the angle of inclination is equal to the normal angle a for the maxi-
mum velocity. Choosing D, and 7, as the parameters of the sys-
tem we shall have

The maximum gradient G, = ea
ro
(10)

The maximum velocity U, = pide bed Do

o "9
In the neighborhood of the equator with o = 0.1199, a = o and
k = 0.00002, we have U, = 51 oe assuming that the system of par-
r

0
allels has a breadth of 27, = 20° and that the total depression is 2™™
we shall find G, = 0o.2™™ and U, = 10 meters.

Variable Latitude

We employ the same notation as in §11, and we consider only the
case in which the gradient coincides with the meridian. Take the
origin at the equator, and write the latitude

a
where
9 7
<> Toh

Here the sign plus indicates that the gradient is directed toward
the north and the sign minus that the gradient is directed toward
the south. Assuming that the velocity is expressed by equation
(2), we again find equations (3) and (4).

Eliminating G from these equations we shallhave

d (tan
ee eae (e+ c)tang¢-: - (11)

Introducing 6 in place of sin 6, we see that equation (11) is satisfied
by
20

tne d= 5 ae a PS ss. te tiles sled)

A; Go

sae pe as ts,
k+e oo

€

202 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

For, by differentiating (12) we have

d (tang ¢) 2w dé 2Zwi

ia wile ee ein Gm GC ecee
Substituting this value and the value of U cos ¢ from equation (2)
we have

9

2wA
bin Te pong te ee) (9 — é«)

WwW
k+2c
Ago tAcx =k + cO = (k+2c)0 — (k +c): (0 — 2)

AG "Ce Be

Whence
AG,

a ea

By eliminating a from equations (3) and (4) we find the gradient

G =" -U cos 9 (b + ¢ + 2w 8 tang $) Pepa GES)

The radius of curvature of the trajectory is found by the equation

ds dx

Hoh aig. acme
From equation (12) we deduce

dd 2w dé 2wa
coz¢dx k+2c dx k+2c

and we thus have

_k+2¢ t

Ras = ee
2w A cos’ ¢

eC)

It is evident that at the point of maximum velocity c¢ changes its
sign, and that in nature at this point the equation c = o must be
true.

In a system of parallels we have two horizontal currents, one along
the surface of the earth and the other in the upper strata, For the
last we can employ the same equations as for the first, but for want

se

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 203

of observations the coefficient of friction remains unknown for the
upper strata. Neglecting the vertical depression /, the sum of the
two horizontal depressions, D, at’ the surface of the earth and D
in the upper stratum, is equal to the difference of the weights of the
columns of air Jsee $20, eq. (12)]. We can approximately calculate
this difference by equation (4) of § 17. To fix our ideas we assume
that the air at the point A has the virtual temperature T, = 298°,
and the coefficient m = 6, if there is an ascending current. At the
point B the calm air has the virtual temperature 7,’ = 294° and the
coefficient m’ = 7. If we assume that the air moves from B to
A and there ascends, we shall find by the formula (6) of §16, that
the ascending current extends up to a height of 4918™ and that the
difference of weight of the columns of air is 3.1™™. Assume D y=
2mm ahd D = 1.1™™, If the extent of the system of wind B A is
20° we shall find by the formula*"(10), U, = 10™. The time the
current requires to move from B to A is expressed in hours.

6 9
10° 200 oe _ = 123.3 hours
9 4U, 3600

If now the air from B can in 123 hours attain the physical state
belonging to the air at A, then this system of wind is realized and,
as we see, the parameters of the system are determined by the physi-
cal state of the air and of the surface of the earth. If we assume the
distance B A = 16°, we shall have U, = 12.5™ and the time equals
103 hours, but in this case the air from B will arrive at A with tem-
perature lower than the temperature at A, and consequently the
depression will diminish and the system of wind cannot be perma-
nent.

$26. Cyclonic system of the second order

We have already in § 12 and § 13 studied the cyclones of the sec-
ond order in respect to the motion along the surface of the earth.
We have assumed that the horizontal current has a constant height
h in the exterior portions and that the horizontal velocity increases
in this part toward the center and attains its maximum value U,
at the distance 7, from the center of the isobars. Then the current
enters into the interior portion, where its velocity decreases at the
same time that the motion is changed little by little into a vertical
motion. Let the mean vertical velocity be w, and the angle between
the gradient and the maximum velocity be ¢; the condition that

204 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the same mass of air passes from the horizontal current to the ver-
tical current is expressed by the formula

rre@wWw=2n7r,hk U,cos py
whence
BN pele cha ee re ree ice
¥.

In cyclones of the second order the ratio //r, is probably so small
that we can neglect the vertical velocity and the vertical depression
E which belongs to the
ha * accelerated motion of
TG ae. \ theverticalcurrent. The
’ rotation of the cyclonic
motion is determined by
the deflecting force T
(fig. 26) of the rotation of
the earth. We have as-
sumed that the cyclonic
system has a barometric
minimum at the surface
of the earth and a ba-

FIG. 26 rometric maximum in

the upper strata. It

follows that the rotation in the upper strata is opposed to that at

the surface of the earth. The intermediate vertical current which

joins the two horizontal currents is consequently rectilinear. The

phenomena are inverse to those of the anti-cyclones. However, the

little that we know about the motions of the cirrus clouds seems to

indicate that the axes of rotation of the lower current andof the
upper current do not lie in the same vertical line.

As parameters of the cyclonic system we can choose the depres-
sion D,and theradius 7, which
depend on the physical state
of the air. We can approxi-

° mately establish the follow-

FIG. 27 ing relations between the max-

imum velocity U, and the gra-

dient G,. Assume that the gradient curve (fig. 27) is composed
of a straight line and of a curve whose equation is

a’

Gate
ro

—

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 205

From §12 we have

a= p Ui we uae
Le cos a
and
pate
u 10°

In the interior portion the depression is equal to

[er {Sr -ie ts
Cy Py

and in the exterior portion, the depression is equal to

{« a (far + Sar) =
r i
2
: = alog.nat. (1) +4. fei
te r

Neglecting the term cl and noticing that

we get the total depression between the center and the point whose

radius is 1,
D, = a(4 4 tog. nat. (“) ) + o
ro Tq

If the radius r denotes the radius of action of the system, we can
determine it by giving to U in the equation
ie,

Pimento!
a conventionally slight value. In violent cyclones we assume U =5
meters per second. It seems that the ratio 7/7, falls between 2 and
IO.
The time that a particle of air requires to pass through the exterior

206 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

portion, that is to say, to go from a point at the distance 7 to a point
at the distance r,, is found by the formula

To = r
ds OS 1
t= ao = = Fa $=
Uv Ucos@,. U5 7, cos: ¢,
r ro To
‘ 2
Es "0 (| i
2 U, cos by 7 5

By the aid of the preceding formule we have calculated the fol-
lowing tables, In the sixth column / is expressed in kilometers and
wW, in meters. We compute the value of U, by successive trials.

Cyclone of the temperate zone

6=60° K=0.00004 ¢,= 72.4°

Do To Uo G 0 Tr Wo h | t
romm ed 21.9m 4 Qui 4.2° 0.12 40 hours
20 I Sr. s 14.0 6:3 O. 17 62
30 I 39.5 21.0 7.9 0.21 79
10 2 15.8 ae 6.3 0.04 | 58
20 2 | 24.4 6.3 9.8 0.07 | 96
30 2 31.2 9.5 12.5 | 0.08 124
40 2 36.8 11.9 14.7 0.10 | 148
Io | 4 11.0 2.0 8.8 0.015 71
20 4 17.2 3.2 13.8 0.023 129
30 | 4 | 22.2 4.4 17.8 0.030 172
40 | 4 | 26.7 Loe 21.4 0.036 | 211
5o 4 30.8 6.7 | 24.6 | 0.042 245
}

Cyclone of the temperate zone

8 = 30° k = 0.00002 bo = 14.7°

Do | To Uo | Go | r Wo: h t
efSEs NRRRERAR Gr A EAR APLi orca. Tage
romm o.1° 3 ym gomm 0. 6° 1s 7 hours
15 (er a4 | 38 144 °.8 1.8 | 9
20 o.1 | 44.5 193 °.9 aor Io
25 o,r 50 | 245 | Have) 2.4 12
\

5 ae) 0.4 | 29 | 22 | gg 0.34 26
15 0.4 35.5 | 33 2.8 0.42 32
20 0.4 awh 44 3:3 0.49 38
25 0.4 46.5 56 Beg 0.55 43
30 0.4 51 67 4.1 0.61 47

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 207

CuapTer VII
VARIABLE SYSTEMS OF WIND
§27. Variation of pressure in a stationary system of wind

In permanent systems of wind the air that flows inward and pro-
duces the vertical current, is always homogeneous. In variable
systems of wind the flowing air is heterogeneous and
consequently the motion of the system varies with

| the time. The intensity of the systems of wind de-

pends especially on the vertical current and we call

the air, which enters into a system of winds and has

such a physical state that it can produce or sustain a

l vertical current either ascending or descending, the

alimentary air. We callthe air which enters a sys-

Ww tem of wind, but which cannot sustain a vertical cur-

FIG. 28 rent the supplementary air. Let us consider a vertical

ascending current whose height is # and in the first

place suppose the motion to be permanent. Denoting the ver-

tical velocities by w and w, (see fig. 28) and the densities by o and

Oo, at the influx and the efflux of the current respectively, the equa-
tion of continuity assumes the form

wi

0O=pw— oy,

Suppose that after a certain time the inflowing air acquires the
density o’ and the temperature t’ and that the vertical velocities
remain unaltered in the first moments, the equation of continuity
takes the form

d (oh) = hdo = (o' w — po, w,) dt

Eliminating o, w,, we find

The change of density produces a change of pressure and assum-
ing approximately
dp dap aS Qs

P
- PEP 9 ys? pean D)

we shall have

1
Aegis leg aE Bree er Oe le, a ad tes)

208 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

We conclude from equation (2) that the pressure diminishes when
the incoming air 1s warmer, and the pressure increases when the in-
coming air ts colder.* Applying this result to nature we infer that
the supplementary air is colder than the alimentary air.

Denoting by 6 the change of the pressure per hour and in milli-
meters and expressing / in kilometers we shall have

3600.760 ap w ’
= 740393" Tooo’ A

and for an average value of o (0.1318) we have

w
Merida! a8 Cia ae, bide SIN Ae Big eee

Let us consider a stationary cyclone whose pressure at the center
varies; 0 represents the variation of the horizontal depression Dp.
In order to introduce the relation given by equation (1) we notice
that this can be written

dp w

In passing from these infinitesimal values of altitude to the
finite differences, it is necessary to consider the whole height h of
the horizontal current, because in the latter we do not know the
variations of velocity with the height and when w expresses the
vertical velocity in the ascending current at the height h, that is
to say, at the level where the motion commences to be purely ascen-
sional, we can introduce the relation given by equation (1) of $26,
and expressing 7, in degrees of a great circle we shall have

= 0. 1 eis SS ee eee

By the aid of equation (3) we can easily calculate the variation
of the pressure in the cyclones given in the tables of $26.

Equation (2) applies only for the first few moments. If the
vertical current is continually being supplied by heterogeneous air,
the change of pressure must depend also on the humidity of the
air. According to § 5 moist air has during ascension a mean tem-
perature higher than dry air. If we consider tand 7’ as approxi-
mately mean temperatures, we arrive at the conclusion that the
supplementary air is colder and dryer than the alimentary air. If

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 209

then the air flowing into a stationary cyclone changes its physical
state and becomes colder and dryer, the horizontal barometric
depression diminishes little by little and the cyclone is destroyed
after a certain time.

-
§28. Instantaneous systems of wind

Let us consider a column of air of the height / that has been heated
so that the pressure p at the upper end (see fig. 29) exceeds the
pressure p’ of the surrounding air. The air commences to leave

, the upper end of the column and at the same
ig P time air enters at the lower end, but the density
of the supplementary air filling the column up
to the height z has a value o different from the
value op’ of the air of the calm atmosphere and
consequently the weight of the column dimin-
ishes so that the pressure p, at the surface of
the earth decreases and produces a depression
Po — Py The pressure , diminishes at the

D P same time that the vertical velocity w ofthe
current increases up to a limit that corresponds
to the maximum value of the vertical velocity,
and after this moment the steady motion goes on. As an approx-
imation we can neglect the variation of density due to gravity and
consider the force that maintains the ascending motion as equal to

Po. P

iy
oe oe i

a The equation of motion assumes the form
| dw Po = 2?
ee. = pl sar et Se ike Soler) ce pe ie (1)

The difference p, — p is equal to the weight of the column of air 2
having the density o and of the column / — z having the density
o’; consequently we have
fu — 6 pe Te pW See)
Introducing this value in eq. (1) we have

dw (0 —p) Ll-e2
di Beet, Seo, ort we ek ee. a Ce)

From equation (1) we conclude that the vertical velocity increases
up to the moment when the pressure has attained the value

P=pt+gol

210 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

At this moment the column is filled with air of the density p and
z = 1 and the motion is steady. Assuming approximately p’ = p
we shall find
Po=ptega'l

and consequently

Y= $= el — pp). so Se eee
Introducing w = — equation (2) will by integration give
s = 1(1 — cos “*s) > Feo Abas at ae
where
syhy sat —f (5)

is the maximum velocity.
The duration of the current up to the moment when thesteady
motion commences, may be ¢, and we shall have

a :
ha 2m, 4 OD
Denoting by ¢ and 7’ the mean temperatures of the column of the
current and of the column of the calm atmosphere, respectively,

we Can assume approximately

po’ 273 +7
o. 24-7

Equation (5) is now written in the-form
ie 2
Wy —— eee < a) on re en {7}
2738 +7
Let

I

Z = 1000,
tT — Tt GP:

273 + 7’ = 290°;

we shall find

w, = 14.2™ and the duration #, = 110 sec.

MOVEMENTS OF ATMOSPHERE——GULDBERG AND MOHN 211

The steady motion continues as long as the alimentary air remains
unaltered. Suppose that after a certain interval of time #, the air
flowing along the surface of the earth enters at the lower end of the
column with the density o’, then the column will little by little be
filled with air at this density, at the same time that the velocity
decreases to zero, and the pressure p, increases to p,’, and the motion
ceases altogether.

The duration of the steady motion depends on the quantity of
air that can supply the current. If for example the system can be
regarded as a radial cyclone, then denoting by r, the radius of the
vertical current, by r the radius of the alimentary air, by hits height,
and by #, the duration we shall have

Tah ee soca

ee
Be Nee oe ements awe)

If, on the contrary, the alimentary air can be reyarded as a stratum
whose length is very great compared with the breadth, we can
imagine that the system of wind consists of a series of instantaneous
systems, such that the cyclone moves along the mean or central
line of the alimentary stratum (tornadoes, hailstorms). Let the
breadth be L and the velocity of propagation be W, we shall have

or

Lhw =xr? wy,
‘and consequently
fal

We me ot eda Wee wectre 79)

The time ¢ that the cyclone consumes in passing any point, is
given by equation
2h
W eae)
Let
Tr, = 200,
kh = 100",
EL = 1200",

we find

W = 14.9™ and
t = 27 seconds.

212 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

$29. Ocean wind and land wind

We consider the ocean winds and the land winds as variable sys-
tems of parallel winds of the second order. The ocean winds be-
long to an ascending system of parallels and the land winds to a

descending system of
P Pp’ parallels. During the
day the land becomes
much warmer than the
sea and consequently the
pressure p at the upper

BR Pe end of the column of air
Yy —— == (see fig. 30) increases and
Up == = === exceeds the pressure 7’;

FIG. 30 the air at the upper end

leaves the column and at
the same time the pressure p, diminishes, because the weight of
the column diminishes, and thus produces a horizontal current which
is the ocean wind. Approximately we can neglect the time neces-
sary to fill the column of air from the ocean and we can consider the
depression p,’ — p, as a function of the temperature.

During the night the land becomes much cooler than the ocean,
the pressure p diminishes at the same time that the weight of the
column of air increases and a descending system of parallels obtains
with a depression Py — Py’.

The barometric depression which depends on the unequal heat-
ing of the ocean and the land is a function of the time and of the
place, and must be determined by observations. This depression
produces a horizontal current which commences with a velocity
equal to zero; the depression gradually increases, the velocity in-
creases and the current extends more and more up to the moment
when the depression attains its maximum value. Then the depres-
sion and the velocity of the current decrease simultaneously up to
the moment when the current ceases.

Consider the horizontal current at any time and denote its max-
imum velocity which occurs near the coast, by U,, its length along
the gradient by x, and the depression in millimeters by D,; it is
evident that D, is a function of U,, of x and of the time.

We approximately assume

10 333

ia ca

7
7

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 213

and introducing a mean value of p we shall have

ee 1

Pea Ite ae
If we suppose that the curve of the gradient can be represented

by two straight lines and if we express x in degrees of a great circle

we have
Dear OI ve cs WIP EO tI. A As)

The gradient G, is determined for the velocity U, by the known form-
ule

G, 0 k
: Bie vane COS ia:
2w sin 0
tang a = k
consequently we have
2 U, cosa 3
x= k = ‘(o)
For example let
6 = 30°,
k = 0.00004,
we have
oO 25-
G,: U, = 0.09
If
Dy = 0.0o5™

we shall have
Oe snout =,

G, = 0.63
x = 1.6°

§30. Movable systems of wind

When the barometric minimum or maximum changes its position
along the surface of the earth, the system of wind is called movable.
The movement of the barometric minimum or maximum is accom-

214 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOR. 51

panied by a movement of the ascending or descending vertical cur-
rent, and the cause of this is due to the heterogeneity of the air that
enters the barometric minimum either at the surface of the earth or
in the upper strata. The alimentary air on entering, produces a
new vertical current at the same time that the supplementary air
suppresses the existing current, and consequently the vertical cur-
rent moves in advance of the barometric minimum and causes its
change of position. When the barometric minimum is situated
in the upper strata its movement is accompanied by the movement
of the barometric maximum at the surface of the earth, and in-
versely.

In any movable system of wind the pressure at any point what-
ever varies with the time and this variation of pressure is closely
connected with the velocity of propagation of the barometric min-
imum or of the central calm region.

Let x and y be the codrdinates of any point, whatever; € and 7
the codrdinates of the movable origin which represents the baro-
metric minimum; we can generally express the pressure as a function
of the location and the time, or

p=f(«%—§,yn-9,

Differentiating we shall have

dp dp d& dp dy | a)

di de ab > Gg db

FIG) 31

Denoting the velocity of propagation the [movement of the mini-
mum] by W and its angle with the axis O X by P (see fig. 31) the
gradient by G and the angle of the direction of the gradient with the

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 215

axis of X by a, we have

f

W oy ts dy
cos B = FF3 sin 2 = Ty.
p dp dp
uGcosa = — ae ge?

: dp dp
uGsina = roy he oe

Substituting these values we shall have

dp =
ae GW cos (a — By e)

Denote the angle between G and W by j7 and let 0 be the total
variation of the pressure at any point (expressed in millimeters per
hour) and 0” the variation of the pressure, if the systemis stationary,
we have

dp 10338 1

dt 760 3600

. (2)
=| 10333 1 ;
at |- 760 ° “3600 ° J
Substituting these values we shall have
O05 NOS2Z4G. W GOSi7 Bares 1s as HCG)
If the pressure at the movable origin is invariable we have
& = 90
and consequently
6=0.0824GWcosy. ..... .. (4)

At the front of a cyclone the angle y > x and consequently 6
is negative and the pressure decreases; at the rear y < z and the
pressure increases.

Example. Let us consider a movable cyclone whose central
pressure is constant and whose velocity of propagation is so small
that we can consider the motion of the system as a geometrical
movement of the isobars; finally we suppose that the radius of action
is so great and the maximum velocity so slight that we can apply the
same ratio between the gradient and the velocity as in rectilinear

”

216 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

motion. At the station A (see fig. 32) we observe the velocity
U, = 12™ and the variation of pressure 0, = —o.5™™; at the sta-
tion B we observe U, = 8™ and 0, = —o.4™™. Assume the mean
latitude equal to 60° and tle coefficient of friction k = 0.00006,
we shall have (see §9) the normal angle a = 64°.6 and the normal
ratioG :U =0.15. From equation (4) by substituting G, = 1.8™™
and G, = 1.2™™, we shall find W,cos7, = —8.6™
andW,cosy.= 10.3".

B

FIG. 32

Let A U, and B U, (fig. 32) be the directions of the veloci-
ties, that is to say, the true directions of the currents of air,
which are different from the direction observed by wind vanes,
because of the different values of the friction in the midst of the
current of air and at the surface of the earth (see §34). Draw the
angles U, AC = U,BC = a then the point of intersection C is
the movable origin or the location of the barometric minimum.
Lay off C a = W cos 7, and C b = W cos 7, and construct a circle
through the three points a, b and C then the diameter C d represents
the velocity of propagation W both in direction and in extent.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 217

§31. Velocity of propagation of a cyclone

As we shall now explain, the movement of the barometric min-
mum is due to the heterogeneity of the air. At the front of acyclone
dj the alimentary air whose tem-

perature is t, enters and pro-
duces a lowering of the pres-

sure that we denote byd,. At

yw therear of the cyclone the sup-
plementary air (see $24) whose
temperature is t,, enters and
produces an increase of pressure
whose value is d,. The air of

FIG. 33 the central part of the cyclone

has the temperature t and we

have t, >t >t, In accord with equation (4) of §27 we write

a, = 0.182208 #o( J iy wpe oa ounels

T9

p= 0.18 78298 #6 (5, ) pre ant Fae)
To

Designating the variation of the pressure at the center by 0, and
assuming that this variation occurs at all points, we can substitute
successively y = z and y = o in equation (3) of §30, then we shall
have

6, = 0, —'0:0822.G.W oe. is oe. (3)

Gp= tt O0828'G wy oo es ls dD

Eliminating between these four equations we shall find

9, Oia UAE Y(t ee ea

ro 2

Teo 780 2 ook pe . 6)
G. te

If we have t = 4(t, + t,), the pressure at the center remains
constant; if t is greater than the mean of t, and t,, the pressure at
the center increases; if t is less than this mean, the pressure at the
center diminishes.

218 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

For example assume

U, = 30",
fy = 72.4°,
r= 4,
Se ett

we have W about 10™.

For
U, = 50™™,
by = 74.7°,
f= Ol,
Gy. = 246™™,

we have W about 3™.

In cyclones of the temperate zones the radius 7, is generally so
great that we can approximately calculate the ratio U, :G, by the
formule deduced for rectilinear isobars. In this case the quantity

U
2.78 G 6° ¢) depends on the latitude 6 and on the coefficient of
0

friction k. Denoting this quantity by B we have

Ca payee

W=B8B

‘9

The value of B is given in the following table:

[ !
|
6 | cheat | k=0.00004 | k=0.00006

| k=0.00008 k=0.00010
50° | BS | t410 | 7.3 | 9.6 10.9 Teo

667) 6 | 3.2 | Si9 | 7.9 9.2 10.0

|

As to the direction of the pro-
pagation of a. barometric mini-
mum that depends on the tra-
jectory of the alimentary air. Let
cc’ in fig. 34 be the direction of
the velocity of propagation W;
the barometric minimum moves
from ¢ to c’ in an infinitely short
time dt; at the same time a par-
ticle of alimentary air moves from
a toa’ withthevelocity U. Draw
c b parallel to ¢ a’; a’ b parallel
to c c’,a’d and be perpendicular |

Fic. 34

to ac and bf parallel to ac.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 219

Make
cco’ =da,aa'=ds,ca=r,¢a=r+dr;
the angles c’ ca = gandcad’ = ¥¢.
We have ,
acb=-—dg,
¢ea=-—dr
ad=ae—-djf

@ a — iy eat of
By substituting the values of these quantities we shall find

cos¢.ds = —dr—cosg.dea i (7)
sing.ds = —rdg+sing.doa | eat renee a

From these equations by substituting

ds = Udt and do = Wat
we find

dr Ucos¢+Weos ¢

rdp Using—W sin 9

and consequently
Usingddr—-Urcos¢d.dg=Wedi(rsing).... . (8)

Supposing that U rcos ¢ is constant and that the angle ¢ is con-
stant and equal to a as in permanent cyclones, then by integration
and determining the arbitrary constants so that gy = o forr = 1,
we shall have

O57, Cos .& | tang a tog. nat. es e| =Wrsing . (9)
i
By this equation we can determine the angle ¢ that alimentary
air must describe in order to reach the interior limit of the cyclone.
The equations that we have developed apply also to the upper
strata of an anti-cyclone where the barometric minimum occurs.
First example.

By equation (9) we calculate the following values:

a = 40° 50° 60° 70°

I

0.44 0.57 0.68 0.77

220 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

This case is that of cyclones that move nearly parallel to the ali-
mentary stratum and where the alimentary air describes a very
small angle in order to reach the interior region.

In the northern hemisphere the wind deviates to the right and
turns around the center against the sun and consequently the cy-

FIG. 35 FIG. 36

clone moves around the alimentary stratum with the sun (see
fig. 35). In the southern hemisphere the inverse phenomenon
occurs (see fig. 37).

When the cyclone passes any point, the temperature increases at
first, but during the passage of the center it lowers (see figs. 36
and 38).

Since in general the mean or normal isotherms do not deviate
much from the direction of the parallels of latitude of the terrestrial
globe, we must expect the cyclone to be formed on the south of the
supplementary air and on the north of the alimentary air and
also that it move in general from west to east.

r
Second example. Assume Z = 10 and = 200°. By equation
(9) we shall find

a =40 45° 50° 3 55°
Ww
—=0.35 0.25 0.41 9,08

Uo
In this case the cyclone also moves nearly parallelto the
alimentary stratum, but the alimentary air describes about half
a revolution around the cyclone before reaching its interior region.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 221

Therefore in the northern hemisphere the cyclone moves around
the alimentary stratum against the sun and inversely in the south-
ern hemisphere (see fig. 37). When the cyclone passes by any point,
the temperature is lowered at first and then increases, and during
the passage of the center it is lowered again to finally increase
(see fig. 38).

FIG. 37 FIG. 38

The cyclones of the inter-tropical regions, at least certain of them
described by the meteorologists of the East Indies, seem to belong
to the last class. However, the thermometric and hygrometric
observations in the cyclones of low latitudes are unfortunately
still too rare for it to be possible to determine the position of the
alimentary stratum and the extent of the arc traversed by the ali-
mentary air before it commences to ascend in theanterior portion of
the interior circle.

§32. Isobars of a variable cyclone

We shall distinguish three cases:

(1) Stationary cyclone.

The isobars of a stationary cyclone are concentric circles that
change their size at the same time that the barometric minimum
varies. Consequently, the curves of equal variation of pressure are
also concentric circles. The variation of the pressure 0, is a func-
tion of the distance r. We can approximately determine this vari-
ation by calculating two cyclones whose parameters are different.
Forexample, suppose that the radius 7, be the same in each and that
the maximum velocity U, diminishes during a certain time. By
the formule of § 13 and § 14 we have calculated the following tables,
assuming 8 = 50° and -k = 0.00010:

_

222 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

FIRST CYCLONE | SECOND CYCLONE
- 7 aT

r U G b — bo U G b — bo

°° o.om 0. oquua o.oo iste || o.oomm | o.oomm

2 6.0 0.97 0.97 5.6 0.90 0.90

4 I2.0 1.93 Be | rr.2 1.78 | 3259

6 18.0 2.90 8.70 16.8 2.69 8.06

7 20.0 3.30 11.80 19.0 3.29 II.00

8 18.7 3.16 15.03 17.7 3-00 14.10

10 15.0 2.55 20.78 14.2 2.41 19.52

12 12.5 2.07 25.38 11.8 1.96 23.86

14 10.7 1.79 29.19 10.1 1.65 27.45

16 9-4 1.52 32.44 8.9 T.43 30.52

18 8.3 1-34 35.29 7.9 | 1.26 | 33-21

20 Fis I.20 37-87 Vis veg 35.60

Assume the radius of action of these cyclones to be about 20° and
that at this distance the absolute pressure is 760™™. The pressure
b, at the center is then in the first cyclone 722.13™™ and in the second
724.40™™, and the increase of the pressure at the center is 2.27™™
at the same time that the maximum velocity has diminished 1™
from 20.0 to 19.0. Adding b, to b — by we shall find the pressure b
and consequently we calculate the increase of pressure at each dis-
tance r. Assuming that the change has taken place in 4 hours, we
find the hourly variation 6, by dividing the increments by 4 as
follows;

=e a |

Ly Oo r Oo rT Oo | Tr bo

0° 0.570m 6° 0.4mm 10° o.25mm | 16° o.ogm™m

2 0.55 7 0.37 12 0.19 18 0.05

4° 0.50 8 0.33 14 0.13 | 20 0.00
72.777. By constructing a curve repre-
a/ senting 0, =f (r) we easily deter-
Q2 mine the distance r for successive
Oz values of 6, and can construct
Ow the curve of equal variation (see

fig. 39).

(2) Moving cyclone with pressure
constant at tts center.

When the pressure at the mov-
ing center remains constant, the
variation of the pressure at any
fixed station is determined by equa-
tion (4) of §30 and we have

FIG. 39 6 = 0.0324 G W cosy

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 223

Assume that W, the velocity of propagation of the center, is con-
stant. For the value 7 = z/2 we have 6 = o, that is to say, the
curve of no variation ts a straight line*that passes through the center,
and is perpendicular to the direction of propagation of the center.

Assuming y = oand y= z, and also G = G, we obtain the maxi-
mum value of 6, which consequently falls at two points at the dis-
tance r, from the center along the trajectory of the cyclone.

The curves of equal variation are determined in general by the
equation

Gcos 7 = constant.

We can easily construct these curves by the aid of the curve of
the gradient.
In the interior portion, we have the equation

G=G,r
and the curves of equal variation assume the form

rcosy = constant.

These curves are straight lines perpendicular to the direction of
propagation.

By using the values of G given in the preceding table we have
constructed, for every o.2™™, the curves of fig. 40, assuming W =
ro™.

If we wish to construct curves of equal variation of pressure for
any date whatever, we can construct two systems of isobars ap-
propriate to the given date, and then determine graphically the
curves of equal variation. It is evident that by choosing two appro-
priate dates so far apart that the distance between the centers
exceeds the diameter of action, 27, the curves of equal variation
and the isobars themselves become identical and the maximum
variations are the centers of the two systems of isobars.

(3) Moving cyclone with variable pressure at the center.

When the pressure at the center varies, the variation of pressure
is determined by equation (3) of §30 and we have

d= 0, + 0.0324 G W cosy

The variation 0, which is a function of 7, is determined as we have
shown in the first case where the system is stationary. Assuming
W = 10™ and introducing the values of G and of 0, given in the
preceding table for the first case, we shall find 0 as follows:

224 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

r r=°0° | =! 30° =) 607 = go° = 120° = 50° = 180°
2 0.86M7M | o.82mm o.771m 0.55MM |) +6,.39MM| 4+56,2gMM!/ 4+5,24mm
4 Tory I.04 0.81 0.50 +0.19 —0.04 —0.12
6 235 Ir.22 0.88 0.41 —0.06 —0.40 —0.53
7 1.44 1.29 0.90 O37 —o.16 —o0.55 —0.70
8 r.30 I.22 0.84 0.33 —o.18 —o.56 —o0.69
10 1.08 0.97 0.66 0.25 —o.16 —0.47 —0.58
12 0.85 0.77 0.53 0.19 —o.15 —0.39 —0.48
14 0.70 0.62 o.41 Oo. 13 —o.15 —0.36 —0.44
16 0.58 0.52 0.34 0.09 —o.14 —0.34 —0.40
18 0.48 ©.43 0.27 0.05 —0.17 —0.33 —o0.38
20 0.39 0.34 0.19 0.00 —o0.19 —0.34 —0.39

FIG. 40

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 225

By the aid of this table we have constructed for every 0.2™™ the
curves of equal variation shown in fig. 41.

FIG. 41

We can also determine the curves of equal variation by construc-
ting two systems of isobars for given dates.

$33. Isotherms of systems of wind

Permanent systems of wind demand a uniform temperature for the
air that enters into the barometric minimum. Assuming that the
temperature of the air varies with the pressure when nearest the
surface of the earth, it is evident that a permanent cyclone must
have circular isotherms around its center. Moreover, the system
of isotherms must itself be permanent.

If we consider a variable and stationary cyclone, the isotherms
must be circular around the barometric minimum but they can vary

226 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLTS

with the time, so that the curves of equal variation of temperature
may be concentric circles around the center of the cyclone.

In the general case where the isotherms have at first any situa-
tion whatever, the system of wind is mobile, and the trajectory
of the barometric minimum depends on the situation of the iso-
therms before the motion commences.

The isotherms at the surface of the earth belong to particles of
air that move without vertical velocity. The trajectories of those
particles of air that remain always at the surface of the earth assume
the form

x = % +7 ()

(1)
v=o FeO
by taking the axis of X and of Y at the surface of the earth, and
designating the time by t¢.
Let the equation of the isotherms for the time t = 0, be

F te 0 2 2 ot ek

If we assume that the particles of air maintain their temperature
during motion, we determine the equation of the isotherms at any
moment by eliminating x, and y, between equations (1) and (2).

If, on the contrary, the temperature of a particle of air varies,
either because the pressure changes its value or because the surface
of the earth causes a heating or a cooling, we shall be obliged to
consider its temperature as dependent on the time while the particle
is moving. The problem will be very complicated but its solution
can be effected approximately by the graphic method by construct-
ing the trajectories of the particles of air and thus following up the
variations of temperature due to the pressure and to the surface
of the earth.

First example. Let the trajectories be straight lines parallel to
a b (fig. 42) and the velocity be constant. Their equations become

4% =X, + at; y = yy + Ot.

Assume that the isotherms for the initial time, ¢ = o are straight
lines parallel to the axis O Y; their equations become

% =f} (t)
Eliminating x, we shall have

x =f (ct) + at

ys

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 227

which equation represents a series of straight lines parallel to the
axisO Y. We conclude therefore that any isotherm, as mn, moves
parallel to this axis.

FIG. 42

Second example. Let the trajectories be logarithmic spirals rep-
resented by the equations
r= — 2at
gy = ¢, — tang a log.nat. ~
in which we have ;
(Tm —a=rUuUcos¢

Assume that the isotherms for the initial time t = o be straight
lines parallel to the axis O X. The equation of an isotherm a b
(fig. 43) assumes the form

To SIN Gy = i (r)

Eliminating r, and ¢g, we shall find

sin(¢ + % tan a lcg nat a = eis cae
t= 92 at V r+ 2 at

228 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Let us consider the cyclone of $32, in which we have a = 48°.
The value of a is Ur cos a, and by introducing hours and degrees of
the great circle we shall have

60 x 60 x 9
10°

a = 150. cos 48°. = 3.25

For the isotherm ab we have j (rt) = 12° and we have calculated
its position at the end of 2, 4 and 6 hours (see the dotted lines in

fig. 43).

FIG. 43

Instead of determining the movement of the isotherms we can
study the variation of temperature and constant curves of equal
variation of r. In a short time the center of the cyclone passes
W oo” from Oa to O” (fig. 44) and we

will consider the mean posi-
tionO. A particle of air de-
scribes the distanceab = ds
and we assume that it main-
tains its temperature con-
stant. Then at the point bthe
temperature will be changed
and the increase of the tem-
perature d rt will be equal to
the difference of the temper-
ature between the isotherms which pass through a and through b.

Let us call the variation of the temperature per degree of a great
circle measured perpendicularly to the isotherm in the direction
toward which the temperature diminishes, the thermometric gradient.

FIG. 44

MOVEMENTS OF ATMOSPHERE——GULDBERG AND MOHN 229

Let ac be the direction of the thermometric gradient J, and draw
b ¢ perpendicular to a c: the temperature is the same at band atc

: , ac .
and the increase of temperature from a to bis J re Introducing

-
ac =dscosyand the value of 1° we have

9
dt = — Jcosyds
ee 4 y

Denoting the variation of the temperature per hour by 2, we have

1 = 3600 ae
dt
Since
a eo
dt
we find

a= 0.0324 J] Ucosy

The angle y depends on the angle 7 between the thermometric
gradient and the axis, and we have

teak ek ew:
Consequently we shall find
a= 0.0324 J] Ucos(eo+q¢-—y7)...... (3)

By the aid of this equation we can construct curves of equal varia-
tion of temperature. Supposing 7 to be constant we shall have for
7— 0,

g=—~—¢+7 =constant.

Nila

Hence, the curve of no variation is a straight line which passes
through the center of the cyclone.

It is evident that there exists some relation between the velocity
of propagation W and the thermometric gradient J. According
to equation (6) of $31 we have

W = 2.78 cos y, 2%
Gy

To

230 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOI a5

The mean value of the thermometric gradient (see fig. 20) is
approximately:

ie ee accat he OS age es

and consequently

w = 5.56 Uo 008 fo

Tow Gt

0

We have then in the examples following equation (6) of section 31
We: | =. 238:

Third example. Let the isotherms be straight parallel lines.
Let us consider a cyclone and distinguish the interior region where
we have U = U,r and the exterior region where we have Ur = m.
Substituting these values in equation (3) we shall find for the inte-
rior region

4

Tr Cos ng — =e
Saar 0.0324 U, J

which represents (see fig. 45) a straight line a b at the distance c
from the origin, and the angle between the axis O X and the per-
pendicular ¢ is (¢ — 7).

ain a
*

FIG. 45

For the exterior region we shall find

0.0324
= OS cos (p +H — 7)

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN ~— 231
which represents (see fig. 46) a circle through the origin and whose
diameter

_ 0.03824 m J
4

d

forms the angle (¢ — y) withthe
axisO X. Considering the cy-
clone of §32, we have ¢ = 48°,
U, = 37, m= 150. Assuming
J =1and do = 60°, weshall have
¢ — 7, = — 12°, which signi-
fies that the perpendicular c and the diameter d are below the axis
OX. Substituting 7 = 0.2, 0.4, etc.,we shall find the curves of fig.
47,in which a b represents the direction of the isotherms.

— Qe iN

--—--~— \
one eae eee

‘\ \ Oe

FIG. 47

232 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL-e5 rE

CHAPTER VIII
SYSTEMS OF WIND IN NATURE

§34. Influence of the surface of the earth

In nature the systems of wind show many deviations from the
ideal systems that we have considered. It is especially the sur-
face of the earth with its irregularities that produces the greatest
disturbances. To take an extreme case, let us consider a valley,
that is to say an uncovered channel in the crust of the earth, it is
evident that the wind follows the direction of the channel, whatever
may be the direction of the gradient in the strata above the valley.

At meteorological stations situated at the surface of the
earth, we must expect that the angle ¢ between the gradient and
the direction of the wind will generally differ from the theoreti-
cal angle, because the value of the friction depends on the irregu-
larities of the surrounding land. We must therefore add a local
correction 4 ¢ which is determined by observations. We believe
that the determination of this correction is of great importance
for the prediction of the movement of systems of wind.

When a system of wind extends over a great part of the surface
of the earth, the variation of the latitude produces disturbances of
the normal angle, and a disturbance of this angle acts also on the
system of isobars.

When the surface of the earth over which the system of wind
occurs offers irregularities, the coefficient of friction varies. The
variation of the coefficient of friction from one point to another
produces disturbances of the angle between the gradient and the
wind and consequently a deformation of the system of isobars.

Example. Let us consider a cyclone of which one half is over
the land and the other half over the ocean. ‘The equation of con-
tinuity is independent of the coefficient of the friction and of the
latitude, and for the exterior portion where the current is considered
as horizontal it is necessary to have

U7, cos. o.5— OU, 7. cos nm,

Assume that the radius of the ascending part be 7° and calculate
the different curves as we have shown them in §12 and § 14; and
we shall find for the two portions of the cyclone;

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 233

OVER THE LAND OVER THE OCEAN
Mean latitude: <c..ccte cc. se 50° | 60°
Coefficient of friction........ 0.00010 0.00005
Normnalwangless--cmss.. 5 6s 48° 10° 68° 24”
Maximum velocity...... fel 20m 30. 7m
Maximum gradient.......... Zngoum 5.34mm
b — bo r (land) r (ocean)

5mm Aa6e Bean

Io 6.4 4-3

15 8.0 aA

20 CRY/ 6.3

25 Ir.47 - 9.2

30 14.4 8.2

35 17-7 9.2

FIG. 48

By the aid of these values taken from the curves of pressure we
have constructed the system of isobars shown in fig. 48.

234 SMITHSONIAN MISCELLANEOUS COLLECTIONS [VoL. ie!

§35. Influence of the movement of the system of wind

In the preceding example we have considered the movement of
a system of wind under the hypothesis that the system keeps its
form unaltered while moving. But this hypothesis is not correct.
A moving cyclone does not transport its system of isobars in the
same way that a system of circles is geometrically transported.
We shall consider the general case in which the cyclone is movable
as to location and variable astothe pressureatthecenter. Wecan,
therefore, by.the aid of the following equations determine directly
the variations of the pressure 0, and 0 that we have already deduced
less precisely in another way in §$§30 and 32.

Exterior portion

Consider a horizontal current; the equations of motion (see §19)
assume the form

Lode... du yet — yt

-.— = —2wsin6.0— ku —-——4—-—v—. . (J)
p dx dt dx dy
BOP by fib gh oh tee oe ee ote)
p dy dat dx dy

Let € and 7 be the codrdinates of the moving origin and assume
that the velocities u and v are expressible in the form
apes en aa Oa
= 5
Bea eee 7) = INGE) :

r

(3)

. 4)

where
= (x — & + (y — 9)
Here M and N like € and 7» are functions of the time ¢, and we

designate their derivatives with respect to t by M,’ N,’ & and 7/
We easily see that the condition

d*p a*p
dydx dx dy °
will be satisfied when we have
du. du

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 235

at the same time that the equation of continuity

du du - i
dx dy
is fulfilled. °
The absolute horizontal velocity U is determined by
: 2 N2
U=av+v= anes Rees we Gy (|
Be

Writing

ak dF

dx’ dy

we shall have

F, =M log. nat. r + N arc ( tang = =)
ay

sa hg
Writing
dF, dF,
apy eee ae
we shall have
FP, = N log. nat.r ~ M are ( tang = —s
A Se
Equations (1) and (2) assume the form
2 2
EGE ee nt po eee
po ax ax ax dxdt dx
2 2
BAS ey ee — oe = ca
p dy dy dy dy dt dy
consequently we have
P2wsin OF, —kF — 4 +6. oe eG)
0

Writing
x—f=rsng
y—-n=rcos ¢

236 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

and substituting the values of F and F,, we shall find

P _[2wsin0.N —kM — M’Jlog nat r

Qe
—[2wsinOd.M+kN+N'J\¢
- (7)
(aio ’ , !
Mie sete al sin ¢ +f DO ere ee
r r
—-4U+C
The condition that the isobars are fixed curves requires that
ZosneOM+kRN+AN=0. 4%. SYR)

Equation (7) shows that the isobars are not circles: they are curves
: a dependent on &’ and 7
which are the compo-
nents of the velocity of
propagation. The gra-
dient no longer coincides
with the radius r and the
angle Y between the ve-
locity and the gradient
differs from the normal
angle a.

Let a’ be the angle
between the velocity U
and the radius r (see

© i fig. 49) by combining
gis ae the equations (3) and (4)
with the preceding equations we obtain

u
tang g —

tang a’ = tang (g —2) = thao lM ; . (9)

1 = tang@ M

Uv
Determining M and N by equations (5) and (9) we find
M = — Urcosa’

» oe = CIO)

N = Ursina’

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 237

By equation (8) we shall find

: /
tang a’ = tang a ere eee et 8)

a

The last equation shows us that for a stationary but variable cyclone
the angle between the gradient and the wind differs from the nor-
mal angle a. Suppose that we have Ur = 150,a = 48° andk =
0.00010, and consequently in the constant cyclone N = Ur sina
= 111.5. In one hour N may increase to 115.1, then we find
N’ = 0.001 and a’ = 44.°7.. Urisincreased by 13.7 and the maxi-
mum velocity by about 1.5™.

Assuming 7/ = o and ¢’ = W that is to say that the cyclone is
propagated with the velocity W and in a constant direction, and
considering the special case in which M and N are independent of the
time and M’ = o, N’ = o, the equations (5) and (7) show that then
U and p are independent of the time and consequently that the
pressure is constant at the center during the propagation, and we
have from equation (11) a’ = a and

p kUr

W
zi aes i =
5 cos 108 nat r 4U : Ursin(@g —a) +C. (12)

Assuming that at the distance R the pressure P remains constant
and that the velocity U can be neglected, the equation is written

P—p RiU¢

1 = UP a i d 13
F Age ognat — +3 + : rsin (gy —d) . (13)

where the influence of the velocity of propagation is represented by
the term

W
| Ursin(g — a)

which term has its maximum value for
pg =90° +a

and consequently the axis of the isobar makes the angle a with the
velocity of propagation. In the direction o b, perpendicular to the
axis 0 a (fig. 50) this term is zero and the pressure has the same value
in this direction as in the stationary cyclone.

238 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 52

In order to determine the angle ¢ between the radius 7 and the
gradient, we notice that the gradient is normal to the isobar and

consequently
dp
dr ( s
Pipes Re ee fe! dtoruh ies oe eA ee
cone rdo dp ae,
"dr

FIG. 50

Assuming that N and WM are independent of the time, we shall
find by differentiating equation (12)

W
es Urcos (vg — a)

tange= 2, WwW ; 0 GEE
ae. Oe sin (ea)
CO5.0) + ‘

Along the axis of the isobar where we have g = a + go° org =
a — 90°,e becomes zero. The maximum value of ¢ occurs for g =a@

and we find

W ‘a
tange,, = Ly « CG

cos a

se os

We conclude therefore that the angle ¢ between the wind and the
gradient has its minimum value (a — ¢,, ) along o b (fig. 50) at the
anterior limit and its maximum value (a + ¢,,) in the opposite direc-
tion.

MOVEMENTS OF ATMOSPHERE—-GULDBERG AND MOHN 239

Interior portion

We have assumed that in the interior portion (see § 14) the ve-
locity and the gradient diminish proportionally to the radius and
that the angle 8 between the direction of the wind and that of the
gradient is connected with the normal angle a by the equation

2U
tanga = tang (1 — 7, cos 2)

\ “a

We make

Cae U 2)
G.=— = —(—

F -COS 2 | r

Consider a variable cyclone and assume that the velocities u and
v have the form ;

uU

alien (17)

eM O17} IN On te)

It is evident that the conditions under which equations (1) and
(2) are integrable are satisfied when we have

dp
dx dy my

Introducing u and v into equations (1) and (2) we shall find the
condition

2wsn0M+kN+2MN+4+WN’=0.... . (18)
Making
S=2wsin@N —kM —M*?+4+N?-M’. .., (19)

we shall have

te aap
—. =S@-H+ME+Ny |
0 x
. (20)
cil at lA )+Ny’ -Ne
o ay ieee 7

240 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 5a

By integration we have

p=2S[%—- s+ y— p+ (ME +N A) - 8)

SM yh NE ti ag) Ae Gal he. Pa ae ee
Making

Me+N7' |? Mir’ —-NE
pale p ue eee | tifyno4 = | (22)
we shall have

=4SP4+C
and
cob egSP. C8)

Hence the isobars are circles about a center different from the moving
origin.
Let the angle between U and r be 8,’ we have

t ‘ : 24
ang #’ = — u . (24)
By the aid of the formula
C= =U AN")?
we shall have
U
M= — x cos f |
. (25)
a ane
Mie re sin §
By aid of equation (18) we shall find
a 7a 8 ine Pe Nr a6
tang @ = tanga + Ee sin f — Lager co (26)

We conclude therefore that also in a stationary but variable
cyclone the angle between the gradient and the wind diflers from
the angle 3 belonging to the permanent cyclone.

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 241

Let us consider the special case in which M and WN are independent
of the time and make

7 =Oand & = W

Then by placitig N’ =o and by comparing the formula for
tan f’ with the first formula for tangent a we have f’ = # and by
eliminating 2w sin 0 between the equations (18) and (19) we shall
find

St

tine (~) -£.6... -. Q9

~ cos B (7, NG
U,W : U,W . 3
— %—§ — Te COs 3 + GU a ee sin 3 (28)

and by introducing the barometric height b in place of the pressure
p, in equation (23) we have

Feehan Jee eon ae es cathe C29)

We infer from these equations that the system of isobars belong-
ing to the stationary cyclone
has been transferred from the
origin O (see fig. 51) to the cen-
ter A, whose distance is

and which falls on the right
line A O making the angle ~

with the direction of propaga-

Y tion of the center of the cy-

FIG. 51 As
clone.

Example. Assume that the cyclone has a velocity of propagation
W = 15™ and that we have for its exterior portion, U r = 150 and
a = 48° and for its interior portion U,= 3™, G, = 0.483™™, B = 57°.5
we shall find

OA = 0°.85

By constructing the isobars for the exterior part and for the
interior part we shall by interpolation find the isobars for the inter-
mediate region.

242 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The isobars in fig. 52 are constructed according to the following
table:

VALUE OF T
b ; Ss
g=a gy = a+ 90 g = a — 90°

760 20.0° 20.8° 19.2°
755 16.3 17.2 15.4
750 53.3 | 14.2 12.2
745 10.8 rr. 7 10.0
740 8.9 9.7 8.1
735 7-9

730 6.3

9725 4.5

|

FIG. 52

The maximum value of the angle ¢ between the gradient and the
radius is determined by equation (16). Assumingr = 9°, U = 16.7™,
k = 0.00010, we shall have ¢ about 5° and consequently the angle
of inclination ¢ varies from 43° at the anterior edge to 53° at the
posterior edge of the progressing cyclone.

\

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 243

§36. Influence of the rotation of the earth on the vertical currents

As we have shown in §19, the force produced by the rotation of
the earth depends also on the vertical velocity. Let us consider
in the first place a steady vertical current and assume the horizon-
tal velocities u an@ v to be zero. The equations of motion assume
the following form, denoting by a the angle between the axis O X
and the meridian (see fig. 53):

So —2w cos 8 sinaw
p ax
ee —2wcos 8 cos aw
p dy
1 dp _ ee tad
o dz dz
N 5, @
a
WwW E
(Ds
5 a
RIG. 54

It follows that the vertical motion goes on in the same way as
we have developed in §15, but that there exists a horizontal grad-
tent. Denoting this gradient by G we have

CG = 2 ns cos Om a yaw ee ees a CL)

p

and this gradient is directed toward the east, when wis positive which
is true for ascending currents. For descending currents w is neg-
ative and the gradient is directed toward the west. The gradient
produced by the vertical current has its maximum value at the

244 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

equator where 0 = o and it disappears at the poles where 0 = 90°.

For a mean value of o we have

G = 0.16 cos Ow

Let us consider an inclined current and seek the conditions under
which the horizontal gradient produced by the -vertical velocity
is zero. Suppose that the inclined current lies in the plane Z O X.
We assume the component v = o.

By substituting

ap th <5
ax. ay

the equations of motion take the following form:

du dw

0= —2 cos Osn aw —4 —_—=w— ,. ... . @
dx dz

0=2wsin@u—2wcos@cosaw. ... .« .(3)
ld :
poe 1 astern eta ne ee . (4)

p dz dx dz

From equation (3) we obtain
uh cotg 0 Sat. 3s ee (5)
w

The horizontal gradient being zero, it isnecessary that p bea func-
tion of z only and consequently from equation (4) we shall obtain

Eliminating « between the equations (2) and (5) we shallfind

0 aerate ened ere
dz

Supposing that the density p is a function of z only, the equation of
continuity is put under the form

o w = constant

MOVEMENTS OF ATMOSPHERE—GULDBERG AND MOHN 245

From the last equation we obtain

and consequently we shall find

i w

tanga = — —— :
aT 2wsin 6

- (7)

For the ascending currents the value of w is positive and the angle
a falls between 270° and 360°, that is to say, the direction of the axis
O X is between the west and the north.

By eliminating w between equations (5) and (7) we shall find

See a rn ee ae Pieter ess AO)

g

The maximum value of w occurs for 0 = 0° and then we have
@ = 270°; for T = 273° we shall find # = 1.2™.

For example let 6 = 45,° T = 273° and w = 1 meter, we shall
find a = 309°.5 and u = 0.64™.

The inclination of the ascending current to the vertical being 2,
we have

= 0.64,

S|

tang 4 =

mo whence 1 = 32° 37’.

If the height of the current was 10000™, the center of the baromet-
ric maximum in the upper strata would be moved 0.64 kilometer,
or about 0.06 degree of a great circle from the vertical passing
through the barometric minimum at the surface of the earth. We
come therefore to the conclusion that in cyclones the current axis is
inclined backward by the action of the rotation of the earth, but so
little that we can neglect the effect of this inclination.

24€ SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

§37. Influence of simultaneous systems of wind

In nature we generally find that various systems of wind exist
simultaneously. The simultaneity of two or of many barometric
maxima or minima produces certain disturbances in the systems
of isobars of each system of wind’and especially do the isobars de-
viate from the normal form along the passage from one system to
another.

We shall illustrate the passage of the wind from one system to
another by an example which offers an analogy with certaincases
of nature. Consider a horizontal motion and assume that the vel-
ocities along the axes O X, O Y and O Z assume the form

eS Myo i ean SS 2 ey ee

Substituting these values in equations (1) and (2) of $35, we have

1 dp

—-— =-2wsind>Mx —kMy— M?*x....... (2)
p dx

aioe 2 ind: M kM M? 3
—$ .——_ = @ sin ‘y — fk Se ee eee
ee y y (3)

By integration we shall find

ae = —}4+(2wsin 6° M+M?) —

—-kMxy+4y7 (2wsind@.M — M?)

and by introducing

we shall have

P— Po EM» ( . a hk
=—i_|y? | tanga ——_])— 2xy — x| tanga +— }|...(4
; i | 9? (tanga — > y — 2°( tang a a) (4)

M
i tan "ep then the isobars represented by equation (4) are
hyperbolas.

MOVEMENTS OF ATMOSPHERE—-GULDBERG AND MOHN 247

The asymptotes are represented by the equation

" i M 2
1 aa + tang?a — )
y as: ky Mi ee (5)

B ge tate heh ge
: k

The trajectories of the motions of the air are determined by-

PS yp ande 4 aeee

dt dt

and consequently
a2 — pay =,0:

By integration we shall have
No == CONStAMGM cat 42 4c e bs (OD

We conclude therefore that the trajectories are equilateral hyper-
bolas.

MAX. °

FIG. 54

248 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The absolute velocity U is found by the equations (1) and we
have

LP ee IP eel ck oe ea ee
Assuming @ = 45°; ois k = 0.00006 we shall find for the
asymptotes of the isobars
a2.) 9 SS and =| Ae
x x

We easily construct the hyperbolas by the aid of the asymptotes
and of one point in the hyperbola. By introducing a mean value
of o and expressing the pressure in millimeters of mercury we shall
find by equation (4)

36.37 (b — by)
26.88 (b, — b)

fora =.0>. 5°

for yy =—/0> 36

By giving to the difference b — b, the successive values1™™;
2mm; 3mm; etc., we shall locate the points by which we can con-
struct the hyperbolic isobars, as shown in fig. 54.

To construct a trajectory of the wind we start from any point
whatever.

XII

ON THE THERMODYNAMICS OF THE ATMOSPHERE
BY PROF. DR. WM. VON BEZOLD

[Fourth Memoir, Sitzungsberichte of the Berlin Academy. 1892, pp. 279-309.
Translated from the Gesammelte Abhandlungen von Wm. v. Bezold, Braun-
schweig, 1906, pp. 184-215]

SUPERSATURATION AND SUBCOOLING. FORMATION OF THUNDER-
STORMS

In the third memoir! on the Thermodynamics of the Atmos-
phere, which was devoted to the investigation of the mixture of
masses of moist air as well as the formation of fog and clouds, I
have shown what the consequences must be when condensation
suddenly occurs in air supersaturated with vapor.

On that occasion I remarked that I considered it very probable
that such supersaturations, whose possibility is demonstrated by
laboratory experiments, occur also in the free atmosphere and that
they certainly may be the cause of cloudbursts.

At that time it appeared to me important to restrict myself
to a simple suggestion, as I was not able to adduce any proof of the
correctness of this idea. Meanwhile it has become clear to me that
there exists still another unstable condition for the water contained
in the atmosphere, that is, the ‘‘Subcooling,’”? whose sudden dis-
sipation must result in phenomena similar to those of “‘Supersatura-
tion.”” Now the subcooling of fog and cloud has been often
observed. In regard to this I recall the investigations that Assmann
made on the Brocken,? as well as the results of the very interesting
balloon voyage made fromBerlin, June 19, 1889, by Moedebeck and
Gross, and described in an excellent manner by the latter.®

The above mentioned observations give convincing evidence
that at temperatures below the freezing point there occur clouds
that contain no ice but are true water-clouds, but from which there

1See p. 272 of the preceding collection of translations. Smithsonian
Miscellaneous Collections, Vol. XXXIV.

2 Met. Zeit., Vol. II, 1885, pp. 41-47.

3 Zeit. f. Luft-schiffahrt, 1889, Vol. VIII, pp. 249-262.

249

250 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. SI

precipitates ice of the same peculiar structure as is observed in
Glatt eis and which gives rise to the formation of the so-called
Anraum or ice storm. —

If now we try to reason out how the sudden cessation of the state
of subcooling or the supersaturation ought to become manifest,
we find that it must be followed by a phenomenon that has long
since been recognized as a regular accompaniment of thunder-
storms, namely, a sudden rise in the atmospheric pressure. This
rise, with the subsequent less prominent fall, must show exactly the
same peculiarities in continuous barograms that are prominent in
the so-called ‘‘Gewitter nase” or ‘‘thunder nose.”

Moreover, by the more accurate prosecution of the study we have
arrived at ideas about the constitution of thunder clouds and of the
processes going on therein that appear likely to throw new light on
the whole theory of the formation of thunderstorms.

But in order to understand these questions it is first necessary to
investigate from a purely theoretical point of view the consequences
of a sudden disruption of the condition of supersaturated vapor
or subcooled water.

SUPERSATURATION

The influence that the dissipation of any existing state of super-
saturation must exert on the thermal condition of the atmosphere,
under the assumption of constant pressure, is explained in the pre-
ceding third memoir,* although only as a pure hypothesis in the
course of the investigation of the mixture of masses of air having
different temperatures and humidities.

It was shown that in such a case there occurs a rise of tempera-
ture whose extent can be most easily determined by graphic
methods.

If we know the pressure prevailing in the supersaturated air,
y we then represent the normal quantity of water
y’ corresponding to saturation or the quantity
contained in a kilogram of the mixture by the
ordinate of a curve F’F”’ in a rectangular sys-
tem of codrdinates whose abscisse represent
the temperatures. (See fig. 30.)

If now, y, = F,T, or the quantity of vapor
contained in the mixture of air and vapor, ex-
ceeds the normal quantity required for satura-
tion by y, — y,!=F,T, — F,!T, then the temperature ¢, that will

*See the preceding collection of translations, p. 272 —C. A.

a Z

FIG. 30

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 251

prevail after the dissipation of the supersaturation will be found by

if

drawing through F, a straight line making an angle a = tg™ 25)

the temperaturés are above freezing, but a* =fg"' if the tem-

2.9
peratures are below freezing.

The abscissa O T, of the intersection F, of this straight line with
the curve of saturation F’ F’ will be the desired temperature #,.

The graphic construction just given may also be applied with a
slight but very important modification to the case now under con-
sideration.

In the investigation above mentioned it was assumed that the
pressure remains constant since the assumption of supersaturation
served only as a numerical artifice, when the actual process must go
on gradually, and therefore the expansion due to the rise in tempera-
ture can also follow quietly. Therefore the adopted value of the ther-
mal capacity of air was that for constant pressure.

Now, on the other hand, emphasis is laid on the assumption that
the disruption takes place so rapidly that the volume is to be con-
sidered as constant at first,so that the rise in temperature must
make itself felt as a change in pressure.

Of course an equilibrium must eventually be attained, the air
must expand until its pressure comes into equilibrium with that
of the surrounding atmosphere, which process must again cause a
cooling.

Therefore, whereas corresponding to the problem previously dis-
cussed, we had

for which we may now more appropriately write

2 1000c,
-

: 1Z Ay

where the subscript p indicates that we treat of constant pressure,
now, on the other hand, for the present case we introduce the angle
a, for which we have the equation

_ 1000¢,
1 i

ig a,

where ¢, is the specific heat of moist air under constant volume.

252 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 5.

For the value of this quantity we obtain

Cy = 0.1685 + 0.000175 y’

by considerations quite analogous to those that Hann has adopted
in his determination of the value of c,.

At the temperatures with which we have to do y’seldom exceeds
the value 1o and then only slightly, and since r varies about the
value 600 therefore the quantity

can be considered as constant and without incurring important
error can be taken as
cot a, = 3.5,

a value that is generally a little too small, but is nearer the truth than
3.6, which is considerably too large.

For temperatures below o°C, we must use, instead of a
a*, determined by the equation

» 4 value

where / is the latent heat of melting ice.

If we introduce the angle a, into the construction of fig. 30,
or its equivalent value into the formula if we prefer numerical
computation, then we can utilize the same method as above
described.

In this method 7, is the end of the abscissa belonging to the
temperature 7#, and y, — y, = F, J is the quantity of precipitated
water.

We see from this that only a part of the excess of vapor over the
amount required for saturation is precipitated while the remainder
remains vapor in spite of the discontinuance, of supersaturation,
since the air now needs a greater quantity of water for its satura-
tion in consequence of the rise in temperature.

But a rise in pressure accompanies this rise in temperature because
of the unchanged volume, at least during the first instant, which
is given by the equation

ps aio =a,
Bf, 2738 —4,

* Zeit. d. Oest. Gesell. fir Met., 1874, p. 374.

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 253

where £, and f£, represent the barometric pressure respectively
before and after the cessation of supersaturation.

But the objection may be raised that the curve of saturation
quantity is drawn under the assumption of a constant initial pres-
sure £,, since such a constant pressure is everywhere assumed in the
diagrams of the previous memoir.

But this assumption is, however, even now justifiable in so far
as concerns the curve F’ Ff’. For a knowledge of the initial pressure
8, 1s only necessary in order to be able to determine the volume that
a kilogram of air occupies at a given temperature; since this volume
experiences no change during the extraordinary short time that we
have under consideration while the change in temperature makes
itself apparent by the increase in pressure, therefore the assump-
tion is perfectly unobjectionable.

In order to judge as to the probability of the occurrence of such
supersaturation as would suffice to explain the observed changes of
pressure in thunderstorms it will be best to consider the supersatura-
tion as a consequence of adiabatic expansion without the accompany-
ing condensation.

Adiabatic expansion, in the absence of dust or ions that can act
as nuclei for condensation, is the only process by which the occur-
rence of supersaturation in the atmosphere is conceivable. On the
other hand adiabatic expansion does play the most prominent part
in the formation of thunderstorms.

In considering the present problem we can profitably make use of
the method of presentation used in the first memoir® but whereas
in that memoir it is assumed that we imagine one kilogram of dry
air to be mixed with x kilograms of aqueous vapor, we shall now
assume that one kilogram of the mixture contains y grams of water.

It is easy to see that within the limits of the ordinary values of x
or y the diagram drawn for one method of consideration also serves
for the other, since only slight changes will be needed which in fact
can only be appreciable when the diagrams are drawn with unusual
accuracy.

Especially is this possible so long as we assume that the precipi-
tated water is carried along with the air; if we drop this assumption
then minor modifications must enter into the treatment of the prob-
lem, but these are not important in the present memoir.

In general it is easy to see that the following equation will hold
good:

11808
1000 — y

5 See No. XV, p. 212 of the 1891 series of these translations.—Eb.

254 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOB. 52

If we assume that the initial condition of the air as it ascends from
the ground is represented by the point a,
= of the diagram (fig. 31), and that S, S,
: is the corresponding saturation-curve, then
supersaturation will occur when the adia-
bat a, a, intersects this curve without
being broken at the point of intersection,
that is to say, when the cooling takes
place according to the same law after pass-
ing the point of saturation, as it did be-
FIG. 31 fore in the dry stage.
But we attain supersaturation or the

quantity
Yi = Wy

when we seek the curve of saturation belonging to a, and with it the
value y,’.. Moreover, we can apply to the supersaturated air the
conception of relative humidity and put

1

R = 100 a

1
‘ where, of course R > 100.
If now by reason of any sudden paroxysm the supersaturation
should suddenly cease, then an increase in temperature would occur,
and since the expansion of the mass of air can only take place gradu-
ally there must also be an increase of pressure, that is to say, the
curve representing the adiabatic condition must rise suddenly from
a, toa,. In this process the point a, always lies below the satura-
tion curve, since a part of the water falls away from the mass when it
attains the final condition represented by a,, and therefore less vapor
is present in a kilogram of the mixture than at the original beginning
of the expansion.

After the cessation of the sudden rise in temperature (which
carries the pressure from f, up to /,) there will, of course, again begin
the process of expansion, but this will now be along the adiabat
of the rain-stage or the snow-stage. The graphic method just
described may be used to locate the position of the point a, for
the purpose of determining the conditions corresponding thereto.

The position of a, is found by considering the line drawn vertically
through a, as the fundamental line, since the pressures increase with
temperature linearly in this direction. We may therefore identify
the points a, and a, directly with the points T, and T, of fig. 30.

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 255

In order to obtain an idea of the magnitude of the changes here
considered it is advantageous to choose a definite case and deter-
mine the magnitude of the sudden ‘rise in pressure when we assume
that the dissipation of supersaturation takes place at different
stages of progress successively far apart.

In the computations I assume that air having a temperature of
25°C. at sea-level contains such a quantity of vapor as would cause
it to cool to its dew-point by adiabatic expansion when rising to
an elevation of about 800 meters. I make this specific assumption
because in the Alps where the mountains offer excellent level marks,
I have often observed thunderstorm clouds whose lower surfaces
had about that altitude above the valleys.

With this assumption we obtain the group of values shown in the
accompanying table.

h 8, Fie aa yy, |u-w | R, ty Yo! B, | B.-A,

° 760 25.0 12.7, | 19.4 —6.7 GG are orsisscks | Maven cha tetera ereienerctateyal| ekarevenatore

834 690 16.6 12.7 | 12.7 0.0 TOO! “ler srceeters adesscodiococuoplgconoar
957 680 15.5 | 12.7 | 12.1 0.6 105 16.2 | 12.6 | 631.6 T.6
1083 670 14.2 12.7 | 11.2 5 I13 15.6 | 12.2 673.3 303
1339 650 TE7 | 12.7 9.8 2.9 130 14.6 Lr.o 656.6 6.6
2000 600 Sia 12.7 6.8 5.9 187 11.8 | 10.5 (arta) |) aeytgh)

|

In this table all quantities having the subscript 1 belong to the
condition of supersaturation before its dissipation; those having
the subscript 2 belong to the condition immediately after supersatu-
ration is broken up. It need hardly be repeated that h is the alti-
tude in meters above sea-level, 8 the barometric pressure in milli-
meters of mercury, ¢ the temperature Centigrade, y, the number
of grams of water contained in a kilogram of the mixture, and
y, the grams of water needed to produce saturation at the tem-
peratures ¢, and #, respectively. Finally, R expresses the relative
humidity just before the dissipation of the supersaturation and is
therefore the measure of the extent of the supersaturation. The
corresponding value R, after the breaking up is always too and is
therefore omitted from the table.

In these computations I have made use of the graphic method
given by H. Hertz,® which, although it does not allowof any great
accuracy, yet is so remarkably convenient and gives the result so

® Met. Zeit., 1884, Vol. 1, pp. 421-431. See No. XIV of these translations.

256 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

quickly that I prefer to recommend it in all cases such as this where
a general orientation is all that is needed.’

The altitude is the only datum not taken from Hertz’s diagram
of adiabats, but has been directly computed since this quantity
as given by the diagram cannot be absolutely relied on if we wish
to avoid large error. But when the object is to attain a general
idea of the magnitude of the quantities in question I think it justi-
fiable to be content with approximations.

From this example we perceive that an ascending sented of air
needs to pass only a very little beyond the saturation point in order
to develop a supersaturation whose dissipation completely suffices
to produce a rise of pressure of such magnitude as is observed in
thunderstorms.

For instance, under the above assumed conditions the rising air
has only to pass 120 meters above the altitude for saturation in
order to produce a rise of pressure of 1.6 mm. when the change occurs
and in fact 75 meters will produce a sudden rise of 1 mm. in pressure.
Hence we utilize no risky hypotheses in explaining by means of
supersaturation the sudden rise in barometric pressure observed
’ during thunderstorms.

In this explanation we must not attribute too much importance
to the fact that hitherto we have not yet been able to prove the
existence of such supersaturation in the free atmosphere. For
independent of the fact that our ordinary apparatus for measuring
humidity, such as the psychrometer and the hair hygrometer, are
not available as indicators of supersaturation, we note that the
greater frequency of fog in the neighborhood of large manufacturing
cities indicates that the point of saturation is not infrequently
attained, and even exceeded, in the free atmosphere without the
attendant condensation because of the absence of thenecessary fog
nuclei. Moreover, the fact recently demonstrated by Hellmann®
that the rainfall from thunderstorms west of Berlin are heavier than
from those over the city or east of it, argues for the occurrence of
supersaturation at places where there is a dearth of nuclei and espe-
cially during thunderstorms.

Furthermore, in the powerful movements and in the peculiar

7 The new adiabatic tables and diagrams by O. Neuhoff as published in
the Abhandlungen of the Preuss. Met. Institute, Vol. I, No. 6, Berlin. 1900,
can now be more conveniently used for such computations. See No. XXI
of this collection of translations.

* Jahresbericht des Berliner Zweigvereins der Deutsche Met. Gesell. fiir
1891, p. 21, Berlin, 1892.

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 257

puffing up and pushing forth of new heads from the cumulus clouds
I perceive evidence that within the cloud itself there must be present
a source of power and that we have not to do with the simple results
of a quickly ascending current of air.

The observations made by Moedebeck and Gross in the interior
of a cumulus cloud during the above-mentioned balloon voyage,
according to which, the balloon was set into great oscillations and
the drops of water whirled in confusion past each other, show that
within the clouds powerful movements take place independent
of the general movement of the air.

Precisely such sources of power must exist within the cloud in
connection with the dissipation of supersaturation.

On the other hand, I cannot conceal the fact that the very low
temperatures observed within the clouds are not easily reconciled
with any such assumption, although the deprivation of the sun-
shine from the interior of the cloud must bring it about that parti-
cles of water which have condensed in the upper portion of the cloud
must fall with lower temperatures into the lower layer of the cloud,
and we thus perceive that we have to do with very complicated
processes that must produce remarkably different temperatures in
different portions of the same cloud.

Moreover, the measurements of temperature made under such
difficult circumstances can only be completely conclusive when they
are made with the perfected apparatus that has lately been described
by Assmann.°

SUBCOOLING

If the above given considerations have to a certain extent the
character of theoretical speculations, since we have not yet experi-
mentally demonstrated the existence in the free atmosphere of true
supersaturation, this is not true of the investigation to be presented
in the present chapter, on clouds containing subcooled particles of
water. Such clouds frequently occur and can exist for a long time
if the subcooling does not exceed certain limits. If, however, we
consider clouds of very great size, in whose highest parts the tem-
perature must be remarkably low, then a small external stimulus
will suffice to dissipate the subcooling and cause a sudden rise of
temperature and pressure.

Let t, < o be the temperature of the mixture of dry air, vapor,
and subcooled water; y, grams the total quantity of water, partly

*Das aspirations-psychrometer. Abhandlungen d. Preussischen Met.
Institute, Vol. I, No. 5, Berlin, 1892.

258 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

liquid and partly vapor, contained in a kilogram of the mixture,
but of which y’, is vapor; then the quantity of dry air in a kilogram
of the mixture is

1 — 0.001 4,.

If now the liquid water suddenly becomes ice then a rise of tempera-
ture must occur because ot the setting free of the latent heat of
melting, but the freezing point cannot thereby be exceeded, since
no further freezing of the remaining liquid masses would be possible
above this temperature.

In the case of very slight subcooling the dew-point is simply
attained, whereas for greater subcooling and not too great a quantity
of subcooled water, 1. e., for moderate degrees of mechanical subcool-
ing, the temperatures remain below the freezing point.

But no equilibrium can be thus attained by the simple conver-
sion of water into ice, for in consideration of the higher final tem-
perature and since the air is to remain saturated, a part of the
existing water must be converted into vapor and hence the final
temperature will not be so high as if this evaporation did not take
place.

It seems to me probable that these processes take place not
exactly simultaneously and not with the same rapidity, but rather
that the freezing takes place suddenly, whereas the evaporation
takes place subsequently and gradually.

Indeed, it is possible that at the first instant the particles of
water all attain the freezing point, but that so long as the sub-
cooling is not extraordinarily large, only a part of the water can
freeze and that afterwards the surrounding air, as well as the
evaporation, have a further cooling influence.

However this may be, it is certainly advantageous analytically
to assume that first there is established a temperature equilibrium
t, between the frozen water particles and the air and that then the
temperature is reduced to #, by evaporation.

The following consideration serves for this determination of the
temperature ¢, depending on the simple conversion of subcooled
water into ice and the corresponding warming of the air.

In the freezing of y, = y, — 9,’ grams of water 80 y,, units of
heat (in small calories) are set free.

This quantity of heat serves first to warm tooo — 7, grams
of moist air from ¢, up to #,, that is to say, by #, — t, = t degrees, and
furthermore to warm y, grams of ice from ?, to ¢, degrees.

ee ee a, i es, ee tiie i ee

a

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 259

Consequently
80 y, = (1000 — y,)c,¢ + 0.51 4,2

since 0.51 is the specific heat of ice,
Since ¢, lies bettveen the limits 0.1693 and 0.1701 under the condi-
tions here considered we can substitute 0.17 for this value and
obtain
80 y, = (1000 — y,) X 0.174 + 0.51 yt
or
80 y, = (170 + 0.34 y,) t
whence
80 . 8 1 =
a te Vee ab ANTS ee
170 + 0.34 y, 17 1 + 0.002 y,

t

By developing into a series the fraction containing y, in the
denominator and retaining only the first two terms we obtain

t = 0.4706 y + 0.00094 9,2

Since 10 isahigh value for y, that is not likely to be exceeded,
and since the second term attains only the value 0.1°C. when y, = 10,
therefore we may ordinarily confine ourselves to the use of the first
term of this equation.

The formula just given enables us to compute the temperature ¢
that prevails immediately after the sudden freezing occurs through-
out the whole of a subcooled mass, assuming that #, is below freezing,
that is to say, that t, < 0.

If this assumption does not hold good, then the computed value
loses its significance and the value 0 must be substituted for it, no
matter how large 1’, may be.

In this case only a part y,* of the subcooled water can be frozen,
which part will evidently be given by the equation

t, = 0.4706 ,*

where for simplicity we have omitted the second correction term.

We have now still to consider how to determine the final tem-
perature f, as it must result when the air, which was no longer satu-
rated at the moment of freezing, becomes again saturated with
aqueous vapor. For although as above remarked, the final condi-
tion is not of importance with reference to the sudden rise in pressure
which is at present our first consideration, since the pressure must

260 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

eventually come to a complete equilibrium, still I hold it to be advan-
tageous to supplement the investigation in this direction also.

We thus obtain a correct idea as to how large the error would be
if the assumption as to the sudden freezing of the whole mass and the
subsequent gradual evaporation should prove not to be appro-
priate.

I have therefore in the example to be communicated later deter-
mined the value f, of the tinal pressure as it would result from the
assumption that the necessary evaporation goes on directly hand in
hand with the sudden freezing.

In this determination we again advantageously make use of the
graphic method.

In fig. 32 again as before in fig. 30 let F,I,=y, and
F,’ T, = y,/: then we Gnd T, by draw-
ing through F,, a straight line that makes
the angle 8 = arc tgo.47 = 25° 11’ with
the axis of ordinates and find the point
of intersection F, of this line with a hori-
zontal line through F,’. Then T, is the
end of the abscissa representing ?, and
consequently T, T, = ¢.

We now draw through F,a straight
line making an angle” a*, = arc tg }
with the horizontal axis of abscissz
(owing to want of room, this angle is
only marked with a in fig. 32).

The abscissa of the intersection F, of
this line with the curve F’F’ of the quantity of vapor needed for
saturation corresponds to the temperature ¢, while the ordinate it-
self F, T, is equal to yg.

In the preceding it is assumed that t, < o and that the whole
process goes on so rapidly that the volume can be regarded as con-
stant.

If the graphic construction or the numerical computation should
give a value t, > o, then this argument loses its significance.

But in this case the temperature ¢, simply rises to 0° C. Hence
only a part of the subcooled water is converted into ice, while another
part remains fluid and a third part becomes vapor.

Since it is not now of importance to determine the magnitudes of
these three parts we may abstain from their evaluation, as well as
from the investigation of the special cases where the subsequent

19 See p. 252 of this translation.

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 261

evaporation again depresses the temperature f¢, below the freezing
point, since this would demand considerable space out of proportion
to its importance.

In order now, as in the preceding case, to obtain a definite idea
as to how large’ are the changes of pressure that may be brought
about by the disruption of the supersaturation, the above given
example is again worked out numerically in the following table, but
under the assumption that there is no supersaturation and that only
various degrees of subcooling occur.

Table 2
| i
h B, | Vy uy,’ ly v, | ty t, Bo Bo Bh, tz Bs s— Pi
m.| mm. grms. grms. | grms. | C. °C mm mm Cc’. | mm / mm.
o| 760 | 12.7 19-4 Sai Satya emta SO | ahctore nyravell ey stereroeene | i cichck clave ovareveye lotellisscecerctere lectteae
834, 690| 12.7 | 12.7 NOM ee OOM hata arte eevee iellsiene ic losin teviermae IapoaDe
2o11| 600/| 12.7 | 10.2 +2.5 TEs: 5 ayei 0 'o1, ovall'oi at's: ohavessllla ate. ave ahelllene, nets) ofei|(esevevevez'ae ISeceroe
3512) 500 | 12.7 reas 50m] Stoll oghae dicooddn diaccndcslauoobeolaoden ox | creer 3
4063| 467 | 12.7 6.1 6.6 | Ou0/ aceite Reece ener {REPO ya yore | lsvahevel cities svencveravevs |ereveneimhe
4360| 450] 12.7 Sasy | 7.2 | —1.9 0.0 | 453.2 | 3.2 | —1.3 | 451.0]| 1.0
4721; 430 | 12.7 4-9 7.8 | —4.0 | —0.3 | 435.9 5.9 | —2.5 | 432.4 (24
5288) 400 | 12.7 4.1 8.6 | —7.4 | —3.4 | 406.0 | 6.0 |— 5.7 | 402.6 | 2.6
6319) 390 | 12.7 2.7 | 10.0|—14.3 | —9.6| 356.4 6.4 |—11.6 | 353.7 | 3.7
7474 300 | 12.7 Teo. |) eLeae \—22 7 |—17.5 | 306.2 6.2 |—14.6 | 303.7 | 3.7
| |

This tabie shows that under the adopted assumptions of an initial
temperature of 25°, an initial pressure of 760™™, a relative hu-
midity of 66 per cent and adiabatic expansion, condensation
occurs at the altitude of 834 meters and the freezing point is reached
at the altitude of 4063 meters.

If now the water formed by condensation is carried 300 meters
further without freezing (being thereby subcooled 1.9° C.) and if
freezing then suddenly occurs, then the (local) pressure suddenly
imcreases 3.27™.

If the sudden freezing first occurs at the altitude 4721 meters, or
for a subcooling of 4.0°C., then the change in pressure is 5.9™™; for
still later freezings this change increases but slightly and in fact
eventually diminishes.

The reason for this latter diminution lies in the fact that in the
formula

ein
b. — B; = 2, yp eee,

the diminution of 8, with increasing altitude is at higher altitudes

262 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

not fully compensated (or offset) by a corresponding increase of the
factor
t, aia ty
273 + t,

so that 8, — 2, must attain a maximum which in this special
example is to be found at an altitude of about 6500 meters. In
this connection I must especially point out the fact that the num-
bers given in the table for the quantity of water carried upward do
not suggest anything improbable. If we compute the volume that
a kilogram of air occupies at different altitudes we find that under
the above given assumption the quantity of fluid water in a cubic
meter amounts at most to 5 grams, that is to say, 5 mg. per liter,
a quantity that can certainly be easily floated in a rapidly rising
current.

The diagram (fig. 33), for the process
here considered, differs from that pre-
sented in fig. 31, which latter related
to supersaturation proper. Whereas in
that the adiabat a, a, simply intersected
the saturation curve S, S,, in the present
case it shows a sharp bend at this inter-
section, since it changes from the adia-
bat of the dry stage to that of the rain
stage. On the other hand, in the former
case of supersaturation the expansion
simply continued along the adiabat of the dry stage even after
passing the point of saturation.

FIG. 33

THUNDERSTORMS

From the above given considerations and developments it results
that both supersaturation of air with aqueous vapor and subcooling
of the water already condensed must, when these conditions
are suddenly dispelled, cause a rapid local rise in atmospheric
pressure which in general will last only a short time (except in so far
as special circumstances yet to be mentioned do not diminish the
restoration of the pressure) and cause a true jump or spring or so-
called step up in pressure or a ‘‘knick’’ in the barogram instead of
an oscillation at the locality.

But such oscillations and jumps, as already mentioned, are almost
always an accompaniment of thunderstorms and it only remains to
investigate whether the processes that come into play in thunder-

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 263

storms are such as would lead us to expect supersaturation or sub-
cooling.

This study leads us unavoidably to the consideration of thunder-
storm phenomena in general and makes it necessary here to say
something on this subject. I must, however, first of all, remark
with reference to the well-known classification into cyclonic thunder-
storms and heat thunderstorms, that it seems to me that often this
classification is not made in an appropriate manner.

Frequently all thunderstorms that arein any way connected with
the forerunner of a barometric depression, or are located on the
edge of the ‘‘low’’ when this is a very flat or feeble depression, are
designated as cyclonic thunderstorms when they may be perfectly
characteristic heat thunderstorms. On the other hand, the term
heat thunderstorms is often applied only to isolated local thunder-
storms, whereas, in my opinion, the majority of all thunderstorms
observed in interior regions, with very few exceptions, are decidedly
heat thunderstorms.

In fact one might say that the circumstance that the division into
these two classes allows of such different points of view, indicates
that this classification is not anatural one. But this is by no means
the case. On the other hand, I consider this classification as of the
highest importance and if the appropriate definitions have not yet
been made so clear and sharp as is desirable, then this is, I think, to
be ascribed to the circumstance that the first attempts to make this
distinction were undertaken in a country where both groups fre-
quently occur and where they merge into each other more than is the
case elsewhere.

So far as I know, this classification originated with Mohn and it is
precisely in Scandinavia that one has opportunity to observe true
cyclonic thunderstorms more frequently than in Germany where
they are confined almost entirely to the coasts and, as above stated,
only in a few exceptional cases occur in the interior.

For this reason therefore one is tempted in Scandinavia to con-
sider as cyclonic thunderstorms many that I should call heat thunder-
storms, but which are not so typically developed as those observed
in the interior of the continent. ‘

In fact Mohn and Hildebrandsson in their admirable memoir™
on the thunderstorms of the Scandinavian peninsula, expressly say:
‘‘However it is in Sweden impossible to find a well-defined boundary
between these two classes of thunderstorms.”

11 Les Orages dans la Péninsule Scandinave. Upsala, 1888, p. 3.

264 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. SI

On the other hand, in the interior of Germany the cyclonic
thunderstorms are among the greatest rarities, but the heat thunder-
storms are so typically developed that one often recognizes their
characteristic peculiarities reproduced in special Scandinavian
storms that Mohn and Hildebrandsson have considered as cyclonic
thunderstorms.

For instance, I should consider the thunderstorm of August 6,
1881, at least after its penetration into the interior of Scandinavia,
as undoubtedly a heat thunderstorm.

It is precisely the possibility of such fundamental differences in
our views that appears to demand that the path to a better under-
standing be indicated and the definitions be made more exact than
has hitherto been the case.

As to this matter the most important indications are given us
by the great differences in the diurnal and annual periods of the
thunderstorms on the coasts and in the interior of continents, as
shown in the above-mentioned observations in Scandinavia, as well
as in material gathered elsewhere.

Whereas in the continental interior the maximum frequency of
thunderstorms occurs in the afternoon hours and in fact only a little
later than the maximum of temperature, while a very feebly indi-
cated secondary maximum in the early morning hours can only be
demonstrated with much labor; on the other hand, in the neighbor-
hood of the oceans the nocturnal thunderstorms are much more
frequent. Thus, for instance, in the coast region of Schleswig-
Holstein the absolute maximum of destructive lightning occurs
between midnight and 3 a.m.” Similarly in the maritime regions
the winter thunderstorms are much more frequent than in the
interior, and it is the winter storms that happen so frequently in the
night time, so that in fact these determine the earie of the
diurnal period in that region.

In this respect the oceanic exposure of Norway as compared with
Sweden makes itself felt to a most remarkable extent; whereas in
Norway in the ten years 1871 to 1880 there were 235 January
thunderstorms as contrasted with 1811 July storms, on the other
hand, during these same years there were in Sweden 14 January and
4419 July thunderstorms.% But in the true coast region of Norway
the numbers for January and July were in fact 198 and 646, respec-

2G. Hellmann, Zeitschrift des Preuss. Statistischen Bureaus, Vol. 26,
1886, p. 179.

13H. Mohn and H. H. Hildebrandsson. Les Orages dans la Péninsule
Scandinave. Upsala, 1888, p. 39.

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 265

tively, so that in this region the secondary maximum for January
in the annual curve of thunder storms attains a very great signifi-
cance.

This comparison plainly shows that we have to do with two
fundamentally @ifferent groups of thunderstorm phenomena which
certainly must owe their origin to very different causes. Indeed it
is the unequal relative frequency of occurrence of cyclonic and heat
thunderstorms in the two regions to which we would ascribe these
peculiarities in the diurnal and annual periods of the coastal and
interior regions, as Hellmann has already clearly stated™ in the year
1885, when he wrote:

The cyclonic thunderstorms occur most frequently in the colder parts of the
year and the day; the heat thunderstorms occur most frequently in the
warmer parts of the year and the day.

In the same place, Hellmann also emphasizes the following:

That the winter thunderstorms, or those of the cold season from October to
March, occur always in connection with cyclonic storms and frequently at
night time; that they often occur rapidly over long stretches of country, but
individually in rather more interrupted succession and in rather narrower
extent of territory than the average thunderstorm of the warm season; that
they are of shorter duration but generally accompanied by some strokes of
lightning which on account of the low altitude of the clouds from which they
emanate produce conflagrations more frequently than in the summer season.

Whereas in these sentences, which I heartily indorse, it is expressly
stated that the cyclonic thunderstorms, even when their paths are
very long, have only a small extent, we also find elsewhere the
remark that the cyclonic thunderstorms are the larger while the
heat thunderstorms, by contrast, seem as rather local phenomena.

On the other hand, it seems to me that most of the thunder-
storms occurring in Central Europe, many of whose fronts extend
from the German coasts to the Alps, must be classed as heat thunder-
storms.

The one feature common to all thunderstorms is the presence
of a strong ascending current of air as the fundamental condition
for the formation of the great clouds that never fail in any thunder-
storm, but the process by which this ascending current comes about
is quite different in the two kinds of thunderstorms.

I will now attempt to give such definitions of the two groups as
will, as far as possible, prevent confusion:

4G. Hellmann, Meteorologische Zeitschrift, II, 1885, p. 445.
1% Sohneke: Meteorologische Zeitschrift, V, 1888, p. 413.

266 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

(a) Cyclonic Thunderstorms.—Cyclonic thunderstorms accom-
pany the central parts of the deeper, well-developed barometric
depressions. They are phenomena characteristic of a rapidly
ascending current of air such as is brought about in cyclones
by the greater disturbances of the atmospheric equilibrium. Hence
they occur during disturbed, cloudy weather and especially in the
neighborhood of the paths of barometric depressions and wherever
these develop into specially well-marked lows, or on the oceans
and on the coasts. During these cyclonic thunderstorms the
general motion of the atmosphere is cyclonic. This cyclonic mo-
tion itself goes on in a horizontal direction with a slightly upward
component around a vertical axis or at least one that is inclined so
as to intersect the earth’s surface. The annual and diurnal periods
of these thunderstorms follow those of the cyclonic storms them-
selves. F

The cause of these thunderstorms is fundamentally the same
as that of the cyclones in general and can therefore at the present
time not be given with any more certainty than that of the cyclones
themselves, which according to the most recent researches are now
no longer to be explained as due to temperature and moisture con-
ditions alone, but to no little extent are consequences of the general
circulation of the atmosphere.

The question whether there are other special circumstances on
which depend the presence or absence of thunderstorms as com-
panions of the cyclones must be cleared up by further investigations.

(b) Heat Thunderstorms.—While, as just stated, the cyclonic
thunderstorms occur, during disturbed, stormy weather and
decided cyclonic movements of the atmosphere; on the other hand,
the heat thunderstorm demands quiet air for its formation without
decided cyclonic or anticyclonic movement and unrestricted power-
ful insolation. These occur neither in the central parts of the
barometric depressions nor in those of barometric highs, but in
the border regions between these two.

The regions in which heat thunderstorms originate when there
is sufficient insolation are the areas of slight depression with
scarcely recognizable centers extending in advance of a large
barometric depression such as are designated as thunderstorm

‘

© These partial depressions or “‘ pockets’’ are often so imperfectly devel-
oped that their shapes on the charts of isobars are entirely changed by slight
changes in the method of reduction of pressure to sea-level, so that one can
hardly speak of their centers.

These slight depressions are most clearly revealed when we make use of

THERMODYNAMICS. OF ATMOSPHERE—VON BEZOLD 267

pockets on our charts of isobars, like shallow furrows or troughs
between two areas of maxima, ridges or tongues of high pressure
between two low areas and especially between shallow depressions
of wide extent.

In other words, heat thunderstorms originate in regions above
which there is neither a decided ascending nor descending current,
so that at the earth’s surface there is opportunity for such an over-
heating of the air as would bring about unstable equilibrium in this
part of the atmosphere.

In this connection, in general, too much importance has, in my
opinion, been given to the depressions present in thedistribution
of atmospheric pressure just described, and thus the difference
between the heat thunderstorm and cyclonic thunderstorm has
been effaced, whereas these depressions are so infrequently devel-
oped in the case of heat thunderstorms that they form a sort of
intermediary condition between barometric maxima and minima.

We may therefore just as properly consider the protruding arm
of the area of maximum pressure which is necessary to the formation
of the so-called ‘‘thunderstorm pocket,” or the ridge or tongue of
high pressure that most emphatically favors the formation of
thunderstorms, as the important feature and give less attention to
the accompanying barometric depression.

The only important consideration is that there be the possibility
of an unusual rise in the temperature of the lowest layer of air
so that the potential temperature below may be higher than above,
i. e., so that unstable equilibrium may occur.

But this is only possible when in the preparatory stage there is
neither a decided ascending current (such as occurs in areasof low
pressure where the lower air being warmed is carried along and
moreover by reason of the cloud necessarily formed by the ascent
checks the superheating) nor a strong descending current (such as
is present in the interior of an anticyclone causing a steady outflow
of the lower layer or the rapid dissolution of individuai local ascend-
ing clouds).

my method of partial isobars, which however assumes a very accurate reduc-
tion of atmospheric pressure to sea-level,

Compare M. v. Rohr (Die gewitter, etc.): ‘‘The thunderstorm of December
tz, 1891, in connection with the simultaneous weather.’’ Publications of
the Royal Preuss. Meteorological Institute. Results of thunderstorm ob-
servations in the year 1891. Berlin, 1895, pp. xi-xxxv.

Also
W. Wundt (Barometrische Theiledepression-en, etc.): ‘‘Barometric
pockets and their wave-like repetition.’’ Memoirs of the Royal Prussian

Meteorological Institute, Vol. II, No. 4, Berlin, 1904. Note added 1905.

268 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

That the superheating of the lowest layer of air and conse-
quently the accompanying unstable equilibrium within it, is a
regular precursor of heat thunderstorms, can certainly be con-
sidered as a fact, even now, although the further establishment of
its certainty is very desirable by means of observations such as can
be furnished in necessary completeness only by self-registering
instruments.

Thus from the observations at Freiburg in Bavaria and on the
Hoéchenschwand, 719 meters higher, Sohnke” has shown that in
general the difference of temperature between these two stations
before the thunderstorm breaks, exceeds its normal value, while in
three cases (1881, June 3 and June 26,and 1882, July 22) it passed
the limit of unstable equilibrium; indeed on June 3, 1881, it exceeded
this limit by a very considerable amount, since on that day the
temperature diminished at the rate of 1.53° C. per 100 meters.*

Similarly, in the memoir by Assmann” on The Thunderstornis in
Central Germany, we find on p. 68 a collection of observations of
temperature on the Inselsberg and at various lower stations made at
special moments before the outbreak of thunderstorms, including
a series of cases in which the diminution of temperature with altitude
exceeds 1°C. per 100 meters and where consequently the limit of
unstable equilibrium is exceeded.

An excessive superheating of the lower strata of air was found in
the case of the thunderstorm of March 29, 1888, minutely studied
by Assmann,” on which day there were observed gradients as high
as 2.26° C. per 100 meters.

17 Sohnke (Der Ursprung, etc.): The origin of the electricity of thunder-
storms, etc. Jena, 1885, pp. 69 et seq.

18 But I cannot agree with Sohnke when he thinks that from these observa-
tions he is warranted in drawing the conclusion that on such days as these
the isothermal surface of o° C. lies especially low in the atmosphere. In the
majority of the cases quoted by him the temperature is above its normal value
evenin the higher levels of the atmosphere, and although inthe lower levels
the departure from normalis still greater than in the upper, yet this does not
warrant us in applying the corresponding temperature gradient to higher
levels. We are no more justified in doing this than we are in arguing as to
the temperature at very high levels from the vertical gradients observed in
the anticyclones of the winter season. Moreover I don’t understand why
Sohnke attaches such great importance to the special low position of this
surface before a thunderstorm, since in support of his theory we need only
to consider where this surface is within the thunder cloud itself, a matter that
we can only determine at present by computation based on the assumption
of adiabatic expansion.

12 Assmann: Die Gewitterin Mittel Deutschland. Halle a. S. 1885.

20 See von Bezold (Ergebnisse, etc.). Results of Met. Obs. in Prussia for
the year 1888, p. lvii. Berlin, 1891.

THERMODYNAMICS OF ATMOSPHERE——VON BEZOLD 269

lf now the conditions above described are fulfilled; if there be no
decided ascending or descending movement of the air, while the
sun heats the ground very hot, then unstable equilibrium will be
produced at different portions of the earth’s surface and especially
where this heating is favored by the character of the ground.

Thus, during the summer months at least, at any given moment
the heating effect may be about the same all along a line inclined
to the meridian and trending NNW. and SSE. since points on
such a line will have experienced equal durations of insolation.

Consequently, and independently of the influence of the general
distribution of pressure, an approximately equal and simultaneous
superheating of the lower air and hence unstable equilibrium will
occur on any given day along such a nearly meridional line.

Thus, then, at first there will be a series of centers arranged along
this line, where favored by local peculiarities the lower air will rise;
on account of the increase of buoyancy due to the condensation,
this ascending current will rise higher and higher until it is no longer
able to raise and carry up the condensed mass of water, when it
falls and we say the thunderstorm has broken.

As will be shown later on, this fall generally begins at altitudes at
which the temperature is below freezing and in most cases therefore
the precipitation at the higher levels consists of hail or sleet, which,
however, seldom reaches to the ground but melts during the falland
therefore reduces the temperature of the lowest stratum in the
well-known manner.

Hence, after the thunderstorm begins there is a sudden fall of
temperature, the surfaces of equal barometric pressure press closer
together within the region of precipitation, while the air rising at the
front or eastern edge of the thunderstorm and adjoining the still
warmer parts of the atmosphere overflows toward the cooled side
and causes a rise of pressure there.

On the other hand, in the lower stratum, the air flows with great
force eastward out of the region of precipitation, the air resting in
front of it is disturbed and, if not already so, is now forced to a
rapid ascent without necessarily being itself in a state of unstable
equilibrium.

Thus the thunderstorm renews itself continually on its front edge
and if the original superheating was great enough, and the atmosphere
in general sufficiently quiet, to allow the individual thunderstorms
developed along the above-mentioned meridional line to unite into
one large band, then the thunderstorm front thus originating rolls
farther eastward as a great whirl with horizontal axis until the

270 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5I

declining of the sun and the accompanying cooling of the lower air
gradually enfeeble the conditions that favor the process and thus
during the night time bring about a gradual extinction of the
thunderstorm.

As a special indication of the existence of well-developed whirls
and horizontal axes, must be mentioned the fact that the wind then
blows nearly perpendicularly to the isobars, constituting an
apparent exception to the basic law of the winds and for which
Moller” has given an explanation.

The preceding explanation does not exclude the existence of
individual small vortex whirls around a vertical axis, since it may
be that the thunderstorm roll is not continuous or that irregular-
ities in special places develop such vortices. But it seems to me
that such details are not sufficient to justify designating such storms
as vortex or cyclonic thunderstorms.. The description here given
corresponds substantially with the presentation of the subject of
the propagation of thunderstorms as given by Koeppen” ten years
ago in his ‘‘Untersuchungen, etc.,” ‘‘Investigations Relative to
the Thunderstorm of August 9, 1881.”

I must return, however, to this subject again because I recognize
the characteristics of ‘‘heat thunderstorms” in this method of
origination and propagation, which, indeed, has been subsequently
confirmed in the case of many great thunderstorms both by the
investigations of Ciro Ferrari* as also by the investigations carried
on in Bavaria and the neighboring States and later also in North
Germany. |

I have also intentionally attached small importance to the pres-
ence of areas of depression or barometric lows, but more rather to
the fact that there exists a region in which neither the cyclonic nor
the anticyclonic character is especially well marked.

I have therefore entirely omitted to consider the circulation of
the upper atmosphere as dependent on the general distribution of
pressure over large areas and have made this substantially pro-
visional study under the assumption that the general circulation of
the atmosphere does not come into consideration.

It seems important to me to make it clear that under this assump-
tion we must expect a propagation of the thunderstorms from west

1 Zeitschrift d. Oest. Gesell. fiir Met. 1884, XIX, pp. 80-84.

” Ann. d. Hydrographie, 1882, X, pp. 595 and 714. Compare also Sprung,
Lehrbuch, etc.: ‘Treatise on Meteorology,’’ pp. 294 et seq.

7 Annali dell Ufficio Centrale di Meteorologia, 1883, Vol. V, part 1, and
1884, Vol. VII.

THERMODYNAMICS OF ATMOSPHERE-—VON BEZOLD oy

to east, whereas it is a well-known fact that under the influence of
the general circulation of the atmosphere™ the opposite direction of
motion can sometimes occur. ;

The thunderstorms that come from the east are, however, always
relatively infrequent and moreover in comparison with those from
the west are feebly developed and have a smaller progressive veloc-
ity. 25

I find the reason for this in the consideration that without the
cooperation of the general circulation of the air the direction of
propagation must always be from west to east, and that therefore
in those cases where the region in question lies under the influence of
a barometric depression located to the southward so that the general
atmospheric movement is from east to west, there are two opposing
factors that disturb the vigorous and typical development of the
phenomenon.

Finally, I may add that it seems to me appropriate to designate

s “Front gewitter’ those thunderstorms that present the just
described band advancing perpendicularly to its length or ‘“‘broad-
side on,’’ whereas the individual scattered thunderstorms, such as
frequently occur under otherwise similar conditions I call ‘Erratic
thunderstorms,” just as was done by Fron.

The fact that in individual years, and often in a series of consecu-
tive years, ‘‘Front’”’ thunderstorms occur, whereas in other years
only ‘‘Erratic’’ storms occur, seems to me to be a question that is in
the highest degree worthy of a thorough study and one to which
I would therefore call especial attention.

Moreover, it is very clear that the occurrence of Front storms

‘ must depend largely on the configuration of the country and on the

features of the soil.

Therefore in accord with this idea such storms attain to a greater
development in the interior of France and Germany than in the
Scandinavian Peninsula or in Italy, where the plains of Sweden and
the Po satisfy the required conditions to a high degree.

It is also apparent that the sloping surfaces of meridional moun-
tain ranges, as in the Vosges, the Black Forest, and the Bohemian
Forest, must especially favor the formation of Front storms.

After these general remarks on the theory of the formation of

24Compare von Bezold and Lang (Beob. etc.): Observations at the
meteorological stations in the Kingdom of Bavaria. Annual volume for 1880,
pp. Xviii-xx.

°C, Lang, in Lang and Erk: Observations at the meteorological stations
in the Kingdom of Bavaria. Annual volume for 1888, pp. xxxvii-xlix.

272 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

thunderstorms (which one may consider as a departure) I will now
return to the principal question, i.e., what réle the supersaturation
and subcooling may play in thunderstorms.

In this investigation I have in mind only the heat thunderstorms,
since the observational material available to me for true cyclonic
thunderstorms is too scanty and especially since I do not know
whether in these latter anyone has observed the peculiar variation of
pressure that can be almost invariably recognized in the barograms
during heat storms.

As has already been stated, it is at present still difficult to decide
to what extent true supersaturations occur, since as yet we have no
sure foundation of experience on this point.

On the other hand, it seems to me that the above-mentioned
observations lately published by Hellmann on the behavior of the
thunderstorm rains that pass from the west eastward over Berlin,
indicate that supersaturations do play a part in thunderstorms.
For the great clouds of dust and smoke that always exist over that
city must hinder the formation of the conditions of supersaturation.

Again the fact demonstrated by me many years ago that buildings
within populous cities are much less frequently injured by lightning
than those in the surrounding country, may indicate that the sever-
ity of the thunderstorms experiences a diminution which may be
referred back to similar causes. However, I readily acknowledge
that such considerations have only slight force as a demonstra-
tion.

It is otherwise with the peculiar movements and uprisings that
the thunder clouds show even when they have not attained to ele-
vations at which we may expect subcooling. The shapes of the
clouds and especially their changes in appearance do not at all
correspond to those that we should expect from currents that are
steadily ascending and are accompanied by condensations that are
only the result of expansion. As already remarked, by. close
observation of the clouds we can scarcely avoid the thought that in
their interior there are forces in action that cause the peculiar expan-
sions and projections of the individual cumulus-heads. One can
scarcely suggest any other forces than the heating that must occur
within the clouds when there is a sudden release from the super-
saturated or subcooled conditions.

This assumption of the occurrence of supersaturation also receives
an important support when we study the variations of pressure dur-
ing thunderstorms in cases where the clouds attain only slight
altitudes, as is not infrequently the case in the Riesengebirge, accord-

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 273

ing to the observations of Reichmann.” It is therefore desirable
that special attention be given to the occurrence of low-lying thunder-
storm clouds of slight power. —

In reference to subcooling we are ina more favorable position than
in reference to*supersaturation. Here we have to do with demon-
strated facts and it is only necessary to give precision to our ideas
as to the formation of clouds by adiabatic expansion and especially
the formation of thunderstorm clouds.

When an active ascending current exists condensation will occur
when the dew-point is attained, insofar as the necessary nuclei
are present. If now the expansion continues, more and more water
will collect on these nuclei while presumably the number of fog
particles is not increased.

Consequently the individual fog particles become larger and
larger, and by this means as well as by the union of manyinto one,
they develop into small drops that may be visible to the unaided eye.

But in a sufficiently active ascending current these droplets will
by no means sink but be carried up to great altitudes, so long as
their magnitudes do not exceed a certain limit, which of course
depends on the velocity of the ascending current and on the density
of the air.

If this process did not proceed in this manner and if the water par-
ticles at once fell down as rain, then a progressive increase in the
size of rainless clouds would be impossible.

Moreover, the clouds could never attain that appearance that we
are accustomed to see in the cumulus clouds which reminds us of
compact masses, but they could only produce the impression of
streaks of fog or mist, which would be thinner. and more transparent
as the altitude increased without having any sharp boundary on the
upper side.

Since all this is not the case in nature we must assume that the
fog particles formed in the lower part of the cloud are at least to
some extent carried up to the upper boundary, after which, by falling
through the lower layers of the cloud, they grow larger.

If in this ascension the particles pass through the isotherm of
o°C. or freezing, stillit does not follow that they will freeze into ice,
but it is quite possible that they may retain their fluid condition
while being carried up into regions where the temperature is far
below freezing.

Now the ascending current of air has by no means ceased at that

7 Met. Zeit., 1886, III, pp. 249 et seq. and 1887, IV, pp. 164 et seq.

274 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

altitude at which the water particles reverse their motion and begin
to fall in consequence of the increased size to which they have
attained by reason of the progressive condensation attending their
long path.

Rather will this current continue far above the possible boundary
of the cloud not only in the case of the summer cumuli proper, but in
all cases where we have to do with the ascension of individual masses
of air and their penetration into upper strata.

But in fact in the case of the heat thunderstorms with their
perpetually renewed whirl about a horizontal axis we have to do
in a certain sense with a steady process even if, as such, it is moving
forward.

In this current of air flowing outward from a “‘thunderhead’”’
condensation must again occur in consequence of the progressive
cooling.” But in this case, on the one hand, the quantity of aque-
ous vapor coming into consideration is slight; on the other hand,
the precipitation will be directly in the form of crystals of ice or
snow because of the temperature prevailing at these altitudes.

In this process which is comparable with sublimation, the super-
saturation or the subcooling can no longer play any important rdle
even when that might otherwise be possible because of the small
quantity of water remaining present. Hence in these clouds there
do not exist the protruding and expanding heads, but in accord
with the steadily ascending current they develop rather in the screen-
like form of a layer of cirrus.

Doubts have indeed been expressed as to whether the screen of
cirrus that accompanies the thunderstorm cloud really consists
always of ice or snow, since the characteristic optical phenomena
are not always observable in it. Hence it seems to me to be impor-
tant to point out that between ice clouds at comparatively low
altitudes, such as correspond to the layer of cirrus, and those in the
highest layers of the atmosphere, there may be very considerable
differences that may exert an influence on the optical behavior.”
Thus, at very low temperatures ice needles easily form, whereas at
temperatures that lie near the freezing point the precipitation takes
place in the form of starlike crystals of snow or indeed masses of
snow, which latter must be less conducive to the development of the
well-known optical phenomena.

27 Compare pp. 237 et seq. of the preceding collection of translations.

28 According to recent investigations it must be recognized as very prob-
able that the ions play an important part in the formation of the cirrus screen
(overflow or false cirrus or cirrus veil or cirrus screen) as indeed in the for-
mation of cirri in general. (Note added in 1905. W. v. B.)

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 275

From these remarks on the cirrus overflow we now again turn our
attention to the thunderstorm cumulus itself.

When this cumulus penetrates upward into regions where the
temperature sinks considerably below freezing the subcooling of
the cloudy elerfent (vapor) must finally attain its limit and some
exterior shock will alone be needed to initiatea sudden freezing. But,
as was shown in the first part of this memoir, a warming and sudden
increase of pressure must go hand in hand with this freezing. Of
course an expansion must follow this rise of pressure and thus we
may explain the fact that new cumuli of considerable size often
suddenly burst forth from the thunderstorm cumulus.

Thus, on the 6th June, 1889, on the Summit of the Santis, Assmann
took some photographs of an increasing thundercloud, from which
in a very short time there broke out of the cloud atypical cumulus
dome which afterwards developed into a cirrus of mushroom shape
with broad cirrus screen.

This change of form corresponded completely with the above
given formation of the cirrus screen.

When in consequence of such a dissipation of the subcooled con-
dition as above assumed, and as appears to make itself known in
the variations of pressure, the now frozen masses are thrown far
above the altitude that they would have attained in the subcooled
condition, then, after the extinguishment of the upward impulse
there must occur a sinking downward, at least of the heavier masses,
while the current that blows through the cloud, and is the cause of
the whole phenomenon, still continues and thus gives occasion to
the formation of the cirrus screen.”

According to the above-mentioned investigations of Assmann on
the Brocken, as well as in accord with more recent observations by
him*, such subcooled fog particles never form crystals of ice or
snow, but only make lumps of ice without internal structure.

But sleet is formed by their combination. The assumption of a
sudden freezing of subcooled fog particles or very small droplets
therefore explains the formation of both sleet and hail without any
difficulty.

At first the frozen subcooled droplets unite into a little pellet of
sleet, since they, by falling and striking other subcooled droplets,
probably bring these also to freezing and at the same moment con-
geal into one mass. When these pellets drop into lower strata in

2° Compare also Moller: Met. Zeit.. Vol. II, 1890, pp. 220-222.
30 Met. Zeit., VI, 1889, pp. 339-342.

276 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

which the particles of water have a temperature more nearly that of
the freezing point, they cover themselves with a coating of clear
ice, upon which during a second ascent, such as frequently occurs in
the commotion within a thunder cloud, there is deposited a second
layer of subcooled particles, after which the hailstone, now become
heavier, again sinks and is again covered with clear,ice.

In this way is formed the cloudy milky nucleus with its surround-
ing concentric layers such as we find in hailstones.

It seems quite natural that a regelation occurs when the hail-
stones already formed strike violently together and thus grow
together into the irregular forms that are frequent among hailstones.

Thus it is that from the assumption that subcooled water particles
play an important rdle in thunder clouds, there follow easily and
naturally the series of phenomena that actually do accompany a
thunderstorm.

Still there remains one great difficulty to be overcome in that it
is not easy to get any clear idea of the process of dissipation of the
subcooled condition.

According to observations that have been frequently made,
among which I need only mention those of Assmann, Moedebeck,
and Gross, the freezing of the subcooled water at individual points
of the cloud does not spread throughout the whole cloud at once.
Whereas on the Brocken all subcooled microscopic droplets immedi-
ately freeze when they strike a solid body and gradually inclose
this body in a sheet of ice, and whereas in the oft-cited case of the
balloon voyage of 1891, June 19, all the rigging of the balloon became
rapidly covered with ice, still the fog or cloud as such remained
unchanged.

It is not easy to understand how this freezing spreads in a short
time throughout the larger part of a cloud, and yet this must be the
case if in fact the sudden rise in pressure, as already described, with
all its consequences is to occur.

Whether this is brought about by the crystals of ice that fall from
the cirrus screen and by contact with the subcooled water particles
cause this sudden freezing, or whether some electrical process here
comes into play, are still open questions.

Onthe other hand, I must consider the heavy showers characteris-
tic of thunderstorms as a proof that in these phenomena the above-
described dissipation does play a part.

Moreover, it is not improbable that many thunderstorm rains
begin in the upper regions as sleet or hail and only become rain in
the lower strata of the atmosphere.

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 277

At least sleet and hail are certainly observed at elevated stations
more frequently than in the low lands.

Equally do the large drops that not infrequently occur in thunder-
storm showers suggest that in such cases we have to do with melted
hail or sleet. A&A consider this assumption especially reasonable
since I have often had occasion to observe that the occurrence of a
heavy fall of hail is announced by the immediately preceding fall
of very large drops of rain.

In such cases I have observed drops of such a size as can only
exist momentarily and can indeed only be explained as being melted
hailstones.

I therefore consider it probable that sleet and hail play a greater
part in thunderstorms than we have generally assumed, and that
their relatively rare occurrence at the earth’s surface is to be
explained by the fact that they frequently arrive in a melted con-
dition.*!

The above-given presentation of the processes going on within the
thunder cloud appears to greatly favor the hypothesis framed by
Sohnke as to the electricity of the thunderstorms.

On the other hand, I would say that for myself at least I do not,
on this account, accept the Sohnke theory. For, on the one hand,
it is difficult for me to understand how a permanent separation of
the positive and negative electricities can be brought about by the
mutual friction of the falling sleet or hail, since at temperatures
below freezing the water particles must immediately freeze together
with ice particles, whereas at temperatures above freezing the sur-
faces of the hailstones are already covered with water and hence
there can only be friction of water on water.

On the other hand, even if it be possible to overcome this objec-
tion, still I cannot agree with the reasoning by which Sohnke
refers even the normal electricity of the atmosphere back to the
same source. Especially does it seem to me exceedingly improper
to attribute such great importance, even on perfectly clear days, to

31 Tn these earlier investigations the processes that occur in thunderstorms
are considered only from purely thermodynamic points of view and the nuclei
of condensation are only those that have long been recognized. According
to recent investigations it is probable that electrons or perhaps also the
cathode rays proceeding from the sun play a part in the condensation. More-
over in the formation of hail electric processes seem to play an important
part. (See W. Trabert: Die Bildung des Hagels. Met. Zeit., 1889, XVI, pp.
433-447.) But since all these questions are far from being settled, therefore
I have not attempted to rewrite the whole memoir from these new points of
view. (Note added in 1905. W. v. B.)

278 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

the isothermal surface of o° C. or to consider it as the carrier of the
positive electricity, when there is nothing else present in this layer
except atmospheric air and gaseous matter and no condensed aque-
ous vapor.

I could indeed imagine that the cirrus clouds are the carriers of the
positive electricity, but since these clouds are wholly absent on
many clear days while on others they float at very great altitudes,
therefore this assumption would not suffice to explain the diurnal
and annual periods in atmospheric electricity, whose cause Sohnke
thinks he has found in the oscillations of the altitude of the iso-
thermal surface of 0° C.

Moreover, if this surface possesses any such importance then its
entrance into the earth, that is to say, the fall of the air temperature
at the earth’s surface below the freezing point, must cause a con-
siderable diminution of the potential gradient, if indeed it does not
cause a complete reversal, whereas, on the other hand it is precisely
during very cold and dry winter weather that this potential gradient
has especially high values.

But these are questions that really do not belong here. If I
have discussed them, I have done it for fear lest any one should
imagine in the views that I have presented a new support for a
theory that, in my opinion, has found too ready acceptance by
many meteorologists and which we ought to view with critical eye,
although I do not deny that it has some value and is worthy of
closer study.

The expositions contained in the preceding memoir may be
summarized in the following theorems:

(1) If supersaturated vapor or subcooled water is present in the
atmosphere then the sudden dissipation of such a condition must
produce a quick variation of pressure that must make itself visible
by a rapid rise and subsequent fall in the barometer.

(2) If cooling precipitations fall quickly after this dissipation
then the barometric fall will be diminished or even entirely pre-
vented and a jump in pressure or “‘step up” rather than an oscilla-
tion, will take place by reason of the contraction of the surfaces of
equal pressure due to the cooling and the consequent inflow of air
from above.#

%2 On the theory of the origin of barometric jumps compare the following
memoirs by Dr. Max Margules: Vergleichung der Barogramme, etc. Met.
Zeit., XIV, 1897, pp. 241-253. Einige Barogramme und Thermogramme,
etc. Met. Zeit., XV, 1898, p. 1-16. (Note added-in 1905. W. vB.)

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 279

(3) Such variations of atmospheric pressure and barometric
steps occur frequently during thunderstorms and of magnitudes
such as without difficulty may be referred back to supersaturation
or subcooling. ,

(4) It is also a fact that during thunderstorms the conditions
that favor the existence of such unstable conditions are fulfilled,
especially should subcooling occur very frequently in the higher
portions of thunder clouds.

(5) Since the dissipation of such conditions must produce sudden
warming in individual locations, therefore by such processes we
must explain the peculiar changes of form that we observe in the
thunderstorm cumuli and which we cannot consider as a simple
consequence of a steadily ascending current even when this ascent
occurs in connection with vortex motions.

(6) The formation of sleet and hail may without difficulty be
referred back to subcooling.

XIII

ON THE THERMODYNAMICS OF THE ATMOSPHERE

BY PROF. DR. WM. VON BEZOLD
Fifth Communication!

(Sitzb. Berlin Academy 1900, pp. 356-372. Translated from the Gesammelte
Abhandlungen von Wm. v. Bezold, Braunschweig 1906, pp. 216-220)

THE CLIMATOLOGICAL IMPORTANCE OF THE THEORY OF ASCENDING
AND DESCENDING CURRENTS OF AIR

In the second of this series of memoirs? I have submitted to more
precise consideration the idea of ‘‘potential temperature’’ first
introduced by H. von Helmholtz under the designation ‘‘thermal
content,”’ and have therein deduced a theorem that has great simi-
larity with the second fundamental theorem of the mechanical
theory of heat.

From the circumstance demonstrated in the first article of this
series, that the changes of saturated moist air, when heat is neither
added nor abstracted and when the precipitated water or ice falls
from it, are not as a whole reversible but only in their smallest por-
tions, it resulted that in such changes of condition the potential
temperatures never diminish but can only increase.

I then drew various consequences from this theorem that are of
fundamental importance not only in the consideration of individual
processes but also in understanding the most important prominent
facts in the general averages.

Thus, in the first place the average diminution of temperature
with altitude finds its explanation in this theorem, and secondly in
studying the average temperatures for whole circles of latitude,
the results deduced from this theorem stand clearly forth.

1 The substance of the present memoir (which could: only be established
by correct observations after the conclusion of the work then being done on
the ‘‘ Results of the Scientific Balloon Ascensions from Berlin’’) had been
previously communicated to the Berlin Academy at its session of the 5th
of May, 1898. (Note addedin1go05. W.v. B.)

2See Mechanics of the Earth’s Atmosphere, 1891, p. 243. Smithsonian
Miscellaneous Collections Vol. XX XIV.—C. A.

280

a

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 281

The climatological aspect of that second memoir which is now to
be considered seems to have remained quite unnoticed and equally
so the various conclusions as to the “exchange of heat,’’? which I
would also consider of fundamental importance for Climatology.

I will therefore here develop more fully the results of a climatologi-
cal character that were only indicated in the first mentioned memoir
and as preliminary will more clearly illustrate the point of departure.

We must recall the fact that the expansion of saturated moist
air without adding or abstracting heat should only be called adia-
batic when the precipitated water remains floating in the air. As
soon as it wholly or partly falls away as precipitation then this term
is no longer strictly applicable since the whole expenditure of the
internal energy is not converted into external work.

In this case the falling particles of water or ice, since they still
have the temperature of the mixture and not of absolute zero,
withdraw from the mixture energy that has not yet been expended
in the work of expansion.

Therefore I have called such processes ‘‘pseudo-adiabatic.”

Since the quantities of energy that are lost by the falling away of
the condensation are very small, therefore the formule for the adia-
bats and the pseudo-adiabats differ from each other only very slightly.
Therefore in the computations and in the graphic presentations we
may consider them as identical, that is to say, we may use the for-
mulz and curves for the adiabats instead of those for the pseudo-
adiabats.

On the other hand, an incisive difference is manifest as soon as
the expansion changes to compression or when the ascending current
becomes a descending one.

In this case it makes a very great difference whether the water con-
densed during the ascent is carried along with the air or falls away
from it. If it is carried along, that is, if the expansion truly follows

the adiabat, then the compression follows exactly the same law, so

that the change of condition is truly reversible; but if the expansion
is ‘‘pseudo-adiabatic”’ it follows a law entirely different from that
which obtained during the expansion.

Since the water or ice which is formed scarcely ever falls away
completely immediately after its formation, forin that case precipita-
tion would fall from a clear sky, therefore this departure from the
adiabatic law does not immediately follow the passage from expan-

3See my memoir of 1892, Sitzb. Berlin Acad., pp. 1139-1178. or No.
XV, pp. 316-356 of the Gesammelte Abhandlungen (or No. XIX of this
collection of translations).

282 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

sion to compression but only after the last of the water and ice is
completely evaporated. Therefore the pseudo-adiabatic change of
condition is in its minutest features always reversible but in its
entirety is not so. I have therefore designated such processes
as ‘‘partially reversible” or ‘‘pseudo-reversible.”’

But this theorem that the so-called adiabatic changes of condi-
tion of moist air in the free atmosphere are not completely rever-
sible, is one of the most important for all theoretical meteorology
and climatology. By it there become explicable not only the
foehn phenomena, whose study, as is well known, formed the
starting point for all incisive investigations, but also the contrast
in the character of the weather in the regions of high and low atmos-
pheric pressure; the difference in the conditions on the windward
and leeward sides of mountain ranges; the distribution of cloudi-
ness and precipitation in general; and finally, as above mentioned,
the law of the average diminution of temperature with altitude, at
least in its principal features, together with the relatively slight
diminution of the average temperature of whole small circles of
latitudes from the equator up to the “‘horse”’ latitudes.

It is therefore worth while to first examine most carefully the
verbal expression of this theorem and then to deduce more rigor-
ously and elucidate more thoroughly than I did in my first memoir*
the conclusions that result from it.

The shortest and most rigid statement of the theorem is given
when we introduce the idea of potential temperature. I have else-
where done this and expressed the theorem in two ways as follows:

“In the adiabatic change of condition of moist air, the potential
temperature remains unchanged so long as the dry stage is not
passed, but it increases when condensation begins and in propor-
tion to the quantity of water that is abstracted.”

Or otherwise it is expressed as follows when specially applied to
atmospheric processes:

“Adiabatic changes in the free atmosphere and when there is
no evaporation, leave the potential temperature either unchanged
or higher.”

In both of these equivalent methods of expression I have at that
time made it understood that I assumed the adiabatic and pseudo-
adiabatic processes as equivalent, as we may safely do both in the
computations and the graphic presentations.

* See Sitzb. Berlin, 1888, pp. 1189-1206, or pp. 243-257 of the preceding
collection of translations.

THERMODYNAMICS OF ATMOSPHERE—VON BEZOLD 283

But since this is not allowable from a strictly theoretical point
of view, therefore I would prefer to substitute the following method
of enunciation: ‘

‘“‘An adiabatic change of condition of moist air leaves the poten-
tial temperature unchanged, but a pseudo-adiabatic change raises
the potential temperature. The rise increases with the amount of
water that is abstracted.”

Of course these theorems are only applicable so long as we exclude
causes of mixture with air having a different temperature and differ-
ent absolute humidity, as also cases where water is added from any
source whatever.

The precipitation or abstraction of water during adiabatic changes
of condition is also excluded because the very definition of ‘‘adia-
batic change” implies that the mass under consideration, that is, the
mixture of air and water remains the same quantitatively notwith-
standing the change of condition as to aggregation.

On the other hand, under ‘‘pseudo-adiabatic changes” are included
all those in which the condensations that are formed either wholly
or partially fall away so that the quantity of water mixed
with the given quantity or unit mass of dry air is diminished by the
abstraction or precipitation of the condensation. An increase of
this mass of water by addition from outside is also excluded by
this definition.

In consideration of adherence to this latter definition of our
terms, the following theorem may be expressed:

‘“‘An adiabatic change of condition may be either an expansion or
compression. A pseudo-adiabatic change is only possible with
expansion.”

Since the ascension of a mass of air is always attended by expan-
sion, and is pesudo-adiabatic after the beginning of the formation of
precipitation, if this expansion takes place without addition or
abstraction of heat, therefore by this process the potential tempera-
ture of the upper layers of air is increased.

Since the potential temperature remains constant in descending
currents so long as no heat is added or taken away, therefore the
vertical movements of the air without change of heat should be
alone sufficient to make the average diminution of temperature with
altitude smaller than would result if the air contained no aqueous
vapor. Therefore, independent of all processes of gain or loss
of heat the simple ascent and descent of currents of air suffice to
explain why the temperature diminishes with altitude and in fact
slower than 1° (or more exactly than 0.99° C.) per 100 meters.

284 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLS st

Consequently for the reason thus explained the mean gradient
of temperature with altitude is smaller in the actual atmosphere than
for the convective equilibrium of pure dry air, and therefore on the
average the earth’s atmosphere is in stable equilibrium.

This fact was already recognized by Lord Kelvin.®

In the second memoir I have expressed this theorem in the follow-
ing form:

“In general the potential temperature of the atmosphere increases
with the altitude.”

Evidently it will now be of interest to investigate more accurately

what the diminution of temperature with altitude would be were
it dependent only on vertical circulation without addition or abstrac-
tion of heat.
2% When one has first clearly understood this question then he can
obtain from observational data an idea as to how far these processes
actually affect the atmosphere and what réle other circumstances
play such as hitherto have been almost exclusively considered.

[In the original memoir there follows an investigation into ‘‘the
average distribution of temperature in a vertical direction.” In
order to avoid repetition this portion is not reprinted, since this
subject. is treated in fuller manner in the following memoir.®
Moreover, my succeeding remarks on the “influence of complete
convection on the mean temperature of the circles of latitude’”’ are
not reprinted, since these are contained partly in No. VI of this
collection’ and partly in No. XVI of this collection. Note added
1905, W. v. B.]

5On the convective equilibrium of the atmosphere, dated January 21,
1862, published in the Memoirs Manchester Phil. Soc., 1865, (3) II, pp. 1r25—
inne

®No. XIV of these translations.

7See Mechanics of the Earth’s Atmosphere, 1891, p. 254.

8See No. XX of present collection of translations.

ee ee eee enn ee es ——

CUO CT

, XIV

THEORETICAL CONSIDERATIONS RELATIVE TO THE
RESULTS OF THE SCIENTIFIC BALLOON ASCENSIONS
OF THE GERMAN ASSOCIATION AT BERLIN FOR
THE PROMOTION OF AERONAUTICS

BY PROF. DR. WM. VON BEZOLD

[From Wissenschaftliche Luftfahrten, or The Scientific Balloon Voyages
carried out by ‘‘ The German Association at Berlin for the Promotion of Aero-
nautics. Published by R. Assmann and A. Berson by the codperation of
O. Baschin, W. von Bezold, R. Boernstein, H. Gross, V. V. Kremser, H. Stade
and R. Stiring.”” Brunswick, 1900, Vol. III, pp. 283-313]

[Translated from the Gesammelte Abhandlungen von Wm. v. Bezold, Braun-
schweig, 1906, pp. 221-264)

The authors of this publication have asked me to express in a
final chapter the most important results from a theoretical point
of view and thus unite the individual portions by one common
thought.

Willingly as I would respond to this desire, yet I find myself in a
difficult position. Notwithstanding the fact that I have steadily
followed the whole undertaking from the first step in the work, still
I cannot seriously begin this crowning chapter until the individual
memoirs united in these three volumes are available to me; and thus
there remains to me no other choice than either-to limit myself to a
superficial review or to delay the appearance of the whole work.

I have decided to pursue the first of these alternatives in recogni-
tion of the conviction that weeks and months would not suffice for
the completion of my work.

Therefore in a first section of this chapter I confine myself to an
exposition of theimportance that pertains to observations in balloons
from the present point of view of our science. In a second section
I will attempt to develop the ideas as to the processes going on in
vertical columns of air to which we are led by purely theoretical
considerations and by which much may be anticipated that may be
subsequently confirmed by the observations. In the third section
the average vertical distribution of the meteorological elements will
be presented as resulting from the data given by the ascensions.

285

286 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

In the expectation that this work will not be used by technical
meteorologists alone I have labored to write as far as possible in
popular style in order to give a large circle of readers a glimpse of
the kind of problems that have to be solved by scientific balloon-
ing and thus to vividly present to them the full meaning of the
results that are laid before the world in these volumes.

Under these conditions, I must of course in the first two sections
repeat many well-known matters along with others that have not
yet been clearly understood. But as I have tried to do this in a
uniform and, as I hope, in a novel way, therefore these considera-
tions may not be without interest even for the specialist. To the
latter the summaries presented in the third section will be welcome.

Unfortunately, in the short time allowed me I must omit from
this review the many works published elsewhere, some of them verv
recently, especially the beautiful investigations of Messrs. Teis-
serenc de Bort, A. L. Rotch, H. Hergesell, H. C. Frankenfield, H.
C. Clayton, F. Erk, et al., but must restrict myself exclusively to the
discussion of the materials submitted in these present volumes.

I must expressly state that the omission of these highly important
works arises in no wise from any low estimate of them, but is simply
demanded by the necessity of speedily finishing my work.

(1.) THE IMPORTANCE OF SCIENTIFIC BALLOONING

The importance that attaches to the investigations of the atmos-
phere by means of balloons, an undertaking that has been made
possible through the grace of His Majesty the Emperor, as well as
the results attained thereby, can only be reached when we take the
broadest view of the present condition and the ultimate object of
meteorological investigations.

The oldest scientific balloon voyages were made at a time when
men had scarcely begun to systematically study the meteorological
processes going on in the lowest stratum of air. Therefore the
aéronaut found himself in a position similar to that of an explorer
who is the first to enter a country hitherto wholly unknown and
the results that he brings back from his journey must be recognized
as an addition to our scientific data, but can only in a very limited
degree contribute to our deeper knowledge.

Moreover, during the whole long interval of time in which meteorol-
ogy was regarded principally as a statistico-geographical study we
could not possibly recognize the true importance of the exploration
of the higher strata of the atmosphere.

The observations in balloons first attained their true importance

ee

SCIENTIFIC BALLOON ASCENSIONS—VON BEZOLD 287

when we began to investigate the causal connection of the atmos-
pheric processes and to trace the latter back to fundamental physical
laws.

When we enter on this problem we must consider the atmosphere
as a whole. We can no longer be satisfied with observations that
are made in the lowest stratum of air, but have to strive for data
from the upper strata and representing all conditions.

Observations made under ordinary conditions will suffice to give
us a picture of the average distribution of temperature, precipita-
tion, wind, etc., as well as of their variations, that is to say, they
suffice as a basis for climatological studies. By means of such
observations, with the help of the graphic weather charts, the phe-
nomena of the weather as they follow one after the other, and the
connection of the processes that occur together can be made out to
very considerable extent. But the explanation of the phenomena is
impossible so long as the study is confined to the lowest stratum of air.

The fundamental generalization that the areas of low barometric
pressure are accompanied by cloudiness and precipitation, whereas
in the high pressure areas clear, dry weather prevails, becomes
intelligible when we consider that in the first case we have to do
with ascending air but in the second case with descending currents.

From that moment when we recognized what fundamentally
different réles the ascending and descending currents play and what
incisive importance the vertical movements of the air have for
meteorology and climatology, it must have been recognized as
a problem of the highest importance to follow along the path of
these currents and numerically determine their behavior above and
below by exact observations.

The recognition of the importance of these questions prompted
at first the establishment of mountain observatories, and the obser-
vations collected there have contributed not a little to advance
our understanding of atmospheric processes and to the attainment
of new points of view.

The changes that rising and falling currents of air experience
as to temperature and moisture can be followed strictly mathemat-
ically by means of the formule of the mechanical theory of heat,
under the assumption that neither mixture with other masses of
air nor increase or diminution of heat occurs. In fact such con-
siderations enable us to explain a series of phenomena.

But whether these assumptions actually apply, and to what
extent absorption or emission of heat or mixture with other air hav-
ing other temperatures and other moisture content, are to be con-

288 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

sidered, are questions that can only be determined by observations
in balloons.

Moreover the other fundamental question, in what manner the
ascent and descent of air takes place in the areas of high pressure
and low pressure can only be explained in this way. For there can
be no doubt that these movements are by no means so simple as
are represented in the sketches in the text-books, but that hori-
zontal and vertical motions are combined together in the most varied
and intricate manner and that mixtures etc., take place.

Those questions also that belong to pure dynamics, in distinction
from the just mentioned thermodynamic questions, can only be
specifically considered with the help of research by means of balloons.

The great difficulty of this problem forbids its general treatment as
a whole; we must therefore consider the individual portions sepa-
rately and afterwards attempt to establish the connection of these.

Among the results attained for which we have to thank the pres-
ent series of balloon voyages (by the Berlin branch of the German
association for promotion of aeronautics) the first place must be
given to the elucidation that they have given us as to the warm-
ing and cooling of the atmosphere and the general distribution of
temperature and moisture in the vertical direction.

(2.) THE VERTICAL DISTRIBUTION OF TEMPERATURE FROM A
THEORETICAL POINT OF VIEW

In a memoir recently published (No. IX, pp. 216--228, or No.
XIII of these translations) but whose principal contents Icommuni-
cated to the Berlin Academy of Sciences on May 5, 1898, I tried to
state in a purely theoretical manner the influence of adiabatic ascend-
ing and descending currents of air on the average distribution of
heat in the atmosphere.

I started with the assumption that radiation inward or outward
can only be influential at the earth’s surface and at the upper sur-
face of the clouds, and that a gain or loss of heat in the free cloud-
less atmosphere by absorption or emission can only play a subordi-
nate part and may be neglected in our final approximations.

It seems that these assumptions do actually suffice to explain
at least the prominent features of the vertical gradient of tempera-
ture, although further elaborations are needed in respect to many
peculiarities.

At the same time these considerations led to views relative to the
exchange of heat in the atmosphere that had indeed been indicated
by several investigators, especially by Lord Kelvin and by H. von

ig 4 De

a ee oe ae

e

SE —— ST eee

— —

SCIENTIFIC BALLOON ASCENSIONS

VON BEZOLD 289

Helmholtz and had been rather thoroughly developed by W. M.
Davis, but that differed often and sometimes to an important extent
from the views generally adopted.

The Results of Balloon Voyages published in the present work?
(whose complete reductions by A. Berson and R. String have been
accessible to me only within a very short time) allow us to check
by experience the theoretical conclusions given in the above-men-
tioned memoir of May 1898, and to show to what extent they need
to be corrected and supplemented.

Since it is remarkably difficult to perceive the full significance of
the formule that represent the thermodynamic changes of ascend-
ing and descending currents, therefore it is helpful to present them
graphically.

THe first to apply a graphic method to these problems was H.
Hertz. But the diagram prepared by him had for its object only
the replacing of numerical computation by a simpler, less laborious
operation. Some years afterward I attempted to follow the
processes themselves as such by means of appropriate diagrams.

Since in the present work an extensive use will be made of this
method in order to present the condition of the strata of air through
which the balloon passes, it seems appropriate to say a few words
relative to these diagrams in general.

In designing such diagrams one may have in mind many points
of view. If, for instance, we deal only with purely theoretical
investigations then it is most appropriate to consider only the fact
that the condition of a given quantity of atmospheric air is com-
pletely determined when we know the pressure, the temperature,
and the quantity and form of its moisture. This last item is
necessary because particles of water or ice so long as they float in
the air are to be counted as constituents of the atmosphere.

Since the above-mentioned data determine also the volume occu-
pied by the unit mass of atmosphere or the so-called specific volume,
therefore this latter quantity may be adopted as the independent
variable instead of either one of the others, and we may characterize
the condition of the atmosphere by the pressure, specific volume
and water-content. Hence in the graphic presentation, we choose
pressure and volume as the coordinates as has long been customary
in the mechanical theory of heat.

This method which I have hitherto used exclusively offers the
great advantage that for any given change of condition we can take

1 Wissenschaftliche Luftfahrten, 3 volumes. Berlin. 1900.

290 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

directly from the diagram not only the work done but also, with but
little trouble, the increase or diminution of heat.

The altitude above the earth’s surface does not enter into the
formule and graphic diagrams used in this method of treatment, a
circumstance that is of great importance for the complete under-
standing of meteorological processes. From this we can conclude
that such changes of temperature as accompany the ascent or
descent of the air are not to be referred back to the work of eleva-
tion, but are conditioned only by the changes of atmospheric pres-
sure associated with the change of altitude. If this view had been
properly considered earlier, one would never have accepted the
erroneous idea that the cooling in ascending currents is a conse-
quence of the work done in elevating the air.

Notwithstanding all this, it does not seem advisable to make use
of this method in the present memoir since it demands an abstrac-
tion too great to suit the new ideas that are immediately press-
ing for attention.

If we wish to consider the conditions in a vertical column of
air then the altitude of any point above the surface of the earth
is the determining item that seems to us especially characteristic.
Even if we know that the atmospheric pressure diminishes with the
altitude, still this pressure makes no such direct impression on our
senses as does the altitude.

If we introduce the altitude as one of the codérdinates then we
more appropriately choose it as the ordinate, while the other ele-
ment whose relation to the altitude is to be presented should be
laid off as abscissa.

It is evident that this method of presentation can be applied not
only to the temperature but to all meteorological elements that
have any relation whatever to the altitude, such as the pressure,
moisture, electric potential, etc.

If the curve of temperature is plotted in this way, then we obtain
the diagram that W. M. Davis has used (with only a change imposed
by the English system of measures), and from which he has drawn a
system of consequences, to which I also had arrived somewhat
earlier by another method and which I have developed quite recently
in the above-mentioned memoir (of May 5, 1898) from a different
point of view.

In the present memoir the last mentioned style of presentation
is always used and the metric units of 1° C. and 100 meters of alti-
tude are represented by the same equal distances measured along the
axes of abscisse and ordinates, respectively. This offers the great

SCIENTIFIC BALLOON ASCENSIONS—VON BEZOLD 291

advantage that the adiabats of dry air appear almost exactly as
straight lines inclined to the axes at an angle of 45°. On the other
hand we must not forget that by this choice of codrdinates it is
only the temperature that is represented in its dependence on the
altitude and hot the thermodynamic condition properly so called,
to whose determination a knowledge of the pressure or the specific
volume is also necessary.

But whatever method of presentation we may choose they all
have this one point in common, i. e., that each condition charac-
terized by the corresponding variables corresponds to a point on
the codrdinate plane. If now we imagine a given quantity of air
(the unit of mass is best) passing successively through different con-
ditions then the points corresponding to these conditions arrange
themselves in a connected series and form a continuous curve.

In this way we obtain “‘curves of change of condition,’ e. g., as
above, ‘“‘curves of temperature change.”

Since in this study one must know in what direction thechanges of
condition follow each other, it is therefore necessary to indicate this
by an arrow along the curve. If, for instance, the changes follow
the altitude, then the arrow shows whether we have to do with an
ascending or descending current.

But we may just as well apply these graphic methods to repre-
sent the condition prevailing at a given moment, or the aver-
age of a longer interval, along any given line. If, for instance,
we plot as ordinates the altitude and as abscissa the temperature
prevailing throughout a vertical column of air at a definite moment
of time, then the curve becomes a representation of the distribution
of temperature prevailing at this moment, or if we add similar
curves for the moisture and the pressure it becomes a plot of the
total thermal condition along the given vertical.

In this case I call these ‘‘curves of condition” as opposed to the
above-mentioned ‘‘curves of change of condition,” or if we con-
sider only the temperature they become ‘‘curves of temperature”
instead of ‘ curves of change of temperature.” Since the curves
of condition do not relate to conditions that follow each other
consecutively but that prevail simultaneously, aad of course
no arrow is needed.

I do not know that any one has yet dwelt on the Bes difference
between these two kinds of curves, although both kinds have
been made use of. Thus, for instance, the curve for the dependence
of the mean temperature on the altitude given on p. go in the well-
known Lehrbuch of Sprung and constructed from Glaisher’s obser-

292 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. §1
vations, is a “curve of condition,’’ whereas the curves that I have
drawn in my memoirs on thermodynamics are “curves of changes
of conditions.”

The curves of dependence of temperature on altitude that are
always used in the description of individual balloon voyages are
in most cases, strictly speaking, neither curves of condition of the
vertical column of air nor yet curves of change of condition; they are
rather representative of the successive conditions that the balloon
has met during its flight.

If the ascent is very rapid (and the greater number relate specially
to the ascent), then the curvecan beconsidered as approximately the
curve of condition along the vertical; but if the balloon floats in
equilibrium without any ascensive power and in company with the
air surrounding it then the diagram does actually present the curve
of change of condition. If the balloon has attained an altitude
where the diurnal period is very small and if the horizontal path is
not too long the curve will to a high degree of approximation pre-
sent the condition of the vertical column.

These approximations may be pushed further especially when we
have observations at the points on the earth’s surface immediately
below the balloon, which allow of a reduction of the individual
observations to a definite moment of time. The extent of the
error that may be made by the use or neglect of these reductions
can be seen exactly from the curves in dotted lines connecting the
values at the earth’s surface with those observed simultaneously in
the balloons. Especially instructive in this respect are the curves
in Vol. II (of the Wissenschaftlichen Luftfahrten) for ascensions
No. .x2,°p. 136; No. 18, p. 288; No. 19. p, 202; No. 25, p. 27a
No. 32, p. 332, and others, which will be easily recognized by
examining the dotted straight lines.

Where the results of many voyages are united in an average
value the curves that represent the connection between the values
and the altitude can be considered as approximately the mean curve
of condition for the vertical column of air above the lowlands of
Northern Germany. The small systematic error that might be
expected for the reason that the lower parts of the curves belong
largely to the late morning hours while the upper parts belong to the
midday or early afternoon, is of insignificant magnitude.

Now, before I proceed to speak in detail of the curves of results
published in this work (Wiss. Luftfahrten, Berlin, 1900) it seems
proper to apply the just-mentioned difference between the curves

1 Sh e's ars

) a

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 293

of condition and curves of changes of condition to a definite and
more general question to the elucidation of which they are pecul-
iarly appropriate, that is, the so-called convective equilibrium.

The mechanics of elastic fluids offers disproportionately far
greater difficulties than that of liquids. A drop of oil that is placed
at the bottom of a vessel full of water rises. in the water without
experiencing any change in its volume or its temperature. On the
other hand, a particle of air enlarges its volume in proportion as it
approaches the surface, it also cools and consequently its volume
does not change to the same extent as when the temperature
remains unchanged.

Still more complicated is the case when a mass of air that has been
locally warmed rises inan atmosphere whose temperature and density
themselves change with altitude and when, moreover, aqueous vapor
is mixed with the air which condenses at a definite temperature.

In order to deal with this question one must make the simplifying
assumption that the mass of air after being once warmed over the
region receives or loses no heat thereafter, that is to say, the expan-
sion during ascent is adiabatic. Under this assumption the tem-
peratures through which the ascending air will pass can be com-
puted and corresponding to these the curve of the change of con-
dition or the so-called ‘‘adiabat”’ can be drawn.

This adiabat is a straight line inclined 45° to the axes of the
coérdinates so long as the saturation temperature is not attained.
At this point the line experiences a sharp bend and thence rises
more or less steadily as a flat curve convex to the right and above.
It rises steeply so long as the temperatures are high, that is to say,
so long as large quantities of water are present whose latent heat
of condensation is able to perform much work; it approaches more
and more the adiabat of the dry stage the lower its temperature,
that is, the less the water contained in the saturated air.

Fig. 34 shows three adiabats that I take from the memoir
of O. Neuhoff? now in press and to be published in the “‘Abhandlun-
gen’’ or Memoirs of the Prussian Meteorological Institute. These
curves correspond to masses of air that ascend from the earth’s sur-
face with temperatures of —10°C., + 10° C.and + 30° C. respectively
and a barometric pressure of 760™™. and relative humidity of 62
per cent.

If in this way we have attained an idea of the course of such curves

20. Neuhoff: Adiabatische, etc. Adiabatic changes of condition of moist
air and their determination, numerically and graphically. Memoirs Preuss.
Meteorolog. Institute, vol. I. No. 6, Berlin, 1900. [See No. xxi, p. 436 et seq.]

2904 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOTES:

then it is not difficult to study the conditions of equilibrium of a
vertical column of air when the curve of condition is known. Let
such a curve be represented by Z Z in fig. 35.

If we now assume that a particle of air (a) for any reason whatever
experiences a Slight rise in temperature then it will pass over into
the condition represented by the location of the particle a,. But
since the atmospheric pressure must be the same at places of equal
altitude therefore it must be specifically lighter than its surround-
ings, and must rise higher. If this rise occurs without further addi-
tion or subtraction of heat, then it must cool according to the adia-
batic law, i.e., the corresponding curve of change of condition will,
in so far as no condensation occurs, be a straight line inclined 45°
to the axis and cutting the curve of condition at a point lying above
a. When the ascending air attains this altitude it has attained again
the temperature of its surroundings and there is no reason apparent
that should cause a further ascent. The equilibrium temporarily
disturbed is now again restored.

—10° +10° +30°
FIG. 34 FIG. 35

When a particle at a experiences a cooling the inverse phenomena
occur: instead of an ascending straight line from a, it follows the
descending line from a, and the particle warms up until at some
lower altitude it attains the temperature of its surroundings and
thus again the movement comes to an end.

We thus perceive that “when the adiabat, whose direction is
shown by the straight line A A, ascends less steeply than the curve
of condition Z Z the equilibrium is stable.”

When the adiabat ascends more steeply than the curves of con-
dition, as is shown in fig. 36, that is to say, when the temperature
along the vertical column diminishes with altitude more rapidly
than in air that is ascending adiabatically, then the phenomena are
quite different from the preceding case.

In this case no special warming or cooling is needed in order to
make a particle rise or sink with increasing speed, but an initiation

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 295

of motion in either direction suffices to cause the motion to continue
with increasing acceleration. If the particle receives a push upward
or in the direction from a toward b, along the adiabat, then in con-
sequence of the smaller cooling, the temperature difference between
the particle afid}the surrounding air when it arrives at 6, will
steadily increase) in proportion as the motion continues. Con-
versely for a descending particle the temperature, as shown by the
line a b, representing the change of condition, will continually depart
more and more from that of the surrounding air, so that this move-
ment also progresses with increasing acceleration.

FIG. 36 FIG. 37

The condition corresponding to this state of affairs is unstable and
can exist only temporarily. The condition of indifferent or neutral
equilibrium occurs when the change of temperature with altitude
exactly follows the adiabatic line, but since this condition changes
over into the unstable condition with the slightest change of tem-
perature, therefore it rarely occurs in nature but immediately
becomes unstable.

In the neighborhood of the earth’s surface, where the atmosphere
is generally in the dry stage, a temperature gradient of 1° per 100
meters constitutes the limit, that is never or very rarely exceeded.
But the problem changes entirely when saturation occurs, since then
a comparatively much smaller gradient of temperature suffices to
produce unstable equilibrium.

For in this case, as above remarked, the adiabat has a form such as
is shown in fig. 37 by the complex line A, SA, broken at the pointS’.

If then we compute the temperature gradient from observations
at two points, one of which lies somewhat above, but the other
below the limit of condensation, e. g., from the temperatures observed
at A, and A,, fig. 37, then, as is evident from the figure, we obtain a
value of the gradient that is less than 1°C. per 100 meters no matter
whether neutral or even unstable equilibrium prevails. If, for

296 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

example, air having a temperature of 20° C. and a relative humidity
of 67 per cent rises from sea level, then under adiabatic expan-
sion the condensation will begin at the altitude 770 meters.

Then at 1500 meters altitudea temperature of 8.6° C. will prevail.
The difference therefore would amount to 11.4° for 1500 meters;
the rate of decrease would, however, be only 0.76° per 100 meters.
Notwithstanding this we should make a grave error if in this case
we should assume a condition of stable equilibrium. Therefore this
circumstance must never be lost sight of in judging as to the stability
of atmospheric equilibrium, for instance, from observations on
mountains and in valleys, where we generally must rely on observa-
tions at two points only.

This difficulty generally disappearsin the deductions from balloon
observations, since in most cases these give us complete curves of con-
dition for long distances. But this point deserves consideration often
in case of rapid ascensions, where not infrequently the first obser-
vation in the balloon can be made only after passing the limit of
condensation.

It may be incidentally mentioned that Reye even in his time,
although in different form, has shown what importance attaches,
for the whirlwind storms, to this ‘‘knick’’ in the adiabatic curve, or
the steeper ascent in the condensation stage. Of course, these
remarks of Reye hold good, with appropriate changes, for the
thunderstorm phenomena of our regions.

The question as to the “critical” gradient of temperature (a term
that we may properly apply to the limiting value characteristic
of unstable equilibrium) becomes especially complicated in one
particular case that I will now explain more fully.

Assume that the curve of condition has some such appearance as
shown by the line Z Z in fig. 38 and that the
limit of condensation lies at S. Then it can
happen that the adiabat of the condensation
stage has the course S A, while that of the
dry stage is represented by A, S. Under these
conditions stable equilibrium prevails below
the limit of condensation but unstable equi-
librium above that limit.

This case cannot easily occur in masses of
airthat ascend as broad currents, for an ascent
along the curve Z S can only happen when the ascending air after
leaving the ground continually receives so much heat, eitler by
radiation or by mixture with other air, which of course must bring

FIG. 38

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 207

with it sufficient aqueous vapor, that a part of the work of expansion
is done by it so that adiabatic cooling is avoided. But after
passing the condensation limit and thereby entering upon unstable
equilibrium, the ascent goes on with increasing velocity, hence either
the whole cofidition must be different or else the movement must
come to a stop in consequence of the subsidence of the mass of air
cooled by ascent.

On the other hand, similar processes are certainly possible under
anticyclonic weather conditions where in general the temperatures
diminish along a curve such as is represented by Z Z, but where in
between the descending masses of air others are ascending, whose
temperatures follow a different law, and thus may be explained the
occurrence of individual cumulus clouds that attain considerable
altitudes.

If stratifications are present then, after the introduction of such
movements in individual cumulus clouds, masses of air may possi-
bly be drawn from the horizontal stratum that corresponds to its
base, which masses fill up the gap that would be left by the ascension
of the cloud.

Finally it is also possible that counter currents may be caused by
the sinking of air in the neighborhood of the cumulus cloud. Of
course these must be quite dry when they reach the lower level and
thus cause dissolution or evaporation of the cloud. Numerous
observations made during the balloon voyages, showing relatively
great dryness when in gaps between the clouds or in the neighbor-
hood of cumuli, seem to be in harmony with this conclusion.

At least the case represented by fig. 38, as plausible, seems to be
worthy of consideration.

According to what has already been said, one easily recognizes that
the play of ascending and descending currents of air will suffice to
bring about a diminution of temperature with altitude. The prob-
lem is to ascertain to what extent the diminution actually observed
in scientific balloon voyages is really explained as to direction and
quantity by the above-given cause.

If the diminution of temperature with altitude is simply a conse-
quence of ascending and descending currents, then must the average
temperatures of different altitudes be the average of those that
correspond to the ascending or descending branches of the different
currents that move in the same vertical.

Under this assumption the course of the temperature is as shown
in general by fig. 39.

If moist air ascends without increase or loss of heat, then the

298 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

change of condition is shown by the broken line a b c; if now it sinks
from some altitude that cannot be shown in the diagram and after all
the water has fallen from it, then the increase of temperature with
descent follows c d, or the adiabat of the dry stage. The nick at b
lies lower in proportion as the air is moister when the ascent begins
and it is sharper, or the first part of the curve b ¢ rises more steeply
in proportion as the initial temperature is higher.

If air alternately and for equal intervals of time rises according
to the law a b c and descends according to the adiabat c d of the
dry stage, then we obtain the average curve of condition by halving
the horizontal lines between the two curves and joining all the half-
way points, If ¢, and #,are the temperatures corresponding to the
points T, and T,, then the mean temperature t¢,, for the altitude
h is given by

th = 4 (4 +4)

and the curve of average condition is represented by the median line
cm,

Since now in general the currents ascending above any place will
have very various initial temperatures and humidities, therefore
the average of all must give curves whose a ¢ branches correspond

ws

6) @ wh aot

FIG. 39 FIG. 40

only in general to the form of the line a ¢ but individually show
great diversity. On the other hand the average curves correspond-
ing to the descending branch will, under the adopted assumption of
adiabatic descent, run parallel to the line d c but cut the axis of
abscisse at very different places.

Hence as an average curve of condition of the vertical column
there results a curve that must have approximately the course
shown by m b,, cin fig. 40. The lower part of this curve is dotted
for a reason that will be explained at once.

In the views that have just been elucidated we had to consider
that at very great altitudes all the adiabats of saturated air become

Nee ee ene een ene enn eee ee ene ee ee ees

SCIENTIFIC BALLOON ASCENSICNS—-VON BEZOLD 299

approximately asymptotic to the adiabats of the dry stage, since,
for the remarkably slight moisture contents that correspond to the
highest parts of the curves, the latent heat of condensation no
longer suffices to perform any appreciable fraction of the work of
expansion. ,

Moreover, at the greatest altitudes the emission and absorption
can play only a very subordinate réle on account of the extraordi-
nary rarity of the air, so that the changes in these strata take place
nearly adiabatically.

We thus come to the very important result that at great altitudes
the temperature curves more and more nearly approximate to the
adiabats of the dry stage and therefore the vertical temperature
gradient must tend toward the value of 1° C. fall per 100 meters*.

The course of the temperature curve constructed as formerly
according to the numbers deduced from Glaisher’s observations
must therefore from purely theoretical grounds seem very doubtful,
at least in the highest portions. The same is of course true of the
formule of Hann (for moisture) and Mendelieff (for temperature)
which rest on these same observations.

It may be said certainly that one of the most important attain-
ments of the undertaking described in this present publication
(Ergebnisse Wiss. Luftfahrten, etc.) is the fact that, asregards the
diminution of temperature in the highest strata of the atmosphere,
there has been established a complete accord between theory and
experience.

* Here it may be especially stated that all these remarks as to rising and
falling currents are only first theoretical approximations. In fact it will
frequently happen that masses of air that have ascended over very warm
places and with a relatively large humidity arrive overhead with such high
temperatures that it is impossible for them to descend at neighboriug local-
ities. Under such conditions abnormally warm air overhead must spread
horizontally and flow away to great distances above the lower strata of air.
Such phenomena as give rise to very slight vertical temperature gradients
and may in fact lead to temperature inversions have been frequently observed
in recent years even at moderate altitudes, as was, for instance, the case in
September, 1900, when such a warm layer extended from the Alps to the
North Sea (see W. Briickmann “‘ Die, etc.’”” The Temperature inversions
in summer anticyclones. Inaugural Dissertation. Berlin, 1904), whereas
it occurs as a regular phenomenon in the much higher strata and such cases
are certainly referable back to the air flowing out from the tropics (see Assmann
‘“‘Ueber, etc.”’ ‘‘On the existence of a warm current of air at the altitude
of ro to 15 kilometers.” Sitz. Ber. d. Berlin Akad. 1902, pp. 495-504).
It cannot be too often stated that the considerations here set forth are only
crude approximations. (Note added in 1905. W. v. B.)

Ale SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 51

The fact that meanwhile the same results have been confirmed by
observations made elsewhere, can only be incidentally mentioned,
since in this present summary, as already stated, for want of time
I must confine myself to the material submitted in this present
publication.

When heretofore one refused to entertain the idea that such large
temperature gradients existed in the highest strata, the reason lay
in the consideration that the temperature could not diminish to
infinity. But we must not forget that the term temperature of the
air becomes less applicable in proportion to the increasing distance
from the earth, and that for the extremest rarefaction the ordi-
nary oniitndtiins must be replaced by an —— different series
of ideas.

The median portion of the curve shown in fig. 40, which is based
simply on the consideration of currents ascending and descending
adiabatically, already shows in its general course a certain agreement
with facts that will hereafter be more exactly described, but with
certain appreciable limitations.

For instance, it follows from considerations based on the above-
given assumptions that the diminution of temperature with altitude
in the median atmosphere strata must be less than in adiabatically
ascending and descending dry air, and especially so in those layers
in which the condensation is most frequent and most considerable,
namely, between the altitudes tooo and 4000 meters. ‘This is in
fact the case qualitatively; but the diminution actually observed is
much smaller than would result from the above-described method of
formation of averages.

For saturated air at temperatures between + 26° C. and — 30°C.
ascending adiabatically the temperature gradient at 1000 meters
altitude varies between —0.37° and —o.88°. Under the assump-
tion that such ascending currents interchange during equal intervals
of time with adiabatically descending currents whose gradient is
always — 0.99° there should result average gradients that lie
between — 0.68 and — 0.93.

For adiabatically ascending air that leaves sea-level with the
temperature + 10°C. and attains its dew-point at altitude 1000
meters, the gradient at this elevation is — 0.59 and the average
of this value and that of adiabatically descending air is — 0.79
or around — 0.80° C. per 100 meters.

But for this altitude the observations give an average value of
— 0.50, or 0.58 if we exclude those cases in which large temperature
reversals were observed, or values that are far smaller than those

SCIENTIFIC BALLOON ASCENSIONS——-VON BEZOLD 301

above computed. In fact in these strata the average curve of con-
dition rises much more steeply than should be the case under the
assumption above made. ;

This is remarkable inasmuch as thus the problem is to a certain
extent reversed as compared with the older views.

Hitherto it has been believed that we could only explain the higher
temperature of the lower strata by the suspicious hypothesis of
the non-transmissibility of dark rays through the atmosphere,
but now we must seek the reasons why the diminution of tempera-
ture with altitude is not far greater than observation shows it to
be, at least in the lower and middle strata.

For the condensation, which contributes in an important degree
to diminish this gradient, still does not suffice to fully explain the
observed diminution.

The ideal curve sketched in fig. 40 departs from observation even
still further, in its lowest portion. Whereas according to the general
scheme one should expect larger gradients in the lowest stratum
than in the median strata, yet in fact according to the numbers
deduced from the balloon voyages fer the lowest three kilometers
there is a nearly constant and rather small value for the gradient.

It was to be expected that our scheme would fail in this portion,
since near the earth’s surface, where radiation and absorption come
into play to such a large extent, it is only seldom that pure adiabatic
processes can occur.

Especially at times of excessive outward radiation must the ideal
scheme be disturbed, since at such times the lowest strata become
relatively cold, whereas the opposite is the case at times of excessive
inward radiation (or insolation) and thereby an approximation to
unstable equilibrium or even that condition itself may easily occur.

Actually, however, it is only the general average whose course
departs so far from the ideal, on the other hand, the average
values for the summer, which will be considered in the third section
of this memoir, do, especially in the lowest portion, approximate far
more closely to the ideal.

To a much higher degree do various individual cuves resemble the
form of the theoretical scheme. In this respect I recall the curves of
condition given in volume 2 (of the Ergebnisse) for the voyages,
Noun) petzos: Noi4i7p.48; No» 10; pi 106 Nos22y preter; No. 60,
P. 553; No. 67-70, p. 579, and No. 72, p. 601.

Hence the course of the lowest portion of the temperature curve
can be very well explained by the overpowering influence of the
radiation, as will be hereafter more precisely set forth. On the

302 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

other hand, one other most remarkable point offers greater difficul-
ties. For we find that not only does the average curve for the anti-
cyclonic day show in its course a great similarity with the adiabats
of saturated air, but this also holds good for the individual curves,
some of which indeed agree altogether with such adiabats.

For the average curve there is indeed not such close agreement,
but even for it at least the differential gradients follow almost
exactly the same law as does the adiabat of a saturated or ascend-
ing mass of air that left the ocean level with a temperature of 18°C.

For the sake of comparison this adiabat 1s shown by dashes in -

the diagram of annual means for various elements, in fig. 43 of the
third section of this memoir. We see at once that it needs only a
horizontal displacement of 8° toward the left in order to make this
adiabat coincide with the curve ¢,,.

This comparison is of great interest because it shows strikingly
how far the observed change of average temperature along the ver-
tical departs from the average of the adiabats of the dry stage and
the condensation stage, and how the temperature diminution with
altitude, as actually shown by observation, is not only in the lower,
but also in the median strata, much smaller than if it were exclu-
sively the consequence of the play of ascending and descending cur-
rents.

The above-quoted cases in which the gradient of temperature
follows the type theoretically developed, point out the way already
indicated to unravel these peculiar relations. They occur always
at times of the day and year when the insolation is in excess or at
least begins to acquire the greatest importance.

It is probable that this approach to the adiabat of the dry stage
or to unstable equilibrium would be much more frequently observed
if ascensions had been more frequently made in the midday hours,
whereas for reasons easily understood the later morning hours
must preferably be chosen.*

At any rate these cases present the proof of the fact that it truly
is the insolation and radiation processes at the earth’s surface that
strongly influence the course of the temperature curve in the lower
strata.

*The most recent kite ascensions have shown that a temperature gradient

of over r° per roo meters frequently occurs in the lower strata in the morning .

hours in the warmer season of the year; e. g., compare R. Assmann and A.
Berson; Ergebnisse,"etc. (Results of ‘the labors at the Aeronautical Observ-
atory in the years 1900 to 1904. Publications of the Royal Meteorological
Institute, Berlin, 1902, 1904, 1905. (Note added 1905. W. v. B.)

——————————

SCIENTIFIC BALLOON ASCENSIONS—VON BEZOLD 303

In fact, from the consideration of the average curve with its un-
expected slight gradients in the lower portion, that is to say, with
its surprising steep ascents, there’results at first the most astonish-
ing fact that in the general average the influence of the soil makes
itself felt in a gelative cooling of the lower strata of air.

This result is in direct contradiction of theolder views. Formerly,
as already stated, we felt that we must accept some very special
assumption in order to explain why the lowest strata of the atmos-
phere are warmer than the upper, but today we confront the ques-
tion, why the difference in the temperature is not much larger than
it is.

I have already treated this subject theoretically in the above-
mentioned memoir,’ which was published a few weeks ago, and now
I willtonly attempt to briefly repeat the most important points in a
less abstract form.

The explanation is found in one circumstance, namely, the
great difference of the influences that the outward and inward radia-
tion at the earth’s surface exert on the atmosphere; a subject to
which Lord Kelvin and H. v. Helmholtz have occasionally referred
and which W. M. Davis afterwards treated more thoroughly both
in his memoirs on whirlwind storms and also in his admirable “ Ele-
mentary Meteorology.”

Although the cooling and warming of the surface of the globe
stand in a simple antithesis to each other, still the processes by which
these influences are transmitted to the air are fundamentally differ-
ent; they are processes for which many years ago I introduced the
term ‘limited reversible’”’ or ‘‘pseudo-reversible.”’

This distinction impressed me still earlier as I investigated the
processes in adiabatically ascending and descending currents from a
very general point of view. If we consider a saturated ascending
current of air we find that the law of diminution of temperature
(ignoring the hail stage) remains exactly the same down to an
exceedingly small difference, no matter whether the water that is
formed falls from the current or is carried along withit. The for-
mule that we apply to the so-called reversible changes of condition
apply perfectly to this case. In fact the changes in question remain
reversible even to the smallest portions if the water falls away as rain
or snow, for the separation never proceeds so rapidly that the pre-
cipitation disappears immediately from the neighborhood of (or
association with) the mass of air in which it originated.

5 See No. IX of my collected memoirs, (or No. XIII of this collection of
translations).

3c4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL aoe

If therefore the ascent of the air suddenly becomes a descent,
then, at least in the first moments, re-evaporation must take place,
that is to say, the processes attending the immediately preceding
moments will be exactly repeated in the reverse order.

If all precipitation were carried up with the ascending current of
air, as it is in the case of clouds from which no rain has as yet fallen,
then in general by reversing the movement the air would arrive
at its starting point in the same condition in which it had left the
earth. If, on the other hand, water has actually fallen from the
cloud, then by reversing the movement the air enters sooner into the
dry stage and its warming follows a very different law from that of
its cooling.

The process is therefore reversible in its smallest details but not
in the larger nor as a whole, and it is precisely to this peculiarity
that, as is well known, we owe the Foehn phenomena, the differences
of the weather in the areas of high pressure and low pressure, the
peculiarities of the windward side and leeward side of mountain
ranges, etc.

We meet analogous conditions in the warming and cooling of the
atmosphere in contact with a terrestrial surface that is subject to
insolation and radiation.

A limit to the warming of the lowest layer of air is soon set by the
occurrence of unstable equilibrium, but, on the other hand, its cool-
ing can proceed as long as the radiation continues and so long as no
rapid renewal of the air is produced either by the drainage away of
the cooled air or by the wind. It is well known that the very low
temperatures that are observed in valleys are thus produced and
especially on tundras in winter and to a less extent also in other
seasons during very clear calm nights. The same is true of the so-
called inversions of temperature that were first observed in moun-
tainous regions and which for a long time were supposed to be
principally confined to such regions.

Scientific balloon voyages have shown that these inversions occur
regularly at times of overpowering radiation and gentle atmospheric
motion.

Moreover, balloon voyages furnish us far more complete pictures
of the temperature inversions than do simultaneous observations at
a summit station and at a neighboring valley station, in which latter
case such an inversion can pass entirely unnoticed when the location
of the (stratum of) highest temperature lies only slightly above the
level of the lower station, so that the temperature of the upper
station is still lower than that of the lower station. Thus, for exam-

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 305

ple, on the dates and the times when the balloon ascensions Nos. 16,
17, 30, 37, and 51 were made ® the very pronounced inversions would
have been entirely overlooked if one had at hand observations at
only one station in the lower plain and one at an altitude of 1000
meters. “

Again, the full extent of the inversion within comparatively
small elevations can only be observed by means of balloons. For
example, during balloon voyage No. 22, on January 12, 1894, the
following temperatures were observed; at the ground— 6°C.; at
400 meters, + 6.5° C.; giving a temperature gradient of + 3.2°: but
on February 24, 1891 (ascension ‘“‘G,’”’ fig. 41) there had been
observed at 230 meters — 2°, whereas at 340 meters this had risen to
+ 9°, corresponding to a gradient of + 10.0°C. per roo meters. By
experiment with the captive balloon ‘‘Meteor’’ on October 9, 1891,
there was observed at about 5 h. 27 m. p.m. an increase of tem-
perature of 2° between 1.5 meters and 8 meters above the ground
corresponding to a gradient of 25.0° C.

A very interesting diagram is formed by extending downward
the main branch of various curves of this type. as is done in fig. 41,
for the curves of the voyages ‘‘G,”’ Nos. 22, 54,and 55, and then placing
near them the curves for cases that correspond to the heating of the
soil such as are typically represented in voyages Nos. 72 and 69b—7o.

The numerals for the voyages are entered near the respective
lines; the curve marked ‘‘G”’ refers to an ascension made by Captain
Gross on February 24, 1891, and which does not belong to the general
series. The sides of the small squares correspond to 200 meters
altitude and 2° difference of temperature. The whole number of
degrees inscribed on the bottom line indicate the scale numbers
for the observed temperatures on the respective curves. From
this diagram we see at a glance how differently the warming and
cooling of the earth’s surface affects the air and we comprehend how
seriously the cooling influence must affect the average values.

Explanation of fig. 41

ve | DURATION UP TO MAXIMUM Reference
SC. 11> So AUTINGDE Wissenschaftliche
Day | Month| Year | Luftfahrten.

| | |
G 24 «| LUM 1891 lo erdeat ane ramen fates 1 peer Pe vol. I| p." 105-106
22 12 I Tsg4 | 9f15,4.M. to L206 D:Mi,-<2-e ee It} 225-236
54 18 II 1897 |r1o:10a.m. to 4:18 p.m.......
55 18 II 1897 | 9540)8.m. tO 2275 PMs. vic ns 1] ecm
69b So aval 1898 Descent 1 to 3:08p.m.......
70 8 VI 1898 (11:55a.m. to 6:15p.m....... E po ae
72 ELF | yy Jeo 1898 | 2:05 p.m. to 3:05 p.m. ....... | II} 594-604

|

® See the Wiss. Luftfahrten, Vol. II, pp. 167, 176, 305, 371, 457, respectively.

306 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

In general the conditions here presented have led to the follow-
ing results:

(a) ‘The warming and cooling of the atmosphere are determined
principally by the radiation processes at the earth’s surface and to a
less degree by the analogous processes at the upper boundary sur-
faces of the clouds.”

NTT I
es

&
S
S
5

7

:
a
a
a
al
PACH : Re |
AAS

FOOOTIV

ESRB Y Ss

-- by

PNB SIS IE
Pert
ae eee

ran

300077

DER

20007

an

ia ero NIST S fala Rel tara
BER SRSA VERA SRR
SRM RERER LAER ER eee
5 OY a a a a 8 bh
ratty att teeistentttsnati

-UBEERMEG ABE
ESR cea Reale Teale ean

400077

S
Bi
aa

FIG. 41

(b) ‘The latter processes at the cloud surface will on account
of the large evaporation probably be more like those above extensive
surfaces of water, especially above the ocean, for which, as yet, no
observations are available.”

(c) “Of these two processes the warming cannot make itself
felt in the lowest stratum so decidedly as does the cooling, since the
warmed air rises and so much the more rapidly in proportion as the
diminution of temperature with altitude approaches the limiting

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 307

value for unstable equilibrium. After the beginning of condensa-
tion this limiting value is smaller than in the dry stage.”

(d) ‘There is no limit of this kind for the cooling, so that the
increase of temperature with altitude in the lowest stratum at the
time of the so-galled inversion of temperature can attain values
that may amount to many times the greatest possible diminution
of temperature for the same differences of altitude. On the twenty-
fourth of February, 1891, there was observed a positive gradient
of 10°, whereas for the negative gradient — 1.0° constitutes the limit
that can scarcely be exceeded.”

(e) ‘This difference in the processes of warming and cooling
brings about a lowering of the average temperature of the lower
strata or a steeper ascent in its lowest portion of the curve of con-
dition for temperature.”

(f) ‘Similar considerations must obtain with reference to the
absorption and emission by the atmosphere itself which may be
very considerable in the lowest strata as shown by the growth of
ground-fog from below upward. Here, then, these processes must
also contribute to diminish the rate of diminution of temperature
with altitude.”

(g) ‘‘Finally it must not be forgotten that at the season of
excessive transfer of heat (to the atmosphere) above the surface of
water or wet soil, the evaporation also contributes to depress the
temperature of the lowest stratum.”

(h) ‘The masses of air ascending from the ground carry upward
with them the heat acquired below (allowing for that which is used
in expansion) and that too not only the heat shown thermometrically
as they leave the ground, but also that which had been used to
evaporate the accompanying water. The heat used for this latter
purpose becomes appreciable in the strata in which condensation
takes place, where it diminishes the temperature gradient and that
too in proportion as the loss of the precipitation is greater; but as
sensible heat this first becomes evident in the descending current
of air and thus gives rise to that form of transfer of heat that I
have called ‘complex convection.’’’”?

(<) “‘Finally,at the greatest altitudes where absorption and emis-
sion disappear and almost no aqueous vapor is present, the adia-
batic ascent and descent of dry air is the only cause of the change
of temperature with altitude.”

™See von Bezold’s 2d memoir translated in Mechanics of the Earth’s
Atmosphere, 1891, p. 255.—C. A.

“a

308 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

() ‘‘The curve of condition for temperature must consequently
in the highest strata asymptotically approach a straight line that

cuts the axes at an angle of 45°.”

(3.) THE OBSERVED MEAN ANNUAL AND SEASONAL VERTICAL
DISTRIBUTION OF THE METEOROLOGICAL ELEMENTS

Now that we have in the second section endeavored to explain the
‘mean distribution of temperature in a vertical column of air at least
as to its principal features, we will exhibit both numerically and
graphically the mean temperature and moisture as deduced by
Besson and String (from observations in balloons). These quanti-
ties are indicated by t,, and y,,; and then for completeness are added
under f,,, barometric readings corresponding to the different altitudes
when the atmospheric pressure at sea-level is 762" and the
temperatures are such as given by Besson’s computation: on the
other hand under #, are given the pressures that would correspond
to dry air adiabatically rising or falling, and leaving the sea-level or
arriving there from above with the temperature 10°.4.

The numbers under ,, give the average vertical distribution of
pressure for the North German plains just as these under #,, give the
average temperature distribution. Of course these numbers do not
represent any greater degree of accuracy than can be expected from
the relatively small number of observations submitted in the ‘‘Er-
gebnisse’’® but still they afford a very instructive picture.

As representative of the moisture I have chosen the specific mois-
ture for a reason that will be explained immediately. The appropri-
ate numbers are found in the column y,,. Moreover, under y, are
found the values of the specific moisture that represent the condition
of saturation for the corresponding pressures #,, and temperature
tn The quotient y,,/y,, whose value can be at once approxi-
mately seen from the graphic diagram, fig. 43, when multiplied by
100 gives the relative humidity in per cent.

Finally the numbers given under Y,, represent the total quantity
of water in kilograms corresponding to the observed values of
Vm and contained in a vertical column of air 1 meter square extend-
ing from the ground up to the respective altitudes. On account
of the slight accuracy naturally attaching to these numbers they
are only given for each full thousand meters.

With these remarks the following table needs no further explana-
tions:

5’ The Ergebnisse: Results of Scientific Balloon Ascensions.

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 309

Table r. The vertical distribution, of pressure, temper-
ature, and moisture for successive altitudes

h | bn | um Ys Bm | Ba | Ym
m | He | gram gram mm mm | kg.
204) ro. | 5.86 7.68 760 760 | =
500 | is Oni veedier 33 6.97 717 717 ==
1000 | 5.4 4-54 6.24) |e 16975 673; || "6..34
1500 2.9 3.61 5.56 635 | 632 —
2000 + 0.4 3.08 4.95 597 $93 10.14
2500 — 2.3 2.66 4.32 | Soo, |) 555 _—
3000 — 5.0 2.2 3.76 526 519 12.60
3500 OL Nl eS 3.29 494 485 _
4000 —-EO\.03, || 08 2.83 4603 452 14.23
4500 | —13.5 T 4/577 2.35 434 421 =
5000 | =16.7 1.18 I.92 406 391 15.38
5500 | —20.1 0.81 bap y! 380 363 —
6000 | — 23.6 0.67 I.21 355 336 15 99 |
6500 | —27.0 0.57 0.94 331 311 _
7000 | — 30.4 0.30 0.73 | 300-)| 288 "16 30
7500 = 34.0 0.26 0.54 288 | 265 | 4 —
8000 | —37.6 0.22 0.42 267 244 16.42
8500 Aha) == 0.29 | 249 224 _
gooo| —45.6 | — 0.20 231 205 _
9500 | (—49.6) — 0.14 (214) | 187 —
10000 | (—53.6) | — 0.09 (198) | 171 —

Figs. 42 and 43 give graphic presentations of the numbers con-
tained in table 1, the curves being designated iby the same letters
as those that stand at the heads of,the respectivetcolumns offtable r.

IL 7 0 2 UNS AZ ON OGE:
10000 10000 = 2

oO 100 300 300 700mm 00-90-20 30, -2 0 10 Oe 2 20-
FIG. 42 FIG. 43

The axis of ordinates is the zero line for both the pressure and
the specific moisture; the value of the specific moisture in grams
per kilogram of moist air is shown by the numbers at the top of

310 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5!

fig. 43; the pressures and temperatures are given at the bottom.
These curves are curves of condition (Z Z) in the sense explained in
section (2) and are specially appropriate to set forth in clear light
the advantages of this method of representation.

The curves ¢,, of temperature and y,, of average moisture directly
represent the results of observation. The values of @,, and y, are
then obtained by computation with the help of the temperatures
t,, the first of them being computed step by step.

To this latter circumstance is also to be attributed the fact that
irregularities in the course of the temperature curve must also pro-
duce others in the curves for £,, and ),.

The only results of computation exclusively are the barometer
readings} 8, computed for various altitudes on the assumption of a
linear temperature gradient of 1° per 100 meters.

The values of @, are added because it is not uninteresting to
present both numerically and graphically the law of diminution of
pressure for the impassable limiting case of the unstable equilib-
rium of dry air, and thus bring vividly to the eye the fact that
convective equilibrium establishes a limit not only for the rate of
diminution of temperature but also for that of pressure.

Moreover, the dependence of the distribution of atmospheric
pressure on that of temperature finds a very instructive presenta-
tion by the comparison of the curves for £,, and for f,.

Finally, in fig. 43, at the extreme right hand the adiabat for satu-
rated ascending air is added asa line of dashes and as it results accord-
ing to the tables constructed by Otto Neuhoff*® and supplemented by
him for the highest altitudes, and assuming that the ascent began at
the ground at the temperature 18° C.

At the first glance we see this curve has almost the same course as
that for the average temperatures and that by pushing it toward
the left it can be made to nearly cover that. It may, indeed, be ©
asked whether in this peculiarity there be not concealed a deeper
connection, at any rate the fact is so interesting that it should not
be passed by unnoticed.

The value of the mode of presentation here used is especially evident
when we apply it not only to the general mean, but also to average
values for short intervals of time and when we set them beside
each other.

*O. Neuhoff: Adiabatic changes of condition for moist air and their deter-
mination numerically and graphically. Abhandlungen der K6nigl. Preuss.
Met. Institute, Vol. I, No. 6. Berlin, 1900. (See No. XXI of this collection
of translations.)

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD e yall

In such cases the curves give us pictures of thechanges during the
year that have great similarity with those curves that I used pre-
viously for the presentation of the movements of heat within the
soil and which I have called ‘““Tauto-chrones.”!° In order that these
latter should exactly correspond with the former we must use the
pressure instead of the altitude as ordinate, that is to say, the tables
as well as the diagrams must proceed by increase of pressure and not
by increase of altitude.

But first the method of presentation hitherto used will be applied
to the respective seasons individually. Therefore I first of all com-
bine the values deduced by Besson" and String ” in one table, No. 2,
which are then also presented in figs. 44 and 45.

In the temperature curves (see fig. 44) for each season (S = sum-
mer; W = winter; F = spring; H = autumn) the influence of the
ground is evident in the same way as in the curves for individual
days that were collected together in fig. 41.

Table 2. The average conditions as to temperature and moisture for each

season
TEMPERATURE (¢) MOISTURE (y)
ALTITUDE

2 Ww. | F | 5 | # w. | F S H
m eC | SCL ON | Ge gram gram gram gram

° a3.) | 8.7 | rSeahe | 9-3 | 3-00 4.71 8.38 5.71
500 = — _ — 2.61 4-49 7.47 4.83
1000 —o.6 2.5 11.0 myer! 2.17 3.67 6.69 4.40
1500 — —_— | — — 1.88 2.72 Sit) 3.53
2000 —5.1 —2.1 | a3 1.6 1.64 2.41 4.59 2.68
2500 _ _— = | —_— I.36 2.26 3.82 2.43
3000 —10.8 — 3.6 0.9 | —2.6 I.19 me 70 3.03 2.17
3500 _ _ = | —— |) goose mea 2.61 2.03
4000 —14.6 —1.5 —5.0 | —7.7 | 0.06 | L338 2.50 1.59
4500 -- — —_ | — | 0.88 | 1.10 1.84 1.72
5000 — | —- | — | — | 0.68 | 0.78 1.63 1.30
5500 -- —- | — -- S|) SOG 1.59 0.88
6000 — => a _— —_ | 0.65 _— 0.66

The summer curve shows decidedly the character proper to the
season of prevailing insolation whereas in the winter curve the
influence of the cooling of the ground is very evident; the part played

10 See figs. 56 and 57 of Memoir XV. ‘‘The Heat Exchange’’, Sitzungsbe-
richte, Berlin, 1892. (See No. XIX of this collection of translations.)

1 Wissenschaftliche Luftfahrten, Vol. III, pp. 93-95.

” Wissenschaftliche Luftfahrten, Vol. III, p. 166.

312 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. SI

by the ground is also beautifully seen in the changes from winter to
spring and from summer to autumn.

It is also evident that especially in the summer curve between
3000 and 4ooo meters peculiarities may be recognized similar to
those in the lowest thousand meters, although on a much feebler
scale. Perhaps we may in this perceive an indication of the circum-
stance that similar, although perhaps feebler, processes take place
at the upper boundary surface of thick clouds as at the surface of
the earth.

| Be vases

ran 70°

Ww 3

FIG. 44 FIG. 45

The curves in fig. 45 representing the change of the specific
humidity show great similarity to the temperature curves, as indeed
could but be expected. The irregularities shown by them are not
surprising. We would rather wonder that the curves are not still
more irregular when we consider the difficulties that we encounter in
determining the humidity and how small are the psychrometric
differences in the upper strata on which these determinations are
based. We may therefore rather regard these curves as a welcome
proof of the excellence of the observations.

Reference has already been made to the fact that the curves
of temperature condition here used have great similarity to those
that I have previously used in order to study the movements of
heat in the ground and which can be equally well applied to the
corresponding processes in lakes or the ocean.

In that memoir™ I have drawn the depths vertically downward
from the earth’s surface as ordinates and the corresponding tem-

* See Berlin Sitzungsberichte, 1892, pp. 1139-1178; or Memoir No. XIX
of this collection of translations.

O 8 99r

cee i =

2 aes

SCIENTIFIC BALLOON ASCENSIONS—VON BEZOLD 313

peratures horizontally as abscisse. But the curves themselves
representing the temperature conditions at a given moment of time
I called ‘‘tauto-chrones.”” If we assume that the physical peculiari-
ties of the soil are uniform throughout the whole stratum under
consideration or at least, and more properly, that the calorimetric
values for equal volumes or the so-called volume-capacity is uniform,
then the quantities of heat received or given out between any two
moments of time are proportional to the areas included between the
tauto-chrones that belong to these two moments.

This same theorem would be true for the curves of condition as
to temperature and moisture of the atmosphere corresponding to
different moments or intervals of time, if the air had everywhere a
uniform density. But, as is well known, this is not the case in the
atmosphere; however, by appropriate choice of coérdinates we can
obtain curves of condition for which, as in the tauto-chrone, the
area between two neighboring curves is proportional to the quanti-
ties of heat that must be received or given out in the passage from
one condition to the other assuming that the masses of air remain
the same and that the change of temperature is a simple consequence
of gain or loss of heat. Similarly, the curves constructed in a corre-
sponding manner for the specific humidity give the increase or loss
of water or, since we can in this case start from the condition of
absolute dryness, they give the total moisture contained in a given
section of the vertical column of atmosphere.

We obtain such curves of condition if we construct a diagram in
which the pressures diminish as ordinates from below upward
and the temperatures or the specific humidities diminish backward
as abscisse. If we imagine a prism cut from the atmosphere erected
vertically on a base of one square meter, and that the barometric
pressures 6, and #, prevail at the altitudes h, and h, then between
these two altitudes there is included a mass of 13.6 (2, — ,) kilo-
grams of air.

Hence in the prism between / and h + dh the air mass is13.6d8
if the barometric pressure is 8 at the altitude h. If we further
‘assume that at first the air in this prism nas everywhere the uniform
temperature o° C. and that it is to be brought to the temperature t
corresponding to that of its temporary condition, then the infinitely
thin layer between h and h + dh is to receive the quantity of heat
dQ = 13.6 ¢, td@ where c, is the thermal capacity or specific heat
under constant pressure. But the whole mass of air under consid-
eration at whose lower and upper boundary surfaces the barometric

314 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

pressures are /, and £, must receive the quantity of heat

in order to warm it from o° C. up to the temperature corresponding
to its temporary condition—where
B (, is the lower pressure at its upper
boundary and £, the higher pressure
at its lower boundary surface.
Assume that the straight line B,
B, in fig. 46 corresponds to the zero
of the temperature scale and that
8, and B, are the ordinates belong-
ing to B, and B,, and furthermore let
the curves through the points T,T,
and 7,’ T,' be two curves of condi-
tion representing the course of the
temperatures ?’ and ¢ then will

FIG. 46

be the surface bounded by the straight lines B, B,, B, T,, B,T,
and the portion T, T, of the curve of condition where the points
I, and T, correspond to the temperatures ¢, and ¢,.

We can thus convert the above given equation into the form

Q = 13.6 ¢, F

where the surface B, T, T, B, is represented by F.

Now imagine another condition for which we have the tempera-
tures ¢,/ and 7,’ corresponding to the same pressures (, and f, as
before, then the quantity of heat Q’ that is now to be added in order
to bring that portion of the column of air which at first had the
temperature o° C. up to the temperature condition represented by
the second curve will be given by the equation Q’ = 13.6 c, PF’
where F” is the area of the figure B, T,’ T,’ B,.

Finally the quantity of heat that is needed to convert tie portion
of the air column between the pressures 8, and 8, from the condition

SCIENTIFIC BALLOON ASCENSIONS—VON BEZOLD 315

of the temperature ¢ over into that of the temperature ? is
On= Q = 13.6 Cp (F’ — Ff) = D320 yf

where the area J, T,’ T,’ T, is represented by F*.

In the method of graphic presentation here chosen, where equal
lengths of ordinates correspond to equal differences of pressure, the
curves of condition are actually therefore tauto-chrones, and the
surfaces bounded by two horizontal lines and the portions of two
curves of condition intercepted between them, give us a measure
of the quantities of heat that have to be given to the corresponding
portion of the column of air in order to convert it from one condition
to the other under constant pressure.

These considerations are applicable not only to the temperature
but equally well to the humidity: If y is the specific humidity,
i.e., the quantity of water contained in a kilogram of moist air, then
the quantity of water Y contained in the vertical prism erected on
a base of one square meter and at whose limiting end surfaces the
pressures B, and B, prevail, will be

8,
¥ = 13.6 { ydf = 136F
Bs

if the specific humidities are laid off as abscisse.

If the diagram be drawn in such manner that the zero of abscisse
corresponds to the zeroof specific humidity then the total quantity
of water in the vertical column is proportional to the surface
bounded by the two axes and by the curve of condition for specific
humidity.

Hence the last mentioned method of presentation, in which equal
differences of atmospheric pressure correspond to equal lengths
offers specific advantages. |

If we would represent numerically the dependence of any quan-
tity whatever on the atmospheric pressure, we must of course also
proceed by equal differences of pressureinstead of equal differences
of altitude as was done above.

But in this method of presentation one must never forget that
the portions of the vertical column corresponding to equal differ-
ences of pressure have very various altitudes corresponding to the
absolute values of the pressure and to the temperatures. Thus, for
example, the layer above considered between the pressures (, and
8, has different altitudes for the two conditions represented by the

316 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

curves of condition T, T, and T,’ T,’ and in fact the altitude will
be smaller for the first case than for the second.

A clear idea of the operation of the method here used is obtained
from the following consideration.

Assume that the so-called standard pressure of 760™™ prevails
at sea-level and that we ascend step by step in altitude so that
for each step the pressure diminishes 76 ™™ then each layer con-
tains one-tenth of the atmosphere that is present above the given
locality. For 760™™ of the mercurial barometer there is a
pressure of 10,333 kilograms per square meter. Each of these ten
sections into which we have in imagination divided the prism above
one square meter contains therefore 1033 kilograms of air or more
than a metric ton. If now the average specific humidity in such
a section is 4, that is if a kilogram of air contains 4 grams of water,
then there are 4.13 kilograms of water in that section. In a corre-
sponding manner we find that for each such section of the column of
air there are needed 1033 X 0.2375 = 245.3 or in round numbers
245 large calories (kilogram-calories) in order to raise the tempera-
ture of the corresponding air by 1° C.

But these sections, each of which contains one-tenth of the total
column of superincumbent atmosphere, have remarkably different
altitudes. For instance, whereas the lowest sections, according to
the mean temperature deduced from balloon observations will
reach from an initial elevation of 20 meters up to 890 m. the second
section will extend from 890 to 1850 meters.

In the above-described method of representation we imagine these
layers of differing altitudes all brought to the same thickness
exactly as if the air in each were compressed to the same density
and thus formed a so-called homogenous atmosphere.

Conversely, the strata which actually have equal altitudes in the
natural atmosphere would in such an ideal case occupy very
unequal volumes since the higher strata would be crowded together
more and more.

In order to keep the relations clearly in sight, lines of altitude have
been introduced in all the diagrams drawn on this system. These
lines of altitude are based on the average distribution of tempera-
ture deduced from the balloon voyages and therefore correspond
strictly only to the conditions presented by the curve #,, in figures
43 and 47.

Notwithstanding this last-mentioned limitation with reference
to the applicability of these lines of altitude, still in general they
furnish an excellent summary view of the distribution of mass

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 327

throughout the atmosphere and lead to the agreeable conviction
that the observations already given by balloon voyages as to con-
ditions prevailing in the atmosphere apply to a very considerable
fraction of the whole atmosphere.

They also show what an important part the lower and best known
strata plays with reference to the economy of heat in the atmosphere.
In all ascensions above 3300 meters and for the average distribution
of temperature, we have already surmounted one-third of the
whole atmosphere and in the ascensions of sounding balloons above
8400 meters we have passed through two-thirds of the atmosphere.

Furthermore, one sees quite vividly how rapidly the quantities
of heat diminish with the altitude, which fact comes in play when
equal changes of temperature occur in high and low strata, and we
see how erroneous it is to replace the clearly defined expression
‘“Temperature of the air” by that of ‘‘ Atmospheric heat.”

In order to warm by 1° C. a definite given volume of air or a layer
of air of definite thickness at the surface of the earth, there is needed
twice as much heat as under average conditions is needed at the
altitude of 5000 meters. Equal oscillations of temperature in the
upper and lower strata which one naturally assumes to be of equal
mass, i.e., of equal altitude, will therefore have much less importance
in the former than in the latter. Moreover, the expression “ Distri-
bution of heat over the surface of the globe,’’ which is generally
used and therefore not easily abolished, is, strictly speaking, not
correct, since we do not really mean the distribution of heat, which
depends not only on the density but also on the moisture of the air,
but we have in mind only the distribution of the temperature at a
few meters altitude above the ground.

The diagram, fig. 47, is now easily understood, especially when we
add that the full horizontal lines refer to the scale of barometric
pressures given on the left, while the dash lines refer to the scale ot
altitudes given on the right hand of the diagram.

If we consider the vertical line belonging to the temperature — 60°C.
as the axis of ordinates then. the abscisse of the curve of condition
t., are directly proportional to the quantities of heat that must be
given to a unit mass of air having the pressure given at the left-hand
in order to warm it from the temperature — 60° C. up to that of #,.

In a corresponding way the abscisse of thecurve y,, give the grams
of water contained in a kilogram of air of the corresponding stratum ;
the abscisse of the curve y, give the grams of water that would be
contained in this kilogram of air if it were perfectly saturated. The
number of grams is inscribed at the top of the diagram, fig. 47

318 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The numbers used in the construction of this figure are also given in

table 3.

CON IO” ZOO FO?

20° Jo°

FIG. 47

temperature (as shown by the curve #,).
The numbers collected in table 3 show clearly how the aqueous
vapor is distributed throughout the atmosphere above Germany.

Along with the quan-
tities previously con-
sidered this table also
gives, as in table 1,
under the column Y,,
the average quantity of
water in kilograms con-
tained in the whole col-
umn of air of one square
meter section from the
ground up to the al-
titude of the given
pressure, while in the
last column under Y,
is given the number of
grams of water that
would be contained
therein if the air were
fully saturated for the
average distribution of

Table 3. The average vertical distribution of temperature
and moisture for successive pressures

Bm hm

mm m
760 20
750 130
700 700
650 1300
600 1950
550 2650
500 3400
450 4210
400 5110
350 6103
300 7210
250 8490
200 9850

ma Fie
el fe
—I1.
—17.
— 23.
— 31.
— 41.
—54.

ie a ie ie
HI AO H PH HAO O COW

ym

grams |

OOH HH NWR UNH
Ht
_

Or HR NWP HS NAA
I
Ww

Ym Ys
0.0 0.0
4-45 5.91

By a little extrapolation we find that the column of air resting on
one square meter contains on the average only 16.5 kilograms of

SCIENTIFIC BALLOON ASCENSIONS—VON BEZOLD 319

water, and that even for complete saturation under the average
distribution of temperature this quantity can at the most rise only
a little more than 2.5 kilograms. Therefore in the neighborhood of
Berlin the whole atmosphere contains ona average only 1.6 per thous-
and (or one-sixth of one per cent) of water, an amount which can
only be increased to 2.5 per thousand for complete saturation under
the average distribution of temperature.

A graphic interpolation shows at once that on the average we find
one-half of this total quantity of water in the stratum between the sur-
face of the ocean and .1600 meters altitude, so that, for instance, at
the summit of the Schneekoppe we already have one-half of the
total aqueous vapor of the atmosphere below us.

If, on the other hand, we consider that 1 kilogram of water spread
over 1 square meter of ground covers it exactly 1™™ deep, we
can get a standard for determining how rapidly the ascending air
must be renewed over such a surface in order to furnish the quanti-
ties of precipitation actually observed and which may still be very
considerable even at altitudes of 1600 meters.

However, we must not forget that we can obtain from the psy-
chrometric measurements only the water that is present as vapor;
how large the quantities of water may be that are present in con-
densed form in the clouds has up to the present time completely
eluded our observations.

The considerations just set forth enable us not only to follow the
average-content of the atmosphere for each season but also the
increase and loss of heat during great intervals of time. To this
end the curves of average condition as to temperature and mois-
ture as they are already given in fig. 44 and fig. 45 are transformed
into the new system of coérdinates, and thus we obtain figures 48
and 49. From these diagrams by measuring the areas of the surfaces
we obtain the numbers given in the following tables 4a and 46 just
as previously we had done for the values Y,, and Y, in table 3.

As we can deal only with rough approximations, therefore the
following table 4 is arranged only for large intervals.

320 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Table 4. Average kilograms of water contained
in a vertical column of atmosphere, one
square meter section, for each season

(4a) FOR INTERVALS OF PRESSURE

PRESSURE WINTER

mm
760-700
700-600
600-500
500-400

760-400 8.

HH HN WD

.25
OE:
76
28

or

SPRING | SUMMER |AUTUMN

3.68 6.33 4.17
4-93 8.05 5.12
2.70 4.81 3.19
1.61 2.90 2.21
a Ss
12.92 22.09 14.69

(4b) FOR INTERVALS OF ALTITUDE

ALTITUDE | WINTER) SPRING | SUMMER | AUTUMN

mm
o-1I000
1000-2000
2000-3000
3000-4000
4000-5000

o-5000

oO kK UR ON

-96
.07
+23
- 84
- 66

-76

5.54 8.42 5.70
2.00. | 6.10 3.81
EeoSi | (eee 2.11
r.30 | 2.41 Mey ke)
0.88 1. D2 1.26
12.77 21.76 14.58

The numbers here given are of such nature that they have no
claim to great accuracy, since in the passage from the numbers given
by Berson and Suring for different altitudes, as presented above in
table 2, errors slipped in because the relations between pressure and
altitude change for different temperatures.

For the same reason also in the diagrams, figures 48 and 49,

= 202 IO ae (U2 SA

7oomimn

700mm

drawn for different pressures there
should, strictly speaking, be drawn
different scales of altitude for the
different seasons of the year. Since,
however, the application of more ac-
curate methods of computation
would have caused a disproportion-
ate amount of labor and since the
gain in reliability would still be
small, therefore, and for simplicity,
we may be satisfied with the scale
of altitudes based on the tempera-

ture deduced from the totality of all the observations, as we find it

under 7 in table 1.

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 221

We obtain a good idea of the magnitude of the error due to this
“simplification by means of fig. 48, in whose construction only the
values up to 4000 meters could be utilized. We see that the corre-
sponding curves end at different ordinates since thesame altitudes
correspond to*smaller values of the atmospheric pressure when
temperatures are low but to higher pressures when the tempera-
tures are high.

In a perfectly similar way to that by which we have just given the
quantity of water we compute in the following table 5 the differ-
ences of the quantities of heat that are contained, on the average of
the respective seasons,in the several sections of the column of air
resting on one-square meter of ground.

Of course in this summary the tens have but little significance,
exactly as in the above-mentioned table, where the second decimal
figure is a pure result of computation, and is retained only for the
sake of an easier check.

Before I come to the table itself I must first explain the word
‘‘Thermal-content”’ or ‘‘ Warme gehalt”’ used in the title of this table.

By ‘“Thermal-content” I understand the quantity of heat that
must be communicated to a given quantity of air to bring it under
constant pressure from any arbitrary initial temperature up to
any given final temperature. The same expression was, as is well
known, some time since applied by H. v. Helmholtz to this concep-
tion for which, with his approval, I afterward | substituted the term
‘potential temperature.’’ Since, however, this last term has mean-

322 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

while become generally accepted, and since I have not been able
to find another appropriate term for the idea now under considera-
tion, therefore I think it allowable to apply the term ‘‘thermal con-
tent’’ in this place in a different sense.

With this understanding I submit the following table 5. In
this table W, F, S, H, represent Winter, Spring, Summer, and
Autumn, respectively, and therefore the numbers in the column
under F-W represent the number of kilogram-calories that need to
be given to the unit-mass of air at the respective pressures or alti-
tudes in order to bring it under constant pressure from the tempera-
ture of winter to that of spring.

Table 5. Seasonal dtfferences in thermal
content of the atmosphere expressed in
calories, for vertical columns having
I square meter sectional area

(a) FOR SUCCESSIVE PRESSURES

|

B s rae ee —-——
PRESSURE| F-W | S-F S-H | H-W

mm

760-700 1290 1700 | 1530| 1460
700-600 1610 2260 |. 1910 1960

600-500 780 | 2030 | 1390 | 1420

760-500 3680 5990 | 6830} 4840

(b) FOR SUCCESSIVE ALTITUDES

| Nes

ALTITUDE r. ;
: my | se | sa | new
| |

™m |
O-1000 2010 2360 | 2110 | 2260
I000-2000 960 I7IOo | 1400 | 1270
2000-3000 580 1510 | 1040 1050
3000-4000 440 1330 810 960
©-4000 3990 6910 5360 | 5540

The subsequent columns are to be understood in a similar way
but with this difference, that the numbers in tke two last columns
indicate the quantities of heat that are to be abstracted from the
respective sections of the column of air to bring about the transition
from summer to autumn and from autumn to winter.

Of course it is understood that all these numbers are fundamen-
tally only algebraic sums, since in reality the passage from one sea-
son to the next by no means implies continuous progressive addition
or abstraction of heat but processes that frequently alter within

SCIENTIFIC BALLOON ASCENSIONS—-VON BEZOLD 323

short intervals of time and which are here represented only by
this final outcome. ;

These two latter tables 5a and 5) have been especially introduced
because from them and especially from the data by altitudes in
table 5b we seé clearly how rapidly the quantities of heat inter-
changed in given strata, diminish with altitude.

Hence the influence of the highest strata on the economy of heat
in the atmosphere is of subordinate importance even when the
annual range of temperature is larger than we formerly suspected.
Even when ranges at great altitudes are as large as they are at the
ground still the quantities of heat exchanged in strata of equal thick-
ness are proportional only to the density of the air present therein.
This is another reason why it is not recommended to speak of the
heat of the air (luftwarme) instead of the temperature of the air.

Now that we have thus illustrated the vertical distribution of the
meteorological elements from very various points of view, there still
remains the important question to what extent the results attained
by these ascensions are appropriate to remove the doubt that exists as
to the interchange of air between the cyclone and anticyclone or as to
the ultimate origin of these two groups of atmospheric whirl-winds.

It follows from the memoir of Berson" that this important ques-
tion cannot yet be finally answered even from the results of balloon
voyages. But in order that we may at least approach the problem
somewhat more nearly I have requested Berson to prepare for me a
new analysis of the results with reference to the temperatures in the
cyclones and anticyclones for the summer and winter half years
separately. I submit this as table 6 but include in brackets those
numbers that result from one voyage only.

Table 6. Vertical distribution of temperature
during cyclonal and anticyclonal weather

)

| WINTER SUMMER
ALTITUDE} seals r
| Anti- | Anti-
| Cyclone | cyclone Cyclone cyclone
fg he °C. a oo ach
ground i Been +1.5 +15.7 + 20.6
I0ooo =| 22 eas +9). T 13.6
2000 Saisie! Sire) | +13).10 ate
3000 —15.1 —6.7 —o.8 2.1
4000 | —20.8 — 10.9 i710 —3.3
5000 — 27.5 —16.0 | —15.3 | —9.1
6000 —34.0 | —25.8 | (—17.2)
7000 (4g cw) | C30. 2) eter cree ens (— 22.0)
8000 (— 48.5) (- 37.9) a eeest tere (— 30.7)

4 Berson: Wissenschaftliche Luftfahrten, Vol’ III, p. 103 et seq.

324 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

From this table, as well as from the figures 50 and 51 belonging
therewith, in which the curves belonging to the cyclonal and anti-
cyclonal weather conditions are indicated by C and A, we see at
once that in winter as well as in summer the temperatures in the
anticyclones are higher than in the cyclones at the same altitude;
pa the only exception is in the

Ee be eh cot an ts very lowest portion of the

winter curves. Thus from

le a S these voyages we deduce

the same result that Hann

drew from the observations
made in the Alps.

Thus the temperatures
observed in cyclonal and
anticyclonal regions up to
8000 meters altitude donot
suffice to explain the origin
or existence of the ascend-
ing and descending move-
ment that is demanded
by the so-called convection
theory.

This is true, indeed, only for Central Europe, but since the
cyclones generally arrive on the European coasts already well
developed, and since also, on the other hand, for reasons easily
understood, the balloon voyages have given us very few observations
from the highest and central parts of the cyclones; therefore the
question is far from being definitely decided.

Moreover, the fact that in the majority of cases the cyclones tose
their intensity after entering thecontinent and are finally dissipated in
the interior of Northern Asia, indicates that observations over
Central Europe cannot possibly suffice to answer the fundamental
question. At least it will require a much broader base of observa-
tions than is here given to answer this question.

Whether and to what extent a thorough discussion of the simul-
taneous voyages undertaken at a great variety of places in Europe,
or a profound comparative study of the observations made in
America and Europe with balloons and kites, will suffice, may be
left to the future. Personally I incline to the conclusion that the
nature of the cyclones and anticyclones will be understood only after
we begin to study them from broader points of view in connection
with the general circulation of the atmosphere.

6000m.

Jo0om

2000m

/0007TR)

She eA) I et art) ane 10°20

FIG. 50

SCIENTIFIC BALLOON ASCENSIONS—VON BEZOLD 325

For the present one must be satisfied with theoretical considera-
tions concerning this aspect of the question since it will certainly

' g000m

6000m

5000m

40007

S20 Se =e SV Oma Ue OO
FIG. 51

be a long time before obser-
vations are at hand from
the oceans and the Tropics
similar to those for Central
Europe that are presented
by the ascensions described
in the present publication.
At any rate, however,
through these ascensions
the theoretical foundations
have acquired such strength
that we may safely venture
to build further thereon un-
til the conclusions drawn
therefrom once again find
confirmation, just as now
the theoretical work that

has been prosecuted for years is to a certain degree confirmed by
the labors whose results are recorded in this work.

XV

ON THE REDUCTION OF THE HUMIDITY DATA
OBTAINED IN BALLOON ASCENSIONS

BY PROF. DR. W. VON BEZOLD

[Zeitschrijt fir Luftschiffahrt und Physik der Atmosphare. Vol. 13, pp. I-9,
1884. Translated from Gesammelte Abhandlungen, W. von Bezold, 1906,

pp. 264-273]

Ordinarily we use the vapor pressure, the absolute humidity and
the relative humidity as the measure of the moisture in the atmos-
phere.

The determination of these three quantities, or any two of them,
suffices in general to define the condition as to moisture. This
is especially true when one has a definite portion of the atmosphere
under consideration no matter whether one wishes to present its
condition as to moisture at a given moment, or to present the
chronological changes of condition, especially as in climatological
investigations.

It is different when the problem is to follow a mass of air in its
path through the atmosphere and to take into consideration the
increase or decrease of the amount of water.

In order to handle these latter problems a knowledge of the
above-mentioned quantities does not suffice, at least not directly,
rather must we from these deduce still other quantities if we would
attain a correct idea.

If, for instance, we consider a quantity of air with given constant
mixing ratio of aqueous vapor and dry air, and we wish to investi-
gate the changes that this undergoes as it rises higher in the atmos-
phere, then in spite of the constant mixing ratio both the vapor
pressure and also the absolute humidity will in general vary.

The very important circumstance that during these processes
the composition of the air has not experienced any changes cannot
be deduced from the data ordinarily employed.

Inversely, the relative humidity can remain constant, whereas
in fact water is steadily being precipitated, as, for instance, in
case an ascending current of air has exceeded the limit of saturation.

326

REDUCTION OF HUMIDITY DATA——-VON BEZOLD 327

We were therefore forced long since, in our theoretical investiga-
tions tofintroduce two other quantities by the use of which not
only did such investigations first become possible, but which are
also adopted to give a deeper insight into the condition of the atmos-
phere as to moisture. These quantities are on the one hand the
quantity of vapor contained in the unit massof moist air, which can
be conveniently called the ‘‘specific humidity; and, on the other
hand, the quantity of moisture mixed with the unit mass of dry air
or briefly “‘the mixing ratio.”

How important the knowledge of these quantities may be in the
discussion of the observed numerical data gained by balloon ascen-
sions is shown by the simple consideration that these must remain
constant so long as the balloon preserves a course in companion-
ship with the air that surrounds it, no matter how complex the
changes may be that this air experiences as to its pressure and tem-
perature and consequently also as to its absolute and relative
humidity.

So also do these quantities experience no change so long as the
balloon remains within an ascending or descending current provided
that no other air, with a different vapor constant, becomes mixed
with it.

Hence also, conversely, any change in these quantities becomes in
one sense a measure of the admixture of foreign masses of air, a
process whose study is of the highest importance.

This much by way of introduction. We will now first consider
the relations that exist between these two quantities and those
others that are ordinarily used as characteristic of the moisture in
the atmosphere.

To this end I shall use the following notation:

e the vapor pressure in millimeters of mercury.

e’ the maximum possible vapor pressure for the temperature t.

7 the absolute humidity or the number of grams of water vapor in

a cubic meter.

R the relative humidity.

x the mixing ratio or the mass of vapor mixed with a unit mass of

dry air expressed as a fraction of this latter unit.

1 In the mechanical theory of heat, as is well known, the fraction of water,
that is in the form of vapor, in a mixture of saturated vapor and water is
called the ‘‘specific quantity of vapor.’”’ By using the name above proposed
we give expression to the analogy of the two quantities (vapor and humidity),
whereas on the other hand we prevent any confusion in the two different ideas.

328 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

y the specific humidity or the quantity of vapor in a unit mass of

moist air expressed in fractional parts of this unit.

8 the pressure to which this mixture is subjected expressed in

millimeters of mercury.

fy the pressure of the standard atmosphere or 760™™.,

a the coefficient of expansion of air = 0.00367 = 1/273.

t the temperature of the mixture.

Recalling that 1 cubic meter of dry air at o° C. and under a pressure
of 760™™ weighs 1293 grams, and that the density of aqueous vapor
is 0.623 times that of dry air at the same temperature and pressure,
then we have the following equations:

5 1
f = 0.623 x 1298 75 X 745 = 1.060755 - - @)
é€
RSIS ips a oe
0.623 —— 3
= 0.628
Efe. a2irpas AS 4
Pe Ae

Since the quantities x and y arealways among the hundredths there-
fore in many cases it will be advisable to multiply the value by 1000,
that is to say, we use the number of grams of vapor that are mixed
with a kilogram of dry air, or that are contained in a kilogram of
moist air respectively.

If we indicate these values by x, and y, then we have

Hy = 623-5 Lh eee haa

and

i Sate Bie . 0.377 = 1000 a0 4, ~ as

In the headings of the tables that are to follow, as also in thedia-
grams, I will, for the sake of clearness, omit the subscript index g
and will by x and y understand quantities rooo times as large as
those given by the preceding definition.

REDUCTION OF HUMIDITY DATA—VON BEZOLD 320

Since the quantities « and y are in general very small and scarcely
ever exceed the value 0.03 but are generally much smaller, there-
fore they are never very different from each other and for a rough
approximation may be considered briefly as equal to each other.

Now in order to put the meaning of the specific humidity and the
mixing ratio in a very clear light it seems appropriate to investigate
how the other quantities vary when the former is constant.

To this end write equation (3) in the form

x
e= 8 0.623

and substitute this in equation (1), then we obtain

Es pa aeullag Pe kee?
l+at «+0.623

This equation shows that with constant pressure but variable
temperature, the absolute humidity experiences changes even when
the composition of the air remains constant.

We get the best idea of the matter if we assume that we change
the mixture from an initial condition, in which the appropriate
quantities have the subscript index 1, over into another for which
we use the subscript 2.

If then we assume

= t,
By = B,
>t
it results that
&y = €,

but
fh <f, and R, < Ry

If, on the other hand, we imagine that the volume remains
unchanged, then according to the well-known law of Mariotte-Gay-
Lussac we have the relation

or

330 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Habito HS eat
Lipo rnb Sark

and then for x, = x, and #, > 4,, we have
15 =), Dlt ye eke i,

that is to say, the warming of a quantity of air having a given
invariable composition and inclosed within a non-expansible vessel,
causes a rise of vapor pressure and a diminution of relative humidity
while the absolute humidity remains unchanged.

This example is very instructive because it allows us to recognize
very clearly the difference between vapor pressure and absolute
humidity, whereas otherwise not infrequently one tends to consider
these two ideas as equivalent.

The reason for this latter error lies in the fact that the quotient

1.060
l+at

occurring in equation (1) is equal to unity when ¢ = 16.38° C.
and varies less than 2 per cent from unity between the values# = 10°
and ¢ = 22°. Sincein the metric system the numbers for vapor
pressure and for absolute humidity are nearly the same for the
temperatures that most frequently occur, therefore in ordinary
language the difference between these two ideas is frequently
entirely overlooked.

These analyses may suffice to help us clearly recognize the mean-
ing of the specific moisture and the mixing ratio.

I will now pursue the example further and show how the average
distribution of aqueous vapor in a vertical column of air is expressed
by the use of this idea.’

Iassume the atmospheric pressure at sea-level to be 760™™, the
temperature 9.0° C. and the vapor pressure 6.5™™, which corre-
spond to annual average conditions in the neighborhood of Berlin.

As to the diminution of temperature with altitude I have used the
numbers deduced by A. Berson. The value of the vapor pressure
for different altitudes is computed by the formula given by R. String

h h
—# (4 4
fie, 10 g ( 20

* The following portion of this memoir has been revised, taking into con-
sideration the results of recent balloon voyages. [1905. W.v. B.]
® Wissenschaftlichen Luftfahrten., Vol. III, p. 63.

REDUCTION OF HUMIDITY DATA—-VON BEZOLD 331

where ¢, is the vapor pressure at sea-level and h is the altitude in
meters.*

This being premised I obtain the following table 1 and arrange
the columns in the order in which they are derived from each other,
i.e., first the altitude and the accompanying temperature, then the
air pressure and vapor pressure, then values of x and x/x, deduced
from these, where x, is the value at the surface of the ground,
expressed in grams of water per kilogram of dry air, and finally the
computed values of the absolute and relative humidity.

TABLE 1
SS ean ose ee 3 =
h t B B/760 | € x 2 ay Vie oF R
|

m oe mm grams grams grams
eo ©6©| + 9-0 760 1.00, || 6.50 5.38 1.00 6.66 76
I000 | + 4.0 673 0.89 4.34 4.04 0.75 4.53 72
2000 — 1.0 595 °.78 2.79 2.94 O90) 5/296 66
3000 pe 6.4 524 0.69 | 7/3. 2.06 6r38 |) 2.88 61
4000 | —11.7 461 | 0.61 F.03 I.40 0.26 04 55
5000 —18.1 | 404 0.53 0.59 0.91 | 0.87 | 0.67 | 53
6000 — 25.0 | 353 0.46 0.32 | ©..97 O.rr | 0.37 52
7000 — 31.8 | 307 0.40 0.17 O37 “|| “On07 -\. Osaz 53
8000 — 39.0 266 0.35 0.09 0.21 O.04 | O.rL | 60

In order to make the course of these numbers perfectly clear the
quantities 8, e,x and R
are represented by
curves in fig. 52, where
the altitudes are ordin-
ates, and the correspond-
ing values of the other
quantities are abscisse.
In-explanation of this
diagram it need only be
added that the distance
between two consecutive
vertical lines is taken as
unity in plotting the
quantities e and x but is
taken as 10 in plotting
relative humidity and as
50 in plotting barometric
pressure.
The numbers, as also the accompanying diagram, now show clearly

‘Siiring: Wiss. Luft., Vol. III, p.160.

8000 ©

(HSI ee i a
Ho afeeeeS ete a]
BE wiet es Bae

Welelcia ele eames
FC OS Se
Nath a Skeeeae
pina iewieslad WeRCAaIN espe Te TY
SSR ReieeD eaeaeee
CS eae See ae
HEE eae
LPN Bb Ie)

nae

7O0O

6000

2000

2000

IN
Anes ee ees
(a Ol es Se a
Sia sd ele a
oO ©] /0 /

FIG. 52

332 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. Si

the diminution of humidity in respect to the mixing ratio. Whereas
according to String’s formula, the vapor pressure (¢) at an altitude
of scarcely 1000 meters is reduced to one-half of that observed at
the earth’s surface, we must rise to 2000 meters before finding the
mixing ratio (x) or the specific humidity (y) diminished to the same
extent. But at an altitude of 6000 meters the vapor pressure is only
1/20 of that in the lowest stratum, whereas the mixing ratio and the
specific humidity are somewhat less than } of those in the lowest
stratum.

The slight increase of the relative humidity (A) in the highest
stratum, as expressed by the numbers (52 and 60), can hardly have
any general importance for we should not overlook the fact that it
needs only very slight changes in the course of the temperatures to
greatly change the values of the relative humidity and the course
of the corresponding curve.

I omit any further remarks that are suggested by figure 52 and
turn rather to another example that shall relate to the behavior of
ascending air without experiencing any mixture with other air or
any decrease or diminution of heat.

Let this air at its start have the altitude of o meter, pressure
760™™, temperature 25° C., vapor pressure 9.25™™. If this air ascend
adiabatically, then at the altitude 1800 meters ‘condensation will
begin and at 3070 meters it will have attained the snow stage.

In detail we have the series of vaiues given in table 2.

TABLE 2

h B € x t R
m | mm | grams | grams °C. =| per cent

o| 760 | 9.25 7.69 ° 25 39

1000 | 677 | 8.24 7.69 15 | 65

1800 615 7.49 7.69 7 | 100

3070 526 6.60 eke 4 ° 150

6840 322 | 0.61 1.18 —29) || too

Fig. 53, which needs no further elucidation, shows the peculiar
course of these values.

On the other hand this diagram shows clearly how important it is
to take into account the mixing ratio, or if one prefers it the specific
humidity, together with the vapor pressure and the relative humid-
ity, in the reduction of the humidity data for various altitudes.

This is especially important if we keep in mind the fact that the
change of x for any given change of altitude gives directly the quan-
tity of waterthat is precipitated in the ascent of the air through this
vertical distance.

REDUCTION OF HUMIDITY DATA—VON BEZOLD 288

Hence from the above given course of the average values of this
quantity (x) we may conclude, as to the values precipitated in the
individual strata of the atmosphere and thence, in connection with
the precipitation measured at the earth’s surface, may conclude
something as*to the average intensity of the vertical circulation of

the air.

Roses eeee
ELAR as ee
CCR eas ae
Bice a
Je oe ee
Lek Cees ne ae
PEGE ee ee
i aS eee ee
Aaa wae ae
Case eS Sek ee
SREB R EP ake

Eee. Gee

3000

2000

/000

I have already remarked that
from the constancy of the mix-
ing ratio within any part of the
atmosphere we can with some
confidence draw the conclusion
that in that particular portion
no mixture of various kinds of
air has taken place.

Conversely, rapid changes in

the mixing ratio as we pass

through different strata of air
show that there are present
masses of air having different
origins.

|
ASB a elk Nae
LI 2a Ree

FIG. 53

The study of the mixing ratio
acquires increased importance,
in view of the circumstance that
the frequent occurrence of the
Helmholtzian billow clouds forces us to the conclusion that very fre-
quently strata of air of quite different temperatures and humidities
are flowing over each other, since the surest indications of the strati-
fication of the atmosphere are found in the numerical value of this
quantity.

These remarks may suffice to demonstrate how desirable it is that
in the discussion of the results of balloon voyages the mixing ratio
should be regularly taken into consideration.

Perhaps it may indeed be worth the trouble also to include it
in investigations into the humidity condition at the earth’s surface
itself, since for equal vapor pressure the value of the mixing ratio
varies very nearly as the reciprocal of the barometric pressure.
So that the distribution of humidity at the earth’s surface will in
many cases, by utilizing this element have quite a different aspect
from that obtained directly from the vapor pressure alone.

XVI

ON THE CHANGES OF TEMPERATURE IN ASCENDING
AND DESCENDING CURRENTS OF AIR

BY PROF. DR. WM. VON BEZOLD

[Meteorologische Zeitschrift, 1898, XV, 441-448. Translated from Gesammelte
Abhandlungen, W. von Bezold, 1906, pp. 274-283]

When I published my first memoir ‘‘On the Thermodynamics of
the Atmosphere’? I expressed the hope that by the elucidations
therein given we had finally set aside the view that slipped into the
excellent work of Guldberg and Mohn, according to which the cooling
of ascending air depends on the work done in lifting it. But since A.
Schmidt of Stuttgart, not only in the year 1890? but also more
recently? has come forward again as defender of the idea that the
work done in lifting plays a part in the cooling of ascending currents
of air, therefore I think that I ought not to delay to repeat and
supplement in more thorough manner my earlier explanation of this
matter. I will, however, pursue a course directly opposite to that
adopted by Schmidt.

Whereas Schmidt takes the kinetic theory of gases into considera-
tion and thereby unnecessarily obscures such a simple question, I
will attempt to treat it in a manner as elementary as possible.

This course seems to me so much the more advisable since in fact
the principle of Archimedes as also the theorems based on experience
relative to the thermal behavior of gases suffice for the investiga-
tion, whereas the introduction of the kinetic theory of gases has only
the result of causing an unnecessary and therefore injurious com-
plication of the present question.

If we are to consider the subject of the work done in the ascent
of a mass of air, we must first clearly understand the conditions
attending a given volume of air within the atmosphere. Let us
assume that the volume under consideration encloses the mass m1,

1 Sitzb. Berlin Akad., 1888. [See pp. 212-242 of the previous collection of
translations.—C, A.]

2 On the cause of the diminution of temperature with altitude. Tiibingen,
1890.
3 Tilustrierte Aeronautische Mittheilungen, 1898, II, pp. 12-15.

Seb

TEMPERATURE OF ASCENDING CURRENTS—VON BEZOLD 335

then its weight must be P = mg if we consider the mass as enclosed
within an enclosure that has no weight and as located within a
vacuous space such as the receiver of an air pump and at a place
where the acceleration of gravity is g. Underthese suppositions
the full amourit of work required to raise this weight through the
vertical distance h would be m gh or that which Schmidt considers
necessary under the conditions existing in the atmosphere. But
this volume of air thus imagined cut out of the atmosphere, is in
fact surrounded by air. Consequently its weight in the atmosphere
is
P’! = gm — gm’ = g (m— m’)

where m’ is the mass of the air displaced by it. But since the baro-
metrie pressure within the enclosed mass is the same as that in its
immediate neighborhood therefore

where ¢ is the temperature of the mass and ? that of the surrounding
air and where

Hence we find

This latter value can be either positive or negative or zero according
as t is smaller or larger or equal to #’. Hence no work is done in
lifting the enclosed air unless its mass is colder than that of the
surrounding air. If it is warmer then it has a buoyancy and it
rises of itself through the surrounding cool air which flows in to fill
its place, and thus the center of gravity of the whole system sinks
exactly as the theory of equilibrium demands.

But under all circumstances the absolute value of P’ is much
smaller than m g, so that for a mass of air rising through the altitude
h (and whose ascent indeed never occurs alone in the atmosphere
but only in connection with other air descending at some other place,
thus forming a connected whole) it is never allowable to introduce
m g into the computations as representing the work done.

But even when work is really done in lifting, which can only occur
when ascending air is cooler than the descending, as in the case of
cyclones with cold centers, still the work is exceedingly slight in com-

330 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. SI

parison with the work of expansion done by the ascending air, as
will be seen by the formula to be developed hereafter. It is evident
that such processes are in general only possible when actual changes,
that is, motions of the atmosphere sufficient to overcome the exist-
ing gradients, are produced by the buoyancy of other portions of
the atmosphere.

If, however, we ignore such special cases and consider only the
normal interchange of air between cyclones and anticylones under
the assumption that a steady state of motion has been established
and omitting the vortex motions due to the rotation of the earth,
then we may imagine a number of stream lines united to form a
closed ring and we have a process analogous to that in the closed
system of a hot-water heating system.

If now we study the process within such a ring, assuming for the
sake of simplicity that it has only a slight vertical range so that
equal differences of altitude correspond to equal differences of pres-
sure then we may consider it as represented by the scheme outlined
in fig. 54. |

In this figure let A Brepresent the ascending and C D the descend-
ing branch, and so choose the connecting pieces B C
and A D that the masses contained in them are in
equilibrium with each other (that is to say that equal

masses are contained in those portions on the right
| and left hand of the central line) (which of course re-

quires that C shall stand a little higher than B, and D
A somewhat lower than A) then the excess of pressure at
D is equal to the difference of the weights of the fluid
columns A B andC D. If now we further assume
that the horizontal lines or divisions indicated in this
figure correspond to equal differences of pressure, then equal masses
of fluid are contained between two successive sections (if the areas
of the sections of the tubes are uniform), and the weights of the two
vertical columns are proportional to the total number of the sec-
tions.

But the excess of pressure corresponding to the difference of the
weights of these columns is the same at each cross-section of this
closed system.

Now, when vertical motion is set up and a steady condition of
motion is established, the ascent of any mass in A B is always at the
expense of the sinking of equal mass in D C, since the masses that
flow through a unit section in a unit time must be the same for every
section. In consideration of the different densities in the ascending

FIG. 54

TEMPERATURE OF ASCENDING CURRENTS—VON BEZOLD- 337

and descending branches this leads of course to the conclusion that
either the sections of the two branches have a definite ratio to each
- other or else the velocities at different places must be different.

The former of these assumptions is the simpler, whereas changes
of velocity would materially burden our course of reasoning unless
indeed they are neglected entirely. In consideration of this fact
the scheme assumes that there is a variation in sectional areas
of the two branches. But under all conditions the existing surplus
of pressure after initiating the motion or after attaining a station-
ary condition serves only to overcome the friction, and if that did
not exist it would, after equilibration of the temperatures, maintain
the movement forever.

Exactly the same conditions exist in the interchange of air between
ascending and descending currents, as soon as the movements are
started and the steady condition is established. Here also the rise
in the ascending branch takes place at the expense of the mass that
is sinking in the descending branch and there can be no thought of a
work of elevation performed by other forces such as heat introduced
from without or by the loss of internal energy, i. e., cooling.

But these preceding remarks obtain only for the steady condition.
If the motion is to be first initiated then either the center of gravity
must be raised on one side by warming or on the other hand it must
be lowered by cooling. In the first case actual work must be per-
formed to raise the mass and this is to be added to the work done by
expansion; in the second case the energy that is necessary to set in
motion the whole mass that enters into circulation must be obtained
from the descent of the center of gravity of the cooling side of the
whole system.

In this process, however, it is absolutely necessary that the heat
be ‘‘taken in” by the warming side or else ‘‘given up” by the cooling
side unless mechanical acceleration be given to the mass by other
masses of air not belonging to this system, as, for instance, by fric-
tion or pressure or suction.

If we ignore these last mentioned influences and confine attention
to those processes in which only heat comes in play, we get an excel-
lent insight into the behavior of the phenomena by the presentation
given at pp. 107-110 of Sprung’s Lehrbuch der Meteorologie and the
experiment there described. .

If now we apply similar considerations to the rise and fall of the
surfaces of equal pressure, such as occur in the production of land
winds and sea-breezes or mountain and valley winds, then we at
once see that here also in case of warming, work is actually done by

338 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

lifting, or in case of cooling there is a disturbance of equilibrium
by the sinking of the center of gravity, which then brings about a
motion of the mass of air.

If the above-given analysis does not yet suffice to make the sub-
ject perfectly clear, then perhaps the following considerations may
succeed in doing so.

Assume that we have three cylindrical vessels, two of them filled
with mercury to the height of 760™™, the third filled to the same
height with water. Let the external air pressure also amount to
760™™ mercury. Now assume further, that at the base of the
first vessel, filled with mercury, there is a piece of iron that is at the
beginning held down but by some appropriate arrangement may be
suddenly left free. When set free, the iron rises until it swims on
the surface of the mercury. But now this surface itself stands some-
what lower since the floating iron protrudes partly above it and the
center of gravity of the whole system is now somewhat lower.

No one will imagine that the iron cools by rising, but will rather
at once perceive that its rising is at the cost of the sinking of the
mercury.

At the bottom of the second vessel imagine a mass of air enclosed
in a small bell glass whose mouth opens downward. This
air is therefore under a pressure of two atmospheres. Turn the
bell glass over by appropriate mechanism so that its mouth opens
upward and the air rises through the mercury to its upper surface.
In this process the air expands and consequently cools. Assuming
that the ascent proceeds so rapidly that there can be no interchange
of heat between air and mercury or that the process is adiabatic,
then the amount of this cooling can be easily computed.

The formula for the computation of the final temperature ¢, is

K—1
Zit ta K
273 + 4 Pr:
where #, is the initial temperature; p, the initial pressure; and /p,

the final pressure and «x the well-known constant 1.41. Under the
assumptions above made we have

ret
Pr, 2
If now t, = 0° then we find #, = — 50.2° or a coolingof about 50°C.

If now we repeat the experiment last described in the third vessel
filled with water up to 760™™, then the air in the bell glass has the

TEMPERATURE OF ASCENDING CURRENTS—VON BEZOLD 339

initial pressure

760™™

760 + 136

of mercury; corresponding to this we have

p, _ 13.6
p, 14.6
and if z,is o° C. then#, = — 5.6°. In this case therefore the cooling

scarcely amounts to 6° C.

Since we can assume that the piece of iron has the same mass as
the quantity of air used in the other experiments, therefore in all
these three cases we have allowed equal masses to rise through
equal altitudes; and yet in one case no cooling takes place; in the
second case a cooling of about 50°C; and in the third case one of
scarcely 6°C. Thus the cooling is not to be attributed to the work
done in lifting but exclusively to the work done by expansion.

By these considerations it must have been put beyond all doubt
that in the ascent of masses of air in the atmosphere the work of
lifting does not come into consideration during steady motion and
only to a very slight degree during the process of the establishment
of such motions.

In all investigations hitherto made relative to ascending and de-
scending currents the steady motion has been assumed or implied,
therefore nothing need be said as to the work done in lifting.

Now that we consider the error of basing the theory of cooling of
ascending masses of air on the work of lifting to have been fully
demonstrated, we have still to solve the question how it was possible
from this assumption to arrive at the same numerical values as by
the exclusive consideration of the work of expansion.

This most surprising fact is easily explained by the consideration
of the following well-known formule.*

For any given change of condition of the unit mass of dry air
let the quantity of heat communicated to it be Q, the specific pres-
sure p, the specific volume v, the specific heat under constant pres-
sure Cy, the reciprocal of the mechanical equivalent of heat A, we
have then the equation

dQ =c,dt — Avdp

‘See J. Hann. Zeit. Oesterreich. Gesell. f. Met. 1874. IX, p. 321. Or
the translation published in the ‘‘Short Memoirs’”’ Annual Report Smithsonian
Institution 1877.

340 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

but for adiabatic change

o =¢,dt — Avdp
or

65 GE AU 5! ry) et cy iu a

But the diminution of atmospheric pressure with altitude, or the
baro-hypsometric formula follows from the equation

rears | SME PS Pe

where pa is the weight of the air contained in a unit volume, and h
is the altitude, and where we assume that at the point under con-
sideration the force of gravity has its normal value or that thecolumn
of air is located at latitude 45° and that the change of gravity with
altitude may be neglected.

Since now according to the definition here adopted the unit of
weight is the weight of the unit mass, therefore p is the mass of the
air contained in the unit of volume, hence

Hence we can write the equation (2) in the form
Gh = = VAP OO Ge a eee

and now by combination with equation (1) we obtain for the diminu-
tion of temperature with altitude the well-known formula

as gy! 2 Sei

Cp

or after substituting the numerical values

epee : dh = — 0.0099 dh.
424 Xx 0.2375

If now, on the other hand, we ask as to the work necessary to lift
the unit mass, then under the assumption above made, that the
weight of the unit mass is the unit of weight,5 we have the equation *

L=h or dL=dadh

5In the metric system. the mass of a kilogram is the unit of mass, its
weight under normal conditions is the unit of weight and the kilogram-
meter is the unit of work.

TEMPERATURE OF ASCENDING CURRENTS—VON BEZOLD 341

The performance of this amount of work requires the consumption
of a quantity of heat expressed by,

dQ = AdlL = Adh

If this quantity of heat is to be drawn from a body whose specific
heat is ¢c then we have

dQ = — cdt

or

A ak til Pace ae ea A

which is exactly as found above, if we take the heat from the air and
if the abstraction of the heat can go on under constant pressure so
that c can be put equal to c,.

But all this is not possible under the conditions that prevail in a
steady ascending current in the atmosphere. The specific mass of
air is not enclosed in an envelope that has no weight, in a vacuous
space, but it floats in its surrounding atmosphere.

But even if the above-mentioned condition were fulfilled still the
mass would not rise and thereby cool any more than a mass of iron
would rise from the earth without the application of exterior forces
and would thereby cool 2.09° per rise of 100 meters, as results if we
substitute for c the value 0.113 as the specific heat of iron.

On the other hand, the mass of iron will certainly rise and that
too without cooling when it forms one member in an endless chain
that glides frictionless over a roller and to which there has once been
given a velocity, no matter how small.

“Tt is therefore a purely arbitrary arithmetical operation when
in the formula (4) we substitute for c the value c, as the specific
heat of air under constant pressure and thus bring about an apparent
agreement with the values deduced from the formule (1) and (2).”

The fact that in this treatment the introduction of the specific
heat under constant pressure rests on no sccure basis, is evident
also from the fact that Schmidt himself thought that instead of this,
one must substitute the value c, or the specific heat for constant
volume instead of the specific heat for constant pressure as used by
- Guldberg and Mohn.

The only logical conclusion that we ought to draw from this
simultaneous consideration of the work of expansion and the work
of lifting is that of a clearer understanding of the results attained by
the first-named process.

342 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

We may say “The cooling that a mass of air experiences when
rising in a steady current without increase or diminution of heat,
is precisely the same as that which it would experience if under con-
stant pressure a quantity of heat were abstracted equivalent to the
work that would be performed by raising an equal weight through an
equal altitude,”

This theorem is analogous to that which refers to the circulation
of a particle of air under the influence of a gradient and which can be
expressed as follows:

“The acceleration which a particle of air experiences when the
atmospheric equilibrium is disturbed in a horizontal direction, is the
same as that which a heavy mass would experience if it could glide
without friction on the rigid surface of equal pressure.”’

Both these theorems are simple developments or illustrations of
the formula deduced from purely physical considerations.

In order to avoid any misunderstanding I repeat that the work
done in lifting can be neglected only during steady motion.

So long as this condition is not yet attained, as, for example,
in the above-described cases, it cannot be neglected although in fact
in general it is only a small portion of the work done by expansion.
Certainly, however, one can imagine processes in which the work of
lifting becomes quite important.

If, for example, we assume that a partially vacuous tube extends
above the atmosphere while at its bottom there is air within an
enclosure and we now by opening a slot let this air enter into the
tube, then after equilibrium is attained the center of gravity of the
whole mass will lie much higher than before and then of course the
work done in lifting must be considered in addition to the work done
by expansion, as the former, like the latter, will be done at the expense
of the internal energy, that is to say by cooling.®

If we are to investigate such cases then we cannot apply the
ordinary formule of the mechanical theory of heat, but must rather
add to these equations another term expressing the work of lifting.

We must indeed never forget that all the ordinary formule of this
theory are based on the assumption that the work needed to raise

° This example is not strictly appropriate, but rather in this special case
according to the well-known experiments of Joule, the work of expansion will
wholly disappear, or at best is to be considered as a small quantity of high
order wherever the work of lifting comes completely into consideration.
Hence cases may be imagined in nature in which the work of lifting cannot
be neglected; but these are always irreversible processes that must be espe-
cially investigated in each individual case. (Note added in 1905. W.v. B.)

TEMPERATURE OF ASCENDING CURRENTS—VON BEZOLD) 343

the center of gravity so far as this comes into the problem, as also
the energy needed to increase the progressive motion of the whole
mass so far as it occurs, are negligible in comparison with the work
done otherwise.

Hence therefore the two ways that have been used to compute
the cooling of ascending masses of air, and which apparently lead to
the same results, are by no means to be considered equivalent.
They would in fact both be false because of neglect of the supple-
mentary term above mentioned, if the work of lifting is to be
introduced.

But in this case all investigations in this field, beginning with
Kelvin, Reye, and Hann, as also those of Guldberg and Mohn down
to the latest works on the dynamics of the atmosphere would fall
with one blow.

The fundamental importance of the whole question has alone
moved me also, independent of the wish of the editors of the Meteoro-
logische Zeitschrift, and quite contrary to my general habit, to
treat this simple question with so many repetitions of well-known
things, in such breadth and detail, that I feel as though I ought to
apologize to those familiar with the subject.

I hope that I have been successful in finally dissipating any doubts
that may still linger here and there and in proving that under ordi-
nary conditions there can be no work done by lifting in the ascend-
ing atmospheric currents but that in these cases the work of expan-
sion alone comes into consideration.”

7 By later publications of A. Schmidt (see Gerland’s Beitrage zur Geo.-
physik, 1899, IV, pp. 1-25; 1903, V, pp. 389-400) the contradictions between
his views and mine have been considerably diminished. (Added rgo05.
Wie sve.)

XVII

ON THE THEORY OF CYCLONES
BY PROF. DR. WM. VON BEZOLD

5 igs ue of the Berlin Academy, 1890, pp. 1295-1317. Translated
from Gesammelte Abhandlungen, 1906, pp. 284-305]

If one follows up the meteorological literature of recent years he
will not deny that a complete reversal has gradually taken place in
the fundamental views as to atmospheric movements.

Whereas under the domination of the old trade wind theory
nearly all these movements were considered as consequences of the
interchange of air going on between the poles and the equator and
nearly all individual processes were sought to be explained from
this point of view, we now go to the opposite extreme since the
establishment of the so-called ‘‘ Modern Meteorology.”

Since by means of the daily weather charts we have learned the
importance that attaches to the areas of high and low atmospheric
pressure, we now imagine that the old point of view may at the
most still have some value only in explaining the processes in the
tropical zones, but that in higher latitudes only local warming and
cooling, as also the condition of the moisture, are the controlling
feature in the formation of cyclones and anticyclones, and therefore
of all the weather phenomena.

Previously we considered the low pressure in the interior of a cy-
clone-as only a consequence of the whirling motion produced by the
cooperation of the equatorial and the polar currents. Subsequently,
on the other hand, we thought of the whirling motion as exclusively
the consequence of the low pressure which itself had its origin in the
local conditions just mentioned. We need not-go into detail to
show how much of truth there was in this newer view and how much
our knowledge was advanced by it, but it cannot be denied that we
went too far when we thought that in it we had the key to the expla-
nation of all weather phenomena.

Absorbed by the many results offered by the study of individual
phenomena from the new point of view we have almost entirely
lost sight of the general circulation. However, individual investiga-
tors have made distinguished exceptions to this and William Ferrel

344

THEORY OF CYCLONES—VON BEZOLD 345

has prosecuted fundamental work not only in the theory of the
general circulation but also especially in the theory of the dynamics
of the earth’s atmosphere. But independently of the fact that his
views were first made known to a larger circle of students (in Ger-
many) by the “Lehrbuch” of Sprung, even Ferrel considered this
general circulation as a series of phenomena complete within itself,
while for him, as also for the majority of modern meteorologists,
the cyclones and anticylones are independent structures whose
theory he sought to develop in a corresponding way and independent
of that of the general circulation.

On the other hand, already in 1879 Hann! had expressed himself in
favor of a more general view of the problem and in a short article
under the title (‘‘ Einige’”’ etc) ‘‘ Remarks on the theory of the general
atmospheric currents” had developed views that correspond in
general with those toward which the most recent researches are
tending.

But this memoir appears to have attracted but little considera-
tion, and I must confess that only recently I was by Hann himself
referred back to this memoir, since it had previously escaped my
notice, as is easily explained since the publication occurred at a time
when I had first begun to occupy myself with meteorology and had
to first make myself familiar with the details of the accepted current
theories.

The merit of attracting the attention of [German] meteorologists in
general to the treatment of this problem from more general points of
view belongs undoubtedly to Werner von Siemens,? whose memoir
(‘‘ Ueber, etc’’) on the ‘‘Conservation of energy in the atmosphere’’
gave a powerful stimulus to this study quite indepéndent of what we
may think as to some details of the views therein developed.

From this time onward various memoirs have appeared which
either directly had as an object the investigation of the general circu-
lation of the atmosphere, or else attempted to show the unsatisfac-
tory nature of the theory of cyclones and anticyclones as developed
too narrowly.

Of these we mention, first, H. von Helmholtz, who in a memoir,
(‘‘Ueber, etc”) on ‘‘The movements of the atmosphere’? demon-
strated that ‘“‘by the action of continuous forces there can be formed
surfaces of discontinuity,’ and that “‘the anticyclonic movement

1Hann: Zeit. d. Oest. Ges. f. met. 1879, XIV, pp. 33-41.

2'W. v. Siemens: Sitzb. d. Berliner Akad., f. 1886, pp. 261-275.

3 Sitzb. d. Berliner Akad. f. 1888, p.663. [See p.93 of the previous collec-
tion of translations. C. A.]

346 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5I

of the lower stratum and the great and steadily-growing cyclone of
the upper stratum which are to be expected at the pole, break up
into a great number of irregular wandering cyclones and anti-
cyclones with a prevalence of the former.”’

Thus at least the way is indicated by which we have to seek the

connection between the general circulation and the individual ©

phenomena such as cyclones and anticyclones which had hitherto
been considered as quite independent existences.

We need only recall the investigations of Moeller, Oberbeck
and others, which also relate to the general circulation of the atmos-
phere.

While theoretical researches thus pressed forward toward a
more general comprehensive treatment of all movements of the

atmosphere, Hann undertook‘ to give a basis of tact, deduced from,

the observations made at elevated stations, to the doubts that he
had previously expressed as to the incompleteness of the current
views.

He demonstrated that in very various cases the temperatures in
the interior of cyclones and anticyclones up to considerable alti-
tudes are such that it is impossible to explain the existence of these
as due to the specific weight of the central column of air, and that
one is inevitably led to explain them as the result of the influence
of the general circulation.

Therefore the theories hitherto accepted as to the origin and move-
ment of cyclones and anticyclones undoubtedly need important
modifications and it will be important to explain how the above-
mentioned local causes, or the specific gravity of the column of air
due to them, codperates with the general circulation to bring about
the phenomena actually observed.

It is comparatively easy to recognize this codperation in the
arrangement of the mean annual and monthly isotherms of the
globe as I will briefly sketch it in the following paragraph.

The difference of temperature between the equatorial and the
polar regions causes a flow of air in the upper regions of the equa-
torial zone towards the pole. This upper current will by reason of
the deflecting force of the diurnal rotation of the earth be converted
first into one from the southwest in the northern hemisphere but

‘Hann: On the relations between the variations of atmospheric pressure
and temperature on the summits of mountains. Met., Zeit. 1888, V, pp.
7-17. The Maximum pressure of November, 1889. Denkschriften d.
Vienna Akad., LVII, pp. 401-424, 1890. Remarks on the temperature in
cyclones and anticyclones. Met. Zeit., 1890, VII, pp. 328-344.

THEORY OF CYCLONES—VON BEZOLD 347

from the northwest in the southern hemisphere, and then gradually
into a nearly true west wind. At the same time its velocity
increases as it advances into higher latitudes, according to the
theorem of the conservation of areas. At and beyond a certain
latitude the’centrifugal forces thus developed overpower the influence
of the temperature which would cause a steady rise of atmospheric
pressure toward the poles, so that this pressure which at first
increased with distance from the equator now diminishes from this
latitude onward very nearly up to the pole itself. Thus arise two
belts of high pressure which the averages show as nearly continu-
ous but with easily recognized separate nuclei, but which the
individual charts show as broken up into many parts.

These two belts of high pressure are regions of descending currents
as is recognized by the clouds.

Moreover, here the movements of the air are feeble since the kinetic
energy is materially diminished by reason of the enormous change
in section that the air currents experience in their transition from
horizontal to vertical motion.

The trade winds blow on the equatorial sides of the two belts of
high pressure except at the point of interruption introduced into
the whole system by the monsoons; on the polar sides, at least at
great altitudes, the conditions are fulfilled that according to Helm-
holtz must give occasion for whirlwinds to originate.

Thus in these regions cyclone follows after cyclone separated
from each other only by ridges of high pressure as they are carried
eastward in the great whirl that surrounds the pole. But the anti-
cyclones are portions of the ring of high pressure and the tempera-
ture conditions are an important consideration in determining the
locations of their central portions in so far that they always seek
relatively cold regions and therefore in summer and in low lati-
tudes rest on the sea, but in winter and in high latitudes on the con-
tinents.

To these conditions is to be ascribed the fact that the ring of
high pressure in the southern hemisphere shows very closely the
form that is to be expected according to this theory, whereas that
of the northern hemisphere appears greatly modified.

Especially does the influence of the great Asiatic continent make
itself felt to such an extent that the nucleus of the great Siberian
anticyclone is pushed about 25° north from the latitude at which
the average atmospheric pressure for a whole circle of latitude
attains its maximum value. Whereas this value both in the annual
mean and also in the extreme months falls nearly on the 35th

348 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

degree of latitude,® on the other hand, the center of the Siberian anti-
cyclone in January is in the latitude of about 60° north.®

If we develop further the idea suggested in these few lines, we
perceive how easily and simply the average distribution of pressure
at the earth’s surface can be summarized.

The application of analogous methods of consideration to individ-
ual cases and the explanation of definite single phenomena by the
cooperation of the general circulation with local conditions may for
years to come well form one of the most important subjects for
investigations.

A complete and rigorous solution of such questions will indeed
offer very great difficulties and it cannot yet be foreseen when that
will be successful. Hence at first we must satisfy ourselves with
considering especially simple cases from the point of view just
explained.

But first it appears to be important to establish simple criteria
showing whether the temperature and moisture conditions alone
suffice to explain the facts of very definite phenomena or, still
better, those of any given cases of cyclones or anticyclones, or
whether and to what extent we have to consider the coédperation of
motions whose causes lie outside the given whirlwind or at least
outside the portions immediately considered.

The object of the following lines is to make a contribution in this
direction, so that in general it has the same object as the above-
mentioned investigations of Hann. But while in the latter the
main feature consisted in the discussion of data of observation
where the temperature conditions especially were considered; on
the other hand, here theoretical considerations will be carried out
and especially will the atmospheric pressure and the wind be con-
sidered.

The question as to the influence of the general atmospheric circula-
tion on the processes within a cyclone, always assuming a stationary
or steady condition may be formulated as follows:

“Does the actually existing distribution of pressure and tempera-
ture suffice to completely explain the simultaneous observed motions
or does it not?”

Or, in other words,

°’ Sprung: Lehrbuch der Meteorologie; Hamburg, 1885, p. 193. In the
following pages I shall frequently cite this work instead of the original mem-
oirs, since frequently the latter can be obtained only with difficulty and since
the references will be found in the work of Sprung.

® Hann: Atlas of Meteorology. Plate No. VII, Gotha, 1887.

THEORY OF CYCLONES—VON BEZOLD 349

“‘Are the movements observed within a cyclone exclusively the
consequence of the presence of the lighter air at its center or, con-
versely, is the latter wholly or partly the consequence of these
movements, in which case these latter must, of course, result from
exterior causes?”

If we consider only a portion of the whirl, then an affirmative
reply to this last question only shows that the cause of the motion
must lie outside the portion under consideration without forcing
us to seek it outside the whole whirl.

Unfortunately, even the simple question whether in any portion of
the whirl the observed movements are wholly explained by the dis-
tribution of pressure cannot be answered in its generality because
one must still make some more or less arbitrary assumptions as to
the coefficients of friction and as to the influence of neighboring
strata.

* On the other hand, this question can be at once answered in the
negative if the so-called angle of deflection (of the wind from the
gradient) is equal to or greater than 90°, that is to say, if the direc-
tion of the wind agrees with the isobar or has a component against
the gradient.

For under such conditions work is being done that can not be due
to the gradient force present in the cyclone or in the portion of the
cyclone under consideration, since in the first case the gradient force
is perpendicular to the direction in which the work (which consists
of overcoming the friction) is being done; whilst in the second case
there must exist a component of force that is directed oppositely to
the only one that can arise from the distribution of pressure.

Of these two cases, the first is easily accessible to mathematical
treatment, and therefore the following remarks apply to it, that is
to say, this investigation is confined to cyclones with circular iso-
bars and winds whose direction coincide with such isobars, or accord-
ing to Sprung’s notation’ to cyclones of circular symmetrical form
and having angles of deflection of go°.

Perhaps such cyclones might be designated as ‘‘centered cyclones”
or in general such whirls as ‘‘centered whirls” by analogy with
““centered optical systems.”

Now it might appear as if by the limitation of our consideration
to such centered whirls we have pushed the specialization of the
problem to the furthest limit and thus rendered the results quite
valueless. But this thought is not quite justified, for, on the one

7Sprung: Lehrbuch, p. 208.

350 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 52

hand, the synoptic charts show that in strongly developed cyclones
the winds very frequently favor the isobars, i. e., the direction
agrees with that of the tangent to the isobar; and, on the other hand,
we are not yet able in theoretical investigations to free ourselves
from the simplifying assumption of circular isobars.

On the other hand, I can but think that the investigation of this
simplest case should suffice to considerably further our understanding
of the cyclonal and anticyclonal motions and illuminate many points
in reference to which an incorrect view has often been maintained.

Moreover, the centered whirl or the centered portion of such has a
special interest in that it represents the limiting case between
whirls with centripetal and with centrifugal motion or between the
corresponding portions of such a whirl.

It is now necessary first to express exactly the fundamental con-
dition for the existence of the centered whirl, which is very easily
done.

Three forces are acting on every particle of the whirl; the centri-
fugal force p, arising from the rotation about the axis of the whirl;
the deflecting force p, of the earth’s rotation, which we can also
represent as a centrifugal force directed toward the center of curva-
ture of the inertia curve; finally, the gradient force I’ which is the
force arising from the difference of the atmospheric pressure.

In a centered whirl, in which each particle describes a circle,
these three forces all act in the direction of the radius of this circle
and it is only the directions of each that differ according as they
have to do with a gradient directed inward or outward, i. e., with
cyclonal or anticyclonal rotations and distributions of pressure.

The fundamental condition for the maintenance of a centered
whirl is therefore

Poa BAP P SO aoe see eee

where the summation is algebraic and we must first give each quan-
tity its correct sign.

If we consider the absolute values of the quantities p,; p,; and
as known and give each its proper sign, then we have to distinguish
four cases:

(A) Cyclonal rotation with gradients directed inward, or, as
we may appropriately say with cyclonal distribution of pressure.
In this case, which we see presented in the lower strata of the ordi-
nary cyclones, p, and p; have the same signs, but J” the opposite
sign and thus the equation reads

THEORY OF CYCLONES—-VON BEZOLD 351

(B) Cyclonal rotation with gradients directed outward, i. e.,
with anticyclonal distribution of atmospheric pressure. These con-
ditions are met within the upper strata of cyclones with warm cen-
ters. Here the gradient is directed outward but the curvature of
the orbits of the particles of air must be cyclonal up to very con-
siderable altitudes, since the movement of rotation that the mass of
air has under the ordinary conditions brought up from the lower
strata cannot immediately disappear.’

But under these conditions the whirl cannot be centered, since
the equation appropriate to this case, viz: .

is ea am PL =1 Lak cas ea aM)

cannot be fulfilled; hence perfect equilibrium must prevail, that is
to say, each of these three quantities must be equal to zero.

(C) Anticyclonal rotation with gradients directed outward hence
with anticyclonal distribution of pressure. These are the conditions
that we usually meet with in the lower part of the anticyclone.

In this case the equation of condition for the centered whirl is

| es | ss a leo. See ee er een eda ee (5

Although theoretically this is not impossible yet this equation may
still be practically meaningless, since the relations in the lower
part of the anticyclone are always such that an agreement of wind
direction with the isobars is not imaginable. Thus there remains at
best only the very highest portions of the cyclones with warm cen-
ters, in which, indeed, anticyclonal distribution of pressure must
prevail and where perhaps anticyclonal movements of the atmos-
phere can also be present, provided that this system extends so
far upward that the moment of rotation in cyclonal direction as
brought up from below is already completely consumed in over-
coming the resistances.

But since we have no basis of facts for the investigation of this
question it will be better to lay it entirely aside.

8’ The scheme of atmospheric motions in the upper portion of a cyclone
deduced by Clement Ley (Quarterly Journal Met. Soc. London, 1877, III,
P. 437) from observations of the cirrus clouds corresponds to this presentation
of our second case. We attain the same result if we think of a cyclonal move-
ment in which the paths of the air particles are more and more straight-
ened out by the forces p,, p; and J" all acting in the same direction until
finally the paths are curved in the opposite or anticyclonal direction while
the velocity of the outflow increases and at the same time the whole system
is carried eastward in the great whirl of the polar region.

352 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. ‘55

(D) Anticyclonic rotation with gradients directed inward, viz:
with cyclonal distribution of pressure. In this case the condition
as to centering is

Dp Ppl D oe Nine socio

As to this equation also it is doubtful whether it has any practical
importance. In general, in the lower strata of the atmosphere we
meet only with the above-mentioned cases (A) and (C).

We usually assume that in the upper portion of the anticyclone
there is a cyclonal distribution of pressure, that is to say, a gradient
directed inward,® since we consider this necessary in order to explain
the’inflow of air from above. But the presence of such a distribu-
tion of pressure in the upper half of an anticyclone has, so faras
known to me, never been shown by any facts; on the contrary,
thermodynamic considerations make it in the highest degree improb-
able that the low temperatures observed at the lower surface of the
so-called cyclones with cold centers extend to any considerable
altitudes. But if this latter is not the case then also the assumed
change in the curvature of the surface of equal pressure (which
should generally pass from convex above, at great altitudes, to
concave above, at lower altiudes) will not exist. Consequently the
flow in the upper regions toward the anticyclone is not to be
explained as the result of a gradient directed inward, but rather
dynamically as a heaping up phenomenon due to obstruction.

However, if in individual cases the assumption of a cyclonal
distribution of pressure in the highest part of an anticyclone should
be correct, as has hitherto ordinarily been assumed, still by reason
of the slight moment of inertia that is ordinarily present in an
anticyclonic whirl there is no reason why the direction of the rota-
tion should remain the same over extensive regions, as in the case
of cyclones where the pressure distribution is of the opposite type.

These considerations show that of the four cases of centered whirls
that can be imagined, only the first mentioned has any practical
importance in meteorology and the following lines are therefore
devoted to its consideration.

Therefore we consider here only a4 whirl with barometric gradients
directed inward, circular isobars, and cyclonal motion of the air,
under the special assumption that the directions of the wind agree
everywhere with those of the tangents of the isobars.

Under these conditions the equation

oe an aE 2+2;-C =0
® Sprung: Lehrbuch, p. 211, fig. 39.

THEORY OF CYCLONES—VON BEZOLD 353

must be satisfied and the problem consists essentially in the dis-
cussion of this equation.

Consider a special isobar and ‘let its radius be r,, the radius of
curvature of the inertia curve 7;, and the velocity of the wind along
the isobar v, then for a particle of air whose mass is m moving along
the isobar in the prescribed manner we have

y
Pe = mM
ro
and
yy
i i

Let the whole process go on at the geographic latitude y and for
simplicity assume that this latitude is the same for all points of the
cyclone, which of course cannot be the case but will cause no great
error if we assume an average value for g; finally, let T be thelength
of the siderial day expressed in seconds of inean solar time, then we
have’?

vT
ere
z Sin ©
or
4xzmv
p= a. sin @
whence

47 P :
Put k = 0.0001458 = - and I’ = my, where; is the acceleration

communicated to the mass m by the gradient force J’, then the pre-
ceding equation assumes the simpler form

v
y=) + vksing bane epealicen aah ac el)

c

But for the acceleration ; we also have the equation

G 13.6
tibia

g = 0.000 122 87 G Bi fen)

10 Sprung: Lehrbuch, p. 24.

354 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

where G is the gradient, i.e., the difference of barometric pressure
between two points distant from each other by one degree of the
meridian, or 111,111 meters on the spherical surface of the earth,
and in the direction of the maximum change of pressure.

But we also have

h .
f= Pos Pp tan otc. 2 ee ane eee

l
where hi is the altitude by which the surface of equal pressure (iso-
baric surface) drawn through the point under consideration, rises
or falls in the course of the horizontal distance /, and where a is
the angle that the surface of equal pressure at this point makes with
the horizon.

Therefore the acceleration that is given to the air by the gradient
force is equal to that which a heavy point experiences when it glides
without friction along an imaginary rigid isobaric surface, at least
in so far as a is small enough to allow us to consider sine a as equal
to tangent a, which is always thecase in our problem." Theacceler-
ation due to gliding down such a surface is g sin a, whereas the force
g tan a acting on the point horizontally, is required to prevent the
gliding downward.

If we substitute in (7) and (8) the value of 7 given in equation
(6) and write r instead of r, since the quantity r; no longer occurs
in the problem, then the equation of condition for the centered whirl
finally assumes the form

G :
0.000122 37 ¢— =— + ok sine. ~). oe a)
Ne g
or if # is the barometric pressure
2
pede ed FUR aa. . eee ee tee ae
ea? 5 ae
or finally
2
gtana="+vksing. se Stk) ee
r

In my original memoir the first deduction and formulation of this theorem
was attributed to Moeller, but it is due to Hann, who first gave it in his mem-
oir ‘‘On the relations between wind velocity and differences of pressure
according to the theories of Ferrel and Colding,’’ Zeit. d. Oest. Gesell. f. Met.
1875, X, pp. 81-88, 97-106. Compare also my memoir of 1901, XVIII of
this collection of translations. (Note added 1906. W.v.B.) [My transla-
tion of Hann’s memoir will be foundin my ‘‘ Short Memoirs,’’ Smith. Rept.
1877.—C. A,]

Ee

THEORY OF CYCLONES—VON BEZOLD 305

which equation can be still further simplified in special cases since
we can consider g to be constant and put

ksing = K.

The first fofm of this equation could also have been deduced
directly from the fundamental equations of Guldberg and Mohn,
giving attention of course to the algebraic signs” here adopted.

The second form is more convenient for application to special
cases drawn from the synoptic weather charts especially when in
place of tan a we introduce the value

h ar
1° Gh

For definite values of pressure and temperature the heights h can
be taken directly from tables which give the heights of columns of
air corresponding to a pressure of 1™™, such as Table V of Mohn’s
“Grundziige,”’ whilst the distances of the isobars corresponding to
differences of pressure of 1™™ are measured directly on the weather
chart.

Suppose, for instance, we wish to determine the inclinations of
the isobaric surfaces for northern England, for points between
Shields and Bradford, from the weather chart of October 14, 1881,
as published in Sprung’s Lehrbuch, Plate VII; we first find for h the
value 11.4 meters, for the pressure 730™™ and the temperature
10° C. then prevailing; for the distance between the isobars 725™™
and 753™™ we find 180 kilometers and therefore / = 18 kilometers
or 18,000 meters for the distance between 729 and 730 or between
730 and 731™™, whence follows

1.4

Sey ee fe Ost 36
18000

tg a

This example is interesting in that it shows very clearly how
remarkably slight in general is the inclination of the isobaric sur-
faces, since even for the great atmospheric disturbances that pre-
vailed in that region on that day one must go northward 18 kilo-
meters in order to experience a change of pressure equal to that
found by rising vertically only 12 meters.

If now we seek to draw some general conclusions from equa-
tion (9) then we perceive, first of all, that it is essential to the exist-

2 Sprung: Lehrbuch, p. r19, equation (5).

356 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 51

ence of a centered cyclonic whirl that very precise relations must
exist between the wind velocity and the distribution of atmospheric
pressure.

Hence in all cases where the wind circles about a center in the
strict sense of the word there must be a very exact distribution of
pressure that renders possible the continuation of such a whirl,
and inversely for every symmetrical circular distribution of pressure
there must be corresponding definite velocities belonging to it.

The entire omission of the friction in this theorem implies the
assumption that this is overcome by forces that do not appear in
this calculation, as, for instance, the difference of velocity in neigh-
boring strata which on its part must of course be maintained by
causes that are outside the region under consideration. In no case
can these resistances within a centered whirl be overcome by the
forces arising from the distribution of pressure, and this is a funda-
mental point for the following discussion.

The questions that interest the meteorologist with reference to
the centered whirl are the following:

(1) Are there really any cyclones that show, at least at the earth’s
surface itself, such a distribution of pressure and wind as must
exist in the centered cyclone?

(2) Can these conditions be satisfied simultaneously in layers
of great vertical extent, under the conditions prevailing in our
atmosphere, or is it improbable that a cyclone that appears as a
centered whirl at the earth’s surface may also possess the same
peculiarity at greater or even only moderate altitudes?

(3) When the equation of condition (9a) is not satisfied but
when departures therefrom are present in any given direction, what
conclusions can be drawn from that fact?

Let us consider the formula

v ;
giga= —+vk sin g
re
from the point of view proposed in the first of these three questions,
after writing it in the simpler form

2
giga=—+uK
r

since r; no longer occurs in the following discussion and since we
may always limit the investigation to some one definite value of ¢.
We note, first, that for diminishing values of 7, i. e., with approach
toward the center, the inclination of the isobaric surface, or the

THEORY OF CYCLONES—-VON BEZOLD 357

gradient, must increase, except in so far as a compensation does not
occur by reason of a simultaneous diminution of velocity. This
increase of inclination or gradient must obtain to a still larger extent
when the velocity v also increases with approach toward the center.
In immediate proximity to the center, even with a uniform velocity
for the innerand the outer rings the gradient becomesinfinite, which
of course is impossible. On the other hand, the increase of the
centrifugal force due to the diminution of r can be counteracted or
even overcompensated bya corresponding diminution of the velocity
so that in the immediate neighborhood of the center the gradient
again diminishes precisely as has been frequently observed. We
see from what has just been said that at least so far as we limit our-
selves to a purely qualitative consideration of the subject the rela-
tions here expressed as the condition for the existence of the cen-
tered cyclone are in reality frequently met with, and that therefore
the existence of centered cyclones is by no means improbable.

Even when we study the matter more closely and numerically we
come to the same conclusion and find that cyclones which are at
least approximately centered at their base, can scarcely be said to
be rare.

In order to acquire a starting point, I have computed the wind
velocities that would be necessary in order that a cyclone should be
centered when the pressure distribution issuch as Sprung™ found for
the average of four well-developed cyclones.

The velocities that I found for the respective distances from the

center are
Distance Velocity

Kilometers Meters per second
100 10.8
200 20.7
300 21.4
400 23.0
600 18.0
800 13.3
1000 10.4

and these numbers are not contradictory to the wind velocities read
off from the synoptic charts for the respective days.

This is still more easily seen if we assume that the cyclone is
located at latitude 45° and that in the portions under considera-
tion the prevailing temperature is 10° C. and pressure 730™™; or

F §
n5 C. and 745™™, etc.; in such cases 0.co012237 — = 0.001 and
0
0.0001458 Sin g = 0.0001031 or nearly 0.0001.

18 Sprung: Lehrbuch, p. 150.

358 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Under these assumptions the equation (ga) assumes the very
simple form

0.001 G = eZ + 0.0001 v
f

or, if we indicate by £, and £, the pressures at the two ends of a line
whose length is one degree of a great circle, lying in the direction of
the gradient, this becomes

G8 p= 1600 = 0:0Ly ee ee
ji

From this we at onceconclude that in centered whirls there must be
pradients of 2™™ or 11™™ or 1o1™™ per degree of a great circle,
at distances of too kilometers, 10 kilometers, and 1 kilometer
respectively from the center, where there is a wind velocity of 10
meters per second at these points.

Gradients like ror ™™ per degree never occur or at least only over
very limited regions, and ro meters per second is not a strong wind,
but from this paragraph we see very clearly how powerfully cen-
trifugal force comes in play even in moderate winds in the neighbor-
hood of the center, and how remarkably large the gradients must be
(nearly four-fold when v = 20 meters per second) if centrifugal move-
ments are not to replace centripetal.

But in ordinary cyclones, beginning at a definite and often consider-
able distance, the wind velocity diminishes with approach to the
center and soalso does the magnitudeof the gradient, so that evenin
this portion the whirl may remain centered, as was already shown in
the above case of an accurately defined example of the typical cy-
clone.

However, the idea seems not to be excluded that even in these
latter, descending currents may replace the ascending, whenever at
moderate altitudes centritugal movements replace the centripetal,
and in sofaras the masses of air required to supply these cannot be
obtained from below. At least the diminution of the cloudiness in
the neighborhood of the center, which is often recognized as the
“eye of the storm,” speaks very decidedly in favor of this conclu-
sion.

On a subsequent page we will explain how these conditions adjust
themselves in the tornadoes proper and in the waterspouts.

In the second place, we will inquire whether it is probable that a
cyclone that is centered at its base will also possess this peculiarity
at greater altitudes.

THEORY OF CYCLONES—VON BEZOLD 359

Of course this question would be at once answered affirmatively if
it were allowable to assume that the wind movement and the baro-
metric gradient were uniform above every point of a large portion
of the base of such a cyclone.

But since this is only true in exceptional cases and in layers of
moderate thickness, therefore the question is to be modified to the
inquiry whether changes of the two elements in question, such that
the condition of centering still remains fulfilled, are conceivable.

We most easily attain a summary view of these relations by the
following consideration:

Let z be the altitude of a point above the horizontal base, then
in the case of a symmetrical circular form for the whole whirl, we
have the equations

B=7( 2)

v= @(r 3)

and

Making use of equation (9b) and recalling that

B 273
Pea Be ie

where py = 1.293, 8 = 760, and T is the absolute temperature, we
can put this equation in the form

giels-6 Ede eH a
ee tiG Toda ean:

or, if T is constant for each horizontal plane or for every value of
z considered as constant, this assumes a still simpler form

If now we consider the relation above assumed according to which

Pt OAra a)

df
then, instead of the total differential quotient aA we have the partial

differential quotient and get
ie’ 20Gb) 4 [ONG.2)i"
BS acdtied eepialae

SO roan. a 3s 2s KLE)

360 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

This equation shows us that for every given symmetric circular
distribution of pressure there is a system of velocities, for which the
whirl becomes a centered whirl, and that, conversely, for every
system of uniform circular motions about one and the same axis,
provided these merge continuously into each other, there is a definite
distribution of pressure for which these motions are permanent or
steady, that is to say, they correspond to the conditions of the cen-
tered whirl: but of course this is true only insofar as we can neglect
the frictional resistances.

First assume the distribution of pressure as given and imagine the
isobaric surfaces to become suddenly rigid and that velocities such as
are indicated by equation (11) are communicated to heavy points
movable without friction along these surfaces, then these will all remain
on the horizontal circles and move forward as before in similar
manner, since in this case there arises from the resistances of the sur-
face a force directed inward that holds in equilibrium the force giga
directed outward.

In this case the acceleration in the direction of the slope that is
communicated by gravity to a heavy point resting on the surface is
g sina, whereas the component of the outwardly directed horizontal
force g tg a that raises the point upward along this surfaceis g tana
cos a, that is to say it is g sin a also.

Whenever the velocities at any point whatever, or along any
horizontal circle whatever, become greater or smaller than those
required by equation (11) then the point will rise or fall respectively.

Therefore these velocities given by this equation for any particular
distribution of pressure are called the ‘‘critical velocities,’’ whereas
the isobaric surfaces given by this equation (11) for any particular
set of velocities will be called ‘“‘critical surfaces.”

But the gradient corresponding to this critical distribution of
pressure will be known as the “‘critical gradient,” in distinction from
the ‘‘effective gradient”’ ordinarily present, so that the fundamental
condition for the existence of a centered whirl may be expressed
thus: “In centered whirls the isobaric surfaces must coincide with
the critical surfaces and the effective gradients must equal the
critical gradients.”

By the help of this theorem we at once see that it isnot at all prob-
able that a cyclone that is centered at the earth’s surface should also
possess the same peculiarity at great altitudes.

The distance between two isobaric surfaces is in general through-
out their whole extent subject to only moderate variations, since
it is simply proportional to the absolute temperatures prevailing at
the various locations.

“ce

|
|

—."

THEORY OF CYCLONES—VON BEZOLD 361

Hence in the cyclone, on account of thediminution of temperature
with altitude (even when the temperature at the’ earth’s surface does
not diminish with distance from this axis, as is the case in cyclones
with warm centers), the isobaric surfaces will gradually approach
each other with increasing distance from the axis, but this approach
will always be relatively slight.

It is entirely different with the critical surfaces; these rise very con-
siderably as one proceeds outward while the velocities increase with
the altitudes.

Since in general the second term of the equation comes only slightly
into consideration, therefore the inclination of the isobaric surfaces
increases very nearly with the square of the wind velocity.

If, therefore, in any cyclone the isobaric surfaces are such as is
shown by the full lines in fig. 55, and this frequently corre-
sponds to the actual conditions, and if this cyclone is centered for the
horizontal section A A, then it will not be so above or below this
section as the velocities increase with altitude.

FIG. 55. ISOBARIC SURFACES AND CRITICAL SURFACES IN A CYCLONE

Under this assumption the critical surfaces are arranged as is
suggested by the dotted lines in fig. 55, and therefore agree with the
isobaric surfaces only at the section A A, since there they have the
same common tangents.

“Above this section the centrifugal forces are greater than the
gradient forces directed toward the axis and therefore movements
must occur opposed to the gradients.”

Hence the surfaces of this section A A, which is not necessarily
a plane but is here thought of as such for simplicity only, is the
boundary between a region of centripetal and centrifugal move-
ments.

At the same time we easily see that such a reversal in the direction of
the movement must occur without change in the sign of the gradients
when the motion at the surface of the earth becomes approximately
circular. For since the velocities of the wind increase rapidly with
the altitude as shown by experience, while the inclination of the sur-
faces of pressure generally shows a diminution, therefore such a move-

362 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

ment as that above considered, which has a feeble centripetal com-
ponent at the earth’s surface, must change into a centered whirl as
it extends into higher strata and eventually in fact into a centrifugal
whirl.

Therefore the second of the questions above formulated is to be
answered negatively and to the effect that it is most improbable that
cyclones should remain centered through any considerable vertical
extent. We are rather to expect centrifugal movements in the
upper portions of such cyclones even if they must proceed against
the gradients.

The preceding section, which was devoted strictly to answering
the second of the three questions above formulated, contains also
the reply to the third. This latter refers to the conclusions that can
be drawn from the non-fulfillment of the conditions that apply to the
centered whirl.

By the introduction of the idea of the critical surfaces these con-
ditions can be expressed in the following simple form: ‘‘In centered
whirls the critical surfaces and the surfaces of equal pressure must
coincide.”

According to what precedes, the inclination of the isobaric surface
measures the magnitude of the effective gradient toward the axis,
but the inclination of the critical surface measures the component
of the force directed from the axis arising from the centrifugal
force and the rotation of the earth.

If therefore at any given location the critical surface has an
inclination less than that of the isobaric surface, then we have to do
with a resultant directed inward or centripetal, but if the critical
surface is more strongly inclined than the isobaric surface then the
resultant is outward or centrifugal.

But in this matter we must recall that even for symmetrical circu-
lar isobars the critical surfaces are surfaces of rotation only when the
atmospheric motions proceed in circular whirls whose planes are
perpendicular to the axis and whose centers also lie in this axis.

But under these conditions the centered condition is unstable
unless the isobaric surfaces and the critical surfaces have the same
inclination at every point and coincide throughout the whole region
under consideration.

Notwithstanding this instability the study of this case, which is
of course only to be thought of as a transition stage, has some
interest in that, as already mentioned, the observed movements actu-
ally do come extraordinarily near to being circular, whereas, on the

1 vee pe em, «

THEORY OF CYCLONES—VON BEZOLD 363
other hand, the generalization of the problem offers very con-
siderable difficulties. :

Nearly circular movements are to be observed, for instance, in the
case of tornadoes and waterspouts.

If now we apply the considerations just introduced, to these latter
cases, we find that the critical surfaces have extraordinarily large
inclination near the axes and hence there must be present enormous
[counteracting barometric] gradients if these circular movements
are not to turn into centrifugal movements. For instance, from
the approximate formula (10) for r = 10 and v = 30 (or for a
wind velocity of 30 meters per second at a distance of 10 meters from
the axis) we find a gradient of 90,000, 1. e., a diminution of pressure
of 0,81 ™™ for 1 meter of approach to the axis.

Under the given assumptions, the inclination of the critical sur-
face will be about 84°.

If then such motions are maintained at the cost of the energy that
is gained at other points, then great rarefactions of the air must
take place in the neighborhood of the axis that can be computed
when definite assumptions are made as to the diminution of the
velocity with the distance from the axis.

Such computations have already been made for the tornado by
William Ferrel! which he considered as a simple centered whirl and
for which he represented in a diagram the form of the isobaric sur-
faces which, under the assumption of the given velocities, are the
same as our critical surfaces.

It would therefore scarcely be necessary here again to touch on
this point, but that it seems to me that in one respect different con-
clusions are to be drawn from these studies than those drawn by
that investigator.

The enormous gradients that must prevail in a very thin mantle
enclosing the axis of a tornado, if there are to be no centrifugal
movements, make it very improbable that any air penetrates this
mantle from without and moves inward to the axis, or that any
centripetal movements occur.

In order to bring about such movements the isobaric surfaces
actually existing must be more strongly inclined than the critical
surfaces, or, which comes to the same thing, the effective gradients
must be still greater than the critical gradients, which themselves
already have such extraordinary large values.

But if there be no continuous flow of air inward toward the axis

14 Sprung: Lehrbuch, p. 224.

364 SMITHSONIAN: MISCELLANEOUS COLLECTIONS VOL. 51

then the existence of an ascending current in this axis itself is not
conceivable.

On the contrary, I would rather hold it to be probable that in
the axial tube no important vertical movement takes place, but
that this is essentially a moving rarified space, whereby new par-
ticles of air are being drawn into the motion and thus subjected to
the rarefaction.

The assumption of an ascending current in the axial tube is also
by no means necessary, since Ferrel has proved that the rarefaction
of the air produced by the centrifugal force, when no addition of
heat comes in, is sufficient to explain the condensation and the
origin of the filmy cloud. This is quite natural when the trunk of
the cloud axis is first recognized as an appendix hanging below a
cloud and appears to gradually descend lower, since in the earlier
stages of the development of this phenomenon where the friction at
the earth’s surface does not come into consideration, considerable
velocities will occur, which might cause rarefaction of the air and
hence the condensation. Moreover, the air must be most nearly
saturated directly beneath the cloud and hence it requires only very
slight rarefaction of the air to bring about condensation.

It is only when the velocities in the lowerstrata of the atmosphere
have acquired a corresponding increase, that the rarefaction pro-
ceeds to such a degree that the cloudy film extends down to the
earth.

But we are not to conclude from this that the cause of the whole
phenomenon is to be sought in the upper regions; rather is it to be
expected that in even the cases where the process is initiated by over-
heating of the lowest strata of air and the unstable equilibrium
produced thereby, still the larger velocities will be attained at great
altitudes sooner than below.

For since after breaking up the unstable equilibrium the accelerat-
ing forces increase with altitude, therefore not only does the ascend-
ing current (which is to be thought of not as exactly in the axis of
the subsequent tornado but as extending over a large area) itself
acquire steadily increasing velocities, but this is also true especially of
the currents of air streaming inward from all sides, since with increas-
ing height slighter resistances oppose its motion.

In general, the fact that the axial cloud appears to descend from
above justifies no conclusion whatever as to whether the true cause
of its origin is to be sought for above or below.

Neither are we to draw any conclusion from the apparent descent
of the cloud-axis as to any descending movements in its interior.

THEORY OF CYCLONES—VON BEZOLD 365

On the contrary, the existence of the cloud proves that in any such
case these descending motions, which in themselves are not improb-
able, cannot be very important since otherwise adiabatic compres-
sion must occur and thus cloud formation would be impossible.

The matterds somewhat different in the case of large cyclones, for
there it is quite conceivable that in the beginning of these or in case
of their rapid development in the median strata of the atmosphere
(which may either be due to the general circulation or be a result
of local expansion of the air), air may be drawn in as easily from above
as below. .

By simple modifications of the above-given figure we can also
obtain systems of critical and isobaric surfaces in which the down-
draft must extend down to the earth’s surface so that a natural
explanation is found for the so-called ‘‘eye of the storm,” as also
for the remarkable dryness observed in the interior of a cyclone, as,
for example, in the hurricane of 1882, October 28, at Manila.

The investigations which I have here carried out started with the
consideration of the centered whirl. Notwithstanding the limita-
tion to this very special case they seem sufficient to remove the
characterization of abnormal or inexplicable from the peculiar rela-
tions that Hann has shown to exist in cyclones with cold centers and
anticyclones with warm centers.

Not the less arethey appropriate to lead us back to a abtteet
appreciation of the views defended by Faye as to the descending
currents in the interior of cyclones and within certain limits pre-
pare the way for a reconciliation between this idea and that which
has become almost universal.

% Sprung: Lehrbuch, p. 24.

#* Similar phenomena may also be reproduced in rotating liquids. In
these we can even develop whirls in which ascending movements occur in the
mantle but descending in the axis. See v. Bezold. Sitzb. Berlin Acad.,
1887, pp. 261-277.

AVI

ON THE REPRESENTATION OF THE DISTRIBUTION OF
ATMOSPHERIC PRESSURE BY SURFACES OF EQUAL
PRESSURE AND BY ISOBARS

BY PROF. DR. WM. VON BEZOLD

[Archives Néerlandaises des Sciences exactes et naturelles, Series II, Tome VI,
bp. 563-574, 1901. Translated from Gesammelte Abhandlungen von
W. v. Bezold, Berlin, 1906, pp. 306-315]

In order to obtain a clear idea of the distribution of pressure in
the atmosphere we imagine surfaces of equal pressure extending
through the atmosphere for a series of pressures differing from each
other successively by a given constant difference. As such con-
stant we most frequently adopt 5 millimeters, that is to say, we
consider surfaces for which the pressures are given in millimeters by
the equation

B= 70+5n

so that the constant difference is 4 @ = 5. In special cases we may
also choose 4 8 = 2.5 or 4 B = 1.0™™,

If now we seek the ‘‘traces’’ or intersections of these surfaces with
any other surface of known location and form, then we obtain lines
of equal pressure or isobars in the most general sense of this term.

As such surfaces of known location and form we choose either
“level surfaces of gravity’’ in which case the traces are isobars in
the ordinary sense, or we seek the intersections with a vertical
surface in which case we speak, but not quite correctly, of the repre-
sentation by means of “‘baric surfaces.”

Both these methods of presentation have their special advantages
and disadvantages which I will elucidate more clearly in the follow-
ing lines.

If it be not possible to avoid restating many well-known points,
still I imagine such reconsideration by no means superfluous, since
it would appear that many of those who daily make use of either
of the two methods of presentation, in spite of the publications of

366

ee

DISTRIBUTION OF ATMOSPHERIC PRESSURE—VON BEZOLD 367

R. v. Miller-Hauenfels!, Nils Ekholm,? and V. Bjerknes,? stilldo not
appreciate the different peculiarities of these surfaces and lines as
perfectly as is desirable. 3

Especially is this true as to researches on the processes in the upper
strata of the atmosphere, researches that have acquired increased
interest in recent times.

One of the principal questions that comes up in the consideration
of an irregular distribution of atmospheric pressure is as to the
accelerations that the particles of air experience in consequence of
this irregular distribution. Most important is the acceleration in a
horizontal direction, that is to say, along the level surfaces of gravity.
Since the component perpendicular to this direction is in general
very small, therefore it will here be ignored. The acceleration is
greatest in the direction of the greatest change of pressure, that is
to say, in that of the greatest so-called gradient.

This acceleration I will call the gradient acceleration and will
designate it by the letter ;.

In the following paragraphs we will more exactly investigate how
useful the two above-mentioned methods of presentation are in
the determination of this quantity. Especially will be considered
to what extent even a casual consideration of them allows of an orien-
tation in this direction.

To this end it is necessary to discuss more minutely the well-
known formule for this acceleration. Ordinarily one makes use of
the equation

G 13.6

‘ = pene eR A) La ey ee ee Ae:
r 1 1 gE 3 ce)

where G is the so-called gradient, or the difference in millimeters
between the barometric readings that prevail at the ends of a
straight line 111,111 meters long whose direction coincides with that
of the greatest change of pressure; » is the density or the mass in
kilograms of air contained in a cubic meter; and g is the local acceler-
ation of gravity expressed in meters per second. The, negative
sign that should be prefixed to this and the following formule I
omit since I consider only the numerical or absolute value of ;.

Since we cannot assume that the change of pressure is actually

1 Theoretische Meteorologie. Vienna, 1883.

2 Bihang till, K. Svenska Vet. Akad. Handlingar., Bd. XVI. Abt. 1,
No. 5 Stockholm, 1891.

3K. Svenska Vet. Akad. Handlingar, Bd. XX XI, No. 4, Stockholm, 1898.

368 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

uniform throughout such a long distance, it would be more correct
to put this equation in the form

| re ee ee ria © 2)

where d # expresses the change of pressure for the elementary dis-
tance d/in the direction of the greatest barometric change. Hence
the value of G should be deduced from the equation‘

Cc} nn os

dl i ee I

Finally for many points of view it is very advantageous to write

é dB Ap

where 4 ? indicates some definite change of pressure and / the dis-
tance in the direction of the greatest gradient to which one must go
untila difference of pressure 4 7 is attained, assuming a uniform baro-
metric gradient.

Thus the formula assumes the form

aS Se a * pp ocak aonb raeed ails)
L
Instead of these three formule which I will speak of collectively
as the formule (1) since they are in fact only different forms of the
same fundamental formula, one may also use the following very
different form

PS BIE Ge th cl Mas Se eee

where a is the angle that a surface of constant pressure makes with
the horizon, and always in the direction of the steepest gradient.

The formule (1) and (2) are closely associated with the two above-
mentioned geometrical methods of presentation that we used to
express the distribution of atmospheric pressure.

Since we can easily lay off a distance of 111, 111 meters or 111 kilo-
meters on any map, no matter what its style of projection may be,
therefore the formula (1a) is specially appropriate to such investiga-
tions as those based on the ordinary synoptic charts.

For this reason also in using formula (1a) one should not, as is
often done, speak of the length of one degree of the equator, since

‘Compare C. M. Guldberg and H. Mohn: Etudes sur les Mouvements de
PAtmosphere, p. 18. Christiania, 1876. [Supra XI, p, 146.]

j
:
}

—————E— — —“‘“‘i—s OO

DISTRIBUTION OF ATMOSPHERIC PRESSURE—VON BEZOLD 369

many charts contain no portion of the equator, but should speak
of a degree of the meridian, or a degree of latitude, since on every
chart a portion of the meridian appears or can be easily drawn.
The degree measured on the meridian, therefore, under all circum-
stances corresponds closely to a length of 111 kilometers.

Therefore by comparing any distance on any chart with a degree
of latitude we can express it in fractions or multiples of 111, 111
kilometers.

Since the formule (1) collectively contain certain lengths (or
distances on the earth’s surface) therefore they are specially
convenient for studies based on the synoptic weather map. On
the other hand, they suffer from the defect that in contrast with
formula (2) they contain two variables, i.e., G and g or / and 9, or
strictly speaking three, since p itself depends on pressure and tem-
perature.

In the ordinary discussions we consider only one variable G, since
o is assumed to be constant.

But this is only a crude approximation for in fact

Bo ats jc Ge
P~Por6Q 273 +1 Sree °T
where for simplicity 2, = 760,T, = 273, T = 273 + ¢# or the abso-
lute temperature, and o, = 1.293, the value that assumes corre-
sponding to the normal pressure £, and the temperature T>.
If we substitute this value in the formule (1) and recall that
13,,.6 85 a 13.596 Bo

Po" To Po Ty
issimply the gas constant for dry air occurring in the law of Mariotte-
Gay-Lussac and which is ordinarily represented by the letter R,
then we have

= 29.272

T
way iit Bo a
dp T
paay phe arm = ee
ABT
pa GRE es

These formule contain altogether three independent variables,

i. e,,8, T and G, —or 8, T and oP ,— or 8, Tand / — instead of the one

dl’
independent variable that is implied in the ordinary approximate
consideration of this subject.

370° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Hence follow the following important consequences, which
are not always sufficiently kept in mind:

“For equal values of the gradient G the gradient-acceleration y
is inversely proportional to the density of the air, hence it increases
with increasing temperature and with diminishing pressure.”

Of course at the surface of the earth this difference in the density '

of the air is not generally of much importance, especially so long as
we consider only a small part of the surface. But if we do not thus
limit ourselves then its influence can in extreme cases certainly
amount to more than 30 per cent.

Assume, for instance, that at some place on the earth’s surface
the temperature is 37° C. and the barometric pressure 710™™, such
as can happen in whirlwind storms, but that at another place we

ie
have — 33°C. and 780™™, then the values of the quotient = at the

B

two localities will have the ratio 44/31, so that for equal gradients
the gradient-acceleration in the neighborhood of the highest pressure
will amount to only 70 per cent of that within the low pressure.

Even for smaller regions, such as those covered by our ordinary
weather charts, this influence can be considerable.

For instance, assume that in the center of a depression of 715™™
the temperature is 12°C., but in that of amaximum of 775™™ onthe
same weather map the temperature is — 33°C., then the ratio of the

NG :
two values of 8 is as 100/77 and for equal gradients the accelerations

at the two localities would have the same ratio.

Since now the examples here chosen, although slightly exagger-
ated, reproduce the conditions that are ordinarily observed in low
areas with warm centers and high areas with cold centers, therefore
we perceive that in general ‘‘the gradient-accelerations” near baro-
metric maxima would be greater than would be expected from
the gradient itself. It is only in the case of depressions with cold
centers that a partial compensation of the rarefaction of the air
due to the low pressure is brought about by the low temperature.
Therefore the lesser density of the air, such as generally occursin
the lows, contributes still further to increase the velocity of the wind
in this region independent of the closeness of the isobars, i. e., inde-
pendent of the strong gradients.

“Since now in front of the cyclones, where the air flows in from
the equatorial side, the temperature averages higher than in the
rear, so also in general for equal atmospheric pressure, i. e., along
any one isobar, the density of the air in front of the depression is

-_ ——————————————

DISTRIBUTION OF ATMOSPHERIC PRESSURE—VON BEZOLD S37r

less than in the rear and correspondingly the gradient-acceleration
is greater than would correspond to the average gradient.”’

However, even for equidistant successive isobars in the front of a
depression one must expect greater accelerations and correspond-
ingly greater vind velocities than in the rear.

Hence the isobaric charts directly allow a conclusion as to the
gradients in that according to formula (1c) these are always propor-
tional to the reciprocal of the distance between neighboring isobars,
but not any conclusion, or at least only a crude approximation, as
to the gradient-acceleration, which still depends to a large degree on
the density of the air.

Therefore the isobars can in no wise be compared with altitude
lines or isohypsen. For whilst we can from the reciprocal of the
horizontal distance of the isohypsen conclude directly as to the
gravity gradient, i.e., the tangent of the angle of inclination, and
thence as to the acceleration which a heavy point experiences when
it moves without friction on the given surface, we cannot do this
from the isobars. Such a conclusion would only be allowable when
the density of the air is uniform over the whole area under consider-

une TE.
ation, i. e., when B is constant.

But even in summer, when it is generally cooler at the base of the
cyclone than in the anticyclone, this condition is only seldom satis-
fied. For instance, in a region of maximum pressure 775™™ and
another of minimum 745™™ the temperatures must be respectively
27° and 16°C. if the densities are to be the same in both. Butmore
than this there is also the condition, which is almost never satisfied,
that the temperature be constant along each isobar.

If the temperature were uniform over the whole region covered
by a chart of isobars, then certainly we would be in a position to
draw a system of lines whose reciprocal distance would certainly be
proportional to the gradient-acceleration. The formula (1) can
be written

qpT
ora B an g
or
d log B
Ieee ap tae

From this formula by passing to differences we can deduce the fol-
lowing:

AlogB
aaa ERE

372 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5I

If in such a case of general uniform temperature, we draw a system
of lines in such a manner that the logarithms of the atmospheric
pressure proceed by equal differences, then to a high degree of
approximation, the accelerations will be proportional to the dis-
tances apart of the neighboring lines. The lines would then also
be truly comparable with isohypsen, at least so long as the inclina-
tion of the surface in question is so slight that we may consider the
sine and tangent of the inclination angle as equivalent.

From the preceding considerations it follows, that any conclu-
sions as to the acceleration effective at various points can only be
drawn with great care, even in the case of the ordinary charts of
isobars at the earth’s surface.

“The gradient is always inversely proportional to the distance
apart of the neighboring isobars; the gradient-acceleration is in
general greater in proportion as the pressure is smaller. If there-
fore we would adhere to the meaning ordinarily attached to the chart
of isobars, we must think of the isobars in the neighborhood of
the barometric pressure as being closer together than they really
are.”

If we draw isobaric charts for higher levels we incur danger of
drawing still more erroneous conclusions, unless we give special
attention. For instance, the chart for the altitude 5500 meters®
should have its isobars drawn for every 2.5 millimeters, since only
then will its appearance justify general conclusions such as those
suggested by the chart drawn for the sea-level (on which the iso-
bars are drawn for every five millimeters).

If from this point of view we consider the isobaric charts for alti-
tudes 5000 and 10,000 meters communicated by H. Hergesell to
the Met. Zeit. for January, 1900, we are surprised to find how enor-
mous the gradient acceleration is at these altitudes on these dates.

Indeed Hergesell himself intended to indicate this point in that
on page 27 he said that at an altitude of 5000 meters the same differ-
ence of atmospheric pressure corresponds to about twice the gradi-
ent, whereas he evidently should have said that the same gradients
at sea-level and at this altitude produce a gradient acceleration at
the highest level twice that at the sea-level.

It is evident from what precedes that the representation of the
distribution of atmospheric pressure by isobars on a level surface
of gravity has the important advantage of being easy to prepare and
of allowing of a comprehensive view of an unlimited extent of area

5 See the table No. 1, Memoir XIV, p. 309 of this collection of translations.

DISTRIBUTION OF ATMOSPHERIC PRESSURE—VON BEZOLD 373

of any such surface, but that as a basis for theoretical considerations,
especially of acceleration, it must always be used circumspectly.

It is quite otherwise with the presentation of atmospheric pres-
sure by a vertical”section, which, as before stated, has been desig-
nated by the inappropriate name ‘‘presentation by surfaces of
pressure.” This method is difficult to put into practice since the
pressure surfaces can be determined only by a roundabout process,
but it offers many advantages from a theoretical point of view.

It is because of this peculiarity that the ‘‘ vertical sections of iso-
bars,’’ as they should be called, are relatively seldom used and even
then almost never applied to specific cases, but only schematically
for purely theoretical considerations.

So far as I know, the first one to make use of this method was
Julius Hann, who according to his own statement explained it in
1875 in his university lectures and also deduced the law of the acceler-
ation experienced by a particle of air at any point on an isobaric
surface.

The first more detailed publication in reference to this point is
found in Hann’s memoir on ‘‘ Mountain and Valley Winds.’ Sub-
sequently H. Januschke’ in 1882 and L. Teisserenc de Bort® in
1884 made use of this method of presentation. It would lead us
away too far to develop the general formula for such an isobaric sur-
face, although this could easily be done with the help of the well-
known barometric formula, but of course with the uncertainty
inherent in this formula relative to the vertical distribution of tem-
perature and moisture.

On the other hand, certain properties of this surface may at least
be mentioned here.

If there are given two surfaces of constant pressure, one of which
corresponds to the atmospheric pressure f, the other to 8 + 48, then
the vertical distance between these surfaces at any point is given by
the equation

4B
Ba 1S Ge eae. |)

since 0 4 h is the mass of the air contained in a vertical cylinder
or prism standing on the unit of surface and 13.6 4 # is the corre-
sponding mass of mercury.

¢j. Hann: Zeit. d. Oest. Gesel.f. Met. 1879, XIV, p. 444. Compare
also my note 11, Memoir XVII, p. 354 of this collection of translations,

7H. Januschke: Zeit. d. Oest. Gesel. f. Met. 1882, XVII, p. 136.

§L. T. de Bort: Annales du Bureau Central. Année 1882, pp. 73-80.
Paris, 1884.

374 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

Therefore, if we have given a system of surfaces of constant pres-
sure corresponding to the pressures 8; 8 + 48;8 +248, etc., then
the vertical distance between the neighboring surfaces at any point
is inversely proportional to the prevailing density of the air at this
point.

This latter theorem corresponds to that for the isobars according
to which the gradient is obtained from the reciprocal of the distance
between neighboring isobars.

If now for p we substitute in the above expression

BT,
nye
8 T
then equation (3) becomes
1 es i
Ahi = —— >, 4B.
Po B Ty

Hence it follows that

“The vertical distance between two definite isobaric surfaces f and
8 + 4 at any point is proportional to the absolute temperature
prevailing at that point.”

Finally, if in equation (1c) in place of the expression

13.6 4°
0

we substitute the difference 4 h from equation (3) we obtain

Now since / is the distance between the pressure surfaces # and
@ +48 measured horizontally from a point on the surface f,
whereas 4h is the distance of the same surfaces measured vertically,

th . etre ee
therefore “ is the tangent of the angle of inclination of the surfaces

or tga. From this consideration we obtain the well-known equa-
tion (2) above given or/ = g tga. This equation is distinguished
by its simplicity from all of those to which the number (1) was given
in the preceding paragraph.

Translated into words this equation (2) would read

‘The gracient acceleration is proportional to the inclination of the
isobaric surfaces.”’

DISTRIBUTION OF ATMOSPHERIC PRESSURE—VON BEZOLD 375

Or if we recall that the angle a is always very small so that we
can consider sine and tangent as equivalent, we have:

“The acceleration experienced by a particleof air ata given point
on an isobaric surface is equal to that which a heavy mass would
experience ifsit could slide without friction on a similar rigid iso-
baric surface.”

This theorem holds good in general without reference to the
density of the air, that is to say, without reference to the absolute
value of the pressure or the temperature. These two quantities
or the equivalent density of the air have already exerted their
influence on the form of the isobaric surfaces and therefore do not
need to be further considered in the final result.

“Therefore the presentation by the isobaric surfaces allows of
direct conclusions as to the gradient-acceleration, and the density
of the air at different points of thé space under consideration, and, as
to the course of the temperatures between neighboring isobaric
surfaces.”

Since these conclusions are all rigorous, therefore the unprejudiced
consideration of any such presentation suffices to answer the indi-
vidual questions, whereasin theuseof the ordinary charts of isobars
one must always proceed with caution and must consider attendant
circumstances.

Unfortunately this great advantage of the presentation by vertical
surfaces suffers from one defect, that the construction of the isobaric
surfaces or their intersections with a vertical surface, offers the
greatest difficulties practically, so that, as above remarked, it is
generally only employed for schematic considerations.

XIX

THE INTERCHANGE OF HEAT AT THE SURFACE OF
THE EARTH AND IN THE ATMOSPHERE

BY PROF. DR. WM. VON BEZOLD

[Sitz. Ber. of the Berlin Academy of Sciences for 1892, pp. 1139-1178. Trans-
lated from Gesammelte Verhandlungen, Berlin, 1906, pp. 316-356]

(I.) INTRODUCTION.

The ‘‘distribution of heat at the earth’s surface’’ or, morecorrectly,
“the distribution of temperature in the lowest strata of the atmos-
phere”’ has been the object of many exhaustive investigations since
the days of Alexander von Humboldt.

It is especially Dove, Wild, and Hann who have gradually com-
pleted the idea that was sketched out in a few lines by Humboldt
and have worked out its details for a large portion of the surface of
the earth.

In this way we have learned at least in general of those influe:ices
that, together with the predominant radiation from the sun, deter-
mine the distribution of heat, and thus give the lines of equal
temperature (isotherms) the exact form that we find in the charts
drawn by the above-mentioned investigators.

But in general these studies are confined to purely qualitative
considerations. One is satisfied to state the general trend of the
influence of the distribution of land and water, and of the currents
of air and ocean. Hitherto only to the most modest extent have
attempts been made to determine the numerical or quantitative
extent of these influences, or to consider together the general
economy of the heat in the atmosphere and on the earth’s surface.

In this respect a section of Samuel Haughton’s Physical Geog-
raphy must be first mentioned.! To a certain extent the works of
Zenker’ belong to this subject. We also meet with attempts in this

1Samuel Haughton; Six lectures on physical geography. Dublin and
London, 1880.

2 Zenker: The distribution of heat at the earth’s surface. JBerlin, 1888;
also Met. Zeit., 1892, IX, pp. 336-344, 380-394.

376

@4sAa2

INTERCHANGE OF HEAT——-VON BEZOLD 377

direction by Woeikof* and similarly in a recent highly interesting
memoir by W. Trabert.*

Attention has hitherto to a lafge degree been given to only one
side of this problem, namely, the theory of insolation or the radia-
tion from the sun to the earth and that of the radiation from the
earth into space—a chapter on which, as is well-known, there is an
extensive literature.

But although it must be allowed that exact determinations of
these two elements are among the most important points of the
whole question, still we ought not to forget that it is precisely here
that we meet the greatest difficulties unless we restrict ourselves
to purely theoretical considerations as J. H. Lambert, L. W. Meech,
and Christian Wiener have done.

Recently O. Chwolson® has clearly shown how important are
the difficulties and how large the corresponding uncertainty that
still attends this field of work in spite of all the thought that has
been bestowed upon it.

That the degree of accuracy that has hitherto been attained in the
determination of the intensity of the solar radiation is still quite
moderate is seen moreover from the simple fact that we cannot
yet recognize the change from perigee to apogee, although it must
amount to one-fifteenth or 7 per cent of the total amount.

In consideration of the difficulties offered by the solution of this
apparently simple question, and in view of the uncertainty that still
exists with reference to the most important constants, it might
indeed seem premature to attempt to extend the investigation
over the far more complicated process through which the heat
furnished by the sun has to pass, from its entrance into the atmos-
phere until its exit therefrom into celestial space.

But still this labor must be undertaken. We must attempt to
determine, at least approximately, what fraction of the heat which
comes into play at any part of the earth’s surface or of the atmos-
phere, in a given time, is furnished by direct insolation and lost by
direct radiation; how much is brought hitherand removed hence by
simple or complex convection; how much is used in evaporating
water or melting ice; how much is stored in the ground only to be

§ Woeikof: The climates of the Globe. Jena, 1887.

4 Trabert: The diurnal variation of temperature and sunshine on the sum-
mit of Sonnblick. Memoirs of the Vienna Acad. Math. Classe, Vol. LIX,
1892.

°> Chwolson: On the present condition of actinometry. Wild Repertor-
ium, 1892, XV, No. 1. :

378 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

subsequently given up, etc. If ever these questions can be
solved even with only a rough approximation this will be con-
sidered a great advance in our knowledge.

Then first will the many items that go to make up the general

problem be separately treated, and only thus will be attained that

point of view that must even now be kept in mind in assembling the
observations, if indeed we are ever to succeed in more completely
attaining the desired end.

The present memoir and others to follow later will contain an
effort in this direction.

After some introductory considerations I will first present a num-
ber of quite general theorems and then develop the individual
chapters.

With reference to the order in which these individual investiga-
tions will follow each other, I shall not bind myself to any pre-
arranged sequence, but rather let 1t depend on my success in bring-
ing each of the appropriate problems to a definite conclusion.

I will endeavor to give the statement of the general theorems
with the greatest rigor, whereas in treating the individual problems
I must often be satisfied with first approximations, as I do not con-
sider it proper to compute with five decimals when we can scarcely
be sure of the whole units, or to develop elegant formule for a prob-
lem as to whose fundamental character we are still seeking for
light.

But before I consider the problem proper it appears appropriate
first to undertake a rapid survey of the whole field and to attempt
by use of the most important well-known constants to obtain at
least a superficial idea as to the weight with which the processes
that are hereafter to be more accurately studied enter into the com-
putation, since onlv thus can we learn what points must be consid-
ered as of first importance and what may be neglected so long as we
cannot attain a high grade of accuracy.

We most easily attain such a general view of the problem when
we seek for the quantities of heat that are necessary in order to
bring about certain effects at the earth’s surface, and when we com-
pare these with the quantities that suffice to melt a layer of ice of
' definite thickness or to evaporate a layer of water of definite depth—
a method of presentation that has already been frequently used,
especially by Haughton.

I choose the large calory or the kilogram calory, as the unit of heat
the minute as the unit of time, and the meter as the unit of length,
unless some other is expressly mentioned.

a

INTERCHANGE OF HEAT—VON BEZOLD 379

With these preliminaries we find the following as the number of
units of heat required.

Kg. calories,

Required to warm (1™)* water 1° Cio... See RT 1000
to@iarmnG) earth AO: Co. 4.2) eae tide by ore sctaie bids 300-600*
to evaporate 1™™ depth per (1™)?water ... ...2c2..... 600+
to melt 1™™ depth per (1™)? area — 1 cubic deci-

HIDEEET ACOL Ae aie vas Masia a eiten ae eathstate we alee e oe ee 76
to warm by 1°C. the total atmosphere resting on
(US) 2nof oeaumed:. acess tyes. SANS os cee SER ot 2454t
to warm by 1°C. (1™) air at o° C. under pressure of
TOT WE 5 cis, 6 ai Saks RA aS eR eyclatatala aes 0.307
* See p. 414.

+ Temperatures between 0° C. and 30° C. principally occur in the case of
evaporation of water at the earth’s surface. For these temperatures, accord-
ing to Regnault, the heat of evaporation lies between 606.5 and 585.6, hence
600 can be adopted.

{ Under the assumption that the pressure at the earth’s surface is 760 mm.

Although this is a very elementary tabulation, yet it gives some
important indications. First, we see that the difference in the capaci-
ties of water and earth for heat, which is frequently adduced asa prin-
cipal basis for the explanation of the difference between the con-
tinental and oceanic climates, is greatly diminished when we compare
together not equal masses but, what is far more correct, equal vol-
umes, that is to say, when weconsider the capacities per unit volume
instead of per unit weight. But above all it shows what an enor-
mous importance attaches to evaporation in the economy of nature,
and how it is that this, together with the mobility of water, assumes
the first place in the questions now at issue, a fact moreover that
Dove laid stress on in his memoir on monthly isotherms,® whereas
subsequently and notwithstanding this we often find the importance
of the difference of the thermal capacities greatly exaggerated.

The powerful influence of evaporation is still more evident when,
by means of the figures above given, we come to clearly comprehend
that the evaporation of a depth of one millimeter of rainfall demands
as much heat as the melting of a layer of ice about eight times as
thick, and that this same amount of heat would suffice to warm up
the ground by 1° C. to a depth of one or two meters, or to warm up
by one-fourth of adegree Centigrade the whole column of air stand-
ing on the same area of ground and reaching up to the extreme
limit of the atmosphere.

Dove: Memoirs of the Berlin Acad., 1848, p. 219.

380 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

In continuation of these views it is not difficult to form an idea
as to the extent to which the total kinetic energy actually present
in the atmosphere, e. g. in the shape of wind, can in an extreme case
affect these investigations.

Assume that one kilogram of air is moving with the velocity v so
that the corresponding kinetic energy is

yy

—- == h.
9 gn,

where gh is the amount of work corresponding to this energy. If
this work is converted into heat it becomes

h

424
calories, an amount of heat that suffices to raise the temperature
of one kilogram of air under constant pressure by »

h h
ee seen — |. Ieprees.
424 x 0.2375 degrees Centigrade or about 100 §

This latter number expresses the rise in temperature that the
air would experience if the wind could be suddenly brought to
a stop and it be then allowed to expand until equilibrium be attained.

If v have values of ro, 20, or 30 meters per second then this warm-
ing would correspond to 0.05°, 0.20°, and 0.45°, respectively.

But we estimate it too high when we assume that the mean
velocity of the whole atmosphere is 20 meters per second (10 meters
would be too high for the lowest stratum) and yet even so the sudden
conversion of the translatory motion of the whole atmosphere into
heat would cause a rise in temperature of 0.20° C.

But this rise of temperature corresponds to an amount of heat
that would not suffice to evaporate a layer of water even one milli-
meter in depth. The potential energy that we observe in the form
of differences of atmospheric pressure, i.e.,in superposed surfaces
of equal pressure, is of course of the same order as the actual energy
of translatory motion evolved from them, and thus we see that the
quantities of heat present in this form of energy are very small
in comparison with those that are absorbed and evolved in the
change of condition of water especially in its evaporation and
condensation.

Hence in the determination of the total energy of any portion of
the atmosphere, the first matter to be considered is the quantity of
aqueous vapor contained therein.

INTERCHANGE OF HEAT-—VON BEZOLD 381

In order to give the estimates here set forth their full value, it is
necessary to compare the consumption of heat in the processes
above enumerated with the quantity furnished by the sun within
the given time.

Unfortunately here we find ourselves in a very difficult position,
since the solar constant or the number of gram-calories that one
square centimeter of surface at the outer limit of the atmosphere
receives in one minute when the rays of the sun fall perpendicu-
larly on it, has not yet been determined with certainty.

The values that have been obtained for this constant, which I
will designate by s vary between the limits 1.763 and 4.0.7 But
since the greater number lie between 2 and 3, therefore, in order to at
least have a definite proposition, I will here use the value s = 2.5,
or if the equivalent constant be expressed in square meters and kilo-
grams and minutes as units, then S = 25 (kilogram-calories).

Under this assumption the whole earth receives 25 z 7? units of
heat in one minute, where r expresses the radiusof the globe includ-
ing its atmosphere. This quantity of heat is distributed over the
hemisphere illumined by the sun, that is to say, overaspherical sur-
face whose areais 27 7? and hence on the average the sun gives each
square meter of the hemisphere on which it shines 12.5 calories
per minute or 12.5 X 60 X 12 = gooo calories per day since, ignor-
ing the eccentricity of the earth’s orbit, the average length of the
day light is 12 hours for every point of the earth.

This amount of heat would suffice to melt a layer of ice 11.84
cm. in thickness, or to evaporate a layer of water 15 mm. deep per
day; or 550 centimeters of water or 43 meters of ice per year.

If by anticipation (see page 414) we add that the quantity of heat
entering and leaving the soil during one year can in an extreme case
evaporate a layer of 40 mm., and if in general we express all this
data for the whole earth uniformly by the depth of evaporated
water or melted ice we obtain the following table:

CAN CAN
EVAPORATE MELT ICE
WATER.

cm.
‘The sunshine inione averaee GRY... okiccet «0.5 as cine che ocia tieiciee | 1.5 12.0
‘The sunshinelin: oneswhole year. acts ciclo «sles «nya sis ose ,o crete s x" 550.0 4325.0
The heat received and lost annually in the soil is less than ... 4.0 31.6
The heat that warms the atmosphere by 1°..........6....- °.4 Bi2
The kinetic energy of the atmosphere is less than........... 0.08 | 0.6

7™Chwolson: On the present state of actinometry, pp. ro to 14.

382 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 52

If we compare the value of the evaporation here given as the
equivalent of the total insolation with the observed rainfall of the
globe we come to the conclusion that either the value s = 2.5 is still
far too high or that out of the totalinsolation falling on the boundary
of the atmosphere only a much smaller portion arrives in the lower
stratum than one might expect from the measures of absorption
made on very clear days.®

This fractional portion could be easily estimated if the average
precipitation were known for the whole earth; since, as just stated,
the re-evaporation of the fallen precipitation represents the principal
work that the sun’s heat has to perform.

Unfortunately we are not able to give even an approximately
reliable value of this precipitation, since observations of the quantity
of rain are almost wholly wanting for the greater part of the globe,
namely for the ocean. ,

If the average precipitation be 55 centimeters and if s = 2.5,
then the heat consumed in the evaporation of this amount of water
would be one-tenth of thetotal furnished by the sun and we should
therefore have to assume that the heat which reaches the lower
strata of the atmosphere amounts to not much more than one-
tenth. If the average precipitation were 110 centimeters, which
certainly seems to be too high an estimate, then we should conclude
that about one-fifth of the total solar radiation reaches the lower
strata.

In any case the quantity of heat reaching the surfaceof theearth
is a much smaller fraction of the total insolation than has been given
by the measurements hitherto made on perfectly cloudless
days.

Of course a very considerable fraction of the incident radiation
is absorbed by the clouds and certainly a still larger part of it is
reflected by their upper surfaces, and thus a quantity of radiant
energy is rejected at the very threshold.

‘Tt needs but a single glance from the summit of a mountain down
on the ocean of cloud lying below one and illumined by the sun to
convince one that the diffuse reflection from that surface is incom-
parably greater than the similar reflection from the ground or from
a water surface and that therefore this must play a very important
part in the thermal economy of the earth.”

How strong this reflection is (and to it I have moreover often
referred, although it seems to have received but littleattention) may

® See Angot-Pernter: Met. Zeit., III, 1886, pp. 540-546.

INTERCHANGE OF HEAT-——VON BEZOLD 383

be seen from the observations in balloons that R. Assmann will soon
publish.®

It is very important to devise methods that will enable us to at
least approximately measure the reflection from the surfaces of the
earth and thé clouds. But these are questions that will be fully
considered hereafter. At present we are concerned only to obtain
a general view as to the most important of the quantities under
consideration. This object seems now to have been attained and I
will proceed to the closer study of the matter.

Before I treat closely the individual problems that offer them-
selves, I will establish a number of theorems that will serve as guides
for all that follows. These theorems are of such simplenature that
they might seem almost self-evident and can easily be expressed
in words. But I will also put them in theshape of formule, although
these latter become more complex than would be expected from
the simple verbal expressions. Nevertheless, I find it expedient to
give them suchaform. By this means we not only attain accuracy
of expression and thus remove every chance of misunderstanding,
but we can from the formule deduce a number of individual items
that would otherwise be overlooked.

(II.) GENERAL THEOREMS

The next following theorems are all founded on the assumption
that we may consider the thermal condition of the earth as a station-
ary one, or more correctly, one that is periodically stationary.

These therefore assume that there are average values of all the
quantities considered which remain the same within small limits
of error when we have deduced them from a sufficiently long series
of years of observation without regard to the exact length of the
series or to the year with which it began.

These theoremsdepend upon the justifiable assumption that the
earth, at least within the time covered by our observations, has
neither become warmer nor colder and that the succession of
seasons goes on as uniformly as ever at every point on the earth’s
surface.

Hence, all the quantities that we consider except the times, the
dimensions, the coérdinates, etc., represent average values as obtained
from series of observations that are long enough to allow of apply-
ing to them the fundamental laws of averages, and yet notso long

®R. Assmann and A. Berson: Wissenschaftliche Luftfahrten. Volumes
II and III. Braunschweig, 1900.

384 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

as to render necessary the consideration of those changes that have
gone on during the immense periods of geology.

Consequently the equations that will be deduced in the follow-
ing pages should, strictly speaking, include a quantity + ¢, wheree
refers to the uncertainty peculiar tothe nature of their average
values; but for simplicity this will be omitted.

Before I proceed to give the promised theorems, I present first
the notations that will be employed as follows:

t, the time in minutes counted from the beginning of the year.

T = 525949, the duration of a mean solar year in minutes.

q the quantity of heat that, at the time ¢, enters a unit surface
in a unit of time, at any given point of the earth’s surface or
of the atmosphere, or which in a certain sense may be said to
pass through the unit surface.

q” the quantity of heat that passes outward through the elemen-
tary unit surface, or that flows through it in the peppery
direction,

qty 2 and qt. the quantities of heat that enter or leave the unit
surface in the intervals of time between ¢, and #, or briefly g-
and gz when the interval of time ¢,, between ¢, and f, is indi-
cated by t.

q the quantity of heat entering the unit surface in the unit of time
at _the upper boundary of the atmosphere.

qh» = dr and Q the corresponding quantities for the interval t,,
_and for the whole year.

q, qt2 = gr and O the corresponding quantities of heat leaving

the unit surface at the upper limit of the atmosphere.

and q” the quantities of heat entering and leaving a closed sur-

face of definite extent in a unit of time at the moment ¢.

,

q

q and q the corresponding values for the boundary of the atmos-
phere, that is to say, for a spherical surface enclosing the
whole atmosphere and earth.

x2 ire %, 2 V4.2 0r briefly qz, qr, Gr: r the corresponding values
for the interval from i tm. dee

Q’ Q” Qand Othe corresponding values for the whole year, i. e., for
t sys: = r.

qa’ qb qa qo qa’ i qa, etc., the corresponding quantities for definite
portions a, b, of the above-named surface or for the boundary
of the atmosphere for the unit of time.

a,c ,7, etc., the corresponding quantities for the interval 7, ,

INTERCHANGE OF HEAT—VON BEZOLD 385

SE 075, Daea, the quantities of heat respectively entering and
leaving an area a of the surface of the earth or of the boun-
dary of the atmosphere within a whole year.

u the total energy contained in an enclosed portion of the surface
of the earth or the atmosphere at the time t.

u, the corresponding quantity for the time ¢,.

r the radius of a sphere centered at the earth’s center and enclosing
the whole atmosphere, or a quantity exceeding the greatest
radius of the globe by roo kilometers.

do an element of a surface.

8 the geographic latitude.

A the geographic longitude.

S the solar constant or kilogram calories of heat received by
the earth from the sun at’ the earth’s mean distance, per
minute per square meter.

If we consider this system of notation we shall perceive that the

following points of view have been kept in mind:

The quantities relating to the unit of surface have been designated
by Roman letters, those relating to larger areas and the boundaries
of the whole atmosphere by German letters.

The quantities relating to the unit of time are indicated by small
letters; those relating to other intervals except the whole year are
indicated by the same letters but with special index. For all
quantities that relate to a whole year the capital letters are used.

The quantities of heat are considered as absolute quantities and
letters indicating added heat have one accent while those indicating
subtracted or lost heat have two accents. These accents are placed
above and to the right when the heat passes through surfaces that
are within the boundary surface of the atmosphere, but are horizontal
lines placed above the letters when the heat passes through this
boundary itself.

We now proceed to establish the following theorems:

I. ‘‘The quantities of heat received by insolation and lost by
radiation by the whole earth in the course of a whole year are on
the average equal to each other.”

For if these quantities were not equal there would occur either a
progressive warming or progressive cooling, which has not been the
case during the time accessible to more accurate investigation.

Translated into algebra this theorem assumes the simple form

Daan tan) Secale: Hic 6)

ee

8)

386 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Here according to the definitions above given, we have
Do-= fo da

where the integral is to be taken over the whole surface of the sphere
whose radius is 7, hence

— 2x Tefg
B-r | anf" O00s G0 Bo. een

|

Since the quantity of heat Q that comes by insolation to a unit sur-
face at any given point of the boundary surface of the atmosphere
in the course of a year is a function of the geographical latitude only,
this equation becomes

= Palsy —
Baan { Gicts GBH eee
- 7/,

Moreover, as Lambert has demonstrated, for this function of the
latitude Q = ¢ (8), we have

¢ (8) = ¢(- B)

that is to say, points at the same latitude in the northern and
southern hemispheres receive from the sun by radiation equal sum-
totals of heat in the course of a year.

Therefore we can write equation (3) in the form

My oy T/ >
B-aar{ @ (BP) cosif'd Be. A Ve ene)

The value of the function g (8) is known from the investiga-
tions of Meech’ and Wiener" and is only uncertain to the extent
of the uncertainty of the solar constant that enters it as a coeffi-
cient.

Moreover, as is well known, we also obtain the value © in the
simplest way from the consideration that the sum total of the radia-
tion coming to the whole earth within a given interval of time is
equal to that which falls in that time on the great circle of the globe
perpendicular to the line connecting the sun and the earth.

10 Meech: On the relative intensity of the heat and light of the sun. Smith-
sonian Contributions, IX, Washington, 1857.

11 Wiener: Zeit. Oest. Gesell ftir Met. 1879, XIV, p. 113. [See Angot
Réchérches Theoriques. Paris, 1885.—C. A.]

INTERCHANGE OF HEAT—VON BEZOLD 387

Hence we have
eS ee. Boca wan 5)

where S indicates the solar constant as determined for the mean
distance between the earth and the sun.

For © we may also establish similar but not nearly so simple
formule. We have the formula

= 27 Bom eve
B-r | ai { “MO Coseag Ge. 5 - 26)
2 ici

but the quantity Q is not like Q a function of the geographic latitude
only, but also of the longitude, inso far as we take into consideration
the individual peculiarity as to outward radiation of each element
of the boundary surfaces (referring especially to the lower portion
of the atmosphere and the adjacent earth’s surface).

The total insolation that an element at the outer boundary of
the atmosphere receives in the course of a year depends only on the
geographical latitude; the quantity that is returned to space by
radiation through this element varies from point to point of the
earth.

Hence 0 = ¢ (8,4) and the function ¢ is never a simple one and is
scarcely expressible empirically.
The formula

BS 27 + z/,
B-+ { if (BA). cos PAB. 2.2%)
90 —2/,

is therefore not susceptible of further simplification or modification;
but on the basis of the above-given considerations and by the help of
equations (4) and (5) the final result, viz:

O=OQ=xnrTS

i)

may be given directly.

Hence the quantities expressing the gain and loss or insolation
and radiation show a very great difference in that one is expressible
by rigorous mathematical formula but the other is not, unless we
can express the latter in terms of the former by theorems relative
to the equality of the quantities of gain and loss.

The difference between these two classes of quantities would be
still more striking if the so-called solar constant really were properly
so-called, i.e., if the intensity of solar radiation actually remained
invariable.

388 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Under this latter assumption all quantities relating to insolation
would be mathematically rigorous in contrast to those relating to
terrestrial radiation w hich can only be thought of as general average
values.

However, the variations observed on the sun’s surface make it
highly improbable that the intensity of solar radiation.can be invari-
able, and therefore we must certainly also assume that the values
relative to insolation always have only the character of average
values.

II. ‘‘The quantities of heat that are given or lost by a definite
portion of the earth’s surface or the atmosphere in all the various
possible ways in the course of a year are on the average equal to
each other.’’

This theorem is, like Theorem No. I, a direct consequence of the
assumption that the sun and the earth are in a certain sense in a
stationary condition, that is to say, that we are in general justified in
speaking of average values of the various quantities that come into
consideration.

III. ‘‘The quantities of heat that individual portions of the
earth’s surface or of the atmosphere gain by insolation or lose by
radiation, in the course of a year, are in general not equal to each
other, but there are portions of the earth where the insolation is in
excess and other portions where the radiation is in excess.”

The correctness of this theorem follows from the simple fact that
warm air and warm water flow continually from equatorial regions
poleward, while conversely cold air and cold water or ice flow from
polar regions toward the equatorial.

Hence the equatorial belt continuously loses heat by convection
(and also certainly in the form of the kinetic energy of translatory
motion) which must be replaced by excess of insolation if the mean
temperature is to remain constant, whereas the reverse holds good
for the polar regions.

We can therefore subdivide the whole earth into three zones, viz:
one equatorial in which the insolation exceeds the radiation, and
two polar, in which the radiation exceeds the insolation.

These zones I will designate as “insolation zone” and “‘radiation
zone,’ respectively.

The lines that separate these zones from each other at the bound-
ary surface of the atmosphere may be called “‘lines of equal insola-

INTERCHANGE OF HEAT—-VON BEZOLD 389

tion and radiation” or ‘“‘lines of radiation equilibrium” or briefly
“neutral lines.”

There are two such neutral lines where the radiation outward and
inward balance each other, one of which belongs to the northern and
the other to the southern hemisphere. But it is not incredible that,
besides these, other similar closed lines may exist that must be
regarded as boundaries for smaller regions, like islands.

If we give the positive sign to the heat radiated from the sun to
the earth and the negative sign to that radiated by earth to space,
then the algebraic sum of the quantities of heat exchanged through
the boundary surface of the atmosphere is positive within the equa-
torial zone but negative in the two polar zones. Wecan, therefore,
as tovannual averages, think of the whole exchange of heat within
the atmosphere and at the earth’s surface as schematically repre-
sented by a current of heat that enters into the equatorial zone
through the boundary surfaces of the atmosphere and after splitting
into two branches departs in the polar zones.

The location of the neutral lines for the balance of radiation and
the determination of the intensities of these ideal streams, i.e.,
the quantities of heat that are interchanged in this way, forms an
important problem in that chapter of the physics of the atmosphere
that we have now under consideration.

In fact we have not to do with such a simple single flow of heat
but with double currents, since warm masses are simultaneously
carried poleward and cold masses equatorward, whose sum
total represents the simple current of the above scheme. Therefore
the considerations to be here set forth have a certain analogy with
those by which one passes from the assumption of a double cur-
rent over to that of a single current as in the case of the double and
single current theories in electricity.

The theorems just stated may be algebraically expressed in the
following forms:

Q> Q in the equatorial zone
O= 6". in, Pheupolan zones. 7°" >” (8)
fa) =Q. along the two neutral lines

which latter may be represented by the equations
®(+ 8’) =0 and ¥(-— BA) =0

where # expresses the absolute value of the latitude, and we reckon
northern latitudes as positive and southern latitudes as negative.

390 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. §1

I may here remark that so far as I can see as yet the values of f
vary about a mean that is to be found between 35° and 40°.

If now we designate the total quantities of heat received and lost
in the equatorial zone by radiation during the whole year by fee and
Be respectively, and the similar quantities for the two polar zones
by 2, and o, respectively, then we have

and

whence recalling that by assumption OQ= 0, we obtain

i, Se ey Het fA ee

that is to say, the excess of insolation received in the equatorial
zone is counterbalanced by an exactly equal excess of radiation
outward lost from the two polar zones and this counterbalance is
effected by the convection into the polar zones of the excess attained
in the equatorial zone.

Hence the difference Q — BH: is equal to the quantity of heat that
by convection (in the broadest sense of the word including the
kinetic energy of moving masses of air) flows through thetwo neutral
sections from the equatorial zone into the two polar zones.

Moreover, the quotient

expresses the average intensity of the currents of heat entering into
the equatorial zone and flowing toward the poles, as we can imagine
them in our scheme replacing the counterbalancing interchanges
that are actually occurring within the atmosphere.

This quotient will therefore be designated by J, So that we
have

ks ony mre Mette Nyt

On the other hand, we divide the quantities representing the two
polar caps into two parts relating to the northern and southern
hemispheres, respectively.

If we give the index to the quantity relating to the northern

es

a

ee ee | ee

INTERCHANGE OF HEAT—VON BEZOLD 391

\

hemisphere and s to that relating to the southern hemisphere, then
we have the following formule:, ;

ae rae 5, + 3 oe
: ro ra o. + 3 a;
and
ey —iieecie Mid rey tage eee Pate)
as also
a, a He
des sae 5 ie
and
ee = = D, P
ile =
whence there follow
O.= O,—JaT
Dp a QD, at: de
== . (12)
Dn DD, a S. y
0,=-0,+ J.T

Since now, on the basis of a definite value of the solar constant,
one can at least approximately compute all the quantities relating
to insolation, when we know the location of the neutral lines, and
since also the approximate determination of the intensities J, and
J, of the two branches of the schematic flow of heat is not a matter
of insuperable difficulty, therefore there is also a possibility of find-
ing the quantity of heat radiated outward in the two radiation
zones, including that reflected outward from the highest regions of
the atmosphere.

These formule teach us that we may hope for information as to
the interchange of heat in the highest inaccessible regions of the
atmosphere as soon as we are successful in determining with suf-
ficient accuracy the solar constant and also the intensity of the flow
of heat through the two neutral sections.

Even this latter problem seems not insoluble, at least within cer-
tain limits, since in this flow the lower accessible strata principally
comes into consideration.

392 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Theorems similar to those just expressed for the whole year can
also be established for shorter intervals of time, some of which may
here be given.

IV. “The quantities of heat that are within special portions of
a year given to and lost by special portions of the earth’s surface or
the atmosphere are in general not equal.”

The proof of this theorem consists in the simple fact that the
thermal condition of the earth’s surface and the atmosphere is sub-
ject to periodical variations, that is to say, this is simply an expres-
sion of the fact that there occur times of excess of insolation and
other times of excess of radiation.

By use of the notation, introduced above, this theorem takes the

following form: ;

BA Vo ea)

fat Sar - <: Wash ale a ae
or also

mn ers
q do ae te fat S 9

where the integral is to be taken over the whole closed area a and
where the omission of the accents over g; and q, 7 indicates that the
quantities are to be considered as algebraic and can therefore have
correspondingly different signs.

If we consider not a closed surface but only a definite portion of
the boundary surface of the atmosphere then we have the expression

Ait Mei” Stecoemtenctte ae Pare ee

In this expression we consider the case in which the inequality
> or< becomes an equality =,asan exceptional case and in general

we have to use the sign =

If qr >o then this expresses the fact that there is an excess of
heat added over that abstracted; if q,7<o then this expresses
the deficiency that has been experienced by the masses contained
within the volume a during the interval t from #, to 4).

We can also write

, —
Var: — q""a,t ae Mgt Mat Rees et mea A: (15)

When this difference has a positive sign it indicates an increase

INTERCHANGE OF HEAT—VON BEZOLD 393

of energy within the volume under consideration; a negative sign
indicates a diminution. ;

This increase may consist in an increase of temperature, an
increase of the quantity of vapor, a conversion of ice into water,
a development or an increase of pressure differences (potential
energy) or of motions (kinetic energy).

Frequently such an increase of energy is also called incidentally
a storage of heat.

On the other hand, if q, 7; is negative this teaches that the total
energy has diminished during the interval of time under considera-
tion, which must indicate either a fall of temperature, or conden-
sation or freezing of the water, a diminution of pressure gradient
or the diminution of the existing motions. If we have to do with
changes in bodies that are stationary or scarcely movable, like
water frozen into ice, or like the solid earth, then we could include
also the storage of heat or cold.

For #,—t, = T we have q,7, = © or Ugy, = Ug, Since in accord-
ance with the assumption that lies at the base of this whole investi-
gation the thermal and kinetic condition of the earth at the close
of a year always returns to its same initial condition no matter
what moment of time ¢, we choose as our starting point.

Since therefore the total increase of heat within a year is zero,
whilst it has finite values during the separate seasons, therefore for
each point of the earth the whole year is divided into periods of
excess of insolation and excess of radiation or, briefly, seasons of
warming and cooling.

In the passage from one such period of one kind over to one of the

d
opposite kind the differential quotient = changes its sign, and q

itself at this moment of time therefore attains a maximum or
minimum value.

Such extreme values occur within every day, but the absolute
maxima and the minima in general only once during each year
except twice at the equator.

If we ignore the daily extremes, and at least for regions outside
the tropics, we can by appropriate choice of dates for the beginning
of the year, divide the year into two halves such that for one
we have an increase of heat and for the other a decrease.

These halves will in general be unequal, since the inflow and the
outflow of heat follow very different laws.

If therefore ¢, = o be so chosen that u, is the absolute minimum
and if we remove the secondary maxima and minima by some

394 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
appropriate method of elimination, and if furthermore u,, is the

absolute maximum of u, and ¢,, the moment of time at which this
maximum is attained, then

4a > 0 when t 2
dt

bn
and
d >t
= <0 when t 2 <r
moreover
Wie, bg Uno
and
Vaee Yao = Uatm

if by t, we understand the interval of time from o to ¢,, and by
t, the interval of time from ¢,, to T.
Hence also follows

Gary ST Gar re ee cme res i)

that is to say, the sum total of the heat received by a given portion
of the earth or the atmosphere in the half year when the gain
exceeds the loss, is exactly equal to that which is given up during
the half year when the loss exceeds the gain.

Moreover equation (16) also holds good if the year is divided into
any two perfectly arbitrary portions provided only that t, + t =
T; in every case the heat that is gained in one portion must again
be lost in the other portion; but in any such arbitrary division
Var, cannot have a maximum. If, however, this value is a maxi-
mum then this must be designated as “‘the annual heat exchange
for the portion of air or earth under consideration.”

Hence it follows that ‘‘The annual heat exchange for any portion
of the earth or atmosphere or both is equal to the difference between
the maximum and the minimum quantities of energy contained
in such portion.”

For shorter periods, such as the diurnal periods, this theorem
needs a slight modification, since in general for any such period
not so much is taken away during its season of diminishing heat
as is gained during its season of increasing heat; but less during
one half of the year and more during the other half.

a

INTERCHANGE OF HEAT—VON BEZOLD 395

If therefore again q;, indicates the heat added during the interval
from any moment of one secondary minimum of total energy to
the same moment of the next following secondary maximum, and
qr, the heat lost from the latter maximum to the moment of the next
following secéndary minimum, then we have

Wr, as Ir.

where, however, the difference between the two quantities q;, and
qr, is always small.
Consequently the amount of the daily exchange is

% (Gr, + 4z,)

These considerations lead naturally to the determination of the
total energy contained in any portion of the atmosphere or the
earth.

For the present purpose it is important to choose such portion
of the atmosphere appropriately and to bring it in connection with
a corresponding limited part of the earth’s surface.

By the term ‘‘total energy of any portion of the earth’s surface”
I will therefore understand the total energy in that portion of the
earth’s crust and the atmosphere resting on it, cut out by a straight
line that, starting from the center of the earth, passes around that
part of the earth’s surface while its upper end is at the limit of the
atmosphere, but its lower end is limited by a surface parallel to the
earth’s surface but so chosen that no annual period of temperature
is observable therein.

On the other hand by the expression “‘total energy of a definite
place on the earth’s surface’? I understand the energy withina
truncated cone whose apex is at the center of the earth while its
conical surface cuts a unit of area from the surface of the earth,
and whose upper and lower surfaces are defined respectively by the
upper boundary of the atmosphere and by a surface lying deep
enough below and parallel to the earth’s surface.

The determination of the total energy for the different points of
the earth’s surface, both as to its average value and also as to its
variation with time constitutes an important problem in the theory
of the thermal economy of the earth.

The amplitude of the variation of the total energy, that is to
say, the difference of its extreme values, affords a measure of the
thermal exchange both for the annual period and also, with a
small modification, for the diurnal period.

396 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The dates of these extremes lead to a division of the year into
seasons of warming and cooling, which division opens up other
points of view than the division of the year on a purely astronomical
basis.

The geographical distribution of the total energy over the surface
of the earth gives for the first time an idea of the actual distribution
of heat at the earth’s surface, whereas hitherto we have given this
name to what is actually only the distribution of temperature in
the lowest stratum of air.

But we must first come to an understanding as to a zero point
if we wish to compare together the energies of different points of
the earth’s surface, although this is a matter that need not at all
be considered in the investigation of the annual or the diurnal
changes at any special points. But this is a point on which I will
dwell in a later communication.

At present I need only remark that the approximate computa-
tion of the total energy in the sense just established ought not to
encounter insurmountable difficulties.

In fact the portion belonging to the solid earth’s crust is deter-
mined with relative ease, as will be shown in the second part of the
present communication.

The extraordinary importance of the solution of this problem may
be seen from the remarks that will be made when we speak of the
remarkable variations that the so-called average temperature of
the whole earth (i. e., of the lowest stratum of air over the whole
earth) experiences in the course of the annual period, whereby it
will be found that it is not allowable to reason from this directly to
variations of the total energy of the whole earth. Similarly the
importance of this question will appear in considering the peculiar
behavior that the polar regions show at the time of the maximum
altitude of the sun.

V. “The quantities of heat that enter and leave through the
outer limit of the whole atmosphere in the course of a definite
portion of the year are not necessarily equal to each other.”

If the earth’s surface and the atmosphere were perfectly homo-
geneous, at least throughout each surrounding layer concentric
with the earth’s center, and if moreover the earth’s orbit about the
sun were circular, then the above-mentioned equality would neces-
sarily exist, but since these conditions are not fulfilled, and since
the regions of excess of insolation and excess of terrestrial radiation
change their locations [on the globe] in the course of the year and

INTERCHANGE OF HEAT—-—-VON BEZOLD 397

in fact at regions whose surfaces have entirely different properties,
therefore there is really no reason whatever for such equality.

Hence there probably are, even for the whole earth, some portions
of the year during which the increase of heat is in excess and other
portions in which the loss of heat is in excess; in other words, ‘‘ The
total energy of the whole earth is probably subject to periodic
variations within the year.”

The fact that the average temperature of the lowest stratum of
air over the whole earth is higher during the summer half-year of
the northern hemisphere than during the winter half-year seems to
agree with this idea.

But of course we must not forget that this temperature is by no
means a measure of the total energy. On the contrary it is very
probable that the changes of totalenergy of the whole surface of
the earth including the atmosphere are not so large, by far, as
one would expect from the change of the mean temperature of the
lowest stratum of air.

For since the masses of water that in the course of a year are
frozen to ice and afterward again melted are apparently much
larger in the southern hemisphere than in the northern, and since
the same is certainly true of the quantities of water that are evap-
orated and condensed—therefore a larger portion of the added
energy is applied to the work of melting and evaporating during
the summer of the southern hemisphere than during the summer
of thenorthern hemisphere. Therefore even in the case of equal
values of the total energy [of the two halves of the year] the mean
temperature of the whole earth must be lower in the half-year con-
taining the northern winter than in that containing the northern
summer, since in the winter half-year of the northern hemisphere
the larger portion of the added heat falls in [southern] regions in
which the consumption of energy in [producing] changes of condi-
tion [snow and ice to water and vapor] is far greater than it ever
can be in the northern hemisphere.

But only detail investigation can decide to what extent the com-
pensation just indicated takes place or, in other words, whether
and to what extent the total energy of the whole earth has an
annual period.

Of course in this matter, as indeed throughout the whole of this
class of investigations, one must be content with estimates, but
certainly the problem itself is a striking example of the special
question to which we are led by these general considerations.

In order to put this theorem into algebraic form it suffices to take

398 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

a more general view of the equations (14) and (15) above given
and slightly alter them.

We have indeed only to drop the index a that was introduced
to show that we are considering a definite portion of the earth or
atmosphere, and to add the horizontal line above in order to em-
phasize the fact that we are considering the boundary surface of
the atmosphere, thus transposing the equation into the following:

WS and Ie — Ir = Wy, — Wy oye ies ee Ce

but must always remember that in the present case, where we are
dealing with the whole earth, the difference u,—u, which I will
designate by u, is always small in comparison with the quantities
qr and qr.

Of course the equation (16) also holds good in this case after
corresponding modifications; therefore if we put

Wy, — Uz, = Uz, and u, — wu, = Uz,
and
%Z+ta=
we must have
Ur, = — Uy,

that is to say, if we divide the year into two arbitrary intervals
then the increase of the energy that the whole earth has gained in
one of these intervals is equal to the loss that it has experienced
in the other interval.

If now we imagine the beginning of the year so chosen and the
division into intervals so devised that in one interval u is always
above and in the other always below the annual mean, then the
year falls into two halves that are in general unequal, one of which
we may call the warmer and the other the colder half respect-
ively.

Since the insolation at different portions of the earth’s surface
shows remarkably great differences at all times of the year, being
indeed zero at some places and times, whereas the radiation out-
ward is always effective, and since, on the other hand, the total
energy of the whole earth is only subject to small periodic changes
within the year so that u, is always small as compared with q and

q, therefore we can so subdivide the whole boundary of the atmos-

INTERCHANGE OF HEAT——-VON BEZOLD 399

phere that in one part the insolation is in excess but in the other
part the radiation.

If we indicate by the index a ae quantities that relate to the
region where insolation is in excess, and by tbe index p the other
region then the equation (17) can be rewritten as

Geo tae. ot ee es, Mitek . (18)

where u, is small with respect to the differences that enter both
sides of this equation.

This theorem can be expressed as follows:

‘“‘At any moment of the year the earth’s surface is divided into
regions having insolation in excess and others having radiation in
excess.”

If we ignore the diurnal period, the equatorial zone always
belongs to the region of excess of insolation but the limiting neutral
lines are subject to important variations in the course of the year.

The proof of this theorem consists simply in this, that at all
seasons of the year warm currents flow poleward from the tropics,
whereas insolation and radiation remain apparently uniform in
the tropics through the whole year, and therefore these currents
can be maintained to only a very slight extent by any energy that
may be stored up.

The polar regions belong to the region of excess of insolation
although only during a small part of the year, since during mid-
summer of either hemisphere the corresponding polar region receives
during a limited interval of time more heat from the sun than the
regions of lower latitude or than those of the opposite hemisphere.

Hence, while the two neutral lines depart in the same direction
from the average location that they occupy at the time of the
equinoxes (in the northern spring time both move northward but
in the southern spring southward), therefore the polar region
enclosed by one of these lines diminishes steadily until it entirely
disappears at midsummer.

If then the convection of heat from lower latitudes continues
during the midsummers of the respective hemispheres, this can
only be explained by the fact that the whole of the heat gained by
excess of insolation and by convection is consumed in covering the
loss of energy that the polar region had suffered during the winter
half-year, and which had resulted in the formation of enormous
masses of ice and the diminution of the vapor contained in the
atmosphere.

400 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Hence the equations of the neutral lines for any given moment
of the year take the form

® (+ 8,2, t) =0 and V(— £4, =0

where for definite values of 7 the one or the other of these equations
becomes useless since the line to which it refers vanishes entirely.

If the surface of the earth were perfectly homogenous and the
earth’s orbit circular the following equation between the functions
¢ and ¢ would hold good

¢(— BA, )= 6 (-B Ate)

that is to say, under this assumption the neutral line on either hemi-
sphere would at any given moment have exactly the same location
that it would occupy on the other hemisphere a half-year earlier
or later. Also each hemisphere would belong to its region of excess
of insolation for exactly the same intervals of time as the other.

Now an interchange of heat by convection takes place between
the region of excess of insolation and that of excess of radiation
just as in the annual average.

But the equations for this convection current are much more
complex for short intervals of time than for the annual average,
since in this latter case all quantities that refer to the storage of
energy fall out, whereas for shorter intervals they play an important
role.

In order to understand this we do best to subdivide the energy
U, in equation (18) into two portions u, and u,, one of which relates
to the insolation region and the other to the radiation region.

Thus that equation takes the form

van = =>

Ge Ge ae ge ret ae oe en

where the left-hand side of the equation represents the remnant of
heat that remains after subtracting the radiated heat and the
stored-up heat from the heat received by insolation in the insolation
region. |

Evidently this remnant must flow as a convection current to the
radiation region.

The average [thermal] intensity of this current is

. Fb tees Pe Ae eae
t

INTERCHANGE OF HEAT—VON BEZOLD 401 *

and this is the current that [arriving] in the radiation region partially
replaces the loss due to the excess of radiation whilst the remaining
excess of radiation is represented by actual loss of energy, i. e., by
cooling, formation of ice, etc.

This formula differs in important respects from the equation
(10) as before established for the whole year. Whereas in that
the convection current depended only on the difference between
the insolation and the radiation, here there is also considered the
quantities of energy that are [in any way] received or lost in the
region and within the given period of time.

Therefore it may theoretically be conceivable that the influence
of the difference of radiation may be entirely balanced or even
overcompensated by the storage of energy.

However, this is not now the case on our earth for the whole
region of excess of insolation, since a flow of heat toward the
winter half of the globe[by convection]is always taking place and,
on the other hand, this makes itself felt in most incisive manner in
the polar regions at the time when the sun has his highest altitude.

It is well known that even in midsummer warm currents flow
from lower latitudes toward the poles, whereas cold air and cold
water flow thence away, except where foehn-like phenomena make
an exception in special localities.

Hence the convection current poleward continues even during
that season of the year in which the pole receives more heat than
any other point on the surface of the earth or of the boundary of
the atmosphere.

Now imagine any line surrounding the pole over which this
current is flowing, and let it serve as a dividing line between a polar
portion and the remaining portion of the insolation region, which
latter may therefore be designated as the equatorial region, and
distinguish by the index p all the quantities relating to the polar
region, then for the intensity of the current J, we have the equation

Or ele eben. ih yO)

Since now the current flows toward the pole therefore Jy must have
the same sign as would belong to it if qy and uy, were both equal to

zero, that is to say, as if only radiation were effective within the
dividing line. Therefore J, must be negative.

402 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

But since at the time of the summer solstice we must have

Ng UN ne oo es es ee ee ee
therefore we must also have
Uy > Ay — Ap

Hence the excess of insolation, large as it is in the polar region at
this season, still does not suffice to supply the demand for heat to
increase the energy, i. e., that needed for melting the ice and
evaporating the water. .

It is not difficult to deduce other theorems from these and thus
increase their number.

But these will suffice, since we have only intended to attain a
general point of view in connection with which various individual
investigations are to be conducted, and since the preceding theorems
suffice we will proceed to their application.

The general views thus set forth show that there are essentially
three points to which attention must be given in investigations
concerning the economy of heat:

(1) Insolation and radiation, including reflection.

(2) Increase and diminution of energy over individual portions
of the surface of the earth and in the atmosphere.

(3) Convection, or the transportation of heat by air and water.

The first of these subjects has already been studied by many and
will therefore not here be made the subject of new investigations.

On the other hand, attention will be given to the two other
headings which it seems to me offer less difficulty than the first,
although as yet less attention has been given to them.

(III.) THE THERMAL EXCHANGE IN THE GROUND

During the warmer portions of the day and the year the ground
absorbs heat which it again gives up during the colder portions.
It therefore plays the part of an accumulator or reservoir which
during special times stores up the energy that must be consumed
again at other times.

In this case the energy occurs in its simplest form and therefore
this investigation offers by far the least difficulties of all that refer
to heat exchange.

If the ground contains no water (which, however, can only be the
case approximately in rocks and in the desert) or if the water
content remains unchanged, while at the same time its temperature

INTERCHANGE OF HEAT—-VON BEZOLD 403

does not fall below the freezing point, then the total stored up
energy is present only in the form of heat that can be measured
thermometrically. y

If the ground contains water and if the temperature passes the
freezing poing in either one direction or the other, then the relations
become more complicated, but still problems relating even to
these cases are much simpler than most of the others that occur
in reference to the subject here treated.

Moreover, as will be seen later, this matter [of freezing] does not
at all come into consideration, at least in lower and middle latitudes,
in the determination of the quantity of heat taken in and given out
during an annual period and independent of the diurnal exchange.

To attain our present object the important matter is the solution
of the two following questions:

(1) How great is the difference between the quantities of heat
taken in and given out by a unit area of surface during a given
interval of time, that is to say, how great is the increase or decrease
of energy experienced by the earth beneath that unit of surface
during this interval of time?

(2) How great is the difference between the maximum and
minimum values of the energy present in this portion of earth dur-
ing a given interval of time?

The reply to the first of these questions will give the energy stored
in the earth during a given interval of time or the quantity present
therein at any moment.

The reply to the™second question gives us a measure of the
efficiency of the ground as a regulator of heat, provided we choose
the interval to be studied so that it includes a complete period of
thermal-exchange, such as a whole day or a whole year.

The reply to these two questions is extremely simple, as will be
shown immediately, since it only assumes a knowledge of the tem-
peratures at different depths and of the capacity for heat of the
unit volume of earth, the so-called volume capacity” whereas the
conductivity of the earth as well as the radiation or emission at
the surface do not come into play.

Moreover, in the solution of the second question, it suffices if we
know the earth temperature for that day or season at which the
temperature gradient in the highest layer of earth is zero.

Easy as it would be to answer these questions, and important as

12 As distinguished from the specific capacity which relates to the unit mass.
C.SAc

404 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

they are from the meteorological point of view, still the material
for reply offered by a superabundance of observations of earth tem-
peratures is extremely scarce, since in only very few cases has the
volume capacity of the appropriate earth been directly determined
and therefore the essential datum is missing.

The above questions will now be first answered theoretically and
then an attempt be made to see how far the formula can be con-
verted into numbers; also for simplicity it will first be assumed
either that the temperatures remain always above the freezing
point or that the earth is wholly free from water.

This being assumed the first of the two questions, i.e., the increase
of energy contained in the ground within a given interval of time
t, is answered by the following consideration:

Let C be the thermal capacity of the unit volume, h the distance
of any point from the surface of the earth, reckoned positive down-
ward, 0, the temperature of the earth at this point at the moment f,,
6, the corresponding temperature at the moment ?#,; imagine a
prism cut from the ground beneath the unit surface, then an infi-
nitely thin horizontal element of this prism having the thickness dh
receives in the given interval of time the quantity of heat repre-
sented by

OC ee Weal

The quantity of heat received by the whole prism to the depth H,
that is to say, the change of the energy within the prism results
from the equation

H
uy — ut, = f C (0, — 04) dh
or if C is constant

A
—uy= Cf G-A) dh... .. . (23)

In this equation 0, and @, are functions of h such that with increas-
ing values of h they very rapidly approach toward equality, so that
if great accuracy be not required the difference 0, — 0, may be
assumed to be o when H = ro meters even when #, and ?#, differ
greatly. If we consider only a short interval of time, such as 24
hours, then we may assume that this limit is reached when H = 1
and can put 0, = 0, for this depth.

INTERCHANGE OF HEAT—-VON BEZOLD 405

It we write equation (23) in the form

H . H
, = Cf 0,de —CYO,dh +
4 0 0

and choose #, as the initial point for counting the time so that t, =o
we may write

H
up=C)0,dh+K
J
or briefly, by omitting the index

H
u=CfOdh+K . Mace en ods
0

where K is a constant whose value depends on what we adopt as
the zero of energy. Theoretically it would be most correct to adopt
for this the absolute zero, but frequently it will prove advan-
tageous to start from the zero point of the ordinary thermometer
scale. Of course by doing this one may in certain cases obtain
negative values for the energy, but this will not be objectionable
so long as we are clear as to the meaning of this result.
The last given equation can also be written in the form

H
u=CH. 7 | Odh+K js iy ce

0

where we put
H

pj Otte O. een, ele (2a)
H

0

But this value @ is simply the average temperature of a prism cut
out of the ground to the depth H beneath the unit of surface, while
CH is the so-called water equivalent of this prism if we adopt the
expression used in calorimetry.

If now we designate by 0, and 9, the values of 6 corresponding
to the times ¢, and ¢, we obtain

i, ut = COG = er) nt at L096)

This equation may be interpreted thus:

406 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The change in a given interval of time of the amount of energy
contained in the ground beneath a unit of surface is equal to the
change in the average temperature of the ground from the surface
down to the depth at which the variations are inappreciable,
multiplied by the water value of a prism cut from this ground
from the unit surface down to the same depth.

Hence the energy stored in the earth attains its extreme values
simultaneously with those of the average temperature of the ground
if in determining these latter we consider the temperatures down
to the depths at which the variations become inappreciable.

The equation (23) allows of a,very simple geometrical presen-
tation (see fig. 56).

Let the depths h be shown as ordinates counted positively down-
ward, and the temperatures 0 as abscisse, then will the distribu-
tion of temperature in the ground at the moment # and down to
the depth h be represented by the curve A, B, as in fig. 56.

If now the distribution of tem-
perature is different at the mo-
ment t, and if it berepresented by
the curve A,B,then the area A,
B,B,A, which is included between
the two curves and the axis of
abscisse and the line parallel to

FIG. 56 this at the depth h, and which
may be designated by f, becomes at once a measure of the added
quantity of heat, since

O Ai Als! a

j= (0) dh

At the same time this method of presentation gives immediately
information as to the direction in which the movement of the heat
is taking place zm the different strata of the ground at the given
times, since the course of the lines allows us to recognize immediately
whether the temperatures increase or diminish downward.. The
direction of the flow of heat is shown by arrows in fig. 56.

Because of the great advantages offered by the consideration of
this curve, I will give it a special name, the ‘“‘tautochrone,’’ since
each such curve presents the temperatures that prevail at the
given time at the different depths.

Incidentally it may be remarked that from these curves we can
construct a remarkably instructive picture.

—_----

INTERCHANGE OF HEAT—VON BEZOLD 407

Assume that we have at different depths perfectly similar accu-
rate thermometers, whose scale degrees have exactly the same
length, and that these are placed horizontally, imbedded in the
ground so that all the zero points lie vertically one above the other,
then the curve connecting the ends of all the mercurial columns
is the tautochrone for any given moment of time. See fig. 57.

Since the phase of the oscillations going on daily and annually
in each layer changes from one stratum to the next, therefore the
curves A, B, and A, B, intersect each other at special depths and
generally speaking an infinite number of times; but since these
curves steadily approach each other as the depth increases and
almost coincide at very moderate depths, therefore we shall not
often need to consider more than two such intersections.

Of course, in the computation of the
total heat received and expended, the 94, A, x
areas on each side of such intersecting
points must be given opposite signs, as
is shown by the signs inscribed in fig.
Se

But the consideration of these curves
becomes especially valuable in that y B,
they allow us to recognize at once when
the quantity of heat contained in the
ground below any given horizontal plane attains a maximum or
minimum.

Of course this is only the case when no heat passes through the
plane in question neither in one direction nor the other, i. e., when
the temperature gradient in this plane is zero or

FIG. 57

eee
dh

Therefore at this place the tangent to the curve representing the
temperature is a vertical line.

If, therefore, we know only the daily mean temperatures for
the upper layers of the earth we can then directly find the two days
of the year on which the heat contained in the ground attains a
maximum or a minimum by seeking for those days on which the
above-mentioned condition is fulfilled, 1.e., when the temperature
curve is perpendicular to the earth’s surface.

If then we also know for these days the distribution of tempera-
ture in the strata below, then the area between the tautochrones

408 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

for these two dates gives directly a measure of the difference between
the greatest and the smallest quantities of heat contained in the
ground during the annual period; of course it is assumed that the
volume capacity of the ground is known.

But this difference is the quantity of heat that is exchanged
through the earth’s surface within one year, omitting,of course that
which is exchanged within the diurnal periods and of which the
remnant left over at the close of each day alone enters into this
present computation.

‘““The consideration just expressed has led to the Pe result
that for the determination of the annual exchange of heat it
suffices to know the distribution of temperature in the ground at
those dates of the year when the increase of heat changes to a
decrease and vice versa.”

In temperate latitudes these dates agree approximately with
the equinoxes.

Of course the exchange of heat within the diurnal period can be
determined in a perfectly analogous way.

We find the heat exchange within the diurnal period by select-
ing from the tautochrones for individual hours those two that are
perpendicular to the earth’s surface and then determine the area
included between them or’ from the corresponding integral.

A determination of the moments of time at which this occurs,
i.e., of the hours of the day at which the energy in the ground
attains its maximum and minimum valuesis, of course, only possible
where hourly observations for the upper strata of the ground are
available or at least those for quite short intervals of time.

In general we can at present only state that the changes from
increasing heat to diminishing heat occur some little time after
sunrise and a rather longer time before sunset. At Pavlovsk® this
occurs at the following hours: in December about 11 a.m. and
shortly before 1 p.m.; in January after 11 a.m. and before 2 p.m.;
in June after 5 a.m. and about 5:30 p.m.; in July about 5 a.m. and
before 6 p.m., as shown by the fact that at these hours the dif-
ference between the temperature at depths of o.o1 meter and 0.02
meter changes its sign.

At Nukuss “ these changes occur in January at about 8 a.m. and
4:30 Psat but in July at 6 a.m. and 6 p.m.

”»

_ ae a Wideman beratuton
Band XIII, No. 7, 1890.

4H. Wild: Ueber die Bodentemperatur in St. Petersburg und Nukuss.
Wild Repertorium fiir Meteorologie. Band VI, No. 4, 1878.

in Wild Repertorium ftir Meteorologie.

INTERCHANGE OF HEAT-——VON BEZOLD 409

Unfortunately these moments in the diurnal period can scarcely
ever be determined very accurately since it is precisely in the
upper strata of ground that most disturbances occur.

But circumstances are still more unfavorable to the determina-
tion of the quantity of heat that is exchanged during the diurnal
period, since the volume capacity of the ground is subjected to
continual variations and especially in these upper strata on
account of their varying content of water. ,

Therefore in determining the annual exchange we do well to first
leave the uppermost strata quite out of consideration and confine
ourself to the determination of the quantity of heat that is exchanged
through a plane lying somewhat below the surface, e. g., at a depth
of o.5 meter, and then correct the error thus incurred by an addi-
tion that will, however, intrinsically be less trustworthy than the
other numbers.

All the views hitherto set forth rest on the assumption that we
have to do either with a perfectly dry soil or else that the tem-
peratures 0, and 0, on the Centigrade scale have the same sign.

This latter condition is always fulfilled in evaluating the annual
exchange so long as we confine the investigation to regions where
the ground is free from frost or ice at the time of the equinoxes.

If we wish to free ourselves from the above-mentioned restric-
tions and include also those cases in which #,<o and @,>o0 and
where also the soil contains water, then we obtain the corresponding
formule from the following considerations:

Let c be the volume capacity of the perfectly dry porous earth,
x the water contained in a unit volume expressed as a fraction of
the unit of mass, then for the volume capacity C of the saturated
ground we have

C=c+-x for 0> 0 Centigrade
but for that of the frozen ground
C =c+0.5x for 6 < 0 Cent grade

Moreover, the thawing out of a unit volume of frozen ground at
o° C. requires heat to the extent of 80% calories.

Now assume that in its initial condition at the time ¢, the ground
is frozen to the depth H, and that corresponding to this we have
6, <o for h>H and 0,>0 for h>H,—but that at the time #, the
ground is completely free from ice and therefore 6,>0, then instead
of equation (23) we have the following more complicated one:

410 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

A, A,
=, = — { (645 ) Odi + 80211, + (c + x) 0, dh

0

A Hi,
+ {+8 @%—8) dh—=e { O,-0) dh. (27)
A, :
Hy, H
taf (0,—O)dh + (e+ 2) (Bo . die See.
/ Ms

where, however, we have still always to remember that 6, is always
positive, whereas in the first two integrals 0, occurs with the nega-
tive sign.

We can of course also represent this formula geometrically, but as
the presentation thus obtained is by far not so simple and clear as
above, where the temperatures are either wholly above or wholly
below the freezing point, therefore we refrain from reproducing
them here.

From these two expositions we see how very easy it is to deter-
mine the quantity of heat exchanged through the earth’s surface
if only one knows the course of the temperature at different depths
as well as the volume capacity of the ground and for temperatures
below freezing, as also the water content. :

By so much the more it is to be regretted that there is such a
remarkably small number of series of observations of earth tem-
peratures for which the volume-capacity of the ground is known
from direct experimental determinations.

In a subsequent communication I will attempt to show how far
the available observations can be utilized in order to determine
numerically from them the annual and perhaps also in some cases
the diurnal heat exchange in the ground for different places and
under climatic conditions as various as possible.

’* Such values for the actual soil in which the temperature observations
were made, I have only been able to find in the memoirby Lord Kelvin
(William Thomson ‘‘On the Reduction of Underground Temperature.”
Edinburgh. Trans. Vol. XXII; Part II, pp. 405-427. 1860) in which the
determinations made by Forbes are discussed. The values there given are:
trap rock of Calton Hill, 0.5283; sand from the observation station in the
garden, 0.3006; sandstone of Craigleith, 0.4623.

EE

INTERCHANGE OF HEAT—VON BEZOLD AWD

At present I will restrict myself to communicating the tauto-
chrones for Munich and for Nukuss.

Singer has deduced ten day means” from the observations of
Prof. J. von Lamont at Munich extending over a period of 25 years,
and therefore"this series is especially appropriate for the determina-
tion of the dates on which the heat content of the ground is a maxi-
mum or a minimum and thence the determination of the annual
heat exchange.

Unfortunately this series does not include observations at slight
depths, so that the values for the upper layer of 1.29 meters must be
extrapolated. JI have performed this extrapolation graphically

ZZ)

|
Hid

vit a
AMEE

FIG. 58

5°

but only in a rough way by the utilization of the observed tempera-
tures of the air; but since the temperatures of the highest strata are
subject to important disturbances, as will be shown from the obser-
vations at Nukuss, therefore it seemed unwise to expend much time
and labor in attaining a result that would eventually not have the
assurance of great accuracy.

Hence also in order to enable one to at once recognize this
uncertainty in the diagram the extrapolated portions of the curves
have been drawn in dashes.

Moreover, in fig. 58, the tautochrones have been drawn for inter-
vals of 20 days only, although in the memoir of Singer the data are

Lang and Erk. Met. Beobachtungen im Ké6nigreich Bayern im Jahr.
1889. Anhang, p. Io.

412 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

given for every ten days, since otherwise the diagram would be too
crowded with lines.

However, I thought I must include the curves for April 1 and
September 28, although they would remain unused in connection
with the twenty-day interval beginning with January 1st, since
these are the dates which among those contained in»Singer’s table
seem to come nearest to the dates of the minimum and maximum
heat content of the ground.

It is, moreover, quite possible that this condition is more pre-
cisely fulfilled on the 21st March and 22d September. I therefore

intentionally adhere strictly to the data available without under- .

taking further numerical or graphical operations in order to avoid
giving the appearance of a greater accuracy than I can truly assume
it to have.

The great symmetry shown by both the curves, and easily recog-
nized in fig. 58 by the crowding of the lines at the above given dates
is remarkable, in consideration of the non-artificial and direct
method of utilization of the data.

A special explanation of fig. 58 is hardly necessary since the
scale of temperatures (Centigrade) is given below on the lower line
and the scale of depths in meters on either end. The short dotted
lines at either end give the depths in meters at which the ther-
mometers were placed; therefore the intersection of the correspond-
ing prolonged horizontal lines with the curves gives the points that
were deduced from the observations.

The dates for which the curves are drawn are given at the top
in Arabic numerals for the days and Roman numerals for the
months.

As a contrast to the curve for Munich we give in fig. 59 the
tautochrone for Nukuss.

This offers a special interest because this station situated on the
Amu Darja represents a region of remarkably great insolation and
radiation with very slight amount of precipitation.

Moreover the series of observations is one of the very few that
give the material needed for the determination of the changes of
temperature in the very highest strata.

However, the temperatures of these upper strata are in fact
deduced from only one year of observation, whilst the numbers for
the greater depths are the means of three years.

This fact is remarkably shown in fig. 59 which is constructed
directly from the data published by Wild” without further interpo-

a eS eS ee

=e

, INTERCHANGE OF HEAT—VON BEZOLD 413

lation or smoothing, in that the curves show the greatest irregu-
larities in their upper portions.

This irregularity is easily explained, since on account of the many
disturbances that we encounter just beneath the surface of the
ground, we can only expect fairly reliable mean values frommany
years of observations made at short intervals of time.

Since we have only monthly averages for Nukuss we must regard
it as purely accidental that among the tautochrones constructed
from these values there are any that are exactly perpendicular to
the surface of the earth and correspond therefore to the limiting
values of the energy stored up in the ground. Such cases would in
fact assume that the times at which these extremes occurred fell
quite near the middle of the two months respectively.

FIG. 59

If, however, we consider the values for the very highest strata
as too uncertain and fix our attention first on the curves from 0.4
meter downward we find then March and September as the months
of least and greatest heat stored in the ground. But it looks as if
the September curve does not correspond to the full maximum,
although in August the maximum is not yet attained.

This seems to suggest that in Nukuss the increase of heat comes
to an end and the decrease begins before the autumnal equinox
(September 21), if we may be justified in drawing such a conclusion
from averages that represent so few years of observation.

If now on the basis of these considerations we actually compute
the annual heat exchange for Munich and Nukuss by taking as a
base the earth temperatures of April rst and September 28th at
Munich but the monthly means for March and September at Nukuss,
we find the following approximate maximum values of u, —u,

For Munich 36 Cy

For Nukuss 48 C,,

17H. Wild: Ueber die Bodentemperatur in St. Petersburg und Nukuss.
Wild Repertorium, VI, No. 4, 1878, pp. 45, 46.

414 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

where Ci, and C,, indicate the quantities of heat that are required
at Munich and Nukuss respectively to warm up the unit volume of
the respective soils by 1° C.

Unfortunately we are not able to say anything as to the values
of these quantities except that they can scarcely be smaller than
300 or greater than 600.%

However, the numbers 35 and 48 as just given for Munich and
Nukuss are still affected with great uncertainty since the data for
Munich begins first at 1.29 meters depth whilst those for Nukuss
end at 4 meters, so that in one case we must extrapolate upward,
in the other case downward. In fact this extrapolation downward
is necessary in both cases although to a less extent in the series for
Munich.

As values of the diurnal exchange we obtained for Nukuss 0.56 C,,
in January and 1.5 C,, in July, but again of course only a crude
approximation.

However, these numbers suffice to show the general magnitude
of the part that the solid ground plays as a reservoir of heat or a
regulator of temperature.

Thus, in order to deal with round numbers assume briefly that

n = Cm = 500, then would the quantity of heat exchanged within
the annual period suffice to evaporate a layer of water 30 milli-
meters deep at Munich and 4o millimeters deep at Nukuss.

Therefore, compared with the depth of the total rainfall which
amounts to 800" in Munich but only 85™™ in Nukuss, the
result is that the quantity of heat absorbed into the ground during
the warm season at Munich but given out again during the cold
season is scarcely 1/26th part of that required to re-evaporate the
annual precipitation, and even in Nukuss, the driest region of the
whole Euro-Asian continent, it is not one-half.

On the other hand, the quantity of heat exchanged at Nukuss
within the diurnal period is much larger than required for the evap-
oration of the average daily rainfall at that place.

Of course it must not be forgotten that the heat used in evapora-
tion goes partly to maintain the temperature of the upper strata,
so that the quantities of heat exchanged within the ground must
on this account appear somewhat smaller than they really are.

18 See von Liebenberg: Ueber den gegenwiartigen Stand der Bodenphysik.
Wollny, Forschungen., Vol. I, 1878, p. 3. And further C. Lang: Warme-
kapazitat der Boden-konstituanten. Forschungen I, p. 1og. Compare
also‘Ad. Schmidt :’Schriften’d. physik-oekonomische Gesellschaft zur Kénigs-
berg in Preussen, XXXII, 1891, p. 123.

INTERCHANGE OF HEAT—-VON BEZOLD 415

The investigations carried out in the previous section of this
memoir have led to the following results:

“The quantities of heat exchanged in [i. e., entering and leaving]
the solid earth are in general small as compared with those that are
required to ewaporate the [local] precipitation.

“In middle latitudes the knowledge of the earth temperatures
in spring and autumn, in connection with the knowledge of the
capacity for heat of the unit volume of the local soil, suffices for the
determination of the quantities of heat interchanged in the ground
in the course of the annual period.”

In these theorems, however, the following points must be con-
sidered:

The earth temperature must be determined at least by decades,
still ‘better by pentades during these seasons, if not for the whole
year:

The observations should extend to at least 6 meters in depth
beginning at 5 centimeters befow the surface:

The temperature should be determined for at least three points
within the upper meter arranged so that the successive distances
of the thermometers diminish with approach toward the surface.

“Hourly observations of those thermometers on which the diurnal
period exerts an influence, at least during the hours after sunrise
and before sunset, are needed for the determination of the diurnal
exchange of heat.”

Continuous registrations for these strata are still more desirable,
but these will attain their full importance only when it at the
same time becomes possible even at large intervals of time to make
continuous determinations of the heat capacity of the unit volume
in these strata or at least to keep informed of their water content.

In general all measurements of earth temperatures first acquire
their true value when the thermal capacity of the unit volume of
the local soil with its average moisture is directly determined.

It is very desirable indeed that for all places for which we already
have observations of earth temperatures such determinations be
made as supplementary thereto.”

19 Relative to the exchange of heat in the ground compare also the follow-
ing memoirs by J. Schubert: Der jahrliche Gang der Luft und Boden-tem-
peratur im Freien und im Waldungen und der Warme-austausch im Erd-
boden. Berlin, r900. As also Der Warme-austausch im festen Erdboden,
im Gewdssern und in der Atmosphire. Berlin 1906. [Note added 1906,
W.ov, 3B]

XX

ON CLIMATOLOGICAL AVERAGES FOR COMPLETE SMALL
CIRCLES OF LATITUDE

BY PROF. DR. W. VON BEZOLD

[Sitzungs Berichte der Berliner Akademie fiir 1901, pp. 1330-1343. Translated
from Gesammelte Abhandlungen, Berlin, 1906, pp. 357-370]

In a previous memoir! I have referred to the fact that in the
tabular or graphic presentation of average values for the complete
parallel-circles it is not advantageous to choose the geographical
latitude as argument or as abscissa. By this method of presenta-
tion which has hitherto been exclusively employed we obtain a
picture in which the polar regions are relatively too prominent.

It is well known that the zones included between small circles
having the same difference of latitude correspond to very different
areas according as they lie in high or low latitudes.

In a table progressing by equal angular differences the numbers
between the equator and latitude 30° occupy only one-half as much
space as those relating to the higher latitudes 30-90°, whereas
that part of the earth’s surface between thirty degrees and the pole
is not larger than the zone between the equator and 30°.

A table arranged in steps of 10° gives to the zone from 0° to 10
only the same space as that given to the polar cap between 80°
and go°, whereas the former occupies more than eleven times the
area of the latter.

Similarly a graphical presentation in which the geographic lati-
tudes are chosen as abscisse produces a wholly distorted image
from which one can obtain a correct idea only after careful medi-
tation. But the matter is entirely changed when we introduce the
sine of the geographic latitude as argument or as abscissa. When
this is done then the same tabular differences, i.e., equal differences,
of the arguments or equal distances on the axis of abscissa,
correspond to zones of equal areas on the surface of the earth and
the separate values or ordinates appear to have the weight that

°

1 No. XIII of this collection of translations.
416

CLIMATOLOGICAL AVERAGES—-VON BEZOLD 417

naturally belongs to them, independent of course of the uncertainty
that may affect individual numbers.

“Correct average values can now be deduced at once by simple
mechanical quadratures from the data of the table or from the
ordinates.” #

In the above-quoted memoir I have already referred to these
properties of the method hitherto employed and of the one here
recommended, except as to this last-mentioned point.

This idea will now be further developed and applied to various
meteorological elements, and it will be shown how simply the con-
nection between the corresponding average values can be per-
ceived and what special considerations come to light almost spon-
taneously.

This much being premised I now give the annual average values
of insolation, temperature and pressure of the air, cloudiness and
precipitation, first in tabular and then in graphic form arranged
according to the sine of the geographic latitude.

As fundamental data I use the average values given in the
ordinary way [for degrees of latitude]; for the insolation I use the
values computed by Meech;? for the temperature of the air I use
those given by Spitaler and Batchelder; for the atmospheric
pressure, the numbers given by W. Ferrel; for the amount of precipi-
tation, the figures given by John Murray, and finally for the cloudi-
ness, those given by Svante Arrhenius deduced from the charts of
Teisserenc de Bort; all of which are found collected in Hann’s
““Klimatologie,” p. 217 [or Ward’s translation, p.1oo].

From these values by very careful graphic interpolation the
values were deduced that correspond to the series of values 0.05,
oie oa eee a 0.95 of the sine of the latitude.

The values thus obtained are found collected in table 1 and repre-
sented by curves in fig 60. On the other hand, fig. 61 givescurves
whose ordinates are the arithmetical averages of the pairs of
values belonging to equal north and south latitudes. These latter
averages I call “‘holospherical” to avoid any misunderstanding,
while the two values belonging to each definite circle of latitude I
call “‘hemispherical.”’ I will refer to this point in a subsequent
paragraph.

See Hann: Handbuch der Klimatologie; 2d edition, vol 1, p. 103. [See
also L. W. Meech: ‘‘On the Relative Intensity of the Heat and Light of the
Sun.” Smithsonian Contributions, [X, Washington 1857, or R. de C. Ward’s
translation of Hann’s Handbook of Climatology, 1903, p. roo].

> Hann: Handbuch, p. 200 [or Ward’s translation].

418 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Table I. Fundamental table of mean values for each circle of latitude *

|
TEMPERATURE
| BGs -
Geog. Lat. Insolation | Pressure | pidlere a pais
Spitaler | Batchelder
i F | | | |
: | t t L328 | im | dm | n | dn
Sing | Daya | 4D °C 4t o¢y aera er eae | em o%,
cham, 8) eRe es |
0} goo’ | 151.6 —20.0 '— 20, fea | | — —
fe = s 48 | ts 2 oe Rae i Aa : a 758. 7| | 35] —

6 ena 20.6) _ ie oe hah 6.6 58. | "98. 3} stale ee
Beles ieee 45.5], + ke Nha ned 5 ale ah teak. scl te aalie sel neae
One Se: weil arang| 0.4 0.2 58.8) | Sol 61

21.7 Bor 3.2 + 1.1 +10 —I
0.80} 53 8 | 237.0 8.6 So5 3-4 59.9 | 58} 8 60
o275| 4B a5 |’assve'|~ -o" 6.8) ers as $8 eo gl et Sel Peele me
16.6 3.8 3:4 +0.7 ° 4
0.70, 44 26 | 272.2 aa 10.6 2 10.6 5 61.6 es I ail ul es
0.65} 40 38 | 286.7 a) 13-7 = ne we 62.0 eal 53 ud 5o Bi
0.60 36 52 | 299.4 ou ed Sai ea 16.0 nee 62.0 Stas 53 ol 47 a
0.95) $522 | 3Ir.0 ne 18. 3} oe 18.2 = 61.9 eared 55 ee a8 3
0.96) 30 © | g2r.0 } 1] 20°3 a 20.2 . 162.4 el 60 iss 42) _
0.45} 26 45 | 330.1 Re 22.2 Ge 21.9 a On 0.8 64 a 39 ;
. ~ S| sao [5 | =
0.40, 23 34 | 337-6!) 7 23.9 Naa 60. 3| | 69) , 4) 38
Bia pe ees 6.7 25 r.5 : 7 | 5 —1.0 Bol + 5 ane |
. 2 spate! 5.5 Ales Se Glee Ee ele ene Pel?) 3
0.30 17 28 | 349.8 26.0 25.8 58.7 109 42)
igs, 0.2 On% —o0.6 +29 | 3
0.25) 34 29 | 354.8 3| 26.2) ae 26.5 ie 58.1 er 159) ae 45 +
0.20} Ir 32 | 358.6 | a: 26. 4\ i 27.0 Sales Tea +0 e eS 48) 2
204 0-0 O.t 0.0 +26 (ave!
Git5) & 38 (| s6r-0 | 26.4 P57 fee | | 57.9 | 195 52
| ae | —o-l —o.1 | 0.0 +10 2
0.10 5 44 | 363.6 ss 26.3 Be 27.0 a 57.9 ao 196 roe 54) re
0.05| 2 52 | 364.8 7) 26.1 26.8 a Sauce Li kee Sa Tbe
| 0.4 —oO.2 —0.2 0.0 ° gees
0.00 o o (365.24 25.9) 26.6 58.0 195 58
} — ee ois —0.2 +0.3 — oe HOS
—0.05|\— 2 52 | 364.8 | 25.7 26.4 wot S803 IQI 60
| i—_—*<r..2 | —O»3) 0} -+0.2 | — 4 °
—0.10)— 5 44 | 363.6 ~* 25.4 ey 26.2 | Se 58.5 sa 186) __ 5 60 ie
—o.15|— 8 38 | 361.9 ia sal er -ae ty 25.9 | eye 58.8 eo 178| 8 58 ee
—o.20—11 32 | 358.6 Beall ol Tas § a Goes 1) 162 56)
=oupsl—rg 29 | 354.8) 3.8) 24.2 hehe 24.9 | ee 60.2 ere 130 a8 53 a
“|= 5.0 “| —0.8 ‘ —0.7 ““| +o. 8} — 32 —2
—o0.30\—17 28 | 349.8 e 23.4 24.2 | 61.0 97 51
| — 5.5] —0.7 —1.0 | +0.8 — 33 VG,
—o0.35|—20 30 | 344.3 22.7 23.2 61.8 71 48
| — 6.4] = a —1.4 | +0.8 *.| — 26) | —2
—0.40/— 23 34 | 337.6 21.5 21.8 62.6 |_ 265: 46
| —=—T 729 — Tie | —2.6 +0.6 + 6 —1
—0o.45|— 26 45 | 330.1 I) 20.3 20.2 63.2 \* (65 45
| | — 9.1 . —1.8 |= E35 | 0.3 ° | +1
—0.50!\—30 00 | 321.0 | | 18.5! 18.3 63.5 66 46
| — 10.90 —2.3 —2.0 | —0.5| ete | “Fg
—0.55)/— 33 22 | 311.0 ie cone 1603 | 63.0 72 49
—11.6 —2.3 — 2.1) —1.3 + 6 +4
—o.60!\— 36 52 | 299.4 13.9 14.2 61.7 he teh 53]
| —12.7 —2.4 —2.4 —1.8| + 11 +4
—o0.65/—4o0 38 | 286.7 np aa) | 11.8 | 59.9) | 97 57
—14.5 —2.3 —2.6 =2.7 +14. +4
—0.70/\—44 26 | 272.2 apc 9.2 Ne 9.2 ey 57.2! ag 110 es 61 2
—o.75/—48 35 | 255.6 rel ews r 6.3 si 54.0 2 116 at 65 4
| —18.6 —2.5 — 3.1 —4.0 leet lpatd
—o.80/—53 8 | 237.0 | 4.2 3.2 50.0 I1I3) 69
—o.85|—58 LZ, | 20963 ae! calc eens pee 44.5 ey 105]- 3.2 74 =
care “= j=—25.5 ; —_— 4 — “| —4.2| — 8 |—
—0.90— ’ — — . 5 _
Bae at aa la ees AR Ate a We al ee =| She calle
Beds 1 dilate Ee —15.66 | — _| — — |_|—{_]/=—
00, —9 1 15s. aw.

*The numbers here given under D and ¢ often differ somewhat from those given in the above
quoted former edition of this memoir. The reason for this lies in the fact that the interpola-
tions have been executed much more carefully for this table than in the memoir XIII above
referred to, where only an approximate statement was desired.

The tables and curves relating to the individual elements in these
two methods of presentation are so arranged as to bring out most
clearly the relations between their relative progress. In order to

CLIMATOLOGICAL AVERAGES—VON BEZOLD 419

make this also prominent in the tables the more important extreme
values are set in heavy-faced type.

In the diagram also the ordinates of the first three elements which
are in their nature positive have been plotted positively upward,
while the two others are plotted positively downward [as shown
by the scales at the sides of the diagrams]. Finally the scale of
ordinates is so chosen that the relationship between the neighbor-
ing curves strikes the eye at once.

No further explanations of table I seem necessary. It need
only be added that the insolation D is expressed in multiples of
that for an average day at the equator; the barometric pressure
(2) is in millimeters; the temperature of the air (#) in Centigrade
degrees; the cloudiness (7) is in percentages and the rainfall or
equivalent depth of melted snow (m) is centimeters.

The sines of the geographic latitude are used as abscissex, as
already mentioned in the introduction. The semicircle at the
base of the figure can be considered as one-half of an orthogonal
projection of a diminutive globe whose axis S. N. lies horizontally
and on which parallels of latitude are drawn for each 10°.

Hence it suffices to prolong any ordinate of this figure down to
the periphery of this semicircle in order to at once perceive the
latitude to which it belongs. This figure also elucidates the method
by which the interpolation was carried out.

The numbers on the side of the diagram give the values of the
ordinates for the individual curves. Their significance is easy
to understand by means of the attached letters and symbols, so
that the connection between these numbers and the accompanying
curves is seen at once.

Moreover, the portion of the network projecting above the codr-
dinates and leading up to the inscribed numerals is drawn in like
the corresponding curves, but rather feebler.

If now we consider these curves we at once derive the very com-
forting impression that our knowledge of the distribution of the
most important meteorological elements is far more complete than
would be suspected from the ordinary method of presentation.

That portion of the polar regions for which the averages of tem-
perature and pressure for whole circles of latitude can only be
formed by bold extrapolations amounts to scarcely one-tenth of
the whole surface of the earth, and even for cloudiness and precipi-
tation this is true to very nearly the same extent, at least as concerns
the principal features of this distribution in latitude. ~

Moreover, we see from the tables and especially from the diagrams

420 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

that the distribution of the most important meteorological elements,
which of course depends primarily on the insolation, is modified by
the distribution of atmospheric pressure, and this is the most
important matter.

The curve of average temperatures has the greatest similarity
with that of the theoretical sums of insolation, provided the scale
of ordinates be properly chosen.

But whereas the insolation by its very nature is accurately sym-
metrical on both sides of the equator with a maximum at that
circle, the maximum
of the temperature
curve is pushed into

/0 OS 06 04 O2 O Q2 04 06 08 10

Bas os ea Tans lee Di
SORE ea ee

Oe 4 sae the northern hemis-

~ heals =es8 a phere. At the same

| Fea opagbeeier lo No ; time a second sym-

210 een aes wee pues metrically located but
170d. 2 a ate. 8° .

‘ome Be much feebler maxi-

702mm aa a mum in the southern

758 ne hemisphere is indi-

794 ws —— =16° cated by the change
pee a e S'

750 , N, --507 in the differences, i.
ORS 2 Wd se sce Ses sffcicehth

TAG" axe --- 7070 $F the diff tial

742 LiL | | ahedrehion | || ae aes ‘cane’

ommo| See Pf --120 This peculiarity in

PEPE Shee --200cm the curve of average

s| TN temperatures for

eet
SN ea

whole circles of lati-
tude is still more strik-
ing when we seek to
approximately elimi-
nate the influence of
the unequal distribu-
tion of water and land
in the two hemispheres by uniting into one arithmetical mean the
two values corresponding to equal north and south latitudes.

By this process which has already been once used by my advice,
by E. Sella,* we obtain average values that, as already remarked,
may be designated as ‘‘holospheric” in contradistinction to the
ordinary “‘hemispheric,’’ which apply only to the latitude circles
of either hemisphere alone.

30

FIG. 60. HEMISPHERIC AVERAGES.

4 See Met. Zeit. XIII, pp. 161-166, 1876.

eS err her, errr tC ee eee

CLIMATOLOGICAL AVERAGES—VON BEZOLD 421

Doing this and applying a similar method to the other elements
we obtain the curves given in fig. 61.

In this figure it is still more clearly seen or at least suggested,
that the maximum of the insolation curve is broken into two
separate maXima in the temperature curve. This separation
becomes more striking if we imagine the temperature curve as
formed of two superposed systems, one of which, the simplercurve,
has only one maximum at the equator; the second superposed on
that would therefore show two clearly separated maxima.

If we pass to the
next curve in fig. 60,
that for atmospheric
pressure, We perceive
easily the two well- °”

N
is)
S
og
S
ad
gS
sS
gS
i)
i)
Ss
to
8
y
S
Q
S
os
[Se
iS)

Oey al Bers Sard STi

ee a

Wi aN

known maxima first °° a2"
pointed out by Ferrel. 2/0 -- 16°
The difference be- 0d A -- 8°
tween this present 70mm- Cs GF
method of presenta- %6

tion and the ordinary 752

method such as we 74&mm-. : 50%,
find, for instance, in es 0%,
the ‘‘Lehrbuch” of ei diene
Sprung consists es- = a -120
sentially in the fact Ht tt apc

that the maxima are
separated farther
apart and. that the
regions of low pressure
in the higher latitudes
are compressed _ to
smaller spaces. How-
ever, the ordinary
method of arrangement of the tables and graphic presentation has
one advantage, not to be underestimated especially in the investiga-
tion of the average distribution of pressure, since the differences
in respect to atmospheric pressure for equal increase of latitude
are simply proportional to the gradients toward the pole.

In the present method of presentation the inclination of the
curves to the axis of abscissa gives directly and most appropriately
an idea of the magnitude of the gradients.

In the diagram fig. 60, as already stated, the two maxima of

4

FIG. 61. HOLOSPHERIC AVERAGES.

422 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

pressure are separated farther from each other than in the older
method, that is to say, we perceive that the zone between these
two circles of maximum pressure covers more than one-half of
the whole surface of the earth, whereas in the temperature curve
the zone between the maxima covers only about three-tenths of
the earth’s surface.

Proceeding further in our study of fig. 60 we next consider the
curves of mean cloudiness and of precipitation. As these two ele-
ments diminish with increasing pressure, therefore, as already
mentioned, for the sake of comparability of the curves the ordinates
are drawn positive downward.

This method of collating the different elements reveals the con-
nection existing between them in truly surprising manner and
clearly brings out the great importance of Ferrel’s zones of atmos-
pheric pressure.

Indeed I might go so far as to recommend the considerations here
established as the starting point for lectures on Climatology, and as
a method of passing gradually from the so-called ‘‘solarclimate”’
to the actual local conditions by some scheme that keeps the aver-
age values of whole latitude circles plainly in view.

By always choosing the sine of the latitude as the argument, as
has been done here, we at once attain correct ideas as to the weight
that is to be attached to the individual values in considering the
economy of nature, but independent of course of any uncertainty
that may attach to them by virtue of the method of determination
and which will gradually diminish.

Before I go further and draw certain conclusions relative to the
temperature curve, I first give at the end of this section the table
in accordance with which fig. 61 is drawn, to which I will only add that
the numbers interpolated from Spitaler and Batchelder are indicated
by S and B.

On examining these numbers one is surprised that the averages
of precipitation and cloudiness, resting on rather feeble observa-
tional bases, when combined into holospherical averages show a
remarkably regular progression.

After these general remarks which refer only to the presentation
in general as also to the average values for the whole year, still
further conclusions will be drawn from the whole diagram.

As already remarked, first of all we see the great similarity
that exists between the curves of insolation and temperature as
drawn on the scale here adopted, and which at once shows that
these two quantities can be connected by one empirical formula at
least throughout a considerable portion of their courses.

CLIMATOLOGICAL AVERAGES—-VON BEZOLD 423

Table II. Holospherical averages

Atmospheric} © TEMPERATURE.

; Insolation. Pressure. ee Precipitation) Cloudiness.
Bua Days em per ct.

5 SIC Bs a. 3

mm.
bees eS eee Sele ee
0.9 189.8 749.3 = _— 67 —
0.85 215.5 52.6 0.8 o.1 77 67
0.8 237.0 54.9 3.8 Bg 85 63
0.75 255.6 57.4 6.7 6.7 87 61
0. 7, 272.2 59.4 9.9 9-9 82 57
0.65 286.7 ° 60.9 12.6 12.6 75 53
0.6 299.4 61.8 T5.0 Lie E 68 5o
0.55 3II.0 62.4 17.2 17.7 63 46
°o.5 325.0 62.6 19.4 19.5 63 44
0.45 330.1 62.1 21.4 21.0 64 42
0.4 2270. 61.4 22.17 22.6 67 42
C35) 344.3 60.5 24.0 23.9 75 44
0.3 349.8 59.8 24.7 25.0 98 46
0.25 354.8 59.2 26.2 25.8 144 49
0.2 358.6 58.9 25.6 26.2 173 $2
0.15 361.9 58.4 2517 26.5 186 55
Ont 363.6 58.2 25.9 26.6 I9gl 57
0.05 364.8 58.1 25.9 26.6 193 58
0.0 365.2 58.0 25.9 26.6 195 58
}

In fact one can with surprising accuracy compute the average
temperature ¢ for any latitude circle from the number D of any
thermal days corresponding to that circle by the formula

pas Babe
5.2

The following table 111 shows how far this approximation holds
good, as it gives not only the computed values oftbut also under S
those given by Spitaler and under B those given by Batchelder,
united into their respective holospheric averages. The adjoining
columns give the differences between these averages and the com-
puted 7.

| | | |
7) t S is. | B. | b= Bz | 5 1S. —B.
| | | |
| |
°° 27.7 25.9 1.8 26.6 Teer: —0.7
Io 26.8 | 25.7 | Tver 26.4 0.4 Oi]
20 23.9 | 24.1 | ele 2) 24.1 —i0.2 0.0
30 19.2 19.4 | =O). 12 19.2 0.0 “Oia
40 13.0 12.9 | Our | m0 | 0.0 —oO.1
5o | Pie) 5.7 —0.2 | 55) 0.0 +0.2
60 —2.5 —0.3 —2.2 —1I.T —1I.4 +0.8

424 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

In this table, I first use the ordinary method of presentation in
which one proceeds by equal differences of latitude in order to
simplify the comparison between the values computed by this
formula and those found by Spitaler and Batchelder. Later I
will give the similar table with the sine as the argument.

From latitudes 20° to 50°, or 0.6 of the whole surface of the earth,
this table shows a surprising agreement between the computed
values and those deduced by Spitaler and Batchelder from obser-
vations and here united into general averages for the two hemi-
spheres or into holospheric averages. The error is nowhere more
than o.2° C. within the given latitudes.

It is only in the equatorial zone and in the higher latitudes that
the differences become larger and that too for explanable reasons,
so that thereby the empirical formula acquires higher interest.

In the equatorial zone the computed temperatures are higher
than the observed. This is undoubtedly a consequence of the
larger cloudiness, since this depresses the temperatures in lower
latitudes, as also a consequence of the above mentioned influence®
of the complex convection whereby heat is carried from this zone
into the two surrounding belts, so that the temperatures in the
equatorial zone proper must be lower, but those in the two neigh-
boring zones higher than would be suspected from the insolation
conditions.

Since in higher latitudes the cloudiness hinders the terrestrial
radiation, therefore to this circumstance we must ascribe the fact
that the temperatures beyond 50° of latitude are higher than would
be expected from this formula.

Moreover, the last column of table 111 containing the differences
between the values deduced from Spitaler and Batchelder for
similar latitudes shows that these differences are of about the same
size as the departures of the numbers computed by the formula
from those derived by these authors from observations, excepting
for the above-explained systematic differences in the equatorial
zone.

Hence the formula reproduces the actual existing conditions with
surprising accuracy.

The result of this study may therefore be expressed as follows:

‘““A change of 5.2 thermal days in passing from one parallel of
latitude to another corresponds to a change of 1° C. in the mean
temperature of the whole circle of latitude.”

5 See Mechanics of the Earth’s Atmosphere, 1891, p. 243, and this present
collection of translations, No. XIII.—C. A,

CLIMATOLOGICAL AVERAGES—-VON BEZOLD 425

If we compare this result of the formula, not as above with the
holospheric value t= 3(¢,y9 + t_g), but directly with the numbers
given by Spitaler and Batchelder for the individual latitude circles,
then the departures between computation and observation are of
course somewhat larger but still they are always within moderate
limits.

We see this from the accompanying table 1v, which also provides
an interesting survey of the different relations of the two hemi-
spheres. ;

Table IV. Comparison between the hemispheric values deduced from observa-
tions and the computed values

g t | Ss i—S B. ‘—B | SB
90° N. | —13.4 — 20.0 6.6 — 20.0 6.6 0.0
80 —12.4 —16.5 Hees —16.9 4a5 +0.4
7O | Sera Xa} 0.7 i oY | I.0 ong
60 = 2:5 —o.8 —1.7 — 1.2 =1..3 +0.4
So Sigh) 5.6 —o.1 5.8 —0.3 —0.2
40 I3.0 I4.0 —1.0 Ti.) —0.9 +O. i
30 | 19.2 20.3 —I.I 20.2 = Trad +o.
20 23.9 25.6 a 24.9 —1.0 +0.7
Io 26.8 26.4 0.4 PA gpl hk —0.3 —Oin/7
° 27.7 25.9 1.8 26.6 Tees Sie\e7/
—10 | 26.8 25.0 8 2507 I.1 —0.7
fe 23.9 22.7 1.2 eG 0.6 —o.6
— 20 19.2 18.5 0.7 18.3 0.9 +0.2
—40 G3..0 11.8 L.2 12.2 °.8 —0.4
—So 5.5 5.9 —0.4 ag 0.2 +0.6
—60°S. — 2.5 0.2 —2.7 — Tea —1I.4 +1.3

|
|

If now we use the sine as the argument we obtain the following
tables v and vI.

Table V. Comparison between the holospheric "values deduced from observa-
tions and the computed values

Sin g t | Ss. | #8. B. | t-B. | S.—B.
0.0 27.7 25.9 1.8 26.6 TI —0.7
O.1 27.4 25.85 ToD 26.6 0.8 —0.7
0.2 26.5 25.6 0.9 26.2 0.3 —o0.6
0.3 24.8 24.7 o.1 25.0 —0.2 —0.3
0.4 22.4 22.9 —0.3 22.6 —0.2 o.1
o.5 19.2 19.4 —— ii 19.5 —0.3 —o.1
0.6 DOE 15.0 | o.t a ae E 0.0 —o.1
0.7 9.8 9-9 | — Ont 9-9 Cent 0.0
0.8 sign 3.8 25/4) RS} —0.2 0.5
0.9 — 6.0 a = = = ——
I.0 —13.4 —_— — _— _ —_

|
|
|
|

426 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

If we compare the numbers in table v with those before given
then the departures between the values deduced from observation
and those computed by the formule give a similar picture. But
the positive differences in the lower latitudes stand out more
prominently in correspondence to the greater surface that the
equatorial regions occupy so that the latter receive their proper
weight only in this method of collation.

Similar remarks apply to table v1 which now allows us to recog-
nize the differences of the temperatures of the two hemispheres in
a manner corresponding to the true importance of the individual
zones.

The two tables v and vi show in admirable manner the syste-
matic departures from the formula that are caused by the dissimilar
distribution of water and land over the two hemispheres.

The last columns of these tables are also worthy of notice as they
also show that there are differences between the values deduced by
Spitaler and Batchelder that, so far as concerns magnitude, are of
the same order as the differences between the computation and
observation of holospheric means. We thus perceive how perfectly
the formula is adopted to represent the average distribution of
temperature.

Table VI. Comparison between the hemispheric values deduced from observa-
tion and the computed values

Sin @ t s. | #8. Ss. t—B. S.—B
I.0 —13.4 —20.0 6.6 — 20.0 6.6 0.0
0.9 = 6.0 - 4.6 —1.4 = 4.9 —I.I 0,8
0.8 erg! 3.8 —0.4 3.4 —0.3 oO.
0.7 9.8 10.6 —o.8 10.6 —o.8 0.0
0.6 ES 16.1 = ie) 16.0 =O. o.1
o.5 19.2 20.3 — F010 20.2 —1.0 o.I
0.4 22.4 23.9 —0.9 23.4 —=T JO 0.5
0.3 24.8 26.0 —1.2 25.8 —1.0 0.2
O.2 26.5 26.4 0.x 27.0 —o.5 —0o.6
O°. 37 26.3 oi 27.0 0.4 <7
0.0 As A | 25.9 TS 26.6 Ted —0.7

=—0.2 Cd 25.4 2.0 26.2 La2 —o.6

—0.2 26.5 24.8 ne7 25.0 1.0 —0.7

—0.3 24.8 23.4 5 Ser | 24.2 0.6 —o.8

—0.4 22.4 2x.5 0.9 | 21.8 0.6 =—0.3

—o.5 19.2 18.7 [s55) 18.3 0.9 0.4

—o.6 Ts, L 13.0 Tia 14.2 0.9 —0.3

—0.7 9.8 9.2 0.6 9.2 0.6 0.0

—o.8 hehe 4.2 aie ee 3-2 —9. 1 +1.0

‘These last columns also show that the departures between the
numbers found by the two authors progress quite regularly. From

CLIMATOLOGICAL AVERAGES—VON BEZOLD (427

53° to 17° north latitude the numbers given by Batchelder are
almost invariably smaller than those by Spitaler but are larger
in the equatorial zone and in the southern hemisphere.

-

Especially do we recognize the value of the method of presenta-
tion here developed when we apply it not only to annual averages
but to specific small periods of time.

Thus, for instance, the curves given by Wiener® and which have
been copied in educational works’ showing the distribution of
insolation on March 20,
April 12, May 5, and June
21, present a very different
picture after being redrawn
as shown in fig. 62.

In this figure the scale of
ordinates is chosen, as done
by Hann, so that the sum
total of the solar radiation
received on the 20th March
by a point on the equator
[at the upper surface of the
atmosphere] or the so-called
“Thermal day’’ is taken as
the unit.

If now we examine this
figure in which we havealso
added below for compari-
son, the temperatures for
January and July as given
by Spitaler we see that the
remarkably large sum total
of insolation that comes to the polar regions during the summer
solstice takes up far less space in this diagram than in the older
method of presentation, in other words, that portion of the cir-
cumpolar region that receives such a relatively large insolation is
_ only a very small fraction of the surface of the earth.

It is easily understood what a great advantage this method has
in that the total insolation coming to any zone on a given day, is

1o5'0 O8 O06 0402 O 02040608 |0

FIG. 62. DISTRIBUTION OF INSOLATION.

® Zeit. d. Oesterr. Gesell. f. Met., XIV, plate 1, fig. 3, 1879.
7 See, for example, Hann. Handbuch der Klimatologie; 2d edition;
Vol. 4, *p:..a7:

428 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

always represented by the area of the portion bounded by thecorre-
sponding portion of the curve, the initial and final ordinates and the
intermediate portion of the axis of abscisse.

Similarly the whole of thesurface that lies below the curve for
any given day is proportional to the sum total of the insolation
that the whole earth receives on that date and inversely proportional
to the square of the distance of the earth from the sun.

If now by means of a planimeter or by means of mechanical
quadratures, using the tables in which the argument is the sine,
we convert these areas into rectangles, then the vertical sides of
these rectangles represent the average sum total of insolation for
the whole earth, and of course similar results may be obtained for
all elements that can be plotted in corresponding manner.

By the application of this method to the numbers under D in
table 1 we obtain 299.3 or in round numbers 300 thermal days
as the mean amount of insolation received annually.

If now we imagine the energy given by the sun annually to the
whole earth’s surface as distributed uniformly over this surface,
then on the average every element of the surface would receive
as much as an equal surface element at the equator receives in
300 average equatorial days.

We can thus also determine with great ease the latitudes that
receive annually this average sum total of insolation. We have
only to seek in the preceding tables the places at which D = 300.
This value we find at sing = 0.6 or if we interpolate more accur-
ately sine ¢ = 0.604 which corresponds to g = +37° 9’. Hence
those points on the earth’s surface (or the upper limit of the atmos-
phere) lying between the parallels of 37° 9’ north and south receive
more than the average insolation and those lying poleward of
them receive less. :

For this reason we may appropriately designate these two paral-
lels as the insolation normals or the ‘‘ Median lines of insolation.”

Since the sines are proportional to the surfaces of the corre-
sponding zones, it follows directly that 0.604 or 6/10 or 3/5 of the
earth’s surface receives more and 2/5 receives less than the aver-
age quantity of radiation coming annually from the sun.

In similar manner we can take from these same tables the ‘“‘tem-
perature-normal’”’ or the ‘‘median line of the temperatures” by
seeking that circle of latitude whose temperature is the same as
the average temperature of the whole earth’s surface, which is
aa Os

In the northern hemisphere we find this latitude at sin g = 0.62

CLIMATOLOGICAL AVERAGES-—-VON BEZOLD 429

or g = 38° 18’, and in the southern hemisphere at sin g = 0.57
or g = 35° 00’—so that here also within a zone that covers 0.6 of
the whole surface of the earth there prevail temperatures that lie
above the average, whereas outside of this zone or over the polar
segments, that both together cover 0.4 of the total surface, the
temperatures are below the general average.

These statements may suffice to give an idea of the great advan-
tages offered by the method of presentation here employed.

The important conclusions that we can draw on this basis with
reference to the thermal economy at the earth’s surface and in
the atmosphere will be reserved for a future memoir.

XXI

ADIABATIC CHANGES OF CONDITION OF MOIST AIR
AND THEIR DETERMINATION BY NUMERICAL AND
GRAPHICAL METHODS

BY DR. OTTO NEUHOFF

[Memoirs of the Royal Prussian Meteorological Institution, Vol. I, No. 6.
Berlin, 1900, pp. 271-300]

§ 1. INTRODUCTION

The investigation of the adiabatic changes in the condition of
moist air, that is to say, those changes that a mass of air experiences
when it is expanding as it rises, or when it is being compressed as it
sinks, without addition or diminution of its internal heat, has
achieved a very prominent importance in modern meteorolcgy.
The old view as to the formation of precipitation, in which we
attributed the principal influence to the mixture of masses of air
having different temperatures, and also the idea that the heat of
condensation of water raises the temperature of the place above
which the condensation occurs, became untenable after the more
accurate study of the foehn winds in the Alps by von Helmholtz
(1862) and Hann (1866) had led to very different results. It was by
the application of the principles of the mechanical theory of heat
to the processes in the atmosphere that we attained to the laws of
the changes of temperature in ascending or descending air, and
these lattér were thus established by the most prominent philos-
ophers, such as Lord Kelvin,! Reye,? and Peslin.®

In the publications of Hann,‘ and Guldberg and Mohn,°* the

1'W. Thomson: On the convective equilibrium in the atmosphere. Mem.
Manch. Soc. (3) II, 125-131.

* Reye: Vertikale Luftstr6me in der Atmosphaére. Zeitschr. f. Math.,
1864, IX, S. 250-276.

5 Peslin: Bull. hebd. de 1’Assoc. scient. de France,1868, ITI.

‘Hann: Die Gesetze der Temperaturainderung in aufsteigenden Luft-
strémungen und einige der wichtigsten Folgerungen ausdenselben. Meteorol.
Zeitschr., 1874, 5S. 321-29, 337-46.

°Guldberg and Mohn: Etudes sur les mouvements de 1l’atmosphére.
Christiania, 1876 and 1880. Ueber die Temperaturanderung in vertikaler
Richtung der Atmosphdre. Meteorol. Zeitschr., 1878, S. 113-124.

430

‘i

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 431

behavior of expanding moist air was developed mathematically
more fully and brought into convenient arithmetical solution.

At the same time Hertz® constructed his very practical diagram
which made it possible to determine graphically, by the use of
curves, the changes in condition of moist air, avoiding any compli-
cated numerical computations.

Although this diagram served as a very convenient help in com-
putations, von Bezold’ introduced into meteorology not only the
more exact mathematical development of the changes of condition
of moist air but also the graphic method of presentation by Clapey-
ron® in order to represent graphically the thermodynamic processes
going on in the atmosphere independent of any of the limitations
introduced by any assumptions.

Von Bezold also first called attention to the fact that the processes
going on in the atmosphere are often not reversible except in a
very limited sense and that we have not always to do with strictly
adiabatic changes but with those that can be designated as pseudo-
adiabatic.

W. M. Davis® afterwards sought by diagrams to explain the
changes of temperature and the associated processes in the atmos-
phere in a manner similar to that of von Bezold but by the applica-
tion of another system of codrdinates, in that he used a horizontal
line as the scale of temperatures but a vertical line as the scale
of altitudes. This latter method of presentation had been occa-
sionally used to graphically present the results of Glaisher’s balloon
voyages.?°

In recent times this method has been used by von Bezold for a
great variety of cases where it is important to represent the depen-
dence of any meteorological element on the altitude. In order to
represent the course of the temperature a diagram or network of
squares is used, in which the horizontal side corresponds toa change
of temperature of 1° C, and each vertical side to a hundred meters
in altitude.

Unfortunately, an extensive application of the theoretical results

®° Hertz: Graphische Methode zur Bestimmung der adiabatischen Zustands-
anderungen feuchter Luft. Meteorol. Zeitschr., 1884, S. 421-31.

7yon Bezold: Zur Thermodynamik der Atmosphadre. Sitzungsber. der.
Berl. Akad., 1888.

8’ Clapeyron: Ueber die bewegende Kraft der Warme. Pogg. Ann. 1843,
S. 446-51, 566-86.

9W. M. Davis: Ferrel’s convectional theory of tornadoes. American
Meteorol. Journal, 1889, S. 344.

10 Sprung: Lehrbuch der Meteorologie. Hamburg, 1885, S. go.

432 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

to the atmospheric processes has hitherto been greatly hindered by
the fact that memoirs on this subject are distributed through the
greatest variety of periodicals, most of which are very difficult of
access. On the other hand, the want of tables and diagrams is
felt all the more since even the diagram of Hertz is at the present
time no longer easily accessible. In the handbook of Zeuner™
moreover, in which the changes of condition of moist air are fully
considered this subject is treated only as a side issue.

The present publication has for its object to respond to the
existing needs in the most perfect manner possible. In this memoir
the equations for the determination of changes of condition in
moist air are given under rigorous physical assumptions and with
an exact mathematical treatment of the problems.

It has been possible to so arrange the results that the processes
during the different periods can be expressed by one single, simple,
and general formula, whose application to special cases by means
of the accompanying tables demands only the smallest amount of
time and trouble.

Moreover, a new adiabatic diagram for the diminution of tem-
perature with altitude has been constructed which makes it possible
to accomplish a graphic determination of the adiabatic changes of
condition of moist air and that too by use of the above-mentioned
extremely convenient net work of squares. In this diagram the
pressure is represented by straight lines crossing the page on a slant
and is read off by the scales on either side of the diagram. By
reason of the diversity in the style of treatment of the systems of
lines and by the use of a red tint for the network of squares, the
use of the table is made easier and its perspicacity is increased.

The accompanying tables, 1 to 6, thus serve as auxiliary for the
computation whereas table 7 considered as a table of adiabatics
gives in one view for every 2° C. the associated values of the pressure,
temperature, altitude and change of temperatuure per 100 meters,
of saturated air, ascending adiabatically.

The utility of the tables, their accuracy, and method of use are
illustrated by practical examples.

At this place I would express my sincere thanks to my highly
honored master, von Bezold, for the stimulus that he has given me
in the accomplishment of this work as well as for his kind and active
interest in it.

1 Zeuner: Technische Thermodynamik, Bd. II. Leipzig, 1890.

ADIABATIC CHANGES OF MOIST AIR——~NEUHOFF 433

§2. IN GENERAL

The elements that represent tHe condition of a mass of air at any
given moment are temperature (t), pressure (p) and moisture; the
latter being considered as to quantity and form of aggregation.
If now the mass of air is by any influence whatever forced to rise
or sink, then the most important questions are as to the changes
that it will experience and as to the altitudes at which these occur.

The problem is simplest when we assume that the mass of air
neither gives up heat to its surroundings nor receives heat from
them. Under these circumstances we have to do with adiabatic
changes of condition, and the equations that express the relation
between the different variables for this condition are called adia-
batic: equations. If we represent adiabatic conditions by curves,
then we obtain adiabatic curves, or, for brevity, ‘“‘adiabats.”

If a mass of airis carried upwards to greater heights it comes under
lower pressure since the pressure in the atmosphere diminishes with
the altitude. Consequently its volume increases and the mass
becomes specifically lighter. But by the increase of volume and
the overcoming of the external pressure a work of expansion is per-
formed; the quantity of heat necessary to perform this work, if the
change is an adiabatic one must be drawn from the internal energy
of the air. But in the case of gases, this internal energy is deter-
mined only by the temperature. Consequently the result of
adiabatic expansion is a lowering of temperature.

In this case for dry air the diminution of temperature for a given
diminution of pressure can be expressed by a simple law which
reads |

Pippy = (T/T)
or
log p — m log T = log p, — m log T, = constant . . (1)

This law was derived by Poisson by an elementary course of reason-
ing but entirely in harmony with the developments of thermody-
namics, hence this equation is known as Poisson’s equation. In
this equation p and p, express the atmospheric pressure and T
and T, the absolute temperature of the free air; the exponent is

where

434 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

is the ratio of the specific heat of dry air under constant pressure
to the specific heat of dry air under constant volume;
Cy = 0.2375; C, = 0.1685 therefore

k
= | —— ae — cS
k=1.4land m ran 3.441

The equation of Poisson is here written in the form usually used
in thermodynamics where the “specific pressure p” in kilograms
per square meter corresponds to the weight of a column of mercury
having the height b and the sectional area of one square meter,
therefore we have p = 13.6 bor, still better,

p = 13.596 b 8
845

where g is the acceleration of gravity at the location in question
and g,, corresponds to the acceleration of gravity at sea-level and
45° latitude.

Since in this equation there occurs only the ratio p/p, of the
pressures therefore instead of specific pressure We may introduce
the heights of the corresponding columns of mercury, which is
always done in the following memoir.”

If now the air contains aqueous vapor, then for adiabatic expan-
sion we must take into consideration the condensation of the
aqueous vapor at the different stages of expansion according as
the result of the condensation and precipitation is liquid (i.e.,
rain) or solid (i. e., ice and snow), and these stages are best charac-
terized by the terms introduced by Hertz as the dry stage, the rain
stage, the hail stage, and the snow stage.

According to this system the first stage is that in which the cool-
ing of moist air by virtue of adiabatic expansion proceeds without
saturating the air with aqueous vapor. So long as this condition
holds good there is no precipitation of water, wherefore this stage
is called the dry stage.

The second stage begins as soon as saturation occurs in con-
sequence of diminishing temperature. If the expansion is pushed
further and the cooling goes on with it,then the aqueous vapor is

* Lummer and Pringsheim make k = 1.4025 for dry air.—C. A.
Tt may here be remarked that the notation here used generally agrees
with that of Guldberg and Mohn in their “Etudes.”

ADIABATIC CHANGES OF MOIST AIR—~NEUHOFF 435

partly condensed and falls as rain or is suspended in the air as
water, and this is the rain stage. ,

This stage continues until the temperature has fallen to o° C.;
now the precipitated water freezes while at the same time partial
evaporation takes place while the temperature remains constant.
As soon as all the water is frozen this isotherm of freezing, this hail
stage or third period,is past and the fourth or snow stage begins
as the lowering of temperature proceeds further.

These processes bring about different final results according as
the condensed water falls away from the cooling air, either immedi-
ately or at some subsequent time. But for mathematical study
we may assume that the mass of air rising up to a certain height
carries with it its condensed aqueous vapor and therefore remains
unchanged as to its total constituents.

If the inverse process takes place when the air is sinking, then in
consequence of the increase of temperature the condensed water
evaporates again and the mass of air returns gradually to its former
condition at its initial elevation above sea-level or its initial pres-
sure; in this case we have perfectly reversible changes of condition.

But it is otherwise if the condensed aqueous vapor falls away from
the air as precipitation. The quantity of vapor remaining in the
air at the end of the ascension will, because of the increasing tem-
perature that accompanies its ascent, depart further and further
from its point of saturation. This process is now in descending air
entirely different from that which took place in ascending air,
wherefore von Bezold expresses the changes of condition when we
take into consideration the loss of the precipitation as ‘“‘limited
reversible. ”’

If we have mathematically and numerically considered the first
case, that of the unchanged constituents of a mass of air, then the
further modifications necessary for the second case, that of the
entire or partial loss of the precipitation, are easy to understand
and to apply numerically. But the latter is only possible when we
start, not from the ordinary assumption of thermodynamics which
considers a unit weight 1 kilogram of moist air as the basis of the
computation, but when we separately consider one kilogram of
dry air and x kilograms of aqueous vapor. Under the assumption
that the condensed ‘aqueous vapor is to be assumed constant
then the weight (1 + x) kg. of the moist air during the whole ascen-
sion will also be constant. The quantity x that is mixed with the
weight of 1 kilogram of dry air or the quantity of aqueous vapor
that is contained in (1 + x) kg. of moist air is designated ‘‘the mix-

q

436 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

ing ratio”? by von Bezold, while the quantity of aqueous vapor
contained in 1 kilogram of moist air is “the specific moisture.”

If the precipitation separates from the moist air at a definite
altitude then the weight of x kilograms of aqueous vapor diminishes
toa smaller quantity, €,which is then to be introduced into the subse-
quent computations as the appropriate quantity. of moisture.

If we have a mixture of gases then the total pressure of the mix-
ture is equal to the sum of the partial pressures of the components,
while the volume of the mixture is the same as the volume of each
separate gas, since each gas expands as though the others were not
present.

In computations relative to these changes of condition moist
atmospheric air is to be considered as a mixture of air and aqueous
vapor so long as the condition of saturation is not attained.

The pressure of the saturated aqueous vapor is a function of the
temperature only; its values have been determined experimentally
by Regnault and expressed in numerical tables. * Since the specific
weight of aqueous vapor is 0.804 therefore the relative weight of
this vapor with respect to the air is

If R represents the gas constant for dry air, then the constant for
aqueous vapor is R, = R/e.

We shall now proceed to consider the individual stages of adia-
batic expansion of moist air.

§3. THE DRY STAGE AND THE SATURATION POINT

Let the volume of the mass of moist air containing 1 kilogram
of dry air and x kilograms of aqueous vapor be V cubic meters;
the general temperature of the mass of gas be J = 273° + ¢on the
absolute Centigrade scale; the partial pressure of the dry air be
p’ and the partial pressure of the aqueous vapor p”, therefore the
total pressure of both is p = p’ + p”; then according to the equa-

*The value of R = 29.272. R, = 47.061. The ratio k = 1.4025 for dry
air, and other physical constants, especially the revised values of vapor pres-
sure for water and ice, will be found in the last edition of the Smithsonian
Meteorological Tables.—C. A.

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 437

tion of condition for gases and for each component of the mixture
we have the equations V p’ = RT and

VOe Fr

’ 2

respectively. Hence by addition we obtain

H
ve=(1+")er Sa aT

as the equation of condition for the mixture and by division we
obtain

for the mixing ratio, which is proportional to the ratio of the partial
pressures of the two components, so that if x is constant then this
ratio must also be constant. It is often advantageous to introduce
the barometric pressure p into the equation of condition and in this
case F is specially designated by an index letter ~.

If in this last equation we substitute for the pressures whose ratio
enters therein the heights of the mercurial columns, then the mixing
ratio is expressed in grams by the equation

x = 6 DD eee

2 ae

Let e,, be the pressure for saturated aqueous vapor then we have

@
ie = G22

by the use of which expression the quantity of aqueous vapor con-
tained in 1 + x kilograms of saturated moist air can be determined.
The quantity x,, required for saturation is a function of the baro-
metric pressure p and also of the temperature, since the pressure
for saturation e,, = f(t) is dependent on the temperature alone.

The quantity x in grams of the aqueous vapor contained in (1 + x)
kilograms of saturated air is computed according to this formula
for the temperatures + 30° C. to — 30° C. ordinarily occurring in
meteorology and for different barometric pressures p, and is given
in table 1, columns 4 to 9. This table contains also in the second

438 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

column the values of the vapor pressure e,, of saturated aqueous
vapor corresponding to the different temperatures according to
the data given by Guldberg and Mohn in their “‘ Etudes,” p. 15.

The table for x here given differs from that previously devised
by von Bezold,* in that the latter determined in grams the quantity
of moisture in the form of vapor contained in a kilogram of satu-
rated air and which therefore corresponded to the idea of the
specific moisture of saturated air.

The quantity

or (1 + 1.608 x) R =f (x) can appropriately be called the
mixing constant as [it is dependent on the mixing ratio, x. In
column 3 of table 4 are given the auxiliary quantities needed
for the computation of the mixing constant corresponding to
values of the mixing ratio from o up to 30 grams; we have only
to substitute Kg for R, so that, for example, for dry air Kg = 2.1528
and for x = 12.5 grams we have k’g = 2.1960.

If the quantity of heat d Q is given to any gas then its change of
condition is expressed by the thermal equation

dQ =c,dT + Apdv
_or since we have
Cy =¢, — AR and pu = RT
hence

dQ =c,dT — Avdp =c,daT — ART,

We make use of this latter form of equation in order to obtain
the equations for pressure and temperature, and therefore for any
change of condition of the mixture we obtain the following equa-
tions for the changes in the individual components, the dry air
and the aqueous vapor, which we distinguish by means of the
superscript indices prime and double prime.

do Seat = apr et
Pp p’

dQ” = xc, aT —xA = vg ap

€ Pp"

18 yon Bezold: Zur Thermodynamik der Atmosphire. Sitsb. Berlin Akad,
t890, p. 239 or 390, or Mechanics of the Earth’s Atmosphere, 1891, p. 287.

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 439

Hence as the equation of change for the mixture there follows:

i= @+eyan-a(i+2)er@... .@
E

4
where Ge = 0.2375 indicates the specific heat of air and Gis =. 0.4805
the specific heat of aqueous vapor, both under constant pressure.
In the case of adiabatic changes the quantity dQ =o, hence after
separating the variables we obtain as the differential equation
of the adiabat -

a ak % dp
O= (Cp + * op) > alt )xa
Bee ee Vea
AR x (a
Lee
€
For brevity put
C.
oy iF or
a Pp ality,
AN Ss eae
then by integration we obtain
log p/Po = m, log T/T,
and also
log p — m, log T = constant . (4)

= log po — m, log Ty

as the equation of the adiabat for the dry stage.

This equation is identical with Poisson’s except that the factor
m has various values that depend upon the mixing ratio x of the
air. After substituting the numerical values we obtain

eres eee
1 4+ 1.608 x

m,

In order to establish the numerical value of this factor and to
understand its influence on the result of our computation for

440 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

different quantities of moistures table 3 has been computed progress-
ing from o to 30 gram by gram with x as the argument giving in
column 4 the value m, for the different mixing ratios, for instance,
for x = 12.5 grams the humidity factor ism, = 3.459. The limits
of this table are for « = o grams or dry air m,= 3.44 and for x = 30
grams m,= 3.48.

Equation 4 holds good for the adiabats of the dry stage only up
to the point when the air attains a condition of saturation. Any
further diminution of temperature then causes a condensation of the
aqueous vapor. This saturation point is therefore the bginning
of the rain stage and its determination is therefore necessary
before proceeding to any further computation. The expansion
proceeds not only by reason of the diminution of air pressure but
also by reason of the diminution of vapor pressure. But since so
long as the air is not saturated the weight of the vapor that is
present, or x, remains constant, therefore during the dry stage

is to be considered constant, hence also the ratio e/p is unchanged.
Further in equation 4 in place of the total pressure (p) the vapor
pressure (e) can be substituted (or the dry air pressure is zero)
whence

log e/e, = m, log T/T,
or

log ¢ — m, log T =.conStant . .... «. (6)
log @, — m, log T,

The fundamental condition for the existence of the dry stage
consists in the fact that the actual pressure of the aqueous vapor e
is smaller than the pressure é,» that belongs to air™ of the same tem-
perature saturated with aqueous vapor. This last equation (5)
therefore holds good up to the point when e = @ém. At the moment
of saturation we have equation

log ¢,, — m, log T, = log e, — m, log T, = constant = S. . (6)

where the subscript index , designates the initial condition and 7,
4So in the original but possibly it would be more exact to say ‘“‘that be-
longs to it when in air, etc.”’—C. A.

eEEEEeEEeEeEeEeEEOEeEeEOeEeEeEeEeEeEeEeEeEeeeeeeeeeeeeeeeeeeEeEeEeEeeeEeeEeEeEeEeEeEeEeEeEeEeEeEeEeEeeeEeeEeeEe—e—eEeEeEeeEeEeEE—Ess ee Eee eee

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 441

indicates the temperature of saturation. This value of S can now
be obtained directly from a table such as table 3 that contains the
appropriate values of S computed according to this last equation
(6) for all the temperatures likely to come into consideration, i. e.,
for each degree from + 30 to — 30 and for the values of m, =
3.44 to 3.48. For any value of S computed from the initial values
t, and @, for which also m, log T, can be taken out of table 3, we seek
in the table of corresponding temperatures that one which represents
the temperature of saturation and which can be obtained by
interpolation to the nearest tenth of a degree.

For example, let us now consider a mass of air expanding adia-
batically from the initial pressure p)= 760 ™™” and the initial tem-
perature tf, = 20° C. and the relative humidity 86 per cent. Accord-
ing to table 1 for 4) = 20° the vapor pressure for saturated vapor is
é = 17.4"™ and the quantity of moisture at saturation is x,, = 14.6
grams, hence for relative humidity 86 per cent the vapor pressure
will be e¢, = 15.0™™. The mixing ratio or the weight of aqueous
vapor present in (1 + x) kilograms of moist air is obtained from
the expression

and is 12.5 grams. We may approximately write x/%m = €)/€m,
whence also follows for x the value 12.5 grams. According to
table 4, column 4, there corresponds to this mixing ratio the
humidity factor for the dry stage m, = 3.46. If this mass of air
expands adiabatically to the point of saturation then for the de-
termination of the saturation temperature according to table 3,
column 5, we form the product m, log T, = 8.5355, whence for
@é, = 15.0™™ there results S = 7.3594. With this value of S we
enter table 3 under m, = 3.46 in column 11 and find the corre-
sponding temperature of saturation ¢, = 17.0° C. The correspond-
ing vapor pressure is @ém = 14.4™™.

The corresponding pressure is obtained in millimeters at once
from the equation (4) and is p = 733.2™™, and with this we obtain
Pp’ =p—e=718.8™™. If we wish to know the volume (V) of the
mixture, or (1 + x) kilograms of air, we shall obtain it from the
equation of condition. Thus from table 4, column 3, for x = 12.5
grams we obtain Kg = 2.196. Therefore for the initial condition
p = 760™™ and T = 293° we have V ~o.847 cubic meters and the
specific volume v = V/1.0125 = 0.837 cbm. In the saturated con-

442 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

dition V = 0.869 cubic meters and v = 0.858 cubic meters. Under
diminishing pressure the air becomes specifically lighter, hence for
the same mass the volume becomes larger.

If we wish to form an equation for the direct determination of
t, it is necessary to represent é, as a function of #. For this purpose
we can make use of the empirical formula of Magnus

7.45 t

log é,, = log 4.525 + 235 41
Substitute this value of é@», in the equation (6) and we obtain
for the variables ¢ or T the relation

7.45 t

Se Res m log T — (m log T, — log @ + log 4.525)
but from this equation 7 can only be obtained in an indirect way
by successive trials.

The upper limit of the first stage is determined by the saturation
point. When the expansion continues further, the values just
computed become the initial values for the second or rain stage.

In the dry stage the behavior of moist air differs from the behavior
of dry air only by reason of the value of the factor m which can be
taken from table 4 as a function of the quantity of vapor (x) that
is present. The departures of the value m, from that for dry air
m = 3.44 are only slight.

§4. THE RAIN STAGE

After the attainment of the saturation point the condensation of
aqueous vapor begins and during the further expansion of the air
it continues to be saturated. In orderto obtain the relation between
pressure and temperature in this stage we form the thermo-dynamic
equations. First we have

; dp’
dQ! =¢,dT—ART

in which dQ’ expresses the quantity of heat that is necessary for
the expansion of 1 kilogram of air.

The total quantity of moisture at the beginning of the condensa-
tion, consisting of vapor (x grams) and water (y grams) we will call

EE

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 443

€, so that € = x + y for this stage. On the assumption that all
of the water remains in the air we have € = x, or the same quantity
of vapor that existed in the dry stage. On the other hand, if we
take account of the loss of the precipitation by its fall from the cloud
then € willshave a smaller value on the average.

The heat necessary for any change of condition involving con-
densation when ¢ = (x + y) kilograms of moisture are present is

GY

dQ” =EcdT + Tai)
where c is the specific heat of water or on the average 1.013 accord-
ing to Clausius and 7 is the latent heat of evaporation of water which
latent heat being set free from the condensing vapor does a part of
the work of expansion as the air ascends and thus diminishes the
rate of fall of temperature with altitude. risa function of the tem-
perature and according to Regnault can be expressed by the empiric
formula r = 606.5—o695¢. The total quantity of heat required
for the change in condition of the mixture of dry air and vapor is
equal to the sum of these two quantities or

| Pe
)-arr E
P

xr

iL

40-( +éjaT+Ta(

In adiabatic expansions we have dQ =o whence we obtain the
following as the differential equation of the adiabatic for this case

ae a(=) pete
O= (+ Fc) 7 + rT) ?

If we indicate the initial conditions by the subscript index o we
obtain by integration and a simple transformation

1 id ae Cp + f¢ lo L + M (ee an “st ) =M, log
P's AR Toot ARN os ie
Me ee. a
sieca lt, eelfves Sani lnlete br ae
gal a ”)

where we have introduced the notation

Grok Ec Cy
1 = ee

Cc
: as Bee + fe) = saa ( + 4.265 €)

444 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The value of the humidity factor m,, of the rain stage is given in

table 4, column 5, for quantities of moisture between o and 30 grams.
[M is the modulus of the system of logarithms.]
_ For example, we find for ¢ = o gr., 11 gr. and 30 grams respect-
ively, the following values m,, = 3.44; 3.60 and 3.88. In conse-
quence of the high specific heat of water the differences are con-
siderably larger than those of m, for the dry stage.

For the variable quantity of vapor («) we may again also substi-
tute the partial pressure by introducing the relations

p” Se
LS,
p Pp
and
R
iy aed

é

where €m = f (t) is to be taken from the table of vapor tension for
saturated aqueous vapor as given in column 2, table 1. We have
here assumed that the volume of the saturated aqueous vapor fol-
lows the law of the equation for elastic gases; this assumption, for
the low temperatures we have to deal with, is far more correct than
if we should put V = xwin strict accordance with the law of thermo-
dynamics where u is the specific volume of aqueous vapor, which
must first be obtained for specific temperatures from the equa-
tion given by Clapeyron,®

r dp
ie ae

The volume of any water that may be present is negligible and is
indeed so slight relative to that of the vapor that numerically
speaking it cannot come into consideration.

According to the above reasoning equation (7) now becomes (8),
where the small quantities r and e depend on temperature only.

p' r ce rT - By |

IO a a ass ae. (8)

PT ee

1 Vergl. Zeuner: Technische Thermodynamik., Bd. II, 1890, p. 333.

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 445

If now we put

r lM

T HR's = 4
and ,

fo) MM

BAR ee

then we obtain the equation for the adiabat in the following simple
form
p’ - fe ao
OR pe Mars Gane apes. gO
SP. lane age?

which may be written

a a
log bv’ i p' Se cers log a log Po = a — My log fo constant (9)

0

The factor a which may be designated the condensation factor
is a function of the temperature only and therefore behaves
analogously to the vapor tension @m of aqueous vapor. The law of
variation with temperature followed by ais also analogous to that for
€m. The graphic representation of this quantity shows a curve
analogous to the curve of elastic pressure for aqueous vapor.

In order to determine from equation (9) the value of p’ expressed
as a height of a column of mercury we must also express the
pressure ¢m by its corresponding height in mercury.

The values of the coefficient a are given for the corresponding
temperatures for each degree from o° to 30° in table 5, column 5,
and can be taken from this by using the argument ?. Intermediate
values can easily be determined by linear interpolation. For
instance, for ¢ = 17°, 10°, and 0° we have the corresponding values
@ = 115.71, 75-98, and 39.99.

The volume (V) of the mixture is obtained from the-equation of
condition for dry air Vp’ = RT. The quantity of vapor present x
is obtained from the corresponding equation

Cm

oa Pp
If in equation (9) by the use of the last-mentioned relation we
express the atmospheric pressure p’ in terms of x then we may

446 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

also form the adiabatic equation for the diminution of the quan-
tity of vapor with temperature. We thus obtain

1 2: ; i |! a M “7,
has Oa aR in eke

If we substitute

M r

ria ie

and collect together the constant terms there results
log x + ax + mlog T — log e,, = constant

The coefficient a which is contained asa factor in the coefficient
a can be taken from the same table 5, column 5, as a function of t.

The quantity of moisture € which enters the value of m, in
equation (7) is the sum of the vapor x and the water y, therefore
the difference € — x = y gives the quantity of the condensed water.

The rain stage attains its upper boundary when the temperature
has fallen to o° C. If now the liquid water has remained in the air
then it enters the isothermal hail stage in which the water freezes
to ice.

As an example we will now follow the mass of air, hitherto
considered during its further expansion within the rain stage.

For the point of saturation, which is the initial point of the rain
stage, we had found ¢ = 17.095 p = 733.27"; @ = 1.44™™;
p’ = 718.8™™; € = x, = 12.5 grams.

During the rain stage the connection between pressure and tem-
perature is given by the equation of the adiabat (9): from the table
4, column 5, we have in this case m, = 3.62.

If now the expansion goes on further until the temperature cools
to 10° C. then a = 76.0 and equation (9) in this case becomes

76.0
log p’ — oh 2.6573

From this we obtain the partial atmospheric pressure ~’ = 606.3™™
and p = 615.5, since e = 9.2™™ when ¢ = 10°.
-The amount of the vapor still present is 9.4 grams, hence the
vapor that has been condensed to water is y = € — x = 3.1 grams.
The volume now amounts to V = 1.005 cbm. and the specific

volume v = 0.993 cbm. For further expansion to 0° C. or to the

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 447

end of the rain stage we should obtain the values a = 40.oand
mM, = 3-62.
By making use of equation (9) we obtain

ieee - = 2.6008

whence p’ = 482.6™" and thence p = 487.2™™

The quantity of vapor present is x = 5.9 grams and the quantity
of water is y = 6.6 grams. The volumes are V = 1.218 cbm. and
U = £.203, ebm.

§5. HAIL STAGE

If fluid water is still present in the air during the freezing stage
which begins when the temperature falls to o° C. then the tempera-
ture will remain constant and therefore also the quantities that
depend upon the temperature, namely, e = 4.6™™ and r = 606.50
— 0.695%.

The total moisture € which will be considered as unchanged and
which consists of vapor (x), water (y) andvice (g), is therefore still
E=x+y+2.

The quantity of heat that is needed for isothermal expansion is
now made up of the quantity that is needed for the expansion of
the air added to that which is needed for the evaporation and freez-
ing of water.

If 7, is the latent heat of melting ice then the thermal equation is

dV
Bon 2 Ret

Vv +rdx—r,dz

In the case of adiabatic expansion dQ =o and by integration there
results

BRT. OV
0= Aan. © a aie) rig (2 — 2)

For the freezing period, which when it occurs is generally of very
short duration, we will compute only the condition of the moist
air at the end of this stage.

At the beginning of this hail stage no ice is present, therefore
Z) = o and at the end of the period all the water is frozen, wherefore
o and therefore z = € — x, showing that the initial quantity
of vapor (x,) has been slightly increased to a newvaluex. Thecon-
nection between these quantities is best understood by the use of
the scheme given by von Bezold in his lectures:

448 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Von Bezold’s scheme for the hail stage

Beginning End
z= 0 y=0
fF =X + V f(= Sree

For the final result we have therefore

one ars is P
SS ie OE ede at ce gins ‘

In consideration of the relations

’

Po
— = —'gnd *% =— le

YP p
this equation becomes
} LOM OF wt, , 1: Mr M Yes
OB ES Gira ge open sr eae Bm Oa he eee

In this equation the numerical values for the temperature 0° C.
are as follows:

Mf 4,
Ga val e@ = 45.20
yp
= AR’ ig £@ = 39.99
pie se Re
ETAT ae Tet

and therefore for the determination of the partial pressure of the
air at the end of the hail stage the above equation becomes

’

' 45.20 40.0
log p’ — —,— = log p — —- — 1.82€
P Poa;

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 449

Instead of the temperature term we have another in this equa-
tion, namely, — 1.82 € which contains the total quantity of
moisture €. At the end of this stage the quantity of vapor (x),
which is not €onstant but increased, can be obtained from the
expression

e
Ri AG ae
a
The equation for the change in the quantity of vapor can also be
written directly, viz:

log x + 15.80 x = log x, + 138.98 x, + 1.82 €

After all the water is frozen the snow stage begins.

If at the beginning of the hail stage the partial atmospheric
pressure pi = 482.6™™ is equalto the barometric pressure p =
487.2™™ diminished by the vapor pressure ¢ = 4.6™™, as in our
previous example, and if the quantity of moisture present is € =
12.57 grams of which the vapor is ¥ = 5.9 grams and the water is
y = 6.6, then we obtain from equation (10) for the final pressure at
the end of the hail stage the values p’ = 471.8™™ whence p =
476.4m™m,

At the end of the hail stage there is present x = 6.1 grams of
vapor and z = 6.4 grams of ice, while 0.2 gram of the water that
was originally present has been evaporated.

The new volumes are V = 1.246 cbm. and v = 0.231 cbm.

§6. SNOW STAGE

The behavior of the mass of air during its further adiabatic
expansion is now similar to that which prevailed during the rain
stage. The only difference consists in the fact that in place of
the specific heat of water we introduce the specific heat of ice
Ce = 0.5 and we also add the latent heat of liquefaction for ice
Yr, = 79.24 to the latent heat of evaporation (r) for water, so that
instead of r we have to substitute r + 1,.

In other respects the process is the same as before; as the air
ascends and cools a further condensation of aqueous vapor occurs
but now it condenses directly to snow.

Therefore the differential equation of the adiabat of the snow
stage becomes

% dp’
Oe (Co 6.6,) a4 - fd zr + 7%) mde tetuiapes lee)

45° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLa5a

In this equation € again indicates the quantity of moisture in the
air which is now composed of vapor (x), ice (z) and snow (s) so that
€ has the same meaning as (x,) in the first stage, since we assume
that all the water has remained suspended in the air after conden-
sation. If this is not the case then € has a smaller value in propor-
tion to the quantity of precipitation that has fallen away from the
alr.

The integration of this equation gives us

pled tO ot M (EO r ater
Ps ie a4 0 AR 7 ts

log

If we adopt tke notation

eee «Me (1 oe) = 3.441 (1 + 2.1054) =m,
AR AR \ Cp

and consider that

Ss)

pete
2
there results
ie ae - M r+ Te eG aay T + es aes fi
Bi: -» SATE 5 Cat AA ne elie gee i
If we substitute
1 ae a
Seg ee
AR L

we then obtain the adiabatic equation for the snow stage in the
same form as in previous cases, Viz:

PL am peor so

log = ;
p, a a tiem ial lag 2

which also may be written

log p’ — bolge? m. los T= constant. ~ fs
p’

The humidity factor m,, = f (€) is determined bythe quantity
of moisture or the mixing ratio € and is computed as given in
table 4, column 6, for values of £ from o up to 30 grams. Thus,

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 451

for example, we find for € = 12.5 grams; m,, = 3.53 and for € =
30 grams; m,, = 3.658.

On the other hand, for the rain stage and € = 30 grams we had.
m,, = 3-881 and for the dry stage with € = 30 grams we had m, =
3.482. ’

Therefore in the snow stage the influence of ¢ on m 1s less than
in the rain stage. The coefficient a is a function of the tempera-
ture only; its value is given in table 6, column 6, for each degree
of temperature from 0° C. to — 30°C. Thus, for instance, in the
snow stage for ¢ = o° and for # = — 20°, respectively, we have
@-= 45.20 and a = 10.06.

Thus the equation of an adiabatic line is easily and quickly
written to suit any special case. The solution of this equation
must be made by trial, which is, however, quite simple, when we
start with a correct estimate of the first approximate values.

From the preceding it is evident without further explanation how
we obtain the total pressure p and the quantity of vapor x as well
as the volume of the mass of air.

The diminution of the quantity of vapor with temperature is
deduced from the following equation found by the combination of
equation (11) with the value x = os

/

logx +ax+m,, log T — loge = constant

where
UE OG
Qa — oS SS
lee oh:

is to be taken from column a,, of table 6, column 4, as a function
of the temperature.

The mass of air continues in the snow stage as long as no further
expansion takes place. As the initial pressure of the snow stage
occurs at the level where temperature is 0° C. it is the same as the
final pressure at the end of the hail stage for which e =.4.6 and
Po = 471.8™™. If the expansion goes on until the temperature
becomes — 20° C. then for € = 12.5 grams we obtain from table
4 the value m,, = 3.53. But since from table 6 fort = o we have
a = 45.2 and fort = — 20 we have a= 10.06, thereforefrom equation
(11) we obtain the final pressure p’ = 311.5 and consequently
since ¢ = o.9™™ we have the total pressure p = 312.4.

The guantities are: vapor, x = 1.8 grams;ice,z =6.4 grams, and
snow, S = 4.3 grams.

452 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
The volumes resulting are V = 1.749 cbm.andv = 1.727 cbm.
The mass of air cooled during expansion to — 20° C. in this

example has the same initial value as was used in the example com-
puted by Guldberg and Mohn. The final pressure of 292 milli-
meters as computed by them in their ‘“‘Etudes” is incorrect, as
indeed Hertz has already shown.” 17

$7. THE GENERAL EQUATION FOR THE ADIABATS OF MOIST AIR

Considering all the preceding results connectedly, we perceive
that the law of variability of temperature and pressure in ascend-
ing and descending currents of moist air for the whole series of
stages can be represented with mathematical exactness by the
general adiabatic equation

log p’ — San log T = constant
p’

which without further change is to be used in this form for the com-
putation. This equation differs from the original Poisson equation
only in form by the corrective term — a/p’.

In all previous attempts to make use of Poisson’s equation for
moist air during the stages of condensation, as for instance by a
variation in the factor m and by the introduction of the so-called
virtual temperature, 7, on the absolute scale

we have been led to very complex and obscure formule. For
example, Guldberg and Mohn® found for the rain stage the follow-
ing formula
dr de
Cy +H {€ - — —- r—
Ene ee ( dt a)
AR ie cay ; 1 oe
AR 273 +4

16 Hertz: Postscript to his previous article ona graphic method. Met. Zeit.,
1884, p. 475:

1 Note. This error does not occur in the text of the translation as given
in this present collection which indeed was entirely revised by Guldberg
and Mohn in 1885s, so as to constitute a new edition. - C.738

18 Guldberg and Mohn: Ueber die Temperaturdnderung in vertikaler Rich-
tung in der Atmosphdre. Met. Zeit., 1878, S. 113.

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 453

Sprung, in his Lehrbuch, has followed their course of reasoning
but in place of m he has introduced the quantities

us e
€ o3.4a(1 + 0.2585 ) in the dry stage

aceon gdo sc
: pdt.
a be, ralmstage

AR 30.622 2—
pT

m Il

In the formula now developed we have to distinguish merely a
dry stage and a condensation stage which are separated from each
other by the temperature of saturation, which may equally well
be above or below o° C.

If the condensation stage begins at temperatures above o° C.
then, when the air has cooled to the latter temperature and if the
condensed water remains in the air, the process of condensation is
interrupted by the isotherm of the hail stage, which must be con-
sidered as a special case by itself since its course is conditioned only
on the presence of liquid water in the air.

This also can be at least approximately expressed in the general
form, when with the initial pressure at the end of the second or
rain stage we use the factor a,, = 40.0 and with the final pressure
at the beginning of the fourth or snow stage we use the factor
a, = 45.20. In place of the temperature term we have to sub-
stitute the term

a, € = 1,82 €

which contains the quantity of moisture so that the isothermal
adiabat now reads

log p’ — Sw = log pp - —a,é
p’

or Eee eeey (62)

45.2 40.0

log p’ — = log p, — — — 1.82 &
p Anes

The exact formule for the computation of the final pressure
from the associated temperature and the given initial condition
assuming adiabatic expansion of moist air are therefore as follows:

454 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

I. The dry stage. Adiabat for dry air.
log p — m log T = constant.

II. The condensation stage. Adiabat for saturated air.
log p’ — om log 7 = constant. .
p

In this way the exact determination of the adiabatic changes of

moist air is made dependent on the evaluation of one simple formula. -

$8. PSEUDO-ADIABATS

The adiabatic change of condition in moist air assumes that the
condensed water remains suspended in the air during the expansion
and that the mass of air retains its original total constituents
unchanged, and that there is therefore no diminution in its total
energy by reason of any removal of the results of precipitation.

But when the mass of the water due to condensation becomes
considerable it will partly or entirely separate from the air.

That change of condition which results from the separation of
the precipitation but without addition or subtraction of heat is
called pseudo-adiabatic by von Bezold and is accurately studied
by him mathematically.” The differential equation of the adiabat
of the rain stage is, as already given

Cee ah te eee oe ra(™)

e

but for the case in which the water formed by condensation is

immediately separated, this equation changes to the following
equation for the pseudo-adiabat:

edt aaah Ane ra(*") Sh ie

In the second member of this equation we can substitute € — y

for x oreven x, — y, thatis to say, the original quantity of vapor

diminished by the quantity of water that is formed, and we thus
obtain

he FEDCT eet Vek ee Ral =)
Pp

19Von Bezold. Zur Thermodynamik der Atmosphadre. Sitzungsber. der
Berl. Akad., 1888. Translated in Mechanics of the Earth’s Atmosphere,
LOO Lge) Peele.

ee

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 455

From this equation by integration we obtain

T2
Sac eae iicaiig ace las ee:
AR fee eax ag Di ee ie
. T
By substitution of
SOS
omer
12
and by the abbreviated notation*
Mee,, 7 ecue
UO 9) naa —Y =m
ART
we finally obtain
Ts
log p, = loop, — “1 _ m log Di dane py
pen eyes "eh, AR A Te
T;

which is the rigorous equation of the pseudo-adiabat where m = f (&)
is a constant and corresponds to the initial quantity of moisture.
The last term in this equation

is a corrective term that is not integrable since y is also variable
with the temperature. If now y is assumed constant for any
small range of temperature, which is true in proportion as the
limiting temperatures T, and T, are near together then the integra-
tion would give

T> .
M See ae eee ae!
ALR je eee ame ae oe a
fly)

This value combined with
— m log ue

2
gives

oe eo “
TR Are) aeiae san Mig tep ick

*a and m are essentially the same as in the previous pages.—C. A.

456 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Since moreover € — y = xis the quantity of vapor that is tem-
porarily present, therefore for the pseudo-adiabat we have

Cee
m, =a or m = Ff (x)

that is to say, m is now to be considered as a function of the
quantity of moisture x that is actually present and that can be
assumed as constant for small intervals and is to be taken from
table 4, column 5 or column 6.

Therefore whereas for the adiabat the value m = f (€) = f (x,) wasa
function of the mixing ratio which remained constant during the
whole process, now, in the computation of the pseudo-adiabat, m
is to be taken as variable during the process of change of con-
dition; but in the computation of every new condition developing
from the previous one (m) must be taken as a constant and con-

sidered as a factor of log fe and in fact equal to that value which
corresponds to the average quantity of vapor « whose numerical
value as a function of the temperature and the approximate pres-
sure we take from table 3. Hence we see at once that which the
practical use of the adiabatic equation (9g) has already demonstrated
that by reason of the separation of the precipitation the quantity
of moisture (€) originally mixed with the air gives a smaller value

: £

for m than is shown in table 4. But still m as a factor of log —
2

remains constant within the limits of the change of condition to

be computed. It would be an error to introduce for T, a value
m, and for T, a value m, since in this case the equation would
lose its applicability.

If the moist air is cooled below o° C. then the precipitation
assumes the form of snow. Then, besides the latent heat of
evaporation r we have also to consider the latent heat of liquefaction
of the water r, which enters into the factor a in table 6, and also in
place of the specific heat of water c, there occurs c, the specific
heat of ice which enters into the factor m, table 4, column 6, for
the snow stage.

The hail stage can only occur when liquid water is present in the
air; for pseudo-adiabatic changes of condition the hail stage is
entirely omitted [since the water drops have fallen down] and the
final pressure of the rain stage for o° C. holds good as the initial
pressure of the snow stage.

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 457

In order now to show how the computation of the pseudo-adiabat
differs from that of the adiabat,,as to its results, and in order to
distinguish as to the admissibility of one or the other boundary
limits on the basis of an accurate computation we have computed
the adiabat of"20 C. and 760™™, for saturated ascending air.

Table A. Computation of the pseudo-adiabat for saturated ascending atr
jor the initial temperature 20° C. and pressure 760™™

T,
5 x a log T 108 ml T; on log p’— & p’ em p
& \pableot 2" | "Table 3 2g eee p’
my Table 3 2 ary
(¢4 gr N mm. | mm. | mm
. 466 .6 | 2.685
reas 14 3.64 ieee 0.0030 0.O10y 137 eae 743 a 760
18 5B 63 4639 sr * 122.7 6749 706 15 20
16 , . 4609 ta 9 Io9g.1 6640 671 14 685
12 62 30 109
14 -4579 96.9 6531 639 12 651
II -60 31 TL
12 -4548 85.9 6419 608 | 10 618
Io 59 30 108
10 57 .4518 : ae 76.0 6311 579 9 588
8 a ee - 4487 | a ee 67.1 6200 552 8 560
6 : 4456 3 | Sg. 6089 527 7 | 534
8 56 31 IIo
4 o +4425 aa ne 52.0 5979 503 6 509
2 6 4.55 -4393 i 3 45.7 5866 481 5 486
+ 0 . 2.4362 3 2 40.0 2.57547 460 5 465
,
= -436 c
° 6 as 2.4362 oO Bae 45.2 2.5645 460 Si Gd:
=F 5 48 +4330 25) te 39.0 5534 438 4 | 442
= # «4298 | 33.6 5423 419 3 | 422
5 48 33 TL
— 6 4265 29.0 5308 401 3 | 404
4 -47 32 III
as 7 4233 ae 25.0 5197 385 2 387
—10 : - -4200 33 21.9 5082 369 2 371
3 -46 34 118 |
—12 6 - 4166 | ss 18.5 4964 354 2 356
=i : ic - 4133 a a 16.0 4850 340 2 342
— 16 Sera ce m ae Ha. 7) | 24734. | 3281, = |) 329
—18 : 2.4065 11.7 | 2.4615 315 I 316

The preceding table (A) shows at once how this kind of computa-
tion is best executed; each new condition is computed from the
data given by the preceding one.

Column 1 contains the temperatures, column 2 the quantities of
moisture (x) for the average temperature of the interval after the
condensation water has fallen away. The values for this column are
taken from table 1, and in doing so, approximately estimated
values of the pressure are used. For each value of x we seek the
corresponding value of m in table 4 and enter it in the 3d column
of table A. We have here to distinguish between temperatures
above 0° C, for which we use the value m,, of the rain stage and
temperatures below o° C. for which we use the value m,, of the snow
stage. Columns 4 and 5 give the values of log T and the dif-

458 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

F :
ferences of log —* that is to say the difference between each two
2
successive values. These differences are to be multiplied by the

corresponding values of m and the product is written in column 6.

For the initial condition ¢ = 20° and p = 760™™ we now compute

log p, — ie

Po

The values of a = f (¢) are to be taken from tables 5 and 6 and
placed in column 7 of table A.

We distinguish between +o0° C. as the final temperature of the
rain stage and — o° C. as the initial temperature of the snow stage
since the values of a are different for these two cases.

itp ye =- 760 and: ¢,,. = 19"; they p= 74g sy Smice- a
137.6, therefore

a

log p, — — = 2.6858 for ¢ =20°
Po

and again

log p’ — as 2.6749 for ¢ = 18°
This latter value is now the next initial value so that we obtain
the value for each successive

1 aa
O as
gP p

by subtracting

T,
m log Tr
2

from the preceding value. But this is true only up to the temper-
ature o° C. or the end of the rain stage. With the temperature
o° C. we enter at once into the snow stage, that is to say, we com-
pute with the values a and m that correspond to the snow stage.
The final pressure of the rain stage as it is found from the equation

40.0
log p’ — p = 2.5757 for + 0°C

viz: p’ = 460 is the initial pressure of the snow stage.

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 459

Now for — o° C. we first compute

45.2
log p’ = —~— = 2.5645
P
/
and each corresponding subsequent expression is deduced from the
preceding by the addition of

als
— m log Tr
2

There follows then the solution of all the equations

log p’ = ?’ = N

(the numbers given in column 8) by numerical trials The app oxi-
mate values can easily be estimated from the progressively diminish-
ing differences of pressure, so that with the first or second trial we
shall hit upon the right value and for the computation of the quo-
tient a/p’ we use Crelle or other practical multiplication table.
The values of ~’ resulting from the solution of the equations N are
found in column 9 of table A; adding to each p’ the saturation vapor
pressure @m as given in table 2 corresponding to the temperature
we obtain the values of the total pressure p as given in column 11.
The values of the pressure are only given to the nearest whole
millimeter, which is quite sufficient for present consideration.

We will now compare the final result with that given by the rigor-
ous adiabat for the initial temperature 20° and pressure 760.

The principal difference in the computation itself lies in the fact
that m remains constant for the rigorous adiabat during the whole
course of each stage and that each new condition can be derived
directly from the original initial condition itself.

If we assume as the initial quantity of moisture § = x, = 14
grams and consider this as remaining constant, then from table
4 we have for the rain stage m = 3.64. For the final temperature
+o0° C. we obtain

40.0
log)’ = p = 2.5741

whence follows for the adiabat p’ = 458.5"™ for o° C., whereas for
the pseudo-adiabat we had p’ = 460 in table A, wherefore the dif-

460 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 52

ference is only 1.5. If a hail stage occurs then, for p’ = 458 and
€ = 14 grams we obtain

45.2 : 40.0
log p’ ——,- = log p) — —; — 1.82 € = 2.5486
P P
whence we find ~’ = 447™™ or an isothermal diminution of pressure
of 22°" and the dinal .» .— 452".
With p’ = 447™™ as the initial pressure of the snow stage and

m

My = 3.54 there results for the final temperature — 18° C. and
pene ; 45.2 i; revere
) ——, = lo — —— =n log = = 2:
SP p & Po Pp ie

In this case we find p’ = 303 and p = 304.
The final results for the adiabat as compared with those for the
pseudo-adiabat are given in the following table:

Table B
Pseudo-adiabat Adiabat
Pp Pp
+20 760mm . 760mm
° 465 463
—o 465 452
—18 316 304.

The values of the pressure for the pseudo-adiabat are always
higher than those for the adiabat for the same temperatures. If
we ignore the isothermal diminution of pressure during the hail
stage, which only occurs in special cases, then the departure at the
end is only 1 millimeter and is therefore so slight that it can come
into consideration only in very rigorous investigations. In the
computation of changes of condition of ascending currents of air it is
practically almost indifferent whether we compute by the adiabat
or pseudo-adiabat formula, that is to say, whether we assume that
the condensed water remains suspended in the air or falls away as
precipitation. The only characteristic difference is the omission of
the isotherm of the hail stage in the pseudo-adiabatic changes of
condition.

Since in the actual atmospheric processes neither one nor the
other boundary limit is strictly fulfilled and it is therefore almost
indifferent which of the two isotherms we take in the computation of

ADIABATIC CHANGES OF MOIST AIR——NEUHOFF 461

the adiabats, it is perfectly practicable to introduce into the rain stage
the value m,, = 3.60 as a constant moisture factor corresponding
to an average quantity of moisture of about 8 or 10 grams; in this
case the slight departures for values above or below this have but
little importance.

If we desire to compute the final pressure at o° C. of the adiabat
of 20° and 760™™ assuming m = 3.60 then we have the expression

loan eo nse
Pp

whence we find ~’ = 460™™, or the same value as that which we
found for the pseudo-adiabat.

If now we seek to find how large the difference will be in the
value of mwhen we entirely neglect the influence of the moisture,
that is to say, when we assume for the rain stage the value m =
3.44, or the same as for dry air, then in this same example we
obtain the same equation

log pr rs = 2.5802
Pp’

whence p’ = 464™™ and the departure as compared with the previous
value is only 4™™ in excess.

Therefore the extreme result of the entire neglect of a quantity
of moisture amounting to 10 grams in comparison with the weight
of air, in the factor m, amounts to only a difference of pressure of
47™ in: the expansion and cooling of the air from the temperature
of 20° C. down to o° C. Therefore for small variations in moisture
on either side of ro grams when we use m,, = 3.60 as aconstant for
the rain stage we introduce departures that scarcely come into
consideration.

In many cases when the quantity of moisture in the air is small
it suffices to assume the factor m = 3.44 as a constant even for the
rain stage, especially when we do not keep the higher value in
memory or wish to avoid using the tables.

In the snow stage the original quantity of moisture present will
scarcely ever need to be used. It is always so slight that here also
we may assume an average quantity of moisture of about 2 or 3
grams and a corresponding value of m = 3.46, and since it scarcely
matters in the computation whether we use 3.46, or 3.44 therefore
we adopt for the snow stage m = 3.44 or the value which holds
good for dry air.

462 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOU 5 =

For instance, in the snow stage fort = — 0°C.;p) = 760™™, m = 3.48
(for € = 5 grams) and for a diminution of temperature in conse-
quence of expansion down to — 20° C., we find the value p’ = 527™™,
whereas if we had used m = 3.44 we should have had p’ = 528.
The departure therefore in this extreme case amounts to only 1™™.

Still less important is the influence of the neglect of the weight of
the moisture with respect to that of the air in the factor m in the
dry stage, where m has the value 3.46 even for a moisture content
of 15 grams. In the case of a large moisturecontent thesaturation
point is very quickly attained as the cooling proceeds; if the tem-
perature is much reduced before cooling produces saturation, then
the moisture content must be small. For the dry stage we are per-
fectly justified in adopting in our computations the value m = 3.44,
such as holds good for absolutely dry air if we do not desire to
obtain the values of pressure accurate to within o.1™™.

Sg. ADIABATIC EXPANSION OF ASCENDING AIR

D

The passage of a mass of.air from a given initial condition p,
and ¢t, by adiabatic expansion or compression into another condition
p and t occurs in the atmosphere principally and on the largest scale
through a change in the altitude of the mass.

Assuming that the air is dry and that we have a uniform dis-
tribution of temperature at o° C. through the whole column of air
we arrive, by integration of the equation

Se) ee eens ee ae CS:

at the well-known formula

h = 18401 log feck log Ps

1 Pr

which latter enables us to determine the difference of altitude of
two atmospheric layers from their difference of pressure, approxi-
mately, it is true, but in a very simple way.

K is ordinarily designated the barometric constant and the sig-
nification of the remaining letters in this formula may from the
preceding paragraph be considered as well known. In order to
determine the altitudes Hertz has made use of this formula in the
construction of the scale of altitudes given in his adiabatic diagram.”°

20 Hertz: Met. Zeit., 1884.

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 463

Hann has also determined the altitudes given in his small table ”!
from this formula, in which the initial level of o meters corresponds
to the atmospheric pressure 760 millimeters. If we desire to pro-
ceed more exactly, by considering the temperatures in the deter-
mination of the altitudes, then 7 must be expressed as a function
of the altitude. But since the law of the diminution of tempera-
ture with altitude is not a general one, therefore we ordinarily
assume that in each special case there is to be introduced a value
for T that is equal to the arithmetical mean of the two temperatures
for the upper and lower levels respectively.

In this method we assume that the temperature is a linear
function of the altitude,an assumption that is more or less proper
but occasionally may be entirely false.

The adiabatic diagram shows that with adiabatic changes of
condition this assumption is perfectly justified during the dry
stage, since then the line which indicates the diminution of tempera-
ture with altitude is perfectly straight. To a limited extent this
is also true up to differences of temperature of 10° in the case of
the adiabats of the condensation stage; at least the curvature of
the lineis in this case so feeble that the departure from tke linear
average temperature can have scarcely any influence on the com-
putation of the differences of altitude. We come nearer to the
truth in proportion as the changes of condition are closer together
or in proportion as the interval of temperature for the two conditions
is smaller. We have thus acquired a simple means for computing
the total difference of altitude step by step in the condensation stage
from corresponding values of temperature and pressure by the sum-
mation of small differences of altitude asin mechanical quadrature.

In the determination of the altitudes the quantity of moisture
that is present in moist air is of less influence. The barometric
formula of Koeppen takes account of the average moisture con-
ditions, viz:

h = (18482 + qt) log 2° = K, log 22
P 2
in which t is the average temperature of the upper and lower levels,

q is a factor that has the value 72 when 7 is above o° C., but in other
cases has the value 69.

” Hann: Die Gesetze der Temperatur-Aenderung in aufsteigenden Luft-
stromungen und einge der wichtigsten Folgerungen aus denselben, Met. Zeit.,

1874, Pp. 321-329, 337-347-

404 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Since we shall make use of this formula therefore the value of the
barometric constant K, has been computed for each degree between
the temperatures + 30° and — 30°; these are givenintable 2. In
continuation of the example already treated a tabular view of the
method of computation of the altitudes is given in detail in the
following table C:

Table C
t a | log p |.4 log p Ky | 4h | h
eh p es mm | | | m m
20| — 760 2.8808 | — es °
—/| 18.5 _ _— 0.0156 | 19764 308 =
a (ae | mie | 733-2 | 2.8652 | — nl 308
— | 13.5 — — | 0.0760 | 19404 | 1474) —
1o| — | 615.5 | 2.7892} — | — | — | 1782
--- 5 Rael ea | 0.1015 | 18792 1902 =
+0 — | 487.2 | 2.6877 | a Pale aor er a 3689
_ — | — _ | 0.0097 | 18432 | 179 | =a
—o| — | 476.4 | SrG7B Yl OP = |= eee
—j|-I10 _— — | 0.1833 | 17742 | 3252 sae
—s20 | — || sx2.4 |'2.4047 =~ 6 ieee =| 7220

The initial level of o meters altitude is here taken to be that at
which the temperature is 20° and the pressure 760™”.

Instead of determining the change of altitude for adiabatic
expansion from an initial to a final condition by applying the
barometric formula we may also combine the equation — dh = vdp
with the adiabatic equation f (p, t) and thus directly attain an
adiabatic hypsometric formula. This process has been applied by
Guldberg and Mohn as also by Hann following the precedent of
Peslin in order to deduce a formula for the diminution of tempera-
ture with altitude.

The combination of the adiabatic thermal equation for dry au

O=c,’ dT —Avdp
with the formula (14) gives the adiabatic hypsometric formula

O=c, dT +Adh
or the equation

—dh= 2 dT =Car. saeco eee

In this formula C = 100.7 meters or the change of altitude for a
diminution of 1° C.,and the vertical temperature gradient or the
diminution of temperature for too meters ascent is 0.993° C.

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF 465

For (1 + x) kilograms of moist air where x is the quantity of
moisture we have for adiabatic expansion in the dry stage

i — (c, + xc") dT —A (1+) up =C,dT —A (1 +%) udp
Sf
where we have put
Cy = Ge teh Gy,
By combination of this equation with the formula (14) we obtain
as the adiabatic hypsometric formula
oe ee ee EC iT oe iG)
(l+x)A (l+x)A

According to this formula we may compute the differences of alti-
tude of dry as well as of moist air in the dry stage, without knowing
the pressure and temperature, but only the difference of tempera-
ture for the two levels. The coefficient C, is, however, variable
with the mixing ratio (x) for moist air, as is shown in the following
table D. It is only for small altitudes and for high temperatures

Table D

%.|| Cp eB Cia da

A | Cy
gr. | om
© |0.. 23750) 100.7 | 100.7 | 0.993
5 2400 | I0oI.7 | IOI.2 988
10 2422 | 102.6 | r1o1r.7 983
Lee) 2447 | 103.9 | 102.2 978
20 2475 | 104.7 | 102.7 973
25 2500 | 106.0 | 103.4 968

that larger quantities of moisture occur than are contained in this
table, and in such cases the point of saturation is generally attained
very soon. For high altitudes the mixing ratio amounts to only
0.001 or 0.003, that is to say, only 1 to 3 grams of aqueous vapor
are mixed with a kilogram of dry air, so that on the average C, =
tor meters or 4t can be adopted as being 0.990° C. per 100 meters
in the dry stage.

For the condensation stage we have the adiabatic thermal equation

O=@ +8 dT +Td(%)— arr t

466 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 52
In place of the second term in this equation and since
ta()=d(m) —"ar
i ff
we may by the application of Clapeyron’s equation obtain
*' dT = AV dp”
of hs 5
and since dp = dp’ + dp” therefore in this case the thermal equa™
tion becomes
O=(¢, + &c)dT+d(ar)—AVdp... . 10
This form may also be used as the initial theorem and thence

inversely the equation first given may be deduced from it.
By the combination of equation (17) with the formula

—(1 + é)dh = Vdp

we now obtain as the adiabatic hypsometric formula for the con-
densation stage

0=(, +c) dT +d (@r) +A 1+ 6.dh
or

GATE petite ord

a See Lee fee ORF)
A (1 + &) A (l+€)

and by abbreviating
pes Somat
AEE > 5

and neglecting € in the second term in the denominator we obtain
the equation

-dh=C,aT + 2dr)... .. . (8)

where C, varies with the quantity of moisture €. In the rain stage
¢ = 1.01 is the specific heat of water and in the snow stage ¢ = 0.5
is the specific heat of ice. We have for example the values
given in table E.

EEE

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 467
Table E
| | :
S ep + €e me fe C2
A
a
7 gr.
° 0.2375 100.7 100.7
5 0.2425 102.8 102.3
Io 0.2475 104.9 103.9 Rain Stage
15 0.2925 107.0 LOD'.5
20 0.2975 109.1 107.1
° | 0.2375 100.7 100.7
5 | 0.2400 IOI.2 100.7 Snow Stage
Io 0.2425 101.8 101.8

In-general it is sufficient to adopt for C, in the rain stage an aver-
age quantity of moisture of 8 grams and corresponding to this use
the value C, = 103, whereas for the snow stage, in which only a
small quantity of moisture comes into consideration, we may put
C, = 1o1, the same as in the dry stage.

In order to actually compute the altitudes according to the adia-
batic altitude formula for the condensation stage a knowledge of the
quantity of aqueous vapor (x) at the final condition is necessary
and this must be obtained by the method already described. But
it is not possible to deduce in a simpler form the expressions for

dx ax
mee OT
dt dh
and hence also
dt
dh
for the condensation stage, since these values vary with pressure or
altitude and temperature. Wecan only establish more or less com-
plicated approximate formulae such as Hann has used for the com-
putation of his table for the value

dt
dh

and such as Sprung has given in his Lehrbuch. In general the
adiabatic hypsometric formula (18) presents in the simplest way
mathematically the law of the diminution of temperature with
altitude for the adiabatic expansion of air. The second term corre-
sponds to the change of elevation in consequence of the condensa-
tion of aqueous vapor and becomes o in the dry stage.

468 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 150

The computation of the example graphically worked out by Hertz
in his table will now be given, in order, on the one hand, to discuss
the accuracy of this table and, on the other hand, to show the new
method of computation and the use of the tables.

We consider a. mass of air that is expanding adiabatically as it
rises and for whose initial condition we have p = 750™™,¢ = 27°,
and the relative humidity 50 per cent. According to the table 1
the temperature 27° corresponds to a vapor pressure é,, = 26.5™™
and to a total quantity of vapor at saturation « = 22.8 grams.
Hence for 50 per cent relative humidity we have the existing vapor
pressure ¢ = 13.5 and the mixing ratio x = 11.4 grams. Corre-
sponding to these figures there results from table 4

m, = 3.46 in the dry stage,

m,, = 3-64 in the rain stage,
ry = 3-52 in the snow stage,

in which we assume that the condensed water remains suspended

in the air.

According to equation (6) S is found to be 7.4470, which value
according to table 3 corresponds to the temperature of saturation
t, = 13.2°. The corresponding pressure as given by equation (4) is
p = 637.5 and the partial pressure for e = 11.3 is p’ = 626.2™™,
From the barometric formula there follows the difference of alti-
tude H = 1403 meters.

We further compute the final pressure for three values t = 10° C,
t = 0° C, and ¢ = — 20°C, by the general adiabatic equation (11)
since the temperature of saturation represents the beginning or
initial condition of the condensation stage. If we consider the
hail stage, then in place of

m log 2

we have the value — 1.82 €; the number corresponding to this is
made conspicuous by bold-face type in column 3 of the following
table F.

q

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 469

Table F
| ; |
° T, | U a | , | |
t _m log T | mlog —2 a log p —— va) em DES ee Ah h
aeree dbo Sieeace Weroas pti iced
C A | mm mm mm or | m |im
17 = = = = = | = | we || = bees | =
13.3 | 8.9424 | — 92.37 2.6498 | 626.2 | 11.3 | 637.5 | 11.4 | — | 1403
Io 8.9246 | 0.0178 76.0 2.6320 579.5 9.2 | 588.7 9-9 2605 =
+o | 8.8677 | 0.0747 40.0 | 2.0757 459.6 4.6 | 464.2 | 6.2 |— 4008
= 6) 8.5998 | 0.0207 45.2 | 2.5544 | 451.9 4-6 | 456.5 6.3 |— 4143
== | = — = | as | — =s —s eS |3298 —
—10 | 8.4830 0.1168 10.06 | 2.4384 296.6 0.9 | 297.5 I.9|— 7441

The values for a given in table F are taken from tables 5 and 6
with*the argument ¢. The whole computation is best made in a
systematic tabular form asin Table F. For comparison with other
methods we give in Table G the corresponding results deduced from
the diagram of Hertz.

Table G
Z Pp x h
|

c mm grams m
27° 750 II.o °
Tes 640 II.o 1270
° 472 6.1 3750
—-o 463 6.2 3900
—20 305 2.0 7200

In these tables the values of the pressure show differences of
nearly 8 millimeters in the condensation stage; the differences in
the altitudes exceed 200 meters:and to this extent the results of the
Hertzian diagram are uncertain. This error has been introduced
by the neglect of the vapor pressure in his construction of the
adiabats of the rain stage and snow stage; but this can be eliminated
by a subsequent correction that can be applied to the values
deduced graphically by subtracting from the final value the
difference of the vapor pressures corresponding to the appropriate
temperatures. We thus obtain 295™™ instead of 305, and in this
way the value obtained from the Hertzian diagram becomes too
small by only 2.5™™.

§10. ADIABATIC TABLES

Tables 1, 3, 4, 5, and 6, given in the Appendix, serve as auxiliary
for the computation of the adiabatic changes of condition of moist
air. Table No. 2 offers a numerical auxiliary for the computation

470 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

of the barometric formula of Képpen. Table 7 contains a collec-
tion of the associated values of temperature, pressure, altitude, and
temperature gradient for each two degrees of temperature for air
expanding adiabatically during the condensation stage.

The initial pressure for all the cases of ascending air saturated
at temperatures 30°, 28°, 26° C., etc., has been assumed as 760
millimeters for an initial altitude of o meters or mean sea-level.

In the general adiabatic equation and for temperatures above
o° C. or the rain stage, we have taken m = 3.60 corresponding to
an average quantity of moisture of 8 or 10 grams per kilogram of
dry air; but for temperatures below o° C., orin the snow stage we
have taken m = 3.44. The snow stage immediately adjoins the
rain stage, that is to say, the isotherm of the hail stage is not con-
sidered, therefore the table corresponds to the limiting case of
pseudo-adiabatic ascent in which all the water that is precipitated
separates from the ascending air.

The difference of altitude has always been computed according
to the hypsometric formula of Koeppen for temperature intervals
of 2° from the respective pressures and average temperatures. The
total altitude of the ascension has then been computed by summa-
tion. The temperature gradient, or the diminution of temperature
per 100 meters has been computed for each condition from the
difference of altitude per 2° of diminution of temperature.

Intermediate values can be taken from the table by interpola-
tion and we thus obtain, for example, the following small table H
for the temperature gradients per 1co meters of altitude of satur-
* ated ascending air.

Table H
INITIAL TEMPERATURES
h |
30° 20° 10° °° |— 10° —20° | —30°
m
Oo 60.377 0.44° revs). be 0. 62° 0.75° 0.86° | 0o.91°
I00o} 0.37 0.46 0,56 0.68 | 0.82 0.90 —
2000) 0.38 0.49 0.56 0.75 0.87 _ _—
3000! 0.40 0.51 0.65 0.82 | 0.89 = | —
f 4000! 0.42 0.57 0.73 a.68.19 | — —— a
5000 0.43 0.59 | 0.80 _— | _— _ _
6000! 0.45 0.63 | 0.84 _— _— _ —-
7ooo) 0.48 0.72 | —_ = — —_ _
|

For an adiabat whose initial temperature is ¢ = 10° the freez-
ing point occurs between the altitudes 1000 meters and 2000 meters,
This table H shows most plainly the slower rate of diminution of

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 471

temperature, that occurs at these altitudes. These adiabatic
tables give the values for the graphic presentations to which we
shall row turn our attention.

? Sir. THE GRAPHIC PRESENTATION

It seems to be of importance to represent by curves the results
thus far obtained on account of the great advantage that the
graphic presentation of formule has in meteorological studies,
since by the application of this method not only the connections
between temperature, pressure, and moisture in the atmosphere
are more easily perceived but also because laborious computations
may thus be avoided.

We can express the relations between pressure and tempera-
ture for adiabatic changes of condition of moist air by a system
of codrdinates whose horizontal axis presents the data as to
temperature and whose vertical axis presents those of pressure.
It is unimportant what units of length are used in these diagrams,
but in our case we use a square network in which the individual
sides of the squares represent 1° C. and 1o™™ of pressure, respec-
tively. In the present case the temperatures extend over a range
of from + 30° to — 30° and the pressures from 300™™ to 760™™,

If we consider air expanding adiabatically in the dry stage then
this condition is expressed by the equation (1) between the variables
p and t.

If we compute the pressure for successive diminutions of tempera-

ture of 4° C. each and
SeB enter the corresponding
values of p and ¢ in the
codrdinate network and
connect the individual
points by a continuous
curve which can be as-
sumed as running ap-
proximately in straight
lines between the plot-
ted points, we then ob-
tain the adiabatic curve
of the dry stage for the
initial condition 30° C. and 760™™, which we will call the dry adi-
abat for 30° and 760™™.
In a similar way we compute for each 10° the adiabats for 20°,

472 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

760™™; 10°, 760™™; etc., and plot the results and thus obtain fig. 1,
which represents all these adiabats of the dry stage.

The values of » and ¢ for the dry stage, needed for the construc-
tion of this figure are contained in the following table I.

Table I. Table for constructing the adiabats,
of the dry stage

’° Pp
sie |
2G mm mm mm mm mm mm
|
30 760 — |— = — as
26 726 == = —= = =
22 693 _ — = = —
20 == 760 oan — — =

N
on
P=
“
an
H
”
an
co
co
|
|
|

Adiabats of the dry stage are segments of hyperbolic curves.
This system of curves enables us without any further labor to
deduce the associated values of pressure and temperature for any
given intermediate conditions with sufficient accuracy.

In a similar way the adiabats of the condensation stage are drawn
by means of values that are given in table 7, page 490.

Since the factor (m) varies for different mixing ratios in the
adiabat of the condensation stage, therefore each mixing ratio
corresponds to a special system of curves. But the error due to
the introduction of an average value m = 3.60 in the rain stage
(corresponding to an average quantity of moisture € of 8 or 10
grams) is so small in comparison with the use of other values that

=

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 473

it can not be expressed graphically, therefore the construction of
one single diagram is sufficient.

In the snow stage m = 3.44 1s to be adopted since here in general
only a slight quantity of moisture can occur.

The curve$ given in fig. 2 present the changes of condition for
pseudoadiabatic expan-
sion under the assump-
tion that none of the
water that is present at
the freezing temperature
= o°C. has frozen; these
adiabats of the snow
stage therefore join di-
rectly on to those of the

JOOMM

rain stage.. In conse- 700
quence of the sudden in- : = = i—1 4 760
troduction of the latent

heat of liquefaction (r) FIG. 2. CONDENSATION STAGE
at + o° C. the curves do
not proceed continuously but have a small nick at the o° line.

If at temperature o° C. in consequence of the freezing of water
there should occur an isothermal fall of pressure, for instance,
of 1o™™, then this would be graphically indicated by a parallel
change in the adiabat of the snow stage, as is indicated by the fine
line in fig. 2 drawn above the adiabat for 20° and 760™™

The adiabats of the condensation stage are more steeply inclined
than those of the dry stage but at low temperatures closely approxi-
mate to the latter.

In the determination of the adiabatic changes of condition for
moist air the determination of the point of saturation or the transition
from the adiabats of the dry stage, to those for the condensation stage,
is important.

The point of saturation depends upon the mixing ratio (x): this
is determined in grams for saturated air from the equation

In this equation é,, is a function of the temperature and therefore
the quantity of moisture for saturation xm is a function of the
pressure and temperature.

If x is constant we obtain from the preceding equation the curve

474 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

of constant quantity of saturation for the varying values of p and
t. The associated values of p and ¢ for the individual curves of
saturation, which latter we can for brevity call ‘“‘gram-lines’’ or
lines of equal quantity of moisture, are obtained for individual
gram-lines from table I, page 486. Fig. 3 is constructed by the
values of table J.

Table J
| ; i fe
Dp I gr. were. |. osier: 5 gr. 7 OT. 10 gr. 15 gr. 20 gr. 25 gr.
mm | °C °c | °C 20 °¢ °C °C °C °C
760 —16.7|} — 8.0] — 3.0 3.9 8.8 14.1 20.5 Vibes 28.7
700 7) | nO 4.0 | 2.7 7.6 13.0 19.2 23.6 27.2
600 —19.5 | —11.0| — 6.0 0.5 Shes 10.5 TOL 21.3 24.7
500 —21.7 | —13.4| — 8.3 | =—2.8 2.7 7.9 13.8 18.3 —
400 —24.4| —16.0| —1r.0| —4.7 —0.4 4.5 10.4 => =
300 —27.6| —19.6 | —14.7 —8.3 —4.0 0.4 — _- —

The curves of gram-lines are feebly curved and run nearly parallel
to each other. The distances between them for equal differences
of weight increase approximately logarithmically corresponding to
the curve m= f (2).

od et
LANG a
COA a i

AChE a

SS eee 760

TIO ed? TOF oC” Val ZO 20"
FIG. 3. GRAM-LINES OF SATURATION

These saturation curves may also be transferred to another net-
work of codrdinates whose vertical axis, as before, shows the pres-
sure while on the horizontal axis the number of grams is shown.
In this case therefore p and x are the variable ge in the
equation

e=f@d= aa = constant,
%

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 475

which equation leads us to the construction of the isothermal curves
of saturation shown in fig. 4.,

By using pressute and temperature as codrdinates the adiabats
of the dry stage and of the condensation stage as well as the gram-
lines may all be combined in one diagram, by the use of which it
becomes possible to determine all the adiabatic changes of moist air
in successive series. Such a system of curves is shown in fig. 5.

JOOTN ML

OND IIONZ. 20253095

3B00TR IN 7 \ \
‘ Ls Peet
ek
Dw Seay \ 400
ae ee
SENS N
Niels
500 PN i oe Vs 500
GS EWES es
CRRNGNEXNELNES
oe NSS SIN GING Sie
BUSSES N Kate ye
NBNSNANANiW
A700 bw INS INI a IN | FOO
NANBINENE NEN
9GO J = y 3 ." - SC SS ee eS 760
= 30. —20 = FE) 0 10° 20" a0
FIG. 4. ISOTHERMS OF EG Sis DIAGRAM OF ADIABATS
SATURATION

Every point of the saturation curve that corresponds to a definite
condition p, ¢ shows how many grams of aqueous vapor are con-
tained in (1 + x) kilograms of saturated air. For instance, at 30°
temperature and 760™™ pressure we have the gram line for 27
grams. If this air is still in the dry stage and if the mixing ratio
is 10 grams, then from the ratio

10 x 100
27

we obtain the relative humidity, 37 per cent.

Conversely if for 20° and 760™™ of pressure we have 20 per cent
as the relative humidity then, since the saturation curve at this
point is 15 grams, we find the mixing ratio to be

15 X 20

= 3 grams.
100 2

The expansion continues along the adiabat of the dry stage until
the point of saturation is reached, that is to say, until the adiabat
of the dry stage intersects the gram line that corresponds to the
mixing ratio.

476 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Thus for expansion from 30° and 760™™" upward and with 10
grams as a mixing ratio, we find the saturation point at the inter-
section of the dry stage adiabat with the 10 gram line, which occurs
at 11° C. and 61o0™™ pressure.

Any further expansion must now follow along the adiabat of the
condensation stage which reaches the freezing point at a pressure
of 465™™ and attains a temperature of — 20° C. at 350™™.

The intersection of the condensation adiabat with the gram line
will therefore show at any moment how many grams of aqueous vapor
are still present, for instance, 3 grams at — 13°C. Since the origi-
nal quantity of moisture was 1o grams therefore 7 grams have been
condensed either to water or snow. At o° C. we find 6 grams of
aqueous vapor remaining, therefore 4 grams have been condensed
to water, which would now at once freeze if it were to remain float-
ing in the air.

For the mixing ratio of 3 grams and for initial condition of 20°
and 760™™ the point of saturation is at —7° C. and 545™™ which is
the intersection of this dry adiabat with the 3-gram line:

The adiabats of the dry stage become straight lines if instead of
the codrdinates p and ¢ we introduce log p and log ¢ as the variables
putting log p = X and log T = Y so that X — mY = constant
which is the equation of a straight line.

Hertz used this principle in the construction of his table,” in
which along the horizontal line the values of log p are set off and
along the vertical line the values log ¢t. The numbers themselves
are written along side as indices. This usage has materially facili-
tated the construction of the table. It is only necessary to know
any two points of an adiabat in order to draw not only this one but
all the others that run parallel to it and are distant fromit only by
the differences of the constants.

The value of the constant corresponds to

Jo

which expression is called ‘“‘entropy”’ by Clausius and ‘‘ Warmege-
wicht”’ by Zeuner.
In the condensation stage we have the formula
p’, T
log p’ — bare log J — constant = a dQ
p’ i

Po, To
” Hertz: Graphische Methode usw. Met. Zeit., 1884, S. 426. See previous
collection of translations, 1891, p. 210. C. A,

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 477

If we neglect the vapor pressure and therefore adopt p’ as the
total pressure then we can construct this curve in the same net-
work as the curves of equal “‘entropy.’”’ Inversely therefore, from
given values of p and t we may compute the entropy and allow the
individual ctirves to grow one from the other by the same differences
of entropy. In this way the curves of the Hertzian table have
been represented. The objection to this arrangement, independent
of the error introduced by the neglect of the vapor pressure in the
condensation stage, consists in the difficult reproduction of the
logarithmic network in comparison with the advantage of having
straight lines for the curves of the first or dry stage.

The important question as to the altitude at which the individual
changes of condition occur can also now be easily answered graphi-
cally by constructing level curves or isohypsen or lines of equal
altitude in the adiabat table of fig. 5; that is to say, we seek the
points on the adiabats corresponding to definite altitudes and con-
nect these points of equal altitude by curves.

In doing this we must first consider the two stages separately.
We locate the initial level of o meters in the pressure line of 760
millimeters.

In the dry stage we now obtain the difference of the altitudes in
the simplest manner by the adiabatic hypsometric formula — dh =
CdT. If we take ap-
proximately C =100 then
the temperature diminu-
tion of 10° C. along any
adiabat corresponds to a
difference of level of 1000
meters. Therefore the
intersection of any adia-
bat with two tempera-
ture lines 10° apart gives
points in the altitude -0 : = 30°
line corresponding to . 6. ALTITUDE LINES FOR THE DRY STAGE
Iooo meters, 2000 me-
ters, etc. If now we combine the points having equal altitude we
obtain the level lines and these also are represented as straight
lines. This construction is carried out in fig. 6. The altitude lines
approach each other as the temperatures increase and at the same
time are inclined to each other.

In the condensation stage the altitudes at which certain condi-
tions are attained when the initial level is at 760 millimeters,

JOOmm

\

1.

YL

2
A
S
S

l
y

,

Ia
d
is)
8

V

:
S
S

478 SMITHSONIAN MISCELLANEOUS COLLECTIONS ViOU sal

are determined, first, from the final condition p, t, either step by
step from the equation (14) or from the adiabatic formula (18),
in which case « must first be computed for each final condition.
In table 7 the altitudes are computed for the adiabats of saturated
air, whence we find by interpolation the conditions at any other
definite altitude such as 1000 or 2000 meters as given in table K.

Table K. Table for h in the condensation stage

INITIAL CONDITIONS

h
760 30° |760 20° |760 10° |760 0°} 760 —10° |760 —20°

m mm °C \ mm °C | mm oC °C | mm °C | mm A¢

° |760 30.0 760 20.0) 760 10.0 760 0.0) 760 —10.0| 760 —20.0
1000 |679 26.3) 677 15.5| 673 4.5) 670 — 6.4| 667 —17.8| 663 —28.8
2000 |605 22.5) 600 10.8} 594 — 1.4| 589 —13.6| 584 —26.3| — —
3000 |539 18.7| 532 5.9) 524 ee Ole a5 —21.5| — = == —
4000 |479 14.8 470 0.5| 460 —14 5) 449 —29.8| — — |j— —_
5000 |424 10.6) 415 — 4.8] 402 IE a —— — = — —
6000 |377 6.2 364 —10.8] 349 — 30 5) = = A | Sh —
7000 |334 I.7| 320 —17.5) — —|— = a — =< —

These data of table K are marked on the individual adiabats and
the points of equal altitude are connected with each other; we thus

find that the altitude
mst ttt
a"

lines are also represent-

BSKnene = SFA eee y ed as straight lines as
axeeceo shown in fig. 7; at least
\ ¥

PRT S24 oy the departures there-
ppp ki from are so slight that
Pe NE |e ue they arenot shown
> eal ae a wee] 600 <
ee \ \ a. graphically.
Se Ae
See e a By comparison of is
Ree pA acd level lines for the two
Be Set ear ee al | 760

-30° -20° -10° 0° 70° 20° 30° stages in figs. 6 and 7 we
find a slight departure
FIG. 7: ALTITUDE LINES FOR THE CONDENSA- only at great altitudes;

TION STAGE
thus on the temperature

line —30° for the line 6000 meters the departures are only 60
meters.

Therefore both tables can be united in a single one which can
also contain the curves of saturation, and in doing this we either
smooth out the differences between the two systems of altitudes
and choose an average system or we decide to use either one of

es

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 479

the two by preference. The small error of 1 per cent in the total
altitude will therefore be considered negligible.

Such a table of adiabats and altitudes constructed on a large
scale enables us to solve in the most convenient manner the most
important queStions as to the altitudes at which certain atmos-
pheric conditions occur under adiabatic expansion and as to the
conditions that must be present at certain altitudes.

§ I2. THE ADIABATIC DIAGRAM

The adiabatic diagram facing page 494 is a very practical form for
most problems. The basis of this diagram is a square network and
the units of length are 1° for temperature, and too meters for differ-
ence of altitude. The diagram covers a range of temperatures from
+ 30° to — 30° C. and of altitudes from o to 7000 meters. In
order to explain its construction more conveniently the following
fig. (8) is introduced which allows the individual items to be more
easily perceived.

According to equation (15) the adiabats of the dry stage are
straight lines and exact diagonals if we put C = too. If C = 1o1
then there is a slight departure therefrom. Ordinarily, however,
this difference can be neglected
and we can assume that the adia-
bats are, or run parallel to, the
diagonals of the respective small
squares.

The diagram (see fig. 8) contains
diagonal lines only for each 10° to
10°, since the interpolation for
other values is very easy.

The adiabats of the condensa-
tion stage are constructed point
by point with the proper temper-
atures and altitudes.

The curves are drawn at distances of every 2° of temperature, so
that on the one hand the appearance of the diagram is not confused
and on the other hand interpolations are not made too difficult.
Every fifth curve is emphasized by heavy lines. For the more con-
venient distinction of the adiabats of the condensation stage from
the adiabats of the dry stage, which are drawn across the diagram,
the first mentioned are indicated by dot and dash curves.

On the isotherm of o° there is shown a small bend or nick in the

480 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

adiabatic curves corresponding to the transition out of the rain
stage into the snow stage.

As we have already in the construction of the pressure and tem-
perature diagram as previously explained, constructed lines of
equal altitude from the adiabats, so now the lines of equal pressure
are drawn in order to be able to read off the pressure changes from
this diagram, taking as the basis the initial altitude o meter and pres-
sure 760™™. The isobars run in straight lines, inclined downward
toward the lower temperatures and separated farther and farther
from each other .as the altitudes increase.

But in this diagram there is a special system of pressure lines
for the dry adiabats and another for the condensation adiabats.
The departure of one from the other is first noticeable at consider-
able altitudes and remains always very slight, amounting to only
6™™ even at 6000 meters of altitude. In this diagram the pressure
lines for the condensation stage are drawn as given by the tempera-
tures corresponding to the adiabats that have been constructed.
The value for any other given pressure is easily interpolated from
table 7; -see, for example table L.

Table L
Pp od 8
mm ° ° | ° ° ° °
760 | 30.0 20.0 | I0.0 0.0 | —10.0 | —20.0
700 | 27.3 16.9 | 6.2} — 4.1 | —14.8 | —25.3
600 | 22.2 10.8 | — 1r.0| —212.5 | —24.4 —
500 | 16.1 3.2| — 9.9| —23.3| — —
400 8.3 —6.5 | —22.5 —- | — _—

If we desire exact values of the pressure for the dry adiabats at
great altitudes we can obtain them from equation (1).

In order not to overburden the diagram, the pressure lines are
only drawn through for each difference of 1oo™™ of pressure and the
remaining lines at intervals of 1o™™ are indicated as to their begin-
ning and ending on the two sides of the diagram by short dashes.
By means of these dashes, laying a straight edge across the diagram
or, perhaps, by ruling the lines in another color, such as blue, these
dashes may be utilized.

For the determination of the point of transition from the dry
stage into the condensation stage and to determine the quantity
of moisture at any point of the diagram, the curves of constan

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 481

quantity of moisture needed for saturation are introduced for the
corresponding values of pressure and temperature. The slight
difference between the pressure lines in the two stages does not
come into consideration.

The gram-lines are represented by dashes for each 5 grams.
The use of the diagram is now intelligible after the explanations of
the preceding section.

This diagram of adiabats possesses not only the advantage of
being easily reproduceable but also the advantage that adiabatic
changes of condition can be graphically compared directly with those
that are produced by change of either temperature or altitude alone.

A special diagram for the hail stage which was given by Hertz
canbe omitted entirely by introducing the altitudes in place of
the pressures. Inthe equation for the isotherm of 0° C. of the hail
stage, the final pressure varies with the total quantity of moisture
€. If now we choose as codrdinate log p’ and & then the adiabats
for different values of € can be drawn as
straight lines because of their short length,
and of the relatively small quantity of water
coming into consideration and can all be con-
sidered as running parallel to each other. 797°
These lines all begin together at the saturation #000
curve of o° C. or the dotted line in fig. 9 3000
which indicates that the quantity of moisture 2000
needed for saturation at o° C. must be sub- — j99g —ONI 45
tracted from the total quantity of moisture O
€ that is present; the remainder is the quan- Fic. 9. HAIL STAGE
tity of water present.

If now we introduce the altitudes in place of the pressures cor-
responding to the formula

02010 Ogr

Al]

7000
6000

h = 18432 log

for the constant temperature o° C. then the altitude lines will run
parallel to the pressure lines and at equal distances from each other
for equal intervals of pressure, and we obtain the following simple
result:

The isothermal change of altitude at o° C. ts proportional to the
quantity of water present,
and we find empirically the formula

h—2r yy,

. /
482 SMITHSONIAN MISCELLANEOUS COLLECTIONS * VOL. 52

where h is the change of altitude in meters; y is the quantity of
frozen water in grams; therefore 1 gram of freezing water corre-
sponds to a change of altitude of 27 meters.

The evaporation of water can be assumed proportional to the

quantity of water present; the amount is very slight and is only
o.1 gram for 5 grams of water; this would introduce an error of
three meters in the altitude when there is an isothermal ascent of
135 meters but the empirical value has considered this fact.

If the condensation adiabat reaches o° C. then the gram-line
passing this point gives the quantity of aqueous vapor still present,
for instance, 6 grams at 4000 meters. If the original quantity of
moisture be 10 grams then at the altitude of 2000 meters condensa-
tion occurs and 4 grams of water are condensed. If these grams
remain suspended in the air and freeze while the temperature re-
mains constant at o° then the hail stage would represent a change
of altitude of 108 meters or a jump of this amount at o° C. line; for
further expansion one must then follow the new adiabat.

It is easy to memorize the number 30 meters as the change of
altitude for each gram of water; this results approximately from
the formula

"e

_ 424 x 80
A 1000

The initial level of the adiabat diagram is taken at 760™™ of
pressure. If we have some other initial pressure, as, for instance,
730™™ and a temperature + 20° then must the altitudes be moved
up a corresponding 250 meters, but we easily recognize the fact
that in the use of the diagram where we only care for altitudes and
temperatures it is indifferent whether at the initial level a pressure
of 760™™ prevails or any other pressure.

According to table 7, page 490, for the condensation adiabat we
have the data given in table M.

Table M
Id Pp ALTITUDE
= mm m
30 760 °
20 | 561 2667
Io 419 5137
° 320 7339

With these data we compute the corresponding values for the
initial pressures 750 and 770 as shown in tables N and O.

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 483

Table N. For initial pressure 750™™

Pig eee m lo Po 2 log pe ,

\(m=3.60)| "7p |fromTab.5| 8” ~5| P em P ates Ne
C ” mm mm mm m m
30| 8.9330 — 238.6 2.5238 718 32 750 26 °
20 8.8808 0.0522 137.6 2.4716 536 | 17 553 3 oe 2674
bade) 8.8265 0.1065 76.0 2.4173 403.5 | 9 412.5 a23 5157

2202
° 8.7703 0.1627 40.0 2.3611 310 5 315 7359
| |

Table O. For initial pressure 750™™

t? | log p= p’ em | p Ah h
Pp
CG mm mm | mm m m
| |
30 2.5448 738 32 | 770 e654 °
20 2.4926 552 17 569 | 2654
2442
Bde) 2.4383 417.5 | 9 | 426.5 ae 5096
° Boar || sane. iy). 5) || 4326 94 7290

Therefore for air that is saturated at its initial temperature of
30° and is ascending adiabatically the final temperature o° will be
attained at the following altitudes:

7339 meters altitude for an initial pressure of 760™™

7350 “ “ “ “ “ 750mm
i 90 “ “ “ “ “ 770m:a

This indicates a difference in altitude of from 20 tu 51 meters
or, for the same final altitude an uncertainty in the final tempera-
ture.of o.1° or o:2°:

If we neglect this difference then the diagram gives the diminu-
tion of temperature with altitude for adiabatic expansion as inde-
pendent of the initial pressure.

When pressures are to be read off from the diagram this difference
is to be taken account of, that is to say, the initial point is to be
graphically transferred to the pressure line of the initial pressure.
This must always be done in fact for low pressures; for instance, if
we should locate 7oo™™ initial pressure on the pressure line that is
marked 70o™™ we must then diminish all the altitudes by this
difference with respect to the initial level.

Of the many applications, that the diagram allows, we mention
especially the processes in connection with the occurrence of the
foehn wind. Whereas in considering ascending air it is almost

484 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL Ss

indifferent whether we consider the condensed water to be floating
in the air or to fall away from the air, on the other hand it makes
an important difference in the case of the compression that accom-
panies descending air.

If, for instance, the mass of air again sinks after it has passed
over the ridge of a mountain range, while the total quantity of
moisture € grams remains unchanged so that no precipitation falls
away from the air, then in the course of the descent of the air
exactly the reverse process takes place, so that graphically repre-
sented the air may be said to pass backward along the same adiabats,
first the adiabat of the condensation stage until all the water is
again evaporated or until the saturation curve, € grams, is attained
and then down the adiabat of the dry stage.

But it is otherwise if the precipitation has fallen away from the
air. In this case during the descent of the air no water can be
evaporated and the air follows backward along the adiabat of the
dry stage only.

FIG. 10. FOEHN WIND

An example for the foehn wind is given in fig. ro.

At the initial level the temperature was 14° C. and the relative
humidity was 60 per cent. For this we find the saturation curve
for 10 grams and hence

Io X 60 + I00 = 6 grams

is the mixing ratio. If now the air expands adiabatically then as
shown by the intersection of the diagonal for the dry adiabat with
the 6-gram line of saturation the air will attain a temperature of
5° at goo meters altitude. If further expansion takes place the air
follows the condensation adiabat, it attains the freezing point at
1750 meters altitude where we find the quantity for saturation 4.6

ADIABATIC CHANGES OF MOIST AIR—-NEUHOFF 485

grams and it attains the ridge of the mountain range at 3000 meters
altitude with the temperature — 7°.5 and the quantity of saturation
3 grams. ;

If now the precipitation all falls away so that at the summit of
the ridge the total quantity of moisture or mixing ratio is equal
to the quantity of vapor or 3 grams, and if now in consequence of
the sinking, adiabatic compression takes place, then the air follows
the adiabat of the dry stage in its descent and attains the tempera-
ture of 22°.5 when it reaches its initial level. At this point the
saturation curve is 17 grams hence the relative humidity is only
ne per cent.

These and similar questions which hitherto have been solved
only to a very limited extent and by a crude approximate compu-
tation with the assistance of the small table published by Hann*
can now be quickly answered by the use of thisdiagram. In this
way the graphic presentation allows of the solution of problems
that can be solved numerically only by very tedious interpolations.

3 Hann: Die Gesetze der Temperaturanderung in aufsteigenden Luft-
strémen, usw. Met. Zeit., 1874, p. 328.

Table 2. Koep-

Table I. Pressure @m of saturated aqueous vapor: x weight pen’s barometric
of water in (1+) kilogram of saturated air constant Ky
18432+qT
| % |
P| em | Eem p | p | PB Pn ee es e
760mm 700mm 600 mm 500mm 400mm 300mm
a | reas
°C| mm mm gram | gram | grams grams| grams | grams c°
30°| 31.55 | 19.624 | 26.94 | 29.39 20 592 30
29 | 29.78 | 18.523 | 25.39 | 27.65 20 520 | 29
28 | 28.10 | 17.478 | 23.88 | 26.01 | * 20448 | *28
27 | 26.51 | 16.489 | 22.48 | 24.48 | : 20 376 | 27
26 | 24.99 | 15.544 | 21.15 | 23.03 | 20 304 | 26
25 | 23.55 | 14.648 | 19.89 | 21.65 | 25.43 20 232 | 25
24 | 22.18 | 13.796 | 18.69 | 20.46 | 23.87 20 160 | 24
23} 20.89 | 12.994 17.58 | 19.14 | 22.44 | | 20 088 | 23
22 | 19.66 | 12.229 | 16.52 | 17.99 | 21.08 | 20 o16 22
ar | £8.90)) TT.907 | Lo.02"| XO-90 | 19.77, | | I9 944 21
20 | 17.39 | 10.816 | 14.57 | 15.83 | 18.55 | 22.39 | 19 872 20
19 | 16.35 | 10.170 , 13.68 | 14.87 | 17.41 | 21.01 | | 19 800 19
TS) } ro.36 9.554 12.82 | 13.95 | 16.33 | 19.70 | 19 728 | 18
17 | 14.42 8.969 | 12.03 | 13.08 | 15.32 | 28.45 | 19 656 | 17
16 | 13.54 8.422 | TI25 | toy A sole ie oS | 19 584 16
r5 | 12.90 7.899,| 10.57 | 1X.50| 13.46 | £6.22 |) 20.47 19 512 15
14 | II.91 7.408 | 9.90] 10.77 | 12.60 | 15.18 | 19.09 19 440 14
13 | 12.16 | 6.942 | 9.27 | 10.08 | 11.79 | 14.20 | 17.85 | 19 368 | 13
12 | 10.46 6.506 8.67 9.44 | 11.03 | 13.28 | 16.68 19 296 | 12
It 9.79 6.089 8.22 | 8.83 | 10.32 |. 52.431) ro .6r | I9 224 | It
10 | 9.17] 5.704 | 7.60| 8.26] 9.65 | 11.62] 14.59 I 19 152 10
9 8.57 D. G30" Fabry. 72 9.02 | 10.86 | 13.63 | 19 080 9
8 8.02 4.988: |. “0x03 Yaex 8.43 | 10O.%4 | 12.73 19 008 8
7 7.49 4.659 6.19 65730\) 7060 9.45 | 11.86 18 936 | O]
6| 3.00 | 42354\| 5.98:| 6028 | 9.340) S285.|¢rx.08 18 864 6
5 6.53 4.062 5.39 5.86 | 6.85 8.22 | 10.34 | 13.86 | 18 792 5
4 6.10 3-794 | 5.03 5.47 6.39 7.68 9.63 | 12.90 | 18 720 4
3 5.69 3.539 4.69 | 5.10 5.96 7.16 8.98 | 12.04 18 648 3
2| 5.30] 3-297| 4.37| 4.74| 5.54] 6.66| 8.35 | 22.18] © 18 576 2
I 4-94 3.073 4.07 4-42 5.17 6.21 7.78 | 10.42 18 504 I
° 4.60 2.861 3:99.) d.It 4.81 5.78 7.24 9.68 | 18 432 °
— 1| 4.25 2.643 B250)| “s660)| eas 5.33 | 6.68 8-93 || 18 363 | —1
—2 3.93 2.444 3.23 B05 4.10 4.93 6.17 8.26, 18 294 — 2
— 3 3.64 2.264 2.99 3.26 3.80 4097 5.72 FAS) 18 225 — 3
— 4| 3-36] 2.090| 2.76] 3-00| 350] 4.21| 5.27] 7.04 | 75156) | ae
-— 5 3, 25 1.934 2.55 2.78 3.24 3.89 4.87 6.51 || 18 087 | — 5
— 6| 2.87] 1.785 | 2.36] 2.56| 2.99| 3.59 | 4.49 | 6.01 |} 18 o18 — 6
- 7 2.65 1.648 | 2.18 2.37 2.76 3.32 4.15 5.95 \ 17949 | — 7
-— 8 2.45 1.524 | a.0r | a.18 2505 3.06 3-83 5. x2 || 17 880 | — 8
—- 9 2.27 I.412 1.86 | 2.02 2.36 2.84 2.55 4.74 || 27 S20 ¢) 9 ee
—10| 2.09| 1.300| 1.72] 1.86] 2.17| 2.61 | 3.27] 4.36 |] 17 742 | —1O0
-—I1 1.93 I.200] 2.58] 2.72 2.01 2.41 3.02 4.03 || ry 673 | =x
—12 1.78 I.107 1.46 1.59 Deoo) 2.22 2.78 3-72 |} 17 604 —12
—13| 1.65| 1x.026| 1.35| 1.47| 1.72] 2.06| 2.58| 3.44 | 17 535 = Ty
=ta| “XeSail oro4e)| Keas 1) ce95 | ease Sal| areool -rase7ul weseegal 17 466 =
—15 I.40 0.871 Ero: 1.25 ToAoi |e Tes 2.19 2.91 || 7 307 —15
=56| “x.a9 |) ovBoa: |e 6d x05.) as agau! cele aren ehac Gell 17 328 | —16
-—17 L229 0.740} 0.98| 1.06 I.24 | 1.48 1.85 2.48 17 259 =—17
—18 I.09 0.678 0.89 | 0.97 Teatd rr 36 I.70 2.28 I7 190 | —3z8
Ino T.or | 0.628] 0.83] 0.90 T.09 | 2.26 Toy, 2.10 || jaca | —19
—20 0.93 0.578 | 0.76| 0.83| 0.96] 1.16 1.45 1.93 nyse) eae
—21 0.85 0.529 0.70/| 0.76 0.88 | 1.06 133 r.97 16 983 | —21
—22 0.78 0.485 | 0.64 0.69 0.81 0.97 I.22 1.62 || 16 914 | —22
—23| 0.72! 0.448| 0.59 | 0.64| 0.75 | 0.89 I.12 r.5o | 16 845 | —23
—24| 0.66] 0.411 0.54 | 0.59 | 0.69] 0.82 1.03 1.38 || 16 776 | —24
—25| 0.61] 0.379) 0.50| 0.54] 0.63] 0.76! 0.95] 1.27 16 707. | —25
—26| 0.56) 0.348) 0.46! 0.49 | 0.58 | 0.70| 0.87 ey, 16 638 — 26
=37 | o.51 | 0.327 | 60.42 | 0.45] 0.531 0.64 ©.79'| 1.06 16 569 | —27
—28 0.46 0.286 0.39 o.41 0.48 | 0.58 | 0.72 0.96 16 500 | —28
—29 0.42 | 0.261] 0.35 | 0.37 Os44)|\ 0.03 0.66 0.87 16.4309) ae
=—30/| 0.39 0.243 0.32 0.35 0.41 | 0.49 o.61 0.81 || 16 362 —30

Table 3. For the determination of the temperature of saturation from

t?

log T } ™ = |

°C 3-44
30] 2.4814]8.5360
29| .4800] .5312
28] .4786] .5263
27| .4771| -5212
26| .4757] .5164
25] .4742| -5113
24) .4728| -5064
23| .4713] -5013
22 4698; -4961
21 4684} -4913
20] .4669}] .4862
19| .4654}] .4810
18] .46391 -4759
17] .46241 .4707
16] .4609) .4655
15} .4594) .4604
14] .4579] -4552
13] .4564] .4501
12] .4548} .4445
Ir] .4533] -4393
to] .4518] .4342
9] .4503] -4290
8] .4487] .4236
7] .4472] .4184
6] .4456} .4128
5] .4440] .4074
4| .4425] .4022
3] -4409| .3967
2) -4393] -3912
I] .4378] .3860
oO] .4362] .3806
= +4346] .3750
= +4330] «3695
= +4314] .3640
— -4298] .3585
= ~4281] .3526
= -4265] .3472
= -4249] .3417
= +4233] -3361
= +4216] .3303
—I0} .4200] .3248
—1Il] .4183] .3189
—12] .4166] .3131
—13] -4150] .3076|
—14) .4133] .3017)|
—15} .4116] .2959
—16] .4099] .2901
—17] .4082] .2842
— 18) .4065] .2784
—19) .4048] .2725
—20]) .4031] .2666
—2f .4014] .2608
— 22] .3997] .2550
—23! .3979] .2488
—24) .3962] .24209)
—25] .3945| .2371
—2 -3927] .2309
—27) -3909 pas
—2 3892] .2189
—29) .3874] .2127|

|8.5608

™m,
yar is)

- 5560}
Bei ees
-5460
5411
- 5360
.5311|
.5260
-5208
+5160)

.5109|
5056)
-5005
-4953
«4901
-4850
-4798|
+4747
-4690
- 4638
-4587
-4535
-4481
+4429
+4372
-4318
-4266
+4211
4156
+4104
+4049
+3993)
+3938
- 3883
+ 3828
- 3769
rity ae)
- 3659
- 3603
35945
+3490

+3431
+3373
- 3318
- 3258
+3200
- 3142
- 3083
+3025
2965
- 2906
. 2848
-2790
-2728
. 2669
.2610
2548
. 2486
2428
- 2366

S=m, log T — loge

8.5856
- 5808
-5759
-5708}
-5659|
- 5608)
- 5559}
5507]
5455
+5407]
5355}
-5303
~2292
5199}
5147
- 5096
- 5043
-4992
- 4936
- 4884)

- 4832
-4780
-4726
-4074
Aone
-4563
4510}
-4455
-4400
+4347
+4293
-4237
4181
~4126
24071

-4012|
- 3957

+3902|
- 3846

- 3787

-3732

. 3673

3614
- 3999]
+3499
- 3441)
+3383)
+3324)
3265

- 3206

+3146)
3088 |
3030)
.2968|
. 2908 |
. 2850)
2787

«2729)|
- 2667

. 2605

— 30] 2.385618. 2064)

8. 2303/8. 2541 8.2780 8.3018l9.

487

S
——— ~ log |———— —————————————
| m =| m= e ELS UN fa le se m, = |m =
3-47 | 3.48 ™ | 3.44 | 3-45 | 3.46 | 3-47 | 3.48
|
8.6104 8.6352 1.4990] 7-0370| 7-0618/ 7.0866) 7.1114| 7.1362
-6056| .6304] .4739] -0573| -0821| .1069/ .1317| .1565
-6007| .6255] .4487| .0776| .1024| .1272| .1520| .1768
-5956| .6203] .4234] .0978| .1226| .1474| .1722| .1969
.5906| -6154] .3978] -1186 +1433) -1681| .1928) .2176
-5855| .6102] .3720] .1393| -1640) .1888| .2135| .2382
-5806| .6053] .3460] .1604| .1851|} .2099| .2346| .2593
-5754| .6001] .31r99] .1814| .2061) .2308| .2555| .2802
-5702| .5949] .2936] -2025| .2272] .2519| .2766| .3013
-5654| .5901] .2672] .2241| -2488| .2735| .2982| .3229
-5602| .5848] .2403] -2459| .2706 -2952| -3199| .3445
-5549| .5796] .2135| -2675| .20921| .3168| .3414| .3661
-5498| .5744] .1864] -2895| .3141] .3388| .3634| .3880
-5446| .5692] .1590] -3117| -3363| .3609| .3856) .4102
-5393) -5640] 1316] -3339| -3585| .3831| .4077| .4324
5342| .5588] 1038 -3566, .3812 -4058| .4304| .4550
-5289| .5535] .0759] -3793| -4039| .4284| .4530) .4776
-5238] .5483] .0477] -4024| .4270] .4515| .4761| .5006
-5181| .5427]}1.0195 .4250| .4495| .4741| .4986| .5232
-5129| -5375]o.9908] -4485| .4730| .4976| .S5221| .5467
-5077| .5322lo.9624] .4718| -4963| - 5208) -5453| .5698
-5025| .5270lo.9330] .4960| .5205| .5450} .5695| .5940
+4971| .52T5lo. 9042] .5194 +5439) -5684| .5929| .6173
-4919| .5163]o.8745] .5439| -5684 -5929| -6174| .6418
-4861| .5106]o.8451] .5677| -5921| .6166| .6410|) .6655
-4807| .505rt]o.8149] .5925| .6169| .6414| .6658| .6902
+4755) .4999]0.7853] .6169| .6413) .6657| .6902| .7146
.4699| .4944]0. 7551] .6416| .6660) .6904| .7148| .7393
-4644| .4887]o.7243] .6669| .6913| .7157| .7401| .7644
-4591| .4835]o.6937] .6923| -7167| .7410| .7654| .7898
-4536| .4780]0.6628] .7178| -7421| .7665| .7908| .8152
-4480| .4724]0.6284] .7466| .-7709| .7953| .8196| .8440
-4424| .4668]o.5944] .7751| -7994| .8237| .8480| .8724
-4369! .46£3]0.5611] .8029| .8272 8515) 8758] .9002
+4314) -4557]0.5263] .8322| -8565| .8808) .9051| .9294
+4255) +4497]0.4928] .8598) .8841| .9084| .9327| .9569
-4200| .4442]0.4579| .8893| .9136 9378. -9621/ 7.9863
+4144) -4387]0.4233| .9184 -9426) .9669 7-9911/ 8.0154
-4088| .4331]o.3892] .9469| -9711|7.9954/8.0196| .0439
+4029| .4271]o.3560]7.9743 7-9985 | 8.0227 -0469| .o7II
-3974| »4216]o.3202]8.0046 8.0288] .0530| .0772| .1014
-3915| .4157]0.2856] .0333) .0575| .o817| .1059| .1301
.3856| .4097]0. 2504 0627) - 0869) -Irro| .1352| .1593
- 3801) -4042/0.2175] .ogor| +1143) +1384) -1626| .1867
-3741| .3983]0.1818] .1199| .1440| .1681| .1923| .2165
. 3682) + 392310. 1461 .1498) -1739| .1980) .2221| .2462
.3624, .3865lo.1106| .1795| .2036| .2277| .2518| .2759
- 3565} + 3806]0.0756 . 2086) .2327| .2568/ . 2809) - 3050
-3506| .3746]0.0374] .2410 2651) - 2891) 73132) 3374
-3446| .3687]0.0043 . 2682 -2922| .3163| .3403| .3644
-3387| -362719.9685 2981) -3221| .3461 +3702) .3942
- 3328) .3569] .92094] .3314) .3554| .3794| .4034| .4275
+-3270| .3510}] .8921] .3629| .3869 . 4109) +4349) . 4589
.3208| .3447] .8573] .3915| .4155| .4395| .4635| .4874
+3148) .3388] .8195] .4234 +4474 +4713} -4953| .5193
Saba - 3329] .7853] .4518| -4757| -4997| .5236| .5476
-3026| .3266] .7482] .4827| .5066) .5305) .5544| .5784
.2964| .3204] .7076 5171) .5410 5649 5888 .6128
2906 .3144| .6628] .5561| .5800| .6039 .6278) .6516
-2843) .3082] .6233] .5894) .6133, .6372 -6610 .6849

S9tr18.6153 8.6392 8.6630 8.6869.8.7107

488 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Table 4. The humidity factors for moist)
air containing x grams per (1 + x) kg |
,

x CD m, m, | my | Ch= Cp (1 + 2.023 x)
Ae Ry= Rg (1 + 1.608 x)

00.2375 |2.5928 [3.441 |3.441 |3.44% i fe

I | .2380 -1563 +442 -456 -448 mM, = &p ra ens 22 44 a 2.023 x

2| .2384 -1597 +443 -470 -455 || x — 1 ue 1.608 x

3 | .2389 -1631 445 485 463 AR 1 =

4| .2394 -1666 -446 .500 +470 €

5 | .2399 1700 -448 -514 477

6 | .2404 .1735 -449 .529 | .484 a + &¢

7 | .2408 -1770 .450 544 +492 mM. = ——— = 3441 (1 4.265

8 | .2413 .1805 +452 558 -499 wt A R : ( + )

9 | .2418 | .1840 “0g 7273 506

Io | .2422 .1874 ~455 -588 514 E ae Ec,

Tr.| «2427 || .1900 456 602 Ore ae mM. = —— = 3.441 (1 1

12 | .2432 -1943 P4558 .617 528 | Ny AR : ( + 2.105 )
13 | .2437 -1978 -459 (042) \|"n035

14 | .2442 | .2012 -461 -646 542 r

15 | .2447 -2047 -462 .661 .550 y= pe M

16 | .2452 22082 | .463 | .676 | .557 ws ieee Alin

17 | .2457 .2116 -465 .690 564

18 | .2461 2151 . 466 -705 Piya

19 | .2466 | .2185 -468 -720 -579 | a= Py Ve : M

20] .2471 22220 -469 .734 | .586 Iv i AR.

ar | .2475 | .2255 .470 -749 | .593

22 | .2480 .2289 471 764 . 500 r M

23| .2485 2324 7473 -778 607 ee i PR RAPS

24 | .2490 | .2358 +474 -793 615 il Ase ™ i m

25 | .2495 | .2393 -475 -808 | .622

26 | .2500 | .2428 Ary .822 .629

27 | .2505 2462 -478 837 -636 oS aks Ye M eo eee

28| .2510 | .2497 .480 .852 .644 Iv I AR Iv m

ag | .2515 wangu 481 307 || 655

30 0.2519 (2.2565 3.482 3.881 3.658

ADIABATIC CHANGES OF MOIST AIR——-NEUHOFF

489

Table 5. For the computation of a, and
a,, in the rain stage

Table 6. For the computation of a>
and a,, in the snow stage

te)

bbw DN DD HO dD Dw °C
On HDWwWE UNBAN TOO OD

Ss + + + 4+ SH SS SH HH
On KDWP UAT WOO OH HWE NAN WO

uv
: T
a es
585.650 1.933
586.345 -942
587.040 950
587.735 959
588.430 -968
589.125 977
589.820 -986
590.515 1.995
591.210 2.004
591.905 O13
592.600 023
593.295 032
593.990 -O41
594.685 -O5I
595.380 o60
596.075 .070
596.770 079
597.465 089
598.160 099
598.855 109
599.550 -119
600. 245 .129
600.940 -139
601.635 149
602.330 159
603.025 169
603.720 180
604.415 190
605.110 200
605.805 211
606.500 2.222

ay

I2.
I2.
I2.
12.
2s
12,
I2.
I2.
I2.
12.
12.
T2).
I2.
I2.
12.
Ea
mar
13.
13.
ey
13):
5
13.
I3.
13.
Tae
Tie
mare
130
tse
mae

704.
704.
703.
702.
702.
7Ol.
700.
700.
699.
698.
698.
697.
696.
695.
695.
694.
693.
693-
692.
691.
691.
690.
689.
688.
688.
687.
686.
686.
685.

060

975
280
585

a

18.
18.
18.
18.
hy (
17.
7.
07.
Tv
7
vy fs
7s
T7i5
17)
17.
16.
16.
16.
16.
16.
16.
16.
16.
16.
16.
16.
16.
16.
TD\
5.
TO

Vi

SBP WWW WH ND DY DB WD HH HK HH HH RR RO
UH ODW HO AMNW HO Ow NEW NH OO

Cw Oonrntaanunst

490 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 54

Table 7. The associated values of temperature, pressure, altitude and tem-
perature gradient jor adiabatic expansion of ascending saturated air

40° | repo sl oad | 40
h for a7 h for p h for
10om 100 m 10om
| =
m mm m mm m
4 4 4 44 4

°
544 | 0.37
544 $38 0.37 760 44 | 3 528 0.38

1082 536 0.37 716 41 528 518 0.39 760 43 2 512 | 0.39

1618 ee 675 1046 . 717 512 ;
2143 525 0.38 637 38 | 1552 506 0.39 677 40 ore 500 | 0.40
66 524 0.38 Bae? 5 503 0.40 6 38 APES 500 | 0.40
; 7 523 0.39 66 34 | im = 5o1 0.40 a 35 = 485 | 0.41
5689 499 | 0.40 : 31 oe 495 0.40 ie 32 ae 472 | 0.42
| ted 490 o.41I ae 30 oe 490 0.41 S4l 31 i ; 64 | 0.43
4657 478 0.42 77 28 | ae 480 0.42 AA 29 3 a6 463 | 0.44
5127 470 0.43 2 a 25 | fe 88 46 0.43 286 26 seas 439 | 0.46
5994 467 | 0.43 -F 24 | pe 454 | 0.44 bs 25 4272 37 | 0.46
6057 463 0.44 Be 22 | or 434 0.46 : 8 23 | 4692 420 | 0.48
6504 447 0.45 ae 20 =i 411 0.48 a6 22 | giz 420 | 0.48
Gaze 422 0.47 a 20 6107 42° 0.49 4 6 7° | 1 40° 0.50
9 5 4x4 0.48 3 18 | 97 405 0.49 39 19 55 393 | 0.52
W582 aig | elas |iodee te | Cae | pees Woe? aa lees eens

| . . e
_ 7802 329 |) Trey Nicaea | 38! 18.1 eugene
312 7469 339 16 | 6749 23, | 0.52
323 15 Ue 369 | 0.54

°.
°
0.47 37 423 0.47
0.47 73 35 | 473 417 | 0.48 ha 36 : 409 | 0.49
0.49 688 32 | 840 398 | 0.50 ees 33 nies 388 | 0.52
i Gc6 9 7298 S 691 797 5
0.51 30 | 388 0.52 31 382 | 0.53
626 1626 660 1179 -
0.52 8 28 a Bie, 0.53 ae 29 ; 370 | 0.54
0.52 59 26 nie 363 0.54 re 28 a 369 | 0.54
PP ris lime eon i 3 362 | 0.56 B a6 | 327, 386'| 0.56
0.57 547 23 ih 34 0.58 577 23 ze 327 | 0.61
0.52 4: 24 3°74 373 0.54 - 25 : 367 | 0.54
0.55 sS 22 Pas Say 0.56 ae: 23 « I | 0.97
0.58 47° 26 3°04 335 0.59 300 20 | 33 9 326 0.60
458 4139 486 3645
0.60 19 bq 33° 0.61 66 2° 6. 329 0.63
0.62 uF 18 ee 324 | 0.63 443 18 2368 304 | 0.66
0.64 16 298 0.66 17 297 | 0.68
0.67 | 495-75.|. 598! aoe Wt io. 6a) |” 43 8ire |: 45°) abe | aces
0.70 72, 15 5388 287 0.70 Aas 15 4853 287 | 0.70
oO. 72 ie 13 5°75 272 0.73 oe 1) 5 5 278 | 0.73
oO.95 S02 13 | es 264 0.706 Sait 13 ss 257 | 0.76
0.77 349 12 2m 58 | 0.78 Nie I2 5°75 256 | 0.78
337 6469 360 5931
= 0.79 It 6718 249 0.80 8 I2 6 248 | 0.80
“3 Up °. 34 12 hie. 246 | 0.82
—26 336 a 6425 arth aces
—28 325 6666 8
~30 314 rr 6905 239 | 0.84

A
DIABATIC CH
ANGES OF
MOIST
AIR—NEU
Table 7 (C io
(Continued) “
i : 40
for
" 100 ™ i :
mm m z Ss
| 100 m™ : | : .
; em | | for 29
| Ioo0 m™
F | mm ™m |
| |
37? | |
679 39 | 496 45° | 0.
643 36 | 979 483 | o. |
6002" | 1448 469 | o. 138
ps pee 464 | o. 4a We ane
ae 30 2369 457 || Os 48 eA 0.43 thes 2 | :
520 27 Ee cee 398 4 | oxgar teen” ie :
4 ne || SESE 426 | o. 1841 43 | 0.45 pas | B90 ye out :
iss 3668 424 | oO. 2279 438 | 0.46 Ost | ” aa ou :
ib 3 4091 423 | Oo. 2706 427 | 0.47 618 3 | oe 431 | ee
42 ne || aes! 4tz | o. HERES 414 | 0.48 588 30 | ee 4x5 oa?
= 20 | 4893 390 | 0. 3521 seh} 0.50 560 224 Bee 405 a 1
a 21 | 5280 387 |"o. | 3921 400 | 0.50 534 Be ite 0.31 3
760 19 5710 430 | oO. 4393 382 | 0.52 a9 i 361 ee = ,
3 are errr 40t | o | 4664 won| 0.58. | 459 ea 38 Ona Cee :
xe 15 6486 375 | o. 5°77 oa | 0.48 465 135 35 os
31 14 6831 345 | Oo. 5451 oe 0.53 | 44 | 4 ae a
ee Tam Ts 344 | Oo. 5818 367 | 0.55 422 ne ee 366 aes 2
305 7506 331 || 0 | 6157 339 | 0.59 404. lee 3 ae
4 | 6486 329 | 0.61 387 5534 : oe
| 6804 ae loresn oe I 5534 33 0.60 6
ion a8 562° 5860 cb 0.61 =
| | 7424 305 | 0.66 | 34” ih ee °-63 | ora
329 ue 2 eee 14
| 317 — sees feeds eee
! | FosG a inte Tis
18
—20
760 ne °
26
ih 382 382 | 0.52 |
664 2° st ee ees 7
oie Be PotD 365 | 0.55 i re
68 27 1482 ae 0.55 696 - v8 59 =
: : ne 363 | 0.55 oe 30 Be ee | 0,56 760 , | 5 12
: : ia a2 | 0.57 68 58 086 448 | 0.56 728 30 3 354 | 0 10
: 29 v4 | oe 25 | 1434 me oy =) 698 ae 345 56 8
: ape 364 | 0.5 a yee (Te oe 0.62 669 | ae 342 me 6
492 21 3184 331 | 0.60 24 | 2114 0.56 643 ; : - “
i I 3508 324 | 0.63 am 2446 332 | 0.60 616 2 1701 a os
He w bea80e es 0.67 519. 2759 ae a (ie cat se oy 269 a
do. Pee ore 19972. | goes ee 567 37 | 7354 29, ou :
: : " 285 | 0:79 = 3372 a | 0.66 540 aoe 297 ae é
“| ae 272 | 0. 17 4 0.69 | 7 ;
ae 14 Le 271 | ae 447 17 | 3935 ee 0.71 Je 253 88 or 2
. 46 aa hea 432 ais | Gee ee 0.73 488 3 = 277 0.70 yas
36 | 5428 254 | 0.79 = |) Gast 25 sie 455 : Se a
: sa ee “5 | 4729 5 | 0.78 455 os uw 259 0.75 —14
: : : 3 | of a 4981 252) | 0.79 44° s 4037 251 0.77 —16
S45 6174 246 | 0.8 13 5232 251t | 0.80 426 mt ae 3 =
333 41 239 Se 36 13 | 9479 gp \colSx.| foe i : fess | a
3 iG Ts 3 pie 398 14 | 4782 fe re 82 —22
5958 239 | 0.84 385 | 5026 oi Ls 26
372 ey x9 | om 3
5504 me he a
—30

VOL. 51
TIONS

EOUS COLLEC

N MISCELLAN

SMITHSONIA

492

Table 7 (Continued)

- | 40°
40 | h for P t I0oom
for P | 100m

I00 ™ | | =)
| mm
mm | ™ 4 4
4 a
|
a
eA pega e oetl| ot anltet ° 0.66
0.59 7 3 63 0.64] 7 © 28 302
0.63 73° 28 | e 315 732 30 302 334 0.60
0.59 [eee a 336; 0.60 702 636 310| 0.63
: 2 7 | 62 a7, 6
0 Gr sh O78 oot OE gael Ugh 0756.| to aal laces
aes 646 aa 1301 307| 0.65 649 L255 ae 0.68
0.66 | 622 1608 97| 0.67 625-4 | 1547 ol. o.72
0.68 | 598 2 | 1999 279| 0.71 se Ee Pee
0.72 | 577.. | ae 276| 0.73 582 6/) POST geal ta
0-74 | 557 0 | 249 273] 0.74 50t geo aegleiee
0.75 | 537 pal ease 0.75 543 a 2624 ase | ough
0.77 | 518 ty | ©8073 255| 0.78 525 2876 35, 0.80
6B SOE a. 7|, 25" 250, 0.80 508 3127 245| 0.82
sar] Mgss | ka] ciae | Sober | 3078]
0.83 | 468 en eo0o 240| 0.83 475 «5 | 3614 39| 0.84
OOF | 858 za.) See anal. oie 460.5 | 3853 4] 5.86
0.85 | 439 14 | eee 234, 0.86 445 4 4085 938 0.88
86 | 425 44°) 227| 0.88 431 4313
‘ 411? 4696
| |
| |

- 6] 760 ° 282 | 0.71 760 B65 OSTA ees ell do 67| 0.75

MO 748 of a 276 | 0.73 734 = 269 265| 0.76 a 26 267 ee 0.77

Sah Pie ee ae Re OK a |) ose aha tp. a8 7107+ | 528 253| 0.79

me ag | acs | aia 686 i7' aba| 0.79] «and 781 343| 0.82

mae i ee ee ee 79 | 663 75| 1043 sida lao tas | 104 240| 0.83

—16] 638°" | 1345 med ec et weet pect ae OE Pah el aba 39| 0.84

—18| 61705 | 1594 388 88 Wer ons Tea 236) 2:89.) tere? cen aaal\ onse

—20| 5989? | 1832 437 || 0.84 1 | ae 1772 236| 0.85 604 °° | 1736 230| 0.87

—22| 579 z= 2069 236 | 0.85 582 = 2008 2 34| 0.86 585 7 | 1966 230| 0.87

Ste) Sees 230h ang |: 9186 564, | 2242 Ba|) Oak Sake rg | 2196 227| 0.88

—26 543 18 2538 231 0.87 546 ce 2469 225 0.90 548 I

—28 | 525 ; 2769 228 | 0.89 2694

ADIABATIC CHANGES OF MOIST AIR—NEUHOFF 493
Table 7 (Concluded)
40 40° “
p h for p h for t
P 100 m 100 m
mm m mm m
4 4 4 4 (oN
10
8
6
4
2
760 30 322 | 0.62
730 322 —2
°. °.
°. 0.67 760 28 295 0.68 = :
°. 0.68 ie 26 25 282 | 0.71 am
(oy °. 706 25 577 0.72 res
I —10
On °. 0.75 east
oO. °. 0.76
°. °. °.
°. °. O-
On °. °.
°. °. °.
OL °. °.
°. °. °.
°. °. °.
°. °. °.

O30507 O70 10 OO:50

Oo 10: 0: 6 0 0 O

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7
S i
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C= é
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pf | | |
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=
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can r ey Pa

+) Ske, re Bip oT , ra @ 4 ‘al
4 el Seu! Me geo Te rer ex :
i Mel Aaa yt Dog ma a a

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USGS EBSeeeRewe

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SAH IUN [Iff Ul OANSSILS 8§&

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ADIABATIC DIAGRAM (Neuhoff).

_" Lge engin
=<
7 ;
at
oa fos
. a
:.
as:
a
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_
_ *
ee

ay

.

4 XXII

THE RELATION BETWEEN “POTENTIAL TEMPERA-
TURE” AND “ENTROPY

BY L. A. BAUER

[Reprinted from the Physical Review, Vol. XXVI, No. 2, February, 1908]

In 1888 the late Professor von Helmholtz incidentally introduced
the term ‘‘wermegehalt” in connection with his investigation,’
“On Atmospheric Motions.”’ According to him the ‘‘wermege-
halt” or the actual heat contained in a given mass of air is to be
measured by the absolute temperature which the mass would
assume if it were brought adiabatically to the normal or standard
‘pressure. It remained for the late Professor von Bezold, however,
to perceive the full significance of this term and to reveal its impor-
tant bearing in the discussion of meteorological phenomena.

As the quantity really involved in this new term is not a quantity
of heat, von Bezold suggested that the term be replaced by the evi-
dently more appropriate one of ‘‘potential temperature.’’* This
met with von Helmholtz’s approval.

With the aid of this happy idea of ‘‘potential temperature” von
Bezold was enabled to draw in a simple and beautiful manner a
number of important conclusions governing thermodynamic phe-
nomena taking place in the atmosphere. Thus, for example, he
found that:

“Strict adiabatic changes of state in the atmosphere leave the
potential temperature unchanged, whereas pseudo-adiabatic ones
invariably increase the same, the increase being in proportion to the
amount of aqueous evaporation.”

1 Presented before the Philosophical Society of Washington, March 16,
1907.

2 Sitzungsberichte Berliner Akademie, 1888, Vol. XLVI, p. 652, ‘‘ Ueber
atmospherische Bewegungen,’’ see translation in Abbe’s Mechanics of the
Earth’s Atmosphere, Washington, 1891, p. 83. The symbol @ is used to
denote the ‘‘Wermegehalt.’’

8 Sitzb. Berliner Akad., 1888, Vol. XLVI, p. 1189, ‘‘ Zur Thermodynamik der
Atmosphere;’”’ also in von Bezold’s ‘‘Gesammelte Abhandlungen,”’ Vieweg
und Sohn, Braunschweig, 1906, p. 128. A translation will be found in Abbe’s
Mechanics, etc., p. 243.

495

496 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Von Bez ‘ld called attention to the fact that this law bears a strik-
ing resemb!ance to the well-known theorem of Clausius, now com-
monly known as the second law. of thermodynamics, viz: ‘‘that
the entropy strives towards a maximum;” but, he says, ‘‘it is not
identical with it.”

The purpose of this paper is to examine into the precise relation-
ship between the two functions “potential temperature” and
“entropy”? and to see whether any use can be made advantage-
ously of the former in the treatment of certain thermodynamic prob-
lems as well as to ascertain wherein the potential temperature law
fails to give full expression of the second law of thermodynamics.
To my knowledge no application has as yet been made of the new
term in treatises on thermodynamics. The substance of this paper
was communicated to the American Association for the Advance-
ment of Science at the Springfield meeting in 1895, but publication
pending opportunity for further elaboration was deferred.

The ‘‘ potential temperature’”’ of a body is defined as the absolute
temperature assumed when the body is brought adiabatically to standard
pressure.

Defining the thermodynamic state per unit of mass of a body by
the three variables, T, the absolute temperature, v, the volume per
unit of mass, p, the pressure supposed uniform, the following char-
acteristic equation subsists between them: T = f (uv, p).

If the body be brought now adiabatically to standard pressure
Pp), then the temperature assumed at the end of the process is the
so-called potential temperature as above defined and is designated
by the symbol @. Hence,

ey Oe Cage >) eee aera tet te A 1)

For a perfect gas, since kT = pu, k being a constant for any par-
ticular gas,

gl = bo Ce ee Nae re

or the potential temperature for any particular gas 1s directly propor-
tional to the volume and, hence, as von Bezold showed, the potential
temperature readily admits of a graphical representation on the
usual pu diagram, being simply proportional to the uv abscisse of
points of intersection of the line of standard pressure, p = pp», with
the adiabats.

Hence, were it possible to express the entropy function for pertect -
gases directly in terms of potential temperature, we should likewise

POTENTIAL TEMPERATURE AND ENTROPY—BAUER 497

have for certain cases an easy graphical representation of the
entropy function. :

In the pu diagram, fig. 1, let aa’ and bb’ represent portions of
two adiabats, and o’a’b’ be the line of standard pressure p = fp.

FIG. FE:

Suppose the initial thermodynamic state of the body experi-
mented upon be represented by the point a and some process ab be
carried out. According to definition, the potential temperature,
6,, in the state a will be the temperature at the point along the
adiabat aa’ where it is intersected by the line of standard pressure.
But according to equation (2) the temperature at this point, a’,
is proportional to the volume, i.e., to o’a’. Similarly the potential
temperature in the state b will be proportional to the abscissa o’b’.
Hence if measured on the same scale, o’a’ and o’b’ will represent
directly for the same substance the respective potential tempera-
tures. It is thus easy to represent graphically at any stage of the
process ab the corresponding potential temperature.

If it is desired to determine the numerical value of the potential
temperature, this can be done with the aid of the equation of the
adiabat thus:

or

\ €-1 1 é€-—1 1
pa ae Men Ore she ot cian eS

where ¢ = 1.41

For a perfect gas, the entropy, s, per unit of mass may be ex-
pressed by the following equation:

‘See, e. g., Planck’s Thermodynamics.

498 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
d
s= f — T= clog T + blog v + Const, i ace

C, and ¢, are, respectively, the specific heats at constant pressure
and at constant volume; k is a constant for any particular gas.
Utilizing equation (3) and remembering that
C
e= "and k= (c, — 6)
v

we get

S = Cy log 0 + (e — 1) log . + Const.
Po

or
¥ =f, lor 0 Const... ‘2 oe ee

This gives us the relation sought between potential temperature
andentropy. Since ¢, is invariably a positive quantity, it follows at
once that for any process the potential temperature varies in pre-
cisely the same direction as the entropy. Ifthe entropy is increased
as it invariably is for irreversible processes in accordance with the
second law of thermodynamics, then is the potential temperature
likewise increased. When the entropy remains constant, as for
reversible processes, e.g., a strict adiabatic process, then the poten-
tial temperature likewise remains constant. In other words as far
as perfect gases are concerned it is possible to express the entropy
function in its simplest form by means of a quantity—the potential
temperature—not only readily interpretable but also easy of direct
graphical representation.

Owing to the intimate relationship between entropy and potential
temperature the term ‘“‘entropic temperature’? might appear as
being possibly a more suggestive one for von Helmholtz’s “‘wer-
megehalt” than that of ‘‘potential temperature,” but it may
hardly seem advisable now since von Bezold’s extensive use of the
latter term to recommend a change.

Cyclical process—By turning back to the diagram, it will be
seen that the change in potential temperature in going from a to b
is precisely the same as from a’ to b’, i. e., the same as for a simple
expansion process under constant pressure. Hence, in carrying
out the cyclical process abb’ a’a, it will readily be seen that the sum
total of the potential temperature changes is zero, just as in the
case of the sum total of the entropy changes.

POTENTIAL TEMPERATURE AND ENTROPY—BAUER 499

We have in general:

5, — Sq = 6, (log 6, — log®0,) =, (log G- — log @,-) . . 6)
or the entropy change in passing from a to b by any process what-
soever—revefsible or irreversible—can be measured ideally by the
temperature changes incurred in allowing the body to expand under
standard pressure between the initial and final adiabats.

For other substances.—lf the substance acted upon be not a perfect
gas we have:

b ’ dh (* do (® do
ee ee

Here c, is not a constant as in the case of a perfect gas, but varies
with temperature and may even be discontinuous, hence it is impos-
sible, in general, to carry out the integration of the right-hand
member. This we know, however, that Cy 18 invariably positive,
i.e., heat must always be supplied to a substance to raise its tem-
perature under a constant pressure. Since

dé
ee ae ae ae (3)

6
it follows that the sign of ds is the same as that of d@, so that when-
ever the entropy increases, the potential temperature does likewise.
This, while true for cases treated, is not so, in general, as previously

explained. ©

In the foregoing paragraphs the law of potential temperature has
been deduced from that of entropy; however, an independent deduc-
tion can readily be made if desired.

For example, we may build up the law of potential temperature
in precisely the same manner as in the case of the entropy law by
taking typical examples of natural processes and showing that
nature unaided invariably tends to increase the potential tempera-
ture.

Thus take the well-known case of the sudden expansion of a
perfect gas without the performance of external work. It is very
easy to show on the pv diagram, since the adiabat is a steeper
curve than the isotherm, that the potential temperature in the final
stage is greater than in the initial stage.

So again with the case of heat conduction. Suppose we have
the same mass of the same perfect gas enclosed in each of two
vessels a and b of the same size and enclosed in a non-conducting ~
vessel. The temperature of a is greater than b. Connect now a

500 SMITHSONIAN MISCELLANEOUS COLLECTIONS: VOL. 51

and b thermally, whereupon in accordance with nature’s law heat
will flow from the hotter body to the colder until the two are of
thesame temperature. It will be found that here again the potential
temperature of the entire system at the end of the process is
greater than at the beginning. This may be proven most readily
thus: For a perfect gas we have from (3), when the volume remains
constant;

6=k' T'/e
hence
is ae
e Tr
where » = 1 — 1/e = positive quantity, since 1/e<1. Conse-

quently, the change in potential temperature for a given change in
absolute temperature, the volume remaining constant, decreases with
absolute temperature. Hence, although the two bodies, a and ),
under the conditions imposed, change in absolute temperature by
the same amount, the first losing, the second gaining, because of
the law just stated, the potential temperature of the colder body, },
suffers a greater increase than the decrease in potential temperature
experienced by the warmer body, a, which was to be proven.

So also for imperfect gases the law of increase of potential tem-
perature for natural processes can be established independently
of the entropy principle. It is merely necessary to show that in
general the adiabat is steeper than the isotherm or that the change
in potential temperature varies inversely with the absolute tempera-
ture, when the volume remains constant.

Thus far it has appeared as though the potential temperature law
might suffice equally as well as the entropy law. However, in all
thermodynamic problems where the element of mass enters, the
former law necessarily fails to give as complete a representation of
the second law of thermodynamics as the entropy law. The entropy
function is not alone a function of pressure and volume but also of
mass, whereas the potential temperature is independent of the
latter. Equation (8) shows likewise that the substitution of the
obviously more convenient function—potential temperature—for
entropy cannot be made in general. There are doubtless, how-
ever, a number of thermodynamic problems, as was shown by von
Bezold, as also in this paper, where the application of the potential
temperature law may be found convenient. The main purpose of
this paper, as above stated, has been to show the precise relation-
ship between the two functions.

|
|
|
|
|

XXIII

THE MECHANICAL EQUIVALENT OF ANY GIVEN DISTRI-
BUTION OF ATMOSPHERIC PRESSURE, AND {THE
MAINTENANCE OF A GIVEN DIFFERENCE IN PRES5-
SURE

BY MAX MARGULES

[Read at the meeting of the Imperial Academy of Sciences, Vienna, July
II, Ig01, commemorating the Jubilee of the k.k. Central Institute for Meteorol-
ogy and Terrestrial Magnetism; translated from the Jubilee volume]

In this memoir some minor studies connected with the problem
of the cyclone have been collected together as a contribution to
this memorial volume of the Central Institute for Meteorology.

In Part I there is determined the work that must be done in order
to transfer air from any prescribed condition of equilibrium over
to any other distribution of mass. In a closed atmospheric system
this work is to be considered as potential energy. The comparison
of the kinetic energy of a simple vortex with its potential energy
teaches that the kinetic is by far the greater.

In Part II the discussion relates to the well-known scheme of
circulation for columns of air of unequal temperatures. The cal-
culation of the additional heat necessary for the maintenance of
any given horizontal difference of pressure and its useful effect—
or coefficient of efficiency—still remained to be accomplished as is
now done in this part.

In the concluding Part III will be found a general calculation
as to the loss of energy in moving air. The internal friction can
have only an inappreciable influence on large systematic atmospheric
currents. Even the complex small movements that pervade
general atmospheric currents consume less of the kinetic energy of
the wind than the lowest stratum gives up in starting and main-
taining the waves of the ocean, or in concussion against the obstacles
offered by the solid ground.

501

502 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. §f

PARTI. THE WORK EQUIVALENT TO A GIVEN DISTRIBUTION
OF PRESSURE

(1.) IN GENERAL FOR ANY GAS

Given air in a definite volume k on which no outer forces are
acting.

The initial condition is uniform constant density “, and uniform
constant pressure f). The final condition is wand p. During the
transition we have yp, and p,.

For a small change of condition the elementary mass dm performs
a work of expansion expressed by

ampd(* ) spe LE aoe
far) Ly

and from beginning to end the total work is

le
da= — om Pt d jy,
Ho fy

The air which when brought to the density m is contained in the
elementary volume dk, has the mass ypdk, therefore the work of
expansion done by the whole mass is

a= — frat "ay
Ho Le

If the relation between pressure and density is independent of
the path followed by the particle of air, if for instance it is arranged
that the transition or change of position of the particle of air shall
take place under constant temperature (isothermal), or that it shall
take place without increase of heat and without exchange of heat
(adiabatically), then the value of a will be determined by the initial
and final conditions.

For the final distribution of pressure p the gas has a store of
energy A that is equal and opposite to a. It is demonstrable by
means of the aerodynamic equations that this represents the poten-
tial energy of the pressural forces for the given distribution of

mass, “, OF
EP
A = ( pdk SE ti. ss RO ee
= fu 1% mae (I)

MECHANICAL EQUIVALENT OF PRESSURE——MARGULES 503

(a.) Isothermal change of pressure

Let R = gas constant, T = absolute temperature and in the
equation for elastic gases,

, p= RT p
let T be constant and use the relation

fudk =[ugdk

then it follows that

A= RT {db wlog(#) = faep tog(* | acy
Ho

0

(b.) Adiabatic change of pressure

For this case we have

where 7 is the ratio of the specific heat of a gas under constant
pressure to that under constant volume, whence

eae ( a
axa ee Lo :

under the condition that the mass of air within the volume F

remains unchanged, this becomes

1
A= 5 J - po) dk. Ae eee ee GO 10))

Relatively small changes of pressure

The expressions (Ia) and Ib) seem to imply that the elementary
volumes for which pressure and density are above the average value,
give a positive addition to the integral, but that those for which
these are below the average give negative contributions. But this
is not correct.

If we put

fe =a (1 + 0) and p = py (I +8)

504 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
Then for an isothermal change we have
Gig he ye Cas, eg
For an adiabatic change we have

GA
a ee ee <r ())

And always
fo dk = 0

Hence we obtain for isothermal change

3 4 2

‘eS Viele “ +e5 ) far e ) Ga
— Po Toe gene Boa Peres 3 yy
and for adiabatic change

ee C—)'6=7)
A=rpyJ dk aS a MCS eae )

=" far($-...) oak ba at hae

These forms, like the fundamental equation (I), show that the
contribution of each elementary volume whose density deviates
from the average value, is positive. The contribution of a volume
in the low-pressure region is indeed somewhat larger than that of
the same volume in a high-pressure region having the same absolute
value of o.

For very small changes of pressure the first term of the develop-
ment is sufficient. This solution was first given by Lord Rayleigh
(see Vol. II, page 22, of his Theory of Sound, German edition (Bruns-
wick, 1880). For equal values of o the potential energy of any dis-
tribution of pressure is 7 times greater under adiabatic conditions
than it isunder isothermal; but with equal values of eit is only 1/7
times as large.

The work stored in a very large volume of gas, when only a
small portion of it 1s disturbed

Let k indicate the volume that suffers a disturbance of its equi-
librium; k’, the remaining far greater volume whose density is not
appreciably changed by transfer of any mass to or from k; o and

MECHANICAL EQUIVALENT OF PRESSURE—-MARGULES 505

o’ the relative change of density in k and k’; we now have
Jodk 4 fo'dk’ =0
and for the limiting case
for ak =0

which latter equation and similar ones for the higher powers of
o’ hold good for an infinite volume k’ of gas.

Therefore the expressions (Ia*) and (1b*) remain unchanged if the
integrals are extended only over the disturbed portion.

In order to formulate expressions for the work, or potential energy
of *a closed system, we note that the share contributed by the
volume k’ to the potential energy is given for isothermal condi-
tions by

A’ = Lim RT { dk’ pl! tog (* ) =RT pty { 0” dk
0

Sia a

or for adiabatic conditions by
1 Por CH= bo
A= SSP) Ci ae It a
If again A indicates the potential energy of the whole mass of

gas, then we have:
for isothermal conditions:

le | p }
A=RT Sak (elog" eee n)= far (; PES. te ~ p)...(la’)

or for adiabatic conditions:

Ante f[2_1_,(4-1) ae re asai))

The integrals are to be extended over the disturbed portion, or
indeed over the whole volume, since the terms that are added to
the previous expressions (Ia) or (1b) contribute nothing more to
the result that pertains to the volume k + k’.

506 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

(2.) THE ATMOSPHERE OF THE EARTH

If external forces act on the air then in a condition of equilibrium
the pressure varies from place to place. In studying perturbations
the potential energy of these external forces comes into consideration
in addition to the potential energy of the change of distribution of

pressure. Still in many cases the expressions above’deduced can.

easily be applied.

We will designate as an atmosphere, any mass of air on which the ;
force of gravity is acting. For brevity we assume the acceleration:

of gravity, g, to be constant, and the ground to be a smooth plane
and the initial temperature to be a function of the altitude only.
If this atmosphere be divided into individual layers of indefinitely
small thickness dz then under simple assumptions we can carry out
the analysis for each layer with the formule that apply to a mass
of gas of constant initial density.

If the condition of equilibrium is disturbed in only a relatively
small portion of the whole mass, then it will be assumed that the
excess or deficit of gas in each horizontal layer of this disturbed
cylinder comes from or has flowed into the undisturbed portion of
this same layer: hence the potential of the gravitational force
remains unchanged. The potential energy of the distribution of
pressure is given by equation (I) or the formule derived therefrom.
The elementary volume dk is to be replaced by the product of the
elementary area dS and the altitude dz.

If we assume that the equilibrium is disturbed in the horizontal
direction only, and that on the other hand the vertical equilibrium
remains unchanged and that the hypsometric formula is still appli-
cable, then the integration with reference to or along the vertical
direction is easily executed.

(a.) Isothermal solution

Under isothermal conditions and according to equation (Ia’)
the store of work for any layer is

dA =a: § (plo? +p, p)as
0

where the integral extends over a surface that includes all the dis-
turbed portion.

If now we assume the temperature of the atmosphere to be con-
stant and designate by P the pressure at the base over the elementary

MECHANICAL EQUIVALENT OF PRESSURE——MARGULES 5°7

surface dS then we have

p-
Ly fe BT de f (Pigs + P,- P)as.
0

The integral with respect to z between zero and infinity is the
so-called height of a homogeneous atmosphere having the tempera-
ture T. If T is a function of the altitude still nothing is changed
in this expression for the volume of A except that in RT/g in the
value of the integral with respect to z, the T now indicates the
mean temperature of any horizontal layer. If we write

P2P, 46)

we obtain the following formula which is more convenient for
numerical computation:

RT ie 8 e*
=| (5 aaa eee Jas (lla)

Hence the potential energy of the assumed distribution of pres-
sure in the atmosphere is equal to that in a layer of air on whichno
outside forces are acting, whose altitude is RT/g and in which the
distribution of pressure in all upper strata is the same as that at
the base of the atmosphere.

If M is the mass above the surface S in the undisturbed condi-
tion; [e?] the average value of e? in S, if moreover the first term of
‘the above series is very large relative to the others, then we have
the following approximate formula:

A=MRT

[e"]
2

Example. The following example will serve for a preliminary
estimate of the potential energy of the distribution of pressure in a
cyclone:

Let the area of disturbed pressure be a circle of radius p; the
pressure in the center at the base be P, (1 — c) increasing linearly
from that point to the circumference, so that

r
= —e(1 ue)
gee

508 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

For the elementary surface dS in equation (IIa) we have to sub-
stitute 2zrdr and making use of the relation

{"(: — ©) rar = So lh i eolingen Aes
0 p (n + 1) (m + 2)

we obtain for this special case

2 141 14!
Ao eae Bie A alta es)

SE RE 1 5! 6!

as the average value of the potential energy of the system for the
unit of horizontal surface.

If the barometric pressure in the center at the base is 745™™ [in
the disturbed region,] and 760™™ throughout the undisturbed
region we then have

mie yard P, = 103833 9.806 ket? m- sec~?;

for the temperature 0° C. = 273° absolute we have
= = 8000 meters nearly
whence
= = 26210 kg sec-? = 6.3 Kilogram-calories m7?

Assuming the radius of the cyclone to be 5 degrees of a great circle
or P = 555,500 meters, then the whole work needed to produce this.
diminution of atmospheric density is equal to 6.1 X 10” calories.
This work will not appear so large when expressed in other terms;
the equivalent amount of heat would raise the temperature of the
whole volume of the cyclone (under constant pressure) by only
about 0.0026° C. or approximately by the z}5 part of adegree Centi-
grade.

With the above assumed linear formula for ¢ and the values of
c and e we have at sea level a constant gradient of pressure of 3™™
mercury per degree of a great circle. The average value of A/zo?
is independent of o and nearly proportional to the square of the
difference between the normal pressure and that in the center of
the cyclone. A barometric reading of 730™™ instead of 745™™ at
the center would increase the above computed value of A/zp? four-
fold.

MECHANICAL EQUIVALENT OF PRESSURE——MARGULES 509

(b.) Adiabatic solution

If we define the average temperature (T) of the disturbed strata
by the equation

-

oO) = * dz /RT
| af dz
g 0

then under adiabatic conditions in the atmosphere we have

Hee PP pS (5+ as.

a [T] a”
a rip +

If we confine our attention to the first term of this series then it
is true that,as before in (Ia*) and (Ib*) so now for the atmosphere
for equal value of T and for adiabatic changes of conditions, with
equal value of o A is 7 times greater than for isothermal changes,
but with equal values of ¢, A is 1/7 times as large as (i.e., smaller
than) for isothermal changes.

. (IIb)

(3.) STATIONARY WHIRLS IN THE ATMOSPHERE

Let a distribution of pressure of the kind assumed in the preced-
ing article be produced in the atmosphere by a stationary whirl;
we wish to know the ratio between the kinetic energy of the moving
mass and the potential energy of the difference of pressure.

Let the atmospheric particles describe circles around the vertical
axis of the cylinder whose radius is 9; the hypsometric formula
applies as before. Such a motion is possible in frictionless air,
that is to say, the assumptions are compatible with the aérody-
namic equations, provided the velocity is constant along the vertical.

(a.) Whirl in a quiet atmosphere

For the change of pressure in the horizontal direction we have the
relation

Sin Sh PUA ER Se We chee ae

510 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

where G is the velocity of a particle and r the radius of its circular
path. For the kinetic energy of the whirl we have

oe) 2
a eC
0 eo 2
co
-x{ as |" op rv? dr
0 0 or
R

= aici Pe 2 dr
g Yo

where the notation is similar to that of the preceding pages.

The assumptions of a very large volume k’ of quiet air in comparison
with the volume of the whirl k and no change in pressure for poe outer
region where r S p¢, are also retained.

Thus by partial integration we obtain

K= 7 sa [end
g 0
Only negative values of ¢ are possible.
Using the value of ¢ = — c (1 — r/p) adopted in the preceding
example we find:
K= rp" Py: ae 5

If M is the mass of the air in a cylinder of radius p under pressure
760™™ and the temperature T, then for K, the kinetic energy of the
whirl, and for A, the potential energy of the distribution of pressure
produced by the whirl, we have

R= MRT
3

Cc?

Ave eT
12

RA

A C

For ¢ = 15/760 we find K two hundred times larger than A. For
= 30/760 we have K still roo times A.

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES Cae
(b.) Whirl on a revolving horizontal plane

For the case of relative motions above a small area on the surface
of the earth we simplify the equations by the assumption of a con-
stant polar distance and thus attain an approximation to terrestrial
conditions that suffices for certain special cases.

We consider the substratum of the atmosphere as a rotating plane.
In order that the atmospheric pressure in the condition of relative
rest may be a function of the altitude alone, we must also assume
a force directed toward the axis of rotation, opposite and equal to
the centrifugal force. The location of the foot of this axis may then
remain arbitrary.

Now the distribution of pressure in a stationary cylindrical whirl
with vertical axis is given by the equation

where G designates the velocity of the air relative to the rotating
surface of the earth and is positive when the direction of rotation
of the whirl agrees with that of the earth [as in cyclones]. The con-
stant factor of the deflecting force due to the earth’s r<tation is

1 = 2.) Sin.

where v is the angular velocity of rotation of the earth and ¢ is the
geographic latitude of the place.

The potential energy of the distribution of pressure is not changed
by the rotation. But for positive G, the kinetic energy of the rela-
tive motion is smaller than it would have been for an equal pressure
gradient and 7 = o. Therefore the ratio K/A is also smaller.

If G/jr is very large then in the equation (@) the first term on the
right-hand side exceeds the second. In the case of cyclones in low
latitudes whose horizontal extent is relatively small, we can esti-
mate the value of K/A approximately according to the example
just given, where K/A = 4/c.

At latitude 15° and for r = 100 km. we have jr = 3.8 meters
per second. If now G is five times larger than this, then the right
hand of equation (8) becomes (25 jr + jr) so that for such cases
the neglect of the second term will incur an error of 4 per cent or
less. In middle latitudes (40° to 50°) the two terms are in general
of the same order of magnitude.

512 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

If in equation (8) we substitute

OP ot ee Be
be Or or

then for positive values of G we have

* mee
@=rrdri_ es (Vie S71) le

he ar SRT i eRe f

Example. For this example, and for the sake of abbreviating
the computation, we here assume another law for the distribution
of pressure, i. e.:

We thus obtain
ea ir uel Fs, tt Oe ge (af ee eta
2 { 4R fs
If we assume the following special numerical values
log 7 = 6.01337 — 10; RT .= 287 .273 m? sec?

30 4 kT
ie hat

6é=1

corresponding to a whirl of 1080 km. radius, with the barometric
pressure 730™™ at the center, in latitude 45°, then we find

BE ES ET. 5 0.268.

If the earth be not rotating (that is to say if 7 = o) and the other
conditions be retained, we should only be able to maintain this
same distribution of pressure by assuming a whirl whose kinetic
energy is

K = MRT ~

a oS ee? ee oe

ee nat

——

MECHANICAL EQUIVALENT OF PRESSURE——MARGULES Sas

For both these cases, under the newly assumed law fore we find
the potential energy of the pressure distribution to be

C2
Vas Mel Sa eS
6

hence the ratio A/K is 1/20 for the rotating earth, but 1/76 for the
non-rotating earth.
Although this ratio is thus seen to be appreciably increased

from 1/76 = 0.013 to 1/20 = 0.050

by the action of the so-called deflecting force of the earth’s rota-
tion,» still even in whirls of the middle latitudes the potential
energy of the distribution of pressure is far less than the kinetic
energy of the relative motion.

(4.) PROGRESSIVE WHIRLS IN THE ATMOSPHERE

One may ask whether the progressive cyclones are more properly
compared with single waves or with revolving whirls. Cyclones
have one feature in common with waves, i. e., the partial interchange
of the moving masses. On the other hand the dust fall progressing
over broad areas with some individual cyclones (notably from
Sicily to the North Sea on March ro and 11, 1901) is a proof that
a large portion of the atmosphere remains constrained to move
in true whirls.

As regards the ratio K/A of the kinetic to the potential energies,
cyclones are to be considered as whirls rather than as waves.
According to Lord Rayleigh, ‘‘ Theory of Sound,”’ this ratio is unity
for progressive plane waves of air. In our present case we find it
from the following rough estimate:

Let M be the moving mass of air, [G’] the average of the squares
of the velocity, [e?] the average of the squares of the relative
diminutions of pressure, then we have

2 2
a ai cig

where V RT is the speed of propagation of isothermal waves or
the so-called Newtonian velocity of sound and is 280 meters per
second for temperature 0° C.

514 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL 52

For a cyclone wherein the maximum absolute value of ¢ is 3/76
we may estimate the average value [e”] as being at the very highest,
only 3/76? as in the last example, since the smaller values of ¢ cover
by far the larger surfaces. In order that K should equal A the
value of [G?] must be(6.4)*, hence the average value of the velocity
must be not more than 6.4 meters per second.

Observations give even for the lowest layer a greater average
velocity than this for the lowest barometric pressure of 730™™.
If the radius of the cyclone is ro° of a great circle and the average
gradient 3™™ mercury, then the mean wind velocity for the lower
stratum of air (about 20 meters above the ground) at median lati-
tudes is to be estimated at 12 meters per second, but that of all
the higher strata at, at least 18m/sec., and therefore K is at least
8 times larger than A.

(5.) RELATIONS BETWEEN PRESSURE AND WORK

The equation (I) has been based on the conception of work done
by the expansion of the gas and is provisionally spoken of as the
potential energy of the distribution of pressure within the closed
volume k. If this be correct then the work done by the pressural
forces in any elementary portion of time must be equal to the
change in —A.

The work done by the pressural forces on the small mass dm dur-
ing dt is given by the expression

20M, OP aa = ene ae as
pe OS ds

where ds is an element of the path of the moving mass and G is the
velocity in the direction ds. This is equivalent to

- ( « Py Pt w 2 \ dbdt
Ox oy 0z

where u,v, w are the component velocities along the axes of x, y, 2.
We have to prove that

0A _ (uP P+ w ? )ae.
Ot Ox oy 0z

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES 515

In equation (I) substitute

"2 du= FW -F we
Ho

7 0

then with the equation

f ude = J mode

which expresses the constancy of the mass of the gas enclosed within
the volume k we obtain the following:

| d
if ui (w) onstan ; 2
o_ iS oe ( He ) dk
ot ot Lt
The equation of continuity of a mass of gas

an , (uu) , a (nv) | A (nw) _
ot 0x oy 0z

combined with the preceding gives us

Si a (eee 2) | at
pe Ot 0x oy dz

By well-known transformation, the second integral on the right’
hand becomes

alee («2 aes ee, om ) dk - es (u cos Nx + vcos Ny
Ox oy 0z

+ w cos Nz) dO

where O is the surface of the volume k and N is the normal to that
surface directed inward.

The last portion of this expression vanishes when no gas passes
inward or “outward through O. .

516 SMITHSONIAN MISCELLANEOUS COLLECTIONS VO 5a

Under this latter condition we have

se se ek ee
ot lt ot Ox

= f (« a ae + wi? ) ab,
Ox oy 0z

The first and second of these equations state that —dA0dt is the
sum of the works of expansion done by all the elementary masses
within the volume k in a unit of time; the third equation states that
this is also the work done in the same unit of time by the pressural *
forces. In general these two quantities of work differ for each
individual elementary mass; it was therefore important to demon-
strate that starting with the work of expansion we arrive finally
at a correct expression for the potential energy of the distribution
of pressure.

We can also deduce the value of A by another route, i. e., by
computing the work done by the pressural forces during the pas-
sage from the initial to the final stage. We thus arrive at the

expression
Pp
A= fa i anf ae
Ho Po P

whose identity with equation (I) can easily be proved: both of these,
by partial integration under the assumption of the constancy of
the mass of gas within the volume k, lead to the following:

= i) udk ip “t =i dk (p — Po)

Now the simple assumptions that have been made the founda-
tion of the preceding computation of A do not obtain in the atmos-
phere. If we assume the atmosphere to pass adiabatically from
any initial condition in which we happen to find it over into a con-
dition of equilibrium, then this will not be possible unless some
masses of air pass from some one horizontal layer over into another
layer. If an interchange of heat take place, then, except in the

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES 517

case of constant temperatures the whole work done by the pres-
sural forces cannot be expressly or exactly stated, for it depends
on the path along which the transfer takes place. Generally the
question is as to the changes of A with time and these can be com-
puted provided that the serial succession of conditions is known.
But the total potential energy can only be given under certain
assumptions; an estimate of its value can however be obtained by
means of the formule here deduced.

APPENDIX TO PART I

(6.) THE EQUATION OF ENERGY OF A FRICTIONLESS MOVING MASS
OF AIR

Retaining the notation of the last section we have for a unit mass
of air the following equation for the living force or kinetic energy:

1d@)_ ¢ 4 _ _ OV G dp
2 Gt dt os fe OS

where V or the potential of the exterior force is so chosen that

the negative derivative with reference to any codrdinate expresses

the force acting on the unit mass, in the dissection of that codrdinate.
We will also introduce the Eulerian Symbol

a*lé a
dt ot Os
0
SM ool We He apie

ot Ox oy 0z

which expresses the variation with time of the variables associated
with the elementary mass. If V is only a function of the location
then the equation of energy becomes

|
Se (III)
2 di de op \ dt at

This holds good also for movements relative to the earth.

518 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
(a.) Horizontal motion im a steady field of pressure
When gravity is the only exterior force and the distribution of

pressure remains unchanged, the equations of condition for hori-
zontal movements are:

eV aaaaal® &
dt ot
whence
L dG ldp | RT dp
cy eater ae iG

(a) Under isothermal conditions, therefore, the integral becomes

(G — G2) = RT log 2
p

bole

where G,, p) and G, p are associated sets of values.
(b) For movements with adiabatic changes (see Ib) we have the
equation
C aT dp _

0
Ay: Bes eA

Here it should be noted that the second term with its negative
sign represents the work of the pressural forces on the unit mass
in unit time in a steady field, and for subsequent use we also note
that the whole work done on the unit mass in moving it from p, to
p or from T, to T is equal to

Cy (To— T)

This is quite independent of whether the motion takes place with
or without friction. In the case of frictionless motion we have
therefore,

1 p \F/Cy.
D) (G - Ge ( 0 ) Pp 0 ( ( Po ) )

(c) If (p) — p) is small relative to p, then the preceding equations
(a) and (b) give alike the same approximate formula for the increase

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES 519

of the kinetic energy of the unit mass

0

: (@ = 6) = RT, 228

Be daar
Ho

The following small table gives the velocity that a mass of air
acquires in passing horizontally and without friction through a
stationary field from rest and the pressure corresponding to 760™™
Merry tO. a.pressure that is less by 2.2... 300) eit 1s cam-
puted’ from thislast equation, assuming RT, = 287.273 m’sec”*.

Computed G, assuming no friction and small changes of pressure,

Py) = 760 and G, = 0

Po =P &
mm.
I 14.4
2 20.3
5 32.1
10 45.4
20 64.2
30 78.6

From this table we may perceive to what linear distance a
horizontal current of air, in a steady field, can flow, frictionless,
against a given gradient. If its initial velocity is 20 meters per
second then this sinks to zero as soon as the pressure rises by 2/760
of the initial pressure. With an initial velocity three times as
great, or a living force nine times as great, it can Overcome a dif-
ference of pressure of 18™™ mercury in the lower horizontal layer.

(b.) Horizontal motion in a variable field of pressure
Equation III now becomes

1 Compare p. 416 of the recently published Lehrbuch by Hann, where these
same results are deduced in another way.—ABBE.

520 SMITHSONIAN MISCELLANEOUS COLLECTIONS Viola Sm

For relatively small changes of pressure this gives us

separa ee |
2 Po Po ot

If an air mass is flowing toward a place of lower pressure and at
the same time the pressure at every point of its path is changing
with the time, then the increase of the living force of the moving
mass is no longer determined simply by its initial and final pressure.
If the pressure rises with the time then the increase in kinetic
energy is greater than it would be ina steady field, but if the
pressure falls, then the increase is less.

Assume that the barometric pressure in the moving mass under
consideration falls 1o™™ during ten hours, but that in the field
through which the moving mass describes its path it rises 1o™™,
then in this case the increase of the kinetic energy of the moving
mass is twice as great as in a steady field. But if the pressure
in the field surrounding the path had fallen 1o™™ instead of rising
during these ten hours, then the moving mass would not have
needed to move at all and the increase of kinetic energy over that
of the stationary field would have been zero.

PART II. ON THE MAINTENANCE OF A DIFFERENCE OF
PRESSURE BY THE ADDITION OF HEAT

ee. STEADY CIRCULATION IN A DRY ATMOSPHERE

During movements of the air out of regions of higher pressure
into regions of lower pressure, work is being expended continuously
by the pressural forces drawing from a previously accumulated
supply. The potential energy of the system must exhaust itself
and the differences of pressure at any level must disappear, unless
there be compensation from some source. Movements against
the gradient could indeed reconvert kinetic energy into potential
energy, but then the process would develop some sort of wave
action and even then the loss by friction must be replaced.

So far as the study of energy is concerned, one can imagine a.
scheme for a steady circulation between regions of differing pres-
sures as explained in the following diagram and text.

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES 521

Heat abstracted

Temperature... t,t 5 : a
PLesSure: 2s. ./u.scn. | Py eR oy Pr»
(3) t
‘ - E
& Le
O | (4) (2) |
|
& | &
fe) | &
©) =
i ee) RE ASAS
Pressure . . higher P, lower P,
Nemperature . 02°. J; i”, I;
Heat added

(1) At the lower level the air flows from the higher pressure P,,
to the lower P, and at the same time receives an increase of heat.
For the sake of the analysis we assume that the adiabatic change
of condition prevails in the passage from P, to P, and that there
has therefore been a cooling from T, to T’, but that then an
addition of heat under the pressure P, suddenly takes place, pro-
ducing a rise from Tj to T,.

(2) An adiabatic ascent at the location of lower pressure P, and
above it a vertical equilibrium prevails or a condition inappreciably
different therefrom, so that the pressure falls to p, and the tem-
perature falls to t,.

(3) A horizontal movement along the upper level from Pp, to p,
together with cooling by radiation or conduction; this process will
for convenience in analysis be decomposed into adiabatic change
of condition from p, Tt, to p, 7, then abstraction of heat and cooling
from t, to t, under the pressure p, to such an extent that,......

(4) When the air descends adiabatically it arrives at the original
temperature 7, and the pressure P,. Here also we assume that the
equilibrium is maintained between gravity and the vertical diminu-
tion of pressure.

In both the two vertical portions of this path the change of tem-
perature with altitude is at the adiabatic rate — g/C, per unit
of length (fordry air C,, = 987 m’ sec* Centigrade*. On any given
level the difference of temperature between the two vertical columns
is constant. The difference of pressure will diminish with the
altitude and become zero at a certain altitude and above that it
will increase but with the opposite sign.

522 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

We choose an appropriate altitude for the column of air such
that the horizontal motion of the upper layer takes place in the
direction of the gradient—though this is not really important.

The potential energy would diminish by the amount of work
done by the pressural forces, if there were no addition of heat.
The quantity of heat converted into work supplies that potential
energy which is converted into kinetic energy by motion in the
direction of the gradient. This increase of kinetic energy is con-
sumed by friction.

For each kilogram of air that makes this complete circulation,
and during the interval of time occupied in so doing, we have the
quantity of heat added at P,, or below

(T,-T,) Q=C,
The quantity of heat abstracted at p, or above
(c—1,) OW =C,
The quantity of heat converted into work
O-Ceq=6, oh oy >)

Now we have

tZ =T7,- ae
Mell rae
Whence
ee St
or
Lt+y=h+h
and
q=C, (T, — Ty +% — 1) ]
= c, 7,[1—(2)""] — eyn[a- (2) "] {
P, ep ia se) J

As stated in §6 the work done on 1 kilogram of air by the pres-
sural forces in the stationary field along the path P, P, is C, (T,—
T{) and C, (t, — t,) along the path p, p,. According to the assumed
conditions of our problem there is no active effective force and

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES 523

therefore no work done along the remaining portions P, p, and
p, P, of the whole circuit. Hence the quantity of heat q is the
equivalent of the total work done along the horizontal portions
of this circulation.

Since byntroducing the equation for adiabatic change of con-
dition we obtain

therefore for 1 kilogram the total change of entropy or the sum of
the changes during one circulation is

(e oat Aa CN ean pea Parent
™m T pic ig en VP ers

This cycle is reversible. If during the upper path the air is forced
against the gradient, then we have to add as much heat as was
withdrawn in the above-described direct cycle, and similarly in
the lower path we must abstract heat instead of adding it. The
work done against the pressural force is converted into heat and
the difference of pressure remains unchanged. :
The useful effect or efficiency of the heat added in the former
direct cycle is very nearly equal to

Lae oi
Tt ty

and it increases with the difference of level of the upper and lower
horizontal paths.

(8.) STEADY CIRCULATION IN MOIST ATMOSPHERE

A cycle with additions of heat varied so as to imitate the process
in moist air may be constructed in the following manner:

In the preceding scheme let aqueous vapor be added at P, and
let the mixture of air and vapor ascend so high that at p, the vapor
has nearly disappeared. The water condensed in each elementary
portion of the path P, p, is assumed to fall away immediately and
be collected again at P,. In this case using one cycle the addition
of heat to one kilogram of dry air is not only the quantity needed

524 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

to raise its temperature from 7’, to T, but also the additional
quantity needed for the evaporation of the water taken up by that
kilogram of air.

In the case of adiabatic change of condition along the path
P, p, the condensation of vapor causes the vertical temperature
decrease to be smaller than in dry air. The ratio of the masses
of saturated vapor and dry air in any given volume is nearly 0.01
at 15° C. If weneglect small quantities of this order of magnitude
as compared with unity then we have

ldx = C, [ (dz) — dé]

where dx is the mass of vapor condensed per kilogram of dry air
along the path dz; Idx is the corresponding amount of heat of evap-
oration; — dr the corresponding change of temperature in satur-
ated moist air and — (dr) the corresponding change of temperature
in dry air.

The complete treatment of a cycle for moist air requires a great
display of formule. But we can with dry air imitate all that is
important and thus the process becomes more perspicuous.

Instead of adding the heat required for evaporation at the point
P, on the lower path, where it would be used to warm the air ascend-
ing along the path P, p, (that is to say, in diminishing the vertical
diminution of temperature)—we arrange a graduated series of
sources of heat along the path P, p, so as to cause a prescribed tem-
perature to prevail along this whole path so that the change —dt
occurs in the distance dz. Ifthe change of temperature is to be
—(dt) for adiabatic conditions then the quantity of heat to be
added will be dQ = C,[(dc) — dr] where we write dQ instead of
Idx.

We now imagine the following cycle:

(1) Movement along the path P, P, and heat added at P, asin
previous case.

(2) Heat added along the path P, p,in such a manner that the
temperature at every altitude has a prescribed value. Equilibrium
between gravity and the vertical diminution of pressure.

(3) and (4) as before.

The conditions of the second step in this cycle are for the added —
heat

0-6 ea
p

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES 525

and for the vertical change of pressure under static equilibrium

-

whence this second step requires that

But in addition to the quantity of heat C, (7,— T’,) added at
P, there is still to be added

Cy ( % —1,+ ze)
C.

Pp

along the path P, p,; and as before there is to be subtracted
at p, the quantity

Cy (Z — 7),

the quantity converted into work is

q=6,(n-T +£htn-4) ; Bhat A)

Dp

=€, (T,—T, + y= m)

But this expression, which is of the same form and meaning as in
the process for dry air (see tv of §7), has now a different numerical
value. If P,P,7,T, and h remain the same in the two cases but
the column P, p, is warmer now than before, then will p, be larger,
but p, remains unchanged and a larger value of t, — Tt, corre-
sponds to the larger difference p, — p,. In the second case more
heat is converted into work than in the first case; this increase will
be used to maintain the greater difference of pressure that now
exists in the upper layer.

The following numerical data are made the basis of an example
of this second method:

526 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL, 52

m
h = 6000 g=9.8 anAS for the average altitude
RD bl a alee a e
G,-) aeal yy see" Cente
C 5ey m ee Calories
ae sec? Cent.0 fa kg C.°
PP, = tr atercury P= 74 oP mercury.
T= eG, = 288° C.
( =) 2 0.009929 a (2 006
Pee aaa Mee a “" m dz inetd
t, = 225.4° tT, = ope 2

We assume the vertical temperature gradient in the column
P, p, to be constant: it is very nearly equal to its average value for
moist air saturated at the temperature 15°C. at the sea level.
Using the hypsometric equation for linear vertical temperature
gradient

; aT
p t leg R dz
pai

we compute

p, = 343.62™ b, = 345.92™™ mercury

and using the analogous equation for adiabatic temperature
gradient

we compute

Pf, = 2er° 7a G. r= elo ke

The quantity of heat to be communicated to a kilogram of air along
the vertical path P, p, is 23.6 C, = 5.6 calories. Air saturated at
15° C. and 740™™ contains 0.01086 kg vapor for each kilogram of
dry air; assuming the latent heat of evaporation to be 595 there-

MECHANICAL EQUIVALENT OF PRESSURE—-MARGULES 527

fore the heat in this quantity of vapor is equal to 6.46 calories and
can do the corresponding amount of work.

(1) The heat added to a kilogram of air during a com- Glories

mlet@ey cles \5e,< eewtacee seinen causa ae bine Se 29.87 Cp = 7.09
(2) The heat withdrawn during the cycle............. 26.11 Cp = 6.20
(3) he heat converted into work... -2)¢ 8-8 22401.) 3:76 Cy = 0.89

(4) The efficiency of the added heat 3.76/29.87 = 0.126

We will now, for comparison, compute an example for dry air
by the first process: the h, P,, P,, T, remains as before, but T, is so
chosen that the average difference of temperature of the two verti-
cal paths is nearly the same as before in the example for above,i.e.,
ne C208

. (2) 5 Ce

Assumed data for h = 6000™

Ea th . |
Poa tie T, = 273 | (=) = — £/ Gs | t, = 213.4
| |
mm. oly ; |
P, = 740 te 28S. | Py a Ce T, = 228.4
| dz /2
Computed data
Pp, = 330.077" = T, = 269.87
ae ste T= 22 1
Calories
Added heat per kilogram.... 0:23... ...0+2+e+2022--- 18.13 Cp = 4.31
Abstracted heat per kilogram.......-------+-+-+-+e:- 14.34 Cp = 3.41
HeaticonverteauntonwOrlcs .clece <5 oe me eieneia tre) ne ee 3-79Cp = 0.90
(Dbitien oyna ey neler eee ee 3270/1853. =o, 20

In these examples of these two processes, for equal differences of
temperature between the two vertical columns of air we have
almost equal quantities of heat (0.89 and o.go calories) converted
into work; but in the second example for dry air the efficiency is
greater than in the first (for moist air).

The quantity of heat converted into work in the unit of time is
nq/0, where is a factor depending on the sectional area of the

528 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

circulating stream and @ is the length of time required for one cycle.
If other conditions are the same then @ increases with the length
of the path, but qisindependent of it. Thelongerthelength of path
the less Feat must be expended in maintaining an equal difference
of pressure in the two vertical columns.

(9.) COMPARISON OF THE PRECEDING SYSTEM WITH NATURE

The preceding scheme was formerly a favorite one when it was
assumed that the anticyclones of winter are cold; but it has become
obsolete since Hann has.shown that this is only true for the lowest
calm layer and that on the other hand the higher strata of air in
anticyclones are very warm.

In an area of high pressure the columns of air not only have a
temperature that is high for the season, but also one that is higher
than anywhere in the surrounding region of lower pressure. In
the lower portion the air flows steadily away in the direction
of the gradient: while the anticyclone as a whole remains stationary
and often for a week or more. We therefore must necessarily
assume that in the upper layer there is an inflow [toward the
anticylone].

Under this assumption the upper inflow can only take place
against the gradient. The differences of pressure do not disappear
with elevation. but become relatively larger in the upper level
provided the whole column in the area of high pressure is warmer
than the surrounding air. If we assume a circulation to exist
under these conditions then we cannot assume any heat to be con-
verted into work. The pressural forces do the work below the
lower layer, but for the inflow in the upper layer work must be
expended, and more than we gain in the lower layer. Hence this
system or cycle cannot be considered as in any manner similar to
that hitherto considered but must maintain itself by drawing
directly from a store of kinetic energy that feeds the upper inflow.
Like all other movements on the earth, this kinetic energy can only
have its ultimate source in heat: but in order to get an idea of the
whole process we must consider the conditions prevailing over a
very much larger region and for that purpose must devise some
scheme that shall include the conversion of heat into work.?

2 Compare Ekholm, Met. Zeit. 1891, p. 366.

MECHANICAL EQUIVALENT OF PRESSURE—-MARGULES 529

PART III. FRICTION

(10.) INTERNAL FRICTION OR VISCOSITY

There aré many obstacles to the analytical treatment of great
currents of air; one of these is the difficulty of introducing the
influence of friction in a proper manner into the equations of
motion. This influence certainly is very large: the unequal warm-
ings of the air are continually giving rise to new differences of pres-
sure and new motions, but there is no corresponding steady increase
in the mechanical energy. Hence for large intervals of time the
whole increase of energy is consumed by friction. An argument
for this conclusion can also be based on the motions of individual
masses of air. Thus, near the ground and in by far the most
numerous cases we find a component of the wind in the direction
of the pressure gradient; hence the motion of the wind is thereby
accelerated. The same peculiarity or a motion perpendicular to
the resultant force also occurs in the upper layer, or at least the
study of the winds during balloon voyages has as yet established
nothing as to winds contrary to the barometric gradient. ‘It is
scarcely to be doubted that such cases do occur, but they appear
not to be very frequent. There is no other reason for the diminu-
tion of velocity except movement against the active forces and
friction. If the first of these very rarely occurs then in general it
must be true that the friction prevents the steady acceleration of
the moving mass of air.

And yet the influence of the internal friction or viscosity of the
air on movements that occupy a large volume is certainly very
slight. This has been demonstrated many times and in various
ways by Helmholtz. Perhaps it will not be superfluous to estimate
the consumption of energy by viscosity by using the following
equation deduced by Stokes:

(Sy e(Sye(Sy ye |

au du \?2 dvs ow \? dw du \?
|| ee saat alan es ~ +] ae
ON OIG, Oz Oy OE OR

Qf au av. dw |: }
uae is

3 |

|
|
}
|
|
|
|

0% ay 02

530 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLT 51

This equation gives the quantity of energy consumed by viscosity
in the unit time within the space k.

The coefficient of viscosity of the air may with abundant accuracy
for the purpose of our estimate be assumed to be

x = 0.00002 kg m~ sec™

In order to study a movement that takes place with a very large
amount of internal friction, or in order to greatly overestimate the
influence of this friction it will be assumed that each component
of the velocity, along the direction of each of the three rectangular
axes, increases or diminishes by 10 meters per second per kilometer
of distance traveled, so that

( au ou du

aac oy dz

Ow ow _ dw _ 10 m sec
Ox dy 2 1000 m
Ov Ov Ov

ax aye |

A 2 2
(2) a fea x (=) =...0.0001 sec~?
Ox Oy \ 02
Moreover it will be assumed that the last or negative term with

the factor 3 in the Stokes equation as given above is to be omitted.
Under these assumptions Stokes equation becomes

Z : 2
ok ~« f18(*) dk
ot Ox

= « { 0.0018 dk
= 0.0018 xk

Hence, for a column of the atmosphere standing on a square meter
whose height we will for further exaggeration estimate at 100,000
meters and whose volume is therefore 10°m* we have

= = (2 31052) (10") 18: x10)

ee qs ee

sec?

MECHANICAL EQUIVALENT OF PRESSURE—MARGULES 531

Since the work corresponding to one kilogram-meter is 9.8, expressed
in these same units therefore it will require at least

ee seconds = 7.6 hours
4 0.0036

for an amount of kinetic energy equivalent to one kilogram-meter
existent in a square-meter column of this hypothetical atmosphere
to be consumed by internal friction.

Now the kinetic energy of this column of atmosphere, assuming
each part of it to have a velocity of 10 meters per second is equal
to

8000 x 1.293 x 50 kg m?* sec~?

or more than 50,000 kilogram-meters. Thus we see that the kinetic
energy in the atmosphere would last a very long time if it were to
be consumed only by such internal friction or viscosity asis effective
in strictly parallel or lamellar motions.

(11.) -RESISTANCES AT THE SURFACE OF THE EARTH

Other much greater obstacles to motion must be present. The
roughness of the surface of the earth, the irregularity of the motion,
hence also the numerous small whirls that originate and disappear
in the large currents, and even surfaces of discontinuity must be
taken into consideration. Possibly the first of these is sufficient
so that the loss of energy may not be caused by exterior friction
proper, but by impact and the sudden transmission of the energy
of the lowest layer of air to solid and fluid bodies. So long as
differences of pressure exist the lowest stratum of air will be con-
tinuously accelerated and for this purpose the energy will be fur-
nished by the upper strata. If now the whole system receives no
energy from without, while on the other hand the mth part of the
total supply on hand (£) is consumed per unit of time (either by
maintenance of waves, or by carrying up of dust and water vapor
by pushing or overturning branches, trees, houses, etc.), therefore,
we have

——; ate

The interval of time required to reduce the kinetic energy to }
of the original supply, or to reduce the velocities to } of their original

532 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

values is?

If m = 10° then the one-hundred-thousandth part of the supply of
kinetic energy will be consumed per second and the velocity will
fall to one-halt of its original value in 138,600 seconds or 38.5 hours.
This might be fairly approximate as to its order of magnitude for
cyclones that are on the wane—for we are only endeavoring to get
a rough idea of the magnitude of the forces in action.

The mass of the lowest layer 8 meters deep of the atmosphere
is 1/1000 of the whole. If we assume its average velocity to be
about 1/3 and its energy 1/10 of that of an equal mass of the outer
layer then the lowest layer has 1/10000 part of the total energy
of the whole moving atmosphere. If the tenth part of this is
given up per second to the fixed obstacles that project from the
ground [1.e., the smooth oblate spheroid of the geodesists] or to the
maintenance of oceanic waves, then this would suffice to withdraw
from a cyclone three-fourths of its initial energy in 38 hours.

If in addition to these there are yet other obstacles to motion
stillit is probable that these altogether would not cause so great a
loss of energy as the pseudo-friction of this lowest stratum.

’The notation is lg — Napierian; Log = Briggian. e = Napierian base,

XXIV

ON THE ENERGY OF STORMS
BY MAX MARGULES

[Dated November, 1904. Translated from the appendix to the annual volume
for 1903 of the Imperial Central Institute for Meteorology. Vienna, 190 5]

GENERAL SUMMARY

When the velocity of the wind is 30 m./sec., the living force or
kinetic energy of one kilogram of air is 450 kg. m.? sec.~? or nearly
equivalent to o.1 calorie. This amount, which is not large, in
comparison with the energy corresponding to the quantities of
heat that 1 kg. of air at the surface of the ground receives and loses
during one day, does appear very large when we compare it with
the energy of a wind of average velocity, such as 5m./sec.

It is not probable that such a very large proportion of the heat
communicated to the air is converted into kinetic energy during
stormy weather. We shall now seek for conditions of the atmos-
phere by virtue of which a sufficient supply of potential energy
is stored up to maintain the storm; we shall allow ourselves to
be led by experience and will start with the relations between the
mechanical and the thermal forms of energy in a gaseous mass.

§(1) A mass of air extending from the ground upward and bounded
by a vertical wall (and sometimes even the whole atmosphere) will
serve as our closed atmospheric system. For any such system the
equation of energy’ is

dK +dP + 0A‘ +(R) =0

where OK is the increase in the kinetic energy of the system;
dP is the corresponding change in the potential energy of
position, considering gravitation asthe only external force;
—dA is the work done by the pressural forces;

1T have taken the liberty of substituting capitals with the superscript
dash for the German type used by Margules.—ABBeE.

533

534 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

—(R) is the work done by the frictional forces, or + (R) is
the loss of kinetic energy by the action of friction and
other resistances.

Of these quantities the first two depend only on the initial stage
and final stage, the other two depend on the nature of the motion.

In a closed system the work of the pressural forces [or —§A] is
equal to the whole work done by the expansion of theair. Let
(Q) be the increase of heat, and I the increase of internal energy
then

(0) = 81 —3A.

For motions that occur without any general increase of heat (but
in which internal exchanges of heat or even external additions and
withdrawals that balance each other are allowable), the value of oA
has also this same property, since dI depends only on the final stage.

The general equation of energy for a closed system as deduced
from the preceding considerations,

(2) =8(K+P+D+(®)

tells us that that part of the added heat that does not serve to
increase the internal energy, represents the increase in kinetic
energy and in the potential energy of position and in the consump-
tion of energy in overcoming friction. If there be no increase of
heat then the increase of mechanical energy takes place at the
expense of the internal energy already present.

§(2) By the help of this last equation we will first seek for a closed
dry air system that without any increase of heat can develop such
great kinetic energy as we observe in storms.

Let the air be initially at rest but not in equilibrium. It starts
in motion and tends to attain a condition of stable equilibrium.
In general we know the characteristics of this final condition: every
horizontal layer is a surface of equal pressure and equal tempera-
ture, the entropy (or the potential temperature) increases-with the
altitude. In order to completely determine this final stage we
will assume that every part of the mass behaves adiabatically, or
isentropically, during the motion. We now construct the final
stage by the following process: we seek first the masses having the
least entropy at the initial stage; these will form the lowest stratum,
the other masses will arrange themselves proceeding upward, 1

———eeEeEEEoEEeEeyeyeyyyEEyEEEEEeEeEeEeEeEeEeEeEeEeEeEeEweeeeeeee

ON THE ENERGY OF STORMS—MARGULES 535

the order of the increasing values of initial entropy. Equal masses
of equal entropy can be interchanged at will.

The available kinetic energy of the system, including the loss
by friction, is determined by the relation

6K > Cs) = = 6 (ered) ae Do deed),
where the index a belongs to the initial and e to the final stage.
(P + I), is the smallest value that the sum total of potential and
internal energy can have under adiabatic condition.

If there be no friction then this equation is to be understood as
follows: The largest amount of kinetic energy will be attained when
all the masses pass through their respective appropriate positions
of equilibrium simultaneously; if this does not occur then the
kinetic energy attainable will be less than this which we will desig-
nate as ‘‘available energy.’’ During the pendulous oscillation
of the masses, a part of the potential and of the internal energy
is still latent.’

If there be friction then the kinetic energy increases and be-
comes a larger fraction of the total amount of available energy
in proportion as the influence of the friction is smaller; after the
masses of air have approached their final positions this fraction
diminishes and becomes zero when the final stage is attained.
The condition of isentropic change is not precisely fulfilled since
the friction produces heat. In our analysis we assume that this
heat is again withdrawn from the air-mass. This limitation is of
slight importance in the case of atmospheric motions.

§(3) Of all the different kinds of storms those best known to me
are the gusts of wind (the boe-en) which are accompanied by rapid
increase of atmospheric pressure and rapid fall of temperature.
These were first investigated by Koeppen. Masses of air of unequal
temperatures at identical levels are separated by a sharp boundary
that advances with the storm wind toward the warmer side. The
difference of temperature, which is often 10° C. at the surface of
the ground, continues up to an altitude of nearly 2000 meters. The
pressures at greater altitudes, not far from the boundary, are equal
over the warm and cold regions but at the ground they are greater
in the cold region.

Based on this general experience I have formulated the follow-
ing problem: Let the mass of air in the lower part of a closed
system, A, B, C, D, be initially divided by a screen into two parts

*Helmholtz describes the free (freie) energy, F, of any system, the total
(gesammt) energy, u, and the latent (gebundene) energy, w—F’—EpiTor.

536 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

(see fig. 1a). Let the cold air be in the left hand chamber 1 but
the warm air in the right hand 2; each mass of air to be at rest and
in either stable or neutral equilibrium; the whole mass of air in the
enclosure above these two chambers takes no part in the follow-
ing processes, we can replace it by a movable heavy piston. What
amount of kinetic energy becomes available when we remove the
screen and let the masses 1 and 2 move adiabatically? __

If in the initial stage the entropy of a kilogram of the highest
layer of the mass (1) is smaller than that of the lowest layer of mass
(2), then in the final stage the whole cold mass of air will spread
out below or at (1’), and the warm mass will be spread out above
or at (2’) as shown in fig. 10.

A C
| Tn Ph ils
h | | iz. | 2
( | ae
B i Por Po2 Tos D
FIG. 1a.
A, C
| Ph Tip
| : r rd Tip is
feed widiee. 2a. sSedl ie
B Po’ ye D
FIG. 10.

If the equilibrium was stable on both sides of the screen then
in every part the serial order of the strata is retained after the
overturning.

If the equilibrium in (1) and (2) was neutral in the initial stage
then it will remain so in the final stage (1’) and (2’).

Let T be the absolute temperature of an elementary mass
dm in the initial stage: T’ that of the same mass in the final stage;
C,, the specific heat of air under constant pressure; C, that for con-
stant volume, C, — C, = R, then we find

dP =R f (T’/—T) dm d1=C,f (1? —T)dm
whence the available kinetic energy of the system is

-~8(P+D=cC,f (T-T)dm

ON THE ENERGY OF STORMS——-MARGULES 537

where OP is the change in the potential energy of position for the
whole system including that of the piston. dP and 0/ are the anal-
logs of the exterior work and the change of internal energy of a
small mass of air under constant pressure. These equations hold
good in general for any change of location of the masses of air when
the pressure remains constant in the superposed movable level
surface* The integrals are to be extended over all the masses
lying below this surface.

The quotient of the available kinetic energy by the mass below
the piston gives the averageenergy 4V*perunitof mass. When the
above assumed overturning of the masses takes place and the
volumes of the two chambers are equal, the corresponding value of
V is given by

V=4v ght

where g = acceleration of gravity; h = altitude of the chambers;
T, and T, are the initial average temperatures: t = (T, — T,)/T,.
Assuming 7, = 273°, 7, = 283° and kh = 2000, 3000, 6000 meters
successively, we find V = 13, 16, 23 meters per second respectively.

In the case of cold and warm rooms in dwellings having the same
temperatures as above but h = 5 meters we find V = 0.67 m./sec.

But this computation tells us nothing as to how the available
kinetic energy is distributed within the masses. We see, however,
that with chambers 2000 meters high and a difference of tempera-
ture of ro° C. a storm velocity cannot prevail throughout the
whole mass but only in about one-fourth part of it, and in even a
still smaller fraction of the whole mass if we abstract a large amount
for the loss of the energy due to friction. In boe-en or gusts, strong
winds occur only on the cold side and close to the boundary.*

The ratio of R to C, is that of 1 to 2.5 and by this ratio is the
work done by the force of gravity less than the diminution of
internal energy when the change of location takes place under con-
stant pressure. When the overturning takes place under constant
volume we have the same value of V, and so also when it takes place
with a very slow change of pressure in the level surfaces near the
boundary; but in these cases the ratio 0P/dJ is changed. We
have the same available kinetic energy if we fill each chamber with
an incompressible fluid whose mass is the same as that of the air
in thischamber, but in this case the energy arises from the work
of gravity only.

3 Corresponding to the piston.
4So also in northers, blizzards, chinooks, boras, purgas, etc.—C. A

538 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

§(4) Let us now consider another system. In the chambers (1)
and (2) of fig. ra let two masses of air be enclosed whose respective
entropies are the same at the same altitudes: therefore the greater
pressure will be on the side of the warmer air; a difference of pressure
of 1o™™ mercury at the base implies a difference of temperature
of 1°C. only. Let each of the two masses be initially in stable
equilibrium.

If now the screen be removed and the total volume be unchanged
then the horizontal strata that were initially at the same altitudes
unite to form one new stratum. The vertical succession remains
unchanged and so also the altitude of the center of gravity. The
change of internal energy as computed for the unit of mass depends
only on the initial difference of pressure, not on the height of the
chambers. We may therefore replace this system by a thin hori-
zontal stratum that initially contained air in two equal divisions
at pressures of 765™™ and 755™™ mercury respectively. The
available kinetic energy is that appropriate to a velocity of 1.5 m/sec.
for the whole mass: that which is available for each unit of mass is
far smaller than in those systems that with the same distribution
of pressure at the base have horizontal differences of entropy.

It has already been shown by me, in my treatise, ‘On the work
represented by any distribution of atmospheric pressure’’® that
the energy stored up in such a distribution of pressure as is
observed in our lower strata during a stormy period would not suffice
to develop the observed kinetic energy of the storm, if the masses
of air were only pushed horizontally out of their positions of equilib-
rium.

A great velocity of a mass of air over a broad area under the
influence of a horizontal pressure gradient can only arise when
this gradient is maintained by some outside source of energy;
otherwise it would disappear before any portion of the mass of air
had attained the velocity of a moderate wind. Dry air possesses
such a store of energy when horizontal differences of entropy of
ordinary amount exist at any level; and not only when there is a
sharp boundary between warm and cold air but also when there is
a steady continuous horizontal gradient of entropy.

§(5) The available kinetic energy of a system in which masses of
unequal entropy are superposed in unstable equilibrium can be
computed from the energy equation. Here we find a store of

» Jubilee volume of the Central Institute for Meteorology, p. 329, Denk
schriften, Imp, Acad, Science, Vol, X XIII, Vienna, rg01, See No, XXIII of
this collection of translations,

ON THE ENERGY OF STORMS—MARGULES 539

energy sufficient for the development of storms; hitherto it has
only been assumed that storms start from such beginnings. The
existence of unstable conditions before a storm has never been
demonstrated. Prohaska never found such cases in his numerous
studies of thunder-storms. Even in so-called calms there is still
enough motion to disturb a condition of unstable equilibrium.
The forces that are thus set free are greater than those correspond-
ing to the largest horizontal pressure gradients that have been
observed in the atmosphere. The accelerating force acting on a
foreign particle of air whose temperature is 7, when surrounded by
air whose temperature is T, is

(7, a T)
ae

and therefore, for T= 273° and T, = 274° this becomes iB) whereas

273
the force represented by a barometric gradient of 1™™ mercury per
degree of a great circle, at the base of the atmosphere is AcSu Ss pie
I00O0

vertical distances in our atmosphere are small. Unstable conditions
can scarcely exist for any length of time over extensive areas; they
would disappear very quickly; their existence has not been demon-
strated nor are they probable. Where there are adjacent masses of
air with very large differences of temperature on the same level,
as in the boe-en gusts, then cold air may intrude upon the warm
region, and warm air flow over into the cold region, but in this case
the storm wind velocity arises not only by reason of the barometric
horizontal pressure but also directly by the action of gravity.

§(6) Many seek for the source of energy of a storm in the latent
heat of condensation evolved by the formation of clouds. Iwill now
compute the available kinetic energy for the following initial con-
dition:

In chamber 1 of fig. ra let there be dry air in neutral equilibrium,
but in chamber 2 an ideal fictitious gas that has the property of
expanding only when heat is added [and not by any diminution
of pressure] but otherwise behaves like dry air. ‘This latter gas
replaces the moisture-saturated air [of nature] and the heat added
during its expansion corresponds to the latent heat of condensation ;
for neutral equilibrium the vertical diminution of temperature in
this fictitious gas is smaller than that in the dry air. The initial
condition is to be so chosen that after the removal of the screen the
mass 1 spreads out below and the mass 2 above; we may then omit

540 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

the assumption of neutral equilibrium for the result will hold good
also when stable equilibrium exists initially in each chamber.
The equation of energy is now to be applied in the form

dK + (R) =(Q)-0(P + D)

where (Q) replaces the latent heat of condensation. The mass 2
cools by expansion less than dry air, wherefore it contributes a
smaller portion to the —d(P + J). The difference is exactly made
up by the added heat (Q). It follows that the latent heat of con-
densation contributes nothing to the energy of the storm. The
available kinetic energy remains unchanged, if in the initial stage
we substitute dry air of the same temperature for the fictitious gas.
We must replace the moisture-saturated air with dry air of equal
density, wherefore the latter having the same pressure must have
a somewhat higher temperature.

§(7) The diagram, fig. 1,is not intended to give a complete idea
of the phenomena in boe-en; it only contains that which we con-
sider as the condition for the origin of the storm.

The length of the chamber must be measured by hundreds of
kilometers but the altitude by very few kilometers. It is indif-
ferent whether the separating surface (or screen) is initially vertical
or inclined, if only the wedge-shaped volume is small relative to
that of the whole chamber If the [inclined] boundary surface be
so laid that the colder mass of air 1 extends as a sharp wedge toward
the ground, we have everywhere steady distribution of pressure.
For an angle of 10° between the boundary surface and the horizon
and for a chamber of 3000 meters altitude the length of the wedge
is 17 kilometers; the diminution of pressure at the ground extends
over this distance. If the boundary advances at the rate of 85 kilo-
meters per hour, then in 12 minutes the barometer at any place
will rise by the amount that corresponds to the difference in the
weights of unit columns of cold and warm air. If the length of
the chamber were 500 kilometers, the result would not be notably
different but the computation would be more troublesome. Even
an inclination of 1° for the boundary surface with a distribution
of the fall of pressure over a distance of 170 kilometers would allow
of the existence of a great amount of available kinetic energy.

I have as yet no definite idea as to how a condition involving the
presence of a great store of potential energy arises without the
immediate occurrence of an unloading or diminution of the poten-
tial by virtue of some movement of the air; in the present memoir

ON THE ENERGY OF STORMS—MARGULES 541

we simply assume an initial stage generalized from actual observa-
tions.

The restriction of the mass of air to a closed system, the assump-
tion of a well-defined boundary between the cold and the warm
air, the introduction of level surfaces of equal pressure, are all
analytical auxiliaries that we employ in order to ascertain the
value of the available kinetic energy of a perfectly definite system.

§(8) If we are to give a broad interpretation to the results of our
analyses, we must omit numerical details. The phenomena of
motion in the great storm areas that we call cyclones are less intelli-
gible than those of the boe-en. But these also, at least in median
and higher latitudes, consist of warm and cold masses of air lying
adjacent to each other horizontally; cold air often spreads out over
the earth in the lower strata behind the passing storm. It is there-
fore not unlikely that these storms are fed by the potential energy
of an initial stage similar to that which we have adopted in the
preceding lines.

The opinion that the energy of cyclones arises from the overturn-
ing of masses of unequal temperature has been expressed in recent
years by Prof. F. H. Bigelow. In one,of his memoirs® we find the
following sentence:

“The cyclone is not formed from the energy of the latent heat
of condensation, however much this may strengthen its intensity;
it is not an eddy in the eastward drift, but is caused by the counter-
flow and overflow of currents of air of different temperatures.”

Long ago W. Blasius had vainly labored to introduce a similar
view as to the origin of storms. In his books (Storms, Philadelphia,
1875; and ‘‘Sttrme and Moderne Meteorologie,’”’ Braunschweig,
1893) this idea is found mixed up with other views that are, I
believe, less reasonable; however, they deserve careful considera-
tion. From giving too much attention to the isobars, it has been
generally assumed that the air must ascend only in the central part
of a region of low pressure and that the motions are nearly sym-
metrical about this. Ferrel as well as Guldberg and Mohn have
built on this assumption.

Our analysis gives us only a general idea as to the source of the
energy of storms; a working model of the cyclone with symmetrical
distribution of temperature has not yet been constructed.

6 “Studies on the meteorological effects of the solar and terrestrial phys-
ical processes, Weather Bureau publication, No. 290, Washington, 1903,
P. 37; separate print from the Monthly Weather Review, Feb., 1903, p. 84,
column 2,

542 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL Sw

It is stated of tropical whirlwinds that ordinarily within their
areas there is observed at the earth’s suface no great difference of
temperature and that the cyclonic distribution of pressure only
extends upward to altitudes of a few kilometers. Hence it may
be concluded that near the ground the central part of the storm
area is the warmest. Helmholtz, in his address on ‘‘ Whirlwinds
and Thunderstorms,’’ assumes that the storm begins with an
unstable condition above a small area; according to the computa-
tions of Reye, the vertical distribution of temperature around this
central region may be stable; the lower strata are pushed upward
through this central hole; the layers that at first were above then
sink lower. This process is dependent materially on the vapor
content; and on another occasion we will investigate how the avail-
able energy is to be computed for this case. In order to judge
whether this idea will apply to tropical cyclones we must know
accurately the conditions, especially the temperature both inside
and outside the relatively small area of the storm.

W. M: Davis has shown’ that tornadoes originate only in the
neighborhood of the boundary between cold and warm masses of
air, a circumstance that had scarcely been considered before and
the knowledge of which can be very useful in finding the source
of energy of these enigmatical storms.

ADOPTED NOTATION

§(9) The following notation and the numerical values of the more
important constants will be used:
t, the time.

x ys, the rectangular codrdinates of a point referred to a
system of axes that rotate with the earth, z being ver-
tical and positive upwards

c, the velocity at this point relative to the origin of these
axes.

uvw, the corresponding components of the velocity c.

k, the volume.
m, the mass.

= the symbol for the total differential coefficient of a

function with regard to the time or

d ty 0 Fe 0 0
ae ae ee Pay oS He

7 Hann: Lehrbuch der meteorologie, Braunschweig, 1901, p. 705.

ON THE ENERGY OF STORMS—MARGULES 543

d, round d, the symbol for partial differentiation of any
function or variable.

W, the potential of the attraction of gravitation combined
with the centrifugal force of the diurnal rotation,

g = ——' = the local apparent force of gravity, assumed to be

constant in these present applications and to be
9.805966 m/sec.”

A,, A,, A,, rectangular components of the deflecting force due to the
rotation of the earth, or the general terms of the
equations of motion that must satisfy the condition

uA, +vA, +wA, = 0.

p, elastic pressure within the air.
ft, density of the air.
T, absolute temperature of the air in Oecttrade degrees.
T*, average temperature of large mass of air.
aT ‘
a= = =rate of change of temperature of atmosphere with
altitude.
R, the constant of the equation of elasticity for gas.
p=kKTp, the equation of elasticity for gas.
C,, specific heat of air under constant pressure.
C,, specific heat of air under constant volume.
R GC.
Cy, —-C,=R=kC,; k= rae
For adiabatic change from py,1, to puT we have

mee)

For dry air the numerical values are

0.41
7, =1.41;k a ear
met? Cal
R = 287. 026 a oo 2 Oo = (0. OED Wat
ee Cal
Cp = 987.09 a a ac? C2 Bie

0

g ‘ C
= = 0.009934 23 —.
G. met

544 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

—R, work done by frictional forces or + R the kinetic
energy lost by the whole system through friction.

. the corresponding rectilinear components.

eh quantity of heat added to unit mass of air per unit time.

S, entropy of the unit mass of air.

Q), quantity of heat added to the whole closed system in
whole time.

V, the average velocity of motion throughout any closed
system for the whole time.

K, kinetic energy of the whole mass of air in the system.
OK, increase of kinetic energy of the system.

Ke potential temperature of air whose actual temperature
is T at pressure p.

P, potential energy of the system due to its position and
the action of gravity.
OP, change in potential energy of the system accompanying
the increase of kinetic energy, OK.

i: internal energy of the system.

al, change of internal energy of the system when pressural
forces do external work.

OA, the work done by pressural forces.

For the notation and values of these quantities in moist air see
Chapter IV later.

CHAPTER I

THE EQUATIONS OF ENERGY OF A MOVING PARTICLE AND OF THE
WHOLE MASS OF AIR IN A CLOSED SYSTEM

§(10o) One of the equations that holds good for the motion of the
air relative to the system of codrdinates rotating with the earth is

du aW 1090p a fi
di. ak “mex ets
and the other two are analogous. From these three there results as

the equation of energy of a definite particle of airof unit mass mov-
ing with the velocity c,

A Ba if, a = =
aie tw) + x (Pf) _Recos@. = 0. . (1)

ON THE ENERGY OF STORMS——MARGULES 545

The increase of the total kinetic and potential energy of the particle
is equal to the work done by the pressural forces and the frictional
forces. The deflecting force of the rotation of the earth being
normal to the path does no work; this is also true of the other por-
tions of the term A. Equation (1) differs from the equation of
energy for absolute motion only in respect to the meaning of W
which contains a term depending on the rotation of the earth in
addition to the potential of the attraction.

We combine the dynamical relation (1) with the thermal relation

¢ ee ee
t at < dt

which applies when the quantity of heat dQ is imparted to the par-

ticle of air while describing its path ds during the element of time det.

It is here assumed that just as in air at rest, so here the imparted

heat dQ serves only to increase the internal energy by the quantity

; 1
C,dT and to perform the work of expansion pal a Conse-
quently -

dQ ace ) | ae py
me i Sere ade ely ape er hatin Ausee a 5s '(a)
We must include in dQ not only the heat communicated from with-
out but also that portion of the heat due to friction that belongs
to this small elementary unit mass of air.

§(11) The equations (1) and (3) with the factor ydk when inte-
grated over the space k, assumed to be filled with air, give the rela-
tions for the total energy of the whole mass within that space.

In this integration we make use of the equation of continuity

du O(uu) A(uv) dpw
ot 0x Oy 02

If F indicates a quantity that is considered as attached to a definite
elementary mass and can be expressed by a continuous function of
the place and time, then by using a well-known transformation we
have

dF % oF Pe nt oF aF oF dk
ai k= at ste Heres Ug eta

0
ae pFdk— | uF ccos (n,c)dO

546 SMITHSONIAN MISCELLANEOUS COLLECTIONS VO Sa

where 1” is the direction of the normal directed inward to the surface
O of the space k.
In a similar way we obtain

( (3-2 a Edy Dee fF
We Att oy [li nie — c cos (n,c) dO

The surface integrals disappear in our case when the mass of air
is bounded by fixed walls; and so also when we extend the space
integral or the mass integral over the whole atmosphere, or over a
mass of air that is bounded by the ground and fixed vertical walls
but is open above; assuming that both the pressure and also the
product of pressure by vertical velocity diminish to zero as the
altitude increases.

The equation for the energy of the whole mass of a closed system
as obtained from equation (1) is as follows:

zie SE a ) a fea \R R,o) nd
ry Hat hW k + Tee R ccos (R,c) pdk =0. (4)

We would remark that here in closed systems the work done by the
pressural forces is equal to the sum of the work done by the expan-
sions of all the elementary masses or

Mar ar ade S ea(;)
- {5(g- fn an pe

In a similar way there follows from equation (2)

dQ a ee: ie
a udk = C3, | Tade— ee

C. Les dk — fear
re Zot Lt

From equations (4) and (5) there results the following equation
(6) which we call the equation of energy for a mass of air in a closed
system

dQ d ce at d ee W |dk
ag ee a HOR ay Hae aE ) a3

~ | Rees (Rc) ndk

. (5)

- 6)

ON THE ENERGY OF STORMS——MARGULES 547

These expressions become more perspicacious by the introduction of
the following abbreviating symbols:
= po Hanis 1
ke FF dk = the kinetic energy of the whole mass of air in

the closed system.

p= | uWdk = the potential energy of position.

I = oni Tydk =~ + | pdb = the internal energy.

The changes in the values of these quantities in the time ¢ are indi-
cated by 0K, OP, OI and are completely determined by the initial
and final conditions.

The three following quantities depend on the path that each
elementary mass pursues; these time integrals extend over the
same interval ¢.

d
-oK=~ far) rhe is

— (R) = a (Rc) pudk

the quantity of heat communi-
(Q) = Jaf ud oe ete : cated to the closed system, in the

time t.

the work of the pressural forces,
or the work of expansion in the
time ¢.

or loss of energy, R, by friction,

the work of the frictional forces
y in the time tf.

We therefore write the equations for the kinetic energy, thermal
equilibrium, and total energy of the whole mass, respectively as
follows:

Kinetic energy...... G) (K Pp Ae (R) =(0 . . (4%)
Thermal energy..... (Q) =9@ tay AG ha cieeton ee (5*)
etal Cnere yaten. ene (Q)=0(K +P+I)+ (R) . *)

§(12) In thecase of friction there can be no steady motion without
a corresponding continual addition of heat. K, P, I remain
unchanged in steady motion and the equations reduce to (Q) =
(R) = — OA. The additions of heat (necessarily consisting of posi-

548 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

tive and negative portions), the loss of energy by friction and the
work of the pressural forces are equal to each other.

(Q) =o. Atmospheric motions are primarily dependent on the
heat communicated from without. But it is possible that for cer-
tain general movements of the air, it is not the absorption of heat
during their occurrence that is the determining factor but the
temporary distribution of pressure, temperature and velocity
throughout the mass of air. In the following pages we will treat
these latter movements as though there were no addition of heat
but only an effort to attain equilibrium as the result of some given
initial condition.

It is a characteristic of every motion performed without exchange
of heat that the work done by the pressural forces is determined by
the initial and final stages alone. It is well known that the quantity

A has the significance of a potential energy under certain conditions
such as, when the mass is kept at constant temperature, or when
every elementary particle of mass behaves adiabatically. This
last condition is a special case of (Q) = o. In this case an inter-
change of heat within the interior of the mass is allowable, or such
additions and subtractions of heat as balance each other, or sum
up zero, during the whole time ¢ under consideration. If we confine
ourselves to the case that (Q) = o during every element of time
then the changes of A and Jare continuously equal to each other.
In the case of motion without increase of heat, the quantity A
that I have in other places® called the potential energy of the dis-
tribution of pressure becomes identical with the internal energy
of the mass.
lf (QO), =. 0. then

OK + (R= .— 01D Doe eee

In this case P + J is to be considered as the total potential energy
of the system; in the case of gaseous motions in a closed system this
expression has the same meaning as P alone in the case of motions
of rigid bodies or incompressible fluids under the influence of gravity.
One easily recognizes the meaning of I in the expression for the
potential energy if one considers the case of masses of air pushed
horizontally (by compression or expansion) out of the condi-

8 Max Margules: Ueber den Arbeitswert einer Luftdruckvertheilung und
ueber die Erhaltung:der Druckunterschiede. Jubiléum des KK Central
Anstalt, Vienna. 1901. See No. XXIII of this collection of translations

ON THE ENERGY OF STORMS——MARGULES 549.

tion of equilibrium while P remains unchanged. If the displace-
ment of each element of mass proceeds adiabatically, or if there

be an internal interchange of heat, then I must increase; after this

if the mass is left to itself it strives toward the position of mini-

= -
mum I.

The problem that we would solve by means of equation (6**) is
as follows:

A mass of airin a closed system is at the beginning at rest and has
a given initial internal distribution of temperature and pressure.
It is set in motion by its tendency toward a condition of stable
equilibrium. If there were no friction the individual portions of
the mass would oscillate about their positions of equilibrium. In
the presence of friction the final condition is attained by the gradual
consumption of the kinetic energy. We seek the maximum values

of 0K + (R) which we designate as the available kinetic energy

of the system. Since the initial values of P and I are known our
problem is to compute their values for the final stage.

No special assumption will be introduced as to the frictional
forces; in fact for turbulent motions there is no assumption that
can satisfy all demands. Hence the frictional force will not be
treated as a part of the pressural force, as is usual nowadays in the
treatment of steady motions. The condition (Q) = o demands
that the heat generated in the system by friction be immediately
withdrawn. But this is not of great importance in atmospheric
motions. Even in cases where it is assumed that the addition of
heat has no influence on the motion there are more abundant sources
of heat than this friction. For the present study the important
point is that the heat due to friction shall not give rise to new or
additional kinetic energy [during the interval of time under con-
sideration].

CHAPTER II

APPLICATION OF THE EQUATION OF ENERGY TO THE OVERTURNING
OF STRATA IN A COLUMN OF AIR

§(13) The analyses to be executed in this second section will not
afford much that is new, they serve only as preparatory to the
following sections.

Consider a column of air of unit area section, in which p and T

550° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOI Si

are functions of the altitude z only. The condition of hydrostatic
equilibrium is

lap
mene
or Re ie erty 8 Se
lop g
Pie Va

The analysis is simplified by the assumption that g is independent
of z whence the potential equation becomes

ee eee re ae eae ee

Let us distinguish between a lower part of the column having a
mass M extending to the altitude and a higher mass M,. Let
overturnings of the strata take place in M whereby h is changed
but the pressure

fp BM i We! woe elim ni ee
on the upper boundary of M remains constant.

Let Z be the altitude of the center of gravity of M, then during
all changes Z -- h remains unchanged, since M, rises and falls like
a solid piston.

The potential energy of position for the whole column of air is

aoe oo h
B= | gende =a geudz+gM,2
0 0

By utilizing the relation (a) we have

h Pp h
‘ gzudz= — | cdp = { pdz —hp,
e/ 0 e 1h 0

er h
Pp =i pdz+(Z—-—h)p, = R{ Tam + Constant . (1)
0

where the integral in the last part of the equation is to be extended
over the whole of the lower mass M.
The internal energy of the column is

I = C, { Tdm + Constant be Gee ea

Overturning of the strata can occur spontaneously whenever the

ON THE ENERGY OF STORMS——MARGULES 551

center of gravity sinks thereby; the available kinetic energy in the
initial stage is

dK + (R) = —dO(P4+)D
and for (Q) =o this becomes

—C, {oT dm,

which is in the ratio C,/R or 1.41/0.41 = 3.44 larger than the
work done by gravity; the principal part of the kinetic energy is
derived from the internal energy.

Let T and T” be the temperatures of the elementary mass dm and
T* and T*’ the average temperatures of the whole mass WM at the
initial and final stages, respectively, then we have

OK + (R) = Gye — T’) dm = C, (T* — T*) M . (8)

Under the condition here given, kinetic energy is available; that
is to say, when by adiabatic overturning of the layers the average
temperature of the whole mass of air sinks, then the conditionis
not stable.

§(14) Computation of the available kinetic energy in the case of any
change of position of a layer.

Let the thin layer m, (see fig. 2)
that initially lay beneath M, be adi-
abatically brought to lie above M,.
In this case nothing changes in the
lower mass M, since the upper mass
M, acts like a piston of constant
weight. Let the layers of the mass
M, retain the same consecutive or-
der. The kinetic energy that is
available when the mass m, ascends
in small particles and spreads out over M,,is now to be computed
from equation (3).

Let p, and T, be the initial pressure and temperature of m,;
p, and T’, the same quantities at the end. Then

FIG. 2.

K
nan (2) ren rem

1

Let p,, T, and p’,, T’, be the corresponding pairs of values for
a stratum dM,, then from the adiabatic condition and from

552 SMITHSONIAN MISCELLANEOUS COLLECTIONS VO se

p's = by + gm, and from the assumption that gm, is small relative
to p, there follow

‘popeta ies -7,(1 +O "7 (1 + el)
P2 P2 P2
Ge tae Spent _ gm,
P2 bs

The contribution of the whole mass M, to the right-hand side of
equation (3) is

Cy f(T. — LG Mg = gm fo == — gm, fas = = — gm,h

where h is the altitude of the mass M, at the initial stage.
The overturning of the masses is brought about by the slightest
initial impulse, and kinetic energy develops when the equation

ae +h =m} 6,7 [1 - (£4) "| ee} (4)

has a positive value.

§(15) Continuous distribution of temperature. We will first assume
that the separation between m, and M, was only made for the
convenience of computation and that in the initial stage the tem-
perature is a continuous function of the altitude throughout
these masses. The value of kh must differ from that appropriate
to the final stable position, but it may be chosen small enough
to allow us to assume T, expressible as a linear function, viz.,

f=T, = 1, — a Sih

az.
With this function of the temperature the equation a gives us

Pre a ae
P1 rT,

whence assuming ah to be small relative to T, we get

(25) * 1-2 Gms gh ,&& —C,a) WP
PD, jie oe ci Cant 2

ON THE ENERGY OF STORMS—MARGULES 553

By substituting this in equation (4), the linear term in / disappears
and there remains

-0@ +H = (a - £) SM see (4a)

7
This value is positive and gives the kinetic energy made available
by the overturning of m, provided

a g or eye ea
5 dz Gr

In this case the equilibrium of the column of air is unstable.

If a <g/C, then with every adiabatic overturning of any layer
there is associated an increase of the total potential energy P + I
and the equilibrium of the column of air is stable. In the limiting
case a = g/C,, and the equilibrium is neutral.

§(16) Discontinuous distribution of temperature. If at the bound-
ary between m,and M, the temperature passes suddenly from T, to
T, it will suffice to assume M, to be of an order of magnitude similar
to m, whence we will now indicate it by m,. The interchange of
positions of m, and m, gives us

—3(P +1) =C,{ m,(T, — T’,) +m, (T, — T'2)}

gm, \*
7 (1 2)

gm, \k
re (1 1 m)
2 2 Do

hence when p is the pressure at the boundary and gm is small in
comparison with p we have

2
|

z

ere gR
Fe EEE (l= fe) ee aE)

which corresponds to unstable equilibrium when the warmer mass
lies below.

§(17) The entropy as the criterion of stable equilibrium in a column
of air of untform constant constitution.

The condition for stable equilibrium can be expressed very simply
when we make use of the entropy. If P, 0, S, are respectively the

554 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOR. Si

pressure, temperature, and entropy for a normal condition of the
air, then for any other pair of values, p and T, the entropy for a
unit mass is

T Pp
S = So + C, log 6 — R log

For a column at rest we have from equation (a)

eee ee =
dz fae poz a

az aah?

whence it follows that stable equilibrium exists when S increases
with the altitude, but unstable when S diminishes with increasing
altitude.

This result also holds good for sudden changes of temperature

CARE di

at special localities; in such cases S, — S, = C, MS ; the entropy
1

increases with the altitude when T, > T, and the warmer layer lies

above the colder.

§(18) Potential temperature. Helmholtz and von Bezold* define

the potential temperature T of a mass whose actual temperature is
T and pressure p as being that temperature which the mass will
attain when brought adiabatically to the normal pressure P. Hence
we have

ss ie kK dT =
Te a dS = Ope S=C, log T + Constant.

The equilibrium is stable if the layers are arranged to succeed each
other upward in the order of increasing potential temperature or
increasing entropy.

§(19) Buoyancy of an elementary mass of air that has a temperature
different from that of tts surroundings.

In a mass of air at rest where T is a function of the altitude only,
we will introduce a foreign particle of air m, which has the tempera-
ture 0, at the altitude z, but always the same pressure pas that of

*See the article by Dr. L. A. Bauer, reprinted as No. XXII of this col-
lection.—C_ A.

ON THE ENERGY OF STORMS—MARGULES 555
the surrounding air at the same altitude. Under adiabatic condi-
tions its temperature in all positions is given by the equation

s24(2)
. Po

: 1 dé kdp
oo O0dz pdz

Let us assume that during the motion of the particle m the pres-
sure in the larger mass remains unchanged and that the equation

(a) holds good so that we have

If [v] is the density of m but » that of the surrounding air then
there is acting upward on m the accelerating force or buoyancy

nn?)
—— 1]
(ii
or, since the pressures are the same,
6 ,
E\ 771
If we consider m as an elementary mass moving without friction and
express its vertical ordinate by z we then have the equation of
motion
d?z ( 0 1) - dé
dt? g (ee ae a Ue
Hence follows the equation of energy, assuming that m has no
initial velocity at 2,

m (dz \? ti
a =m { C,.(0,—0) — 8G Fo)
: p \k \
-mica(1-2\"|-se-m

This latter expression is identical with the right-hand side of equa-
tion 4 section 14, substituting m,for m, T, for 0, and h for (z—%).

556 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The deduction of the amount of the available kinetic energy for
the whole system is rigorous as there given, but is inaccurate in the
present article. The mass of air does not remain at rest when m
moves through it; also, even if the energy of every particle of the
mass is small, still the sum total may be of the same order of mag-
nitude as the kinetic energy of m.

With this proviso I will quote some figures computed by these
last equations in order to show how large the velocity may be that
is produced by this force of buoyancy when the initial difference of
temperature amounts to 10°.

When the acceleration is o the greatest absolute value of the
velocity w will be attained at the altitude’, where? =T. Let the
temperature of the larger mass of atmosphere at the initial position
2 be T, = 273° C. and in general T = T, — a (2 — 2,); when a =

oT ;
— = o we obtain
Oz

pee 6,=T1,+10°, C—z,= 988.6 meters, w= 18.8 m./sec.
\ for @=T,—10°, ¢—z——1025 meters, w=—19.3 ees,

Therefore the values of ¢ — 2% and w are larger in proportion as the
rate of vertical diminution of temperature throughout the mass of

Pee
far 6.=T,+ 10°, ¢—2,= 1942meters, w= 26.4 m./sec.
i for 6. =T,— 10°, - ¢—2,=—2090 meters, w=—27.4 m./sec. }

Similar computations for moist air are given by Reye in his “‘ Wirbel-
sturme,” Hanover, 1872, p. 227, etc.

aT
atmosphere is larger; thus when a = 1a = — we have
p

§(20) Computation of fTdm jor linear vertical diminution of

temperature in the column of atmosphere.
Assuming T = T, — az then for the state of rest [or hydrostatic
equilibrium] the pressure is given by the integration of the equa-

tion (a), i.e.,
ae
Pp aS Po oe

whence we deduce the following equation (3), that will often be
used hereafter, for the integral of the product of the temperature by

ON THE ENERGY OF STORMS—MARGULES 557

the mass in a vertical column of atmosphere whose section has the
unit area and for which p = RT p

Pe udz ane pdz

°*T)
ee Ra —9/Ra Siar Gt ACD
— fel / i ak an (5)

ae

For neutral equilibrium throughout the atmospheric column we
haye a = g/C, whence in this case

’ 1 1
ere ieee (Dp 5: PE rer (Sa)

§(21) Overturning of upper strata in the column; computation of
the available kinetic energy in this case.

We will apply equation (3) to the following problem. In one
column (see fig. 3) are at first two masses, 1 and 2, each in neutral
equilibrium;the entropy of the
lower mass 2 is higher than that Barn Ps)
of 1; between these two masses [
as a whole there exists initially hy | 1 g!
unstable equilibrium, after the j{____
overturning and in the final
stable condition the whole mass h,4| 2 1’
1, which now becomes 1’, rests
below and 2 becomes 2’ on top. Pp ; p
In this overturning, the alti- ; ;
tudes of both strata are changed era
and also the location of their
surface of separation 7; the pressure on this surface 7 will be desig-
nated p; for the initial and p; for the final stage; the temperature
of each mass changes but the condition of neutral equilibrium re-
mains true of 1’ and 2’ individually provided it be true as we assume
that the transition from 1 to 1’ and 2 to 2’ is performed isentropic-
ally. The pressures p,at the base and p, at the upper boundary
remain unchanged.

At the boundary surface 7 there is initially a sudden transition
from the temperature T,, to the smaller value Ty.

558 SMITHSONIAN MISCELLANEOUS COLLECTIONS ViOU 5

For this initial condition we have given the data
Po L025 hy, Ty) hy

whence we know

With these values by the help of equations (1), (2) and (5a) we
compute the following equation except the arbitrary constant

sate fk C. 2
(P+ Tom | * Tyg (fo Toa — Pe Tn + Pi Ta— Py Try) + Constant.
For the final condition p’; = p, + (p, — p,) Whence the tempera-

tures of the two masses at the boundaries become

K : > \K
money nen (t)
'\ Pr Ph
: 4 K
T, =T es PA bay
2 02 Po 2 02 Po
and ;
— — C, i Ul , , , /
(P =F I).= g . Phi (2, ies = PD; 1 aE P; sas a Pr (ee) = i Constant.
We find the heights or depths of the masses 1’ and 2’ from
, C, , Ud , Cs U ,
h, rs? g eae a T;,); h, a g (Ty aia T;,,)

The sum of the two masses is Po Dy wherefore the available ki-
X
netic energy of a unit mass is

j (P+I), — (P +I),

V7=
3 Po — Ph

Numerical example. Let h, =h, = 2000 meters and let the other
data for this problem be the numbers indicated by a star (*) as fol-
lows (the pressures being in millimeters of mercury and the tem-
peratures absolute Centigrade):

ON THE ENERGY OF STORMS—MARGULES 559

Initial stage

Py = 760% Pi = 591.690™™ Pr = 450.222™™
Te = 283 Tp, = 263.1315° T= 260,1305° T,.=240,2636°
h,* = 2000 meters h,* = 2000 meters
Final stage
pi — 700 p/ = 618.5327" i= A5e.220—
Pq, =279-773° T's, =263.509° | T’ p= 266.548° T',.=243.034°
h', = 1637.17 meters h', = 2366.97 meters

(P+1}),= Z ieee p;, 233 . 5132 + Constant
P+I ee 233 . 4140 + Constant
(Pp em, ie ee ? + Constan
Ph I Ms
VS Oe O.09G2"
; Po — Pr L+k A
whence V = 14.85 meters per second.

This computation is laborious because the conclusion depends on a
small difference between large quantities. We may find V by a
shorter method without previously computing a number of other
quantities as in the next following article.

§(22) Approximate method of computing V. We first assume that
each of the masses 1 and 2 is initially in stable equilibrium but that
the greatest entropy in 1 is smaller than the least entropy in 2, so
that as before in the final stage the whole of 1’ comes to lie below
2’; the serial order of the stratain each of the masses will be re-
tained provided the overturning proceeds isentropically.

Let p, and p’, be the pressures for the same layer in 1 and 1’,
or in the initial and final stages of mass 1 respectively, and similarly
T, and T’, for the corresponding temperatures. Let p,; p’,; T3;

560 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5a

T’,; be the analogous quantities for any given layer in the mass 2
and 2’. We thus have

Pp’, = Ph + bh — 2; b', = PD, — (Ps — Ph)

T', = r,(B)*- me a mats)

it

Se ( er ee —#) approximately.
\ 1
With this last approximate value, which holds good in proportion
as Py — p;, is small relative to p,, we obtain for mass 1

fo eee pr ahs
Cy
Cp J (Ti — T) dm, = — (Po — Pi) hy

Similarly for the other mass 2 we obtain

f i Rs ‘cP

Pp Us

Cy J (La — T)) dim, = (P; — Py) hy

Hence when h, and h, are small enough to allow of this approxi-
mate method we have

Cy J (T = 1!) dm = (6; — By) hy — (Po — Bi) I

From stable equilibrium we now pass on to the limiting case of
neutral equilibrium within the masses 1 and 2; we have

gh, Te ( gh, ye
= p.{ 1 = d = p;( 1 +
Ph P ( Co, an Po P. ae

p
whence approximately

gh, gh,
a at! of Yo and ae ame ic ee
iP hep and hb -A Me r,
: (pean g
C T LUD Y dia da lg be ee
i ) Uh Poe enna ae
Leer SP, tila til
g R Ta Ty

h, h, (Tx = Ts)

= ae
; h, Tp +h, Tis

ON THE ENERGY OF STORMS—MARGULES 561

If h, = h, and T; = 3 (T;, + T;,) this last equation becomes

yh gr
V? = gh, a an

7

If this approximate formula be applied to the preceding example
as computed in §21, we have

h, = 2000 meters
Tyg — Ty = 3° whence V = 14.82 meters per second.
T, = 261.62° J

a

CHAPTER III

METHODS OF COMPUTING THE AVAILABLE KINETIC ENERGY FOR A
MASS OF AIR THAT PASSES ADIABATICALLY FROM ANY GIVEN
INITIAL STAGE INTO THAT OF EQUILIBRIUM

§(23) Let there be given a mass of dry air, bounded by the
horizontal ground plane and vertical walls, that is, initially at rest
but not in equilibrium. We assume an initial condition of rest in
order to be able to make use of the equation (a) of the preceding
chapter, in our computation of the potential energy. We assume
furthermore that that portion of the mass that is above the level
surface h is already initially in equilibrium, and that during the
changes that occur in the lower portion of the mass, this upper
part acts like a piston of constant weight p,Bywhere: B is the area
of the base or of any horizontal section.

Using a notation analogous to that of §13 we now have as before
the following expression for the potential energy corresponding to
the position of the column of air above the surface element dB

dP =dB{ ("pds + (Z—h) p |

Whence follows the P for the whole mass from the ground up to
the level surface at the altitude h

— h
pe ead pd Bdz + B(Z —h) p, = { pdk + Constant
= a Tdm + Constant.

Similarly for the initial stage we obtain

@ + D: = Gali Tdm + Constant

562 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. §T

The constant on the right hand is the same in both the initial and
final stages.

In the case of an adiabatic passage from the initial over to the
final stage the temperature T of the elementary mass dm becomes
T’ and the total potential energy of the whole mass becomes

(P +1), = Cy f T’dm + Constant
Hence the available kinetic energy in the initial stage is

—8(P+H=C,f (7-1) dm.

§(24) First analysis. The initial stage. The mass of air in the
chamber 1 of our fig. 1 is in neutral equilibrium, and S, is the
entropy of the unit of mass. Similarly in the chamber 2 the air has
the same volume but a higher entropy, S,, and is in neutral
equilibrium. The problem is wholly analogous to that treated
previously, only the mass having the smaller entropy now lies
alongside the other and not above it.

The given data of the present problem are: The temperatures
Ty, and T;, at the altitude h and the values B, h, p,. From these
we find the following initial temperature and pressures at the bases
of the two masses. .

Oy Pe
h
TT (2 Pee )
02 2 Gade
ale ( gh \V/«
see = Pea
Pu = Pr ( Pr C, rT)
Le, \1/% B® Sie
Po2 = ( 4 n(rté )
The Codi

From these and equation (sa) of the preceding chapter, section 20,
there results

a aaa | B
Pit Dae 6p. =: oy: os Pou = Vin + Leta

— Ti.?,} + Constant.

The final stage. The mass 2’ of higher entropy now occupies the
upper part of the whole volume of the trough, the mass 1 having

ON THE ENERGY OF STORMS—MARGULES 563

lower entropy is separted from it by the level suface 7; at this level
the temperature changes suddenly from T’,, to T’,. Each of the
two masses is individually in neutral equilibrium. At the upper
surface of 2’ the pressure is p,, consequently the temperature is
Ty. Sincewthe entropies S,; and S, remain unchanged therefore
the values of the pressures at 2 and at the base (p’, and p’)) are to
be computed from the weight of the mass and thus we completely

know the final stage, as follows:

Location. : Pressure. Temperature.
At the upper boundary 2’ Pr, ie
I \K
U = ot
At the surface of separa- | ie ( Pr )
tion 4 between the | P; = Ph as 4 (Pos aa Pp)
/ / CONTIG
masses 2’ and 1’.... | Tu = Ty 2)
Ph
At the base level we| pj = p, +4 (Poo — P,) ah (# i
have Oh tN
BPR Me A Ga! Satis) 8FS" oh + L (Por = Py) \ Pr

‘We thus obtain all the quantities that enter into the expression
for the total energy of the final stage
1 1

(P+, = lis eras B (To Po- Tatit Te Pi

— Ti. P,} + Constant

except only the arbitrary constant which will itself disappear when
the difference is taken.
We assume that the available kinetic energy, viz.,

IP +) =), Pp,
belongs specifically to the mass M below the piston, and that this
therefore may be written 4 MV’.

In frictionless motion if the final stage be attained simultaneously
by all the masses, then $V? is their average kinetic energy. Since

M= p (Penh De ‘) therefore V is independent of the area of the
g

base.
Finally we compute the heights of the strata 1’ and 2’ from the
temperatures by the formule

, C , v , Cr ,
h = g CF: o— Lin) h, = g a Tio)

564 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Example 1. Given h = 3000 meters; p, = 510™™" mercury
Ty, = 248° Ty. = 248°
These data and the quantities computed from them for the initial
and final stages are arranged in the following tabular form:
Initial stage
h = 3000 meters

Thy = 243° Paste Tp = 248°
To. = 272.8027° Po = 759-1980 | Py=753-4621 To. = 277.8027°

1
: ipar ; Ph x 162 . 7598 + Constant

Final stage

h’ = 1603.2 meters.

Ti = 248° i

8 Tac a Ta
is { T', = 263.9266

Pp; = 631.7310

I

h’ = 1398.9 meters.

1

T;, = 258.6055
p, = 756.3300 { ; }
T = 272.5026

o1

eae eet
(PS ire tae ke 162.7127 + Constant

| aa oe
4" — Cot B09 ~ 0.4880

V = 12.2 meters per second.

Example 2 h = 3000". p, = 510™
Ty, = 243° Ty. = 253° whence V = 17.3 m/sec.

Example 3 h =6000" p, = 3825™™
Ty, = 218° Ty, = 218° whence V = 18.3 m/sec.

Example 4 h =6000" p, = 325™
T;, = 218° T,,= 223° whence V = 25.8 m/sec.

ON THE ENERGY OF STORMS-——MARGULES 565

§(25) Second analysis: approximate method for the case when
the masses 1 and 2 are each initially in stable equilibrium and the
entropy of the highest layer of 1 is smaller than that of the lowest
layer of 2.

Since it is Again assumed that every particle of the mass behaves
adiabatically, therefore the layers in 1 retain their relative positions
when they become 1’; similarly for the layers of 2 when they become
2‘. We will designate the areas of the floors of the chambers by
Gand 6, so that B, + B= B:

If p’; is the pressure in the final stage of any layer of 1’ which
had the pressure p, when it was in the initial stage, then we have the
relation

, B, B, B,
P, =P; +P a Pr) +B Coz aa Pr) Ps + Be (Por cae P;)

Similarly when p’, and p, refer to another equal mass in the
chambers 2’ and 2 in fig. 1 we have

B, B, 3
P= Ph igs (P2 — Pr) = Pa py Cn = Pa)

Hence the temperatures T’, and T’, of these masses in the final
stage are to be computed from their initial temperatures T, and
T, by the following equations:

, B af
rar,(%)* ml te oe ey

B =
= r(1 + ag. 78 = * ) approximately.
1
, B ds K
oa) =F a m= Ps)
B a)
Ae — ,~*_** ) approximately.
2 es Ps Pp y.

The approximate formule hold good for every p, and p, when
Po. — P, iS small relative to pp.

In the computation of the integrals that occur in the expression
for the available kinetic energy we take layers of 1 and 2 as the

566 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLsgt

elementary masses and therefore by making use of the equation
(a) § 13 we have

dp, 12 eee,
g g

dm, = — B,

Substituting hereafter only approximate values we obtain

, K Bp By Paar
she ik 1S dm, = — ooTB T, p; dp,

F K

We may remark that although in the development of the binomials

we previously retained only the terms of the first degree in Po — Ph
Ph
yet on account of the limits of these definite integrals, they are
accurate to terms of the second degree.
From equation (a) there results

Pa T, fro Ie gh
ee ma py ot? — ab hee

If we introduce the average temperatures 7,* and 7,* of the
masses 1 and 2 as determined by the equations

Po. Po2
T* (Por - 2) = J T, dp; Ty* (Por iz. Pr) = i i dp,
Ph Ph
we thus obtain for the above integrals

(T.— T) dm a 77s J re (p — Pp) WES
1 1 1 g B LY? 01 h R fe

, K B, B, gh
jo, — IT) dm, ae ae TOF) R Pr }

These expressions may be still further simplified if we introduce
other average temperatures ©, and ©, which for distinction we will

ON THE ENERGY OF STORMS——MARGULES 567

call barometric temperatures as determined by the barohypsometric
relations*

je Gea imatel
— pe approximately.
Po Pr P Pr Re: 2 RO, PP y

re € gh Bie aes

= z2= ———— = asa

Poz = Pre Pr lr Ro, =F 2\ Ro, approximately.

In the serial development of these exponentials we have stopped at
the terms of second degree in accordance with a preceding remark.
With these values our integrals become ft

, _B gh
for — 1) 6 ie, Ph pe
: {a =| Meas Gr \
OF R\.O; ze)
, B, B, gh
for, os Ts) dm, = — Bo wh R
O, Kk 202

Now in the actual applications to our atmosphere the quantities

T* — ©are always very small relative to se . For the value h=3000

* The e is the base of the napierian logarithms.

+7 = temperature of air at any time or place.

T* = true average temperature of a mass of air as determined by the
mass-relation,

Po
thee”
Po— Ph

T# =

© = Approximate average temperature of mass of air as determined by
the barohypsometric relation
Po = Ph evh/Re

whence
Po gh
los ——. =" Modulus). ——
2 Ph RO
gh 1
© = Mod. —
R ] Po
og —
Ph

568 SMITHSONIAN MISCELLANEOUS COLLECTIONS Vou, Bt

meters this quantity is 102° and the difference between the true
average temperature J* and the barometric average temperature ©
can only attain 2° Centigrade inextremecases. For smaller values
of h the T* — © is also smaller. We can therefore here substitute
T* for the corresponding © and obtain

any lem i seh 1 1
Wes T) dm, = — me Ph T* aa oT, )

Ki BoB, h 1
ina ina 2 AB n(2 ) ( )

R ar
Finally by writing
(TH)? = TE TY,
ft iar ie
ae

ars

gh
Bp, —— = gM (approximatel
Phi e PR y)

we obtain the following expression for the available kinetic energy,

; MVR OM BB,
Cp | (T -T’) dm =° ee gee a ght.

V is independent of the constants Rk and C, that characterize the

physical properties of the gas. Foragiven value of B this expression

for the available kinetic energy is greatest when B, = B, = 4 B; where-

fore when the chambers 1 and 2 have equal volumes then the velocity

is

Die ae es RD

This approximate method suffices completely for the cases above
given as examples of our first method of computation (see section
24). Since in the limiting case neutral equilibrium becomes stable
equilibrium we may also apply this method of computation to
those examples also. In the computation of T we may substitute
4 (1, + T)) for the average temperature. The values of V com-
puted by the approximate formula for those four examples now
become respectively

Example Velocity
mM, P, 8.

GE) el atlene aj Estee brn hae od ges Seat ga eae T2593

(Gy cree ercbe' ve. Soaps ee Reda ee Rote 17.4

C3) ine jx aig Saath Save’ Cokes eres reas 18.6

ON THE ENERGY OF STORMS——MARGULES 569

The assumptions of the approximate computation do not hold
good for h = 6000 meters; but still the final formula gives very good
approximate values; this is also true for systems having still greater
altitudes. 4

§(26) If the overturning of the masses 1 and 2 takes place under
constant volume the computation proceeds in a perfectly similar
manner. These masses considered by themselves now form the
closed system to which equation (6**) of section 20 is to be
applied. The diminution of P will be greater than before and by so
much smaller will be the diminution of J, so that we obtain the
same value of V as for the overturning under constant pressure.

We may also state the problem thus: During the overturning
the pressure at the upper boundary surface changes but has the
same value throughout all parts of this surface. If the change pro-
ceeds so slowly that no appreciable amount of kinetic energy is
thereby produced, then we again obtain the same equation (I)
as just now deduced for the velocity V. This is not a case of a
closed system. In place of the equation (6**) we now have

oK+@=--0@+)-B fran

where the first term on the right hand refers only tothe masses 1 and
2 and can be written in the form

C, f(T = Ed on Bh pl, = hep,)

whereas the second term on the right results from the motion of the
movable piston. When p, is constant the sum of these right-

hand terms becomes C, f (I — T’)dm. The case of constant

volume corresponds to h’ = h.

We will now leave the two chambers system and compute the
available kinetic energy in a special case of continuous distribution
of temperature.

§(27) Third analysis. The initial conditions are a continuous
horizontal distribution of temperature and a vertical diminution
of temperature corresponding to that of neutral equilibrium.

We assume that the trough is a parallelopipedon of air having
a unit breadth and a length / along the horizontal axis of x, and that

570 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5x

in the initial stage the temperature of the lowest surface is a con-
tinuous function of the distance x from the left-hand end of the
trough; therefore the temperature at the point (*, 2) isexpressed
by the equation

T =f) -=
Cp

If the f (x) increases from the left toward the right then the entropy
will also do so, since the pressure /, is again assumed to be constant
at the level h; hence the entropy is only a function of the distance
x or the length of the trough and this is equally true of the pressure
Poq at the base level.

If the mass of air under the pressure p, passes over adiabatically
into the condition of equilibrium, then a horizontal layer is formed
from each vertical column of the initial condition and the masses
will now succeed each other from below upward in the same order
as they were before arranged from the left toward the right. A
mass originally in a vertical column at « having an initial p and
T has in the final stage a p’ and T” such that

1 1
pb’ = Pp, + i ite (Pox — Px) 4%

1 : i
-2-(p-m-4.[ (Pox — Pr) dex )
l—zes

In this last equation we consider the member in the parenthesis as
small relative to p, which is true when the difference between any
two values of the pressure within the mass is small as compared with
the total pressure ~,. Under this assumption we introduce an
approximate computation analogous to that of the last section

§ (25),

/ p’ \k Pr 1 E |
PS TS Pla SS T= Sk ae.
(F) K Ru IRp 1, oe Pr) x

We first seek for the mass-integral of (T — 7’) throughout the
whole mass of the unit column above the point x on the axis of
abscisse; in accord with the previous definition we put T,,* for the
average temperature of this column, then we have

= h h
px Pos — Ph _ px ch ndz = { T pds
g§ 0 i)

ON THE ENERGY OF STORMS——MARGULES Sifu

whence we obtain the mass-integral of (TI — T”’) as follows:

h K .
(TT) pds = © {TE Cre Lyi
’ il 9)

h aly Gs
-2 la, a ee =P) ax | }

This expression multiplied by the factor C,dx and integrated
throughout the whole length / gives the available kinetic energy
of the whole system. But since we take the true average tempera-
ture T* instead of the barometric average temperature therefore
we first substitute

Ea 2 gh LI ne ia

and remark that in the first member, on the right hand side of the
integral (A), both terms of (B) as the serial development of p,, — p,
are to be used, but in the last member of (A) only the linear

term in h or the first term of (B) need be considered, if we desire
to go only as far in the result as terms of the order

For 7% we choose a linear function of the length in which +
is small relative to unity so that

Te - TH (1457) ; pe pg(1- 4)
l T* TH l

This gives for the last term in the integral (A)

ete gh a 2 pe
- — Gi P| Hise pee mc a
i { @. Pr) Pr RT* i 3 p )

and for the complete integral (A)

h k BO (A eae cok een
ete ae ) IS GO Goa
ae Neier, ue roy ey ye cr yr

572 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5x

whence the available energy

l h
Cy) (F -T!) dm = cy f ax { (T —T’) nds

oh ; ee
sept pe ye
2 Kis 12
Using the approximate value
gh
M=1p, RT,#
we obtain
ght
= St | kee eee
"3 (1)

In this case the available kinetic energy for the unit of mass is
smaller in the ratio of 2 to 3 than in the system previously con-
sidered, if we substitute T7,* and T7,* therein instead of 7,* and
T,*. In this first approximation, this energy depends only on
the altitude and on the maximum horizontal difference of tempera-
ture and is independent of the length of the trough and therefore
also of the horizontal temperature gradient.

The result is principally determined by the assumption that the
vertical diminution of temperature is that corresponding to neutral
equilibrium, as is shown in the following section.

§(28) To find the location of the surfaces of equal entropy im a mass
of air when the pressure is constant throughout any level surface and
the temperature ts a function of the length and a linear function of
the altitude.

In the expression for the entropy

S = Constant + C,log T — K log p,
we put
: g Peace
A ee nc. ae and p-nlz)

where T, is a function of x only and ~, is constant. The system
of curves of equal entropy in the xz plane is determined by the equa-
tion

F (x,2) = nlog T, — (n — 1) log T = Constant

ON THE ENERGY OF STORMS—-MARGULES 573

The angle a that is included between the direction of the curve in
the vertical plane of xz and the horizon is given by the equation

(ehal oe =
4

oF hoo wes nN _ yore
ax/ a2 n—1 TIM Oe

For m=1 the angle ais aright angle. If ~>1 with stable equilib-
rium in each isolated column, and if x increases toward the right
hand, then the curves of equal entropy trend downward toward the
right. With increasing values of 1 the inclinations of the surfaces
of equal entropy to the level surfaces diminish very rapidly.

If the horizontal increase of temperature is 1° C. for 20 kilo-
meters or

vi
a = 0.00005° Centigrade per meter

we obtain the following respective sets of values:

Vertical Qo for
| Temp. ap, for Z=0

i | Gradient | z=h h = 6000m

per room Tp = 250°
1.00 0.993 90° (of go° Of
I.O1 0.984 26° 57’ 32° 12’
1.10 0.903 3° Io’ 3° 55°
1.50 | 0.662 (i Kyte ey
2.00 | 0.497 (oho BEY. Ld °° 43’

Even for very large horizontal temperature gradients, the sur-
faces of equal entropy are but slightly inclined to the level surfaces
when the vertical diminution of temperature in dry air is less than
0.9° per 100 meters. If now from such an initial condition the
masses pass adiabatically to the final stage then there is evidently
available a smaller amount of kinetic energy than in the cases where
the entropy surfaces are at first vertical.

§(29) We now return to the two-chamber system.

To find the final stage of two masses of air under constant pressure
with initial linear vertical diminution of temperature.

If the vertical gradient of temperature within the masses 1 and
2 (fig. 4) is smaller than that for neutral equilibrium then the entropy

574 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL.s%
increases with the altitude and it can happen that the entropy at
the altitude c,in the cooler mass 1 is as large as that at the base
of the mass 2; 1. ¢:, at the alti-

‘ea YI) tude (i — c,); the upper layers
entropy as the layers in 2 up to

NA | che aitiudectys b.e dente

final stage the lower part of 1

sisting of 1 and 2 mixed; above this will rest that portion of 2
that initially lay between (kh — c,) and h. At the boundaries be-
tween these three layers the temperature changes are continuous.

¢, of 1 may one after the other ser-
FIG. 4. will become spread out at the
If the temperatures diminish linearly as in the equations

SEO

ially have respectively the same
base; over it will lie strata con-

Tl, = Ty + moe Wi tg = ie ar =)

then we have to seek the altitude at which the entropies are equal
or S,=S, for the same value of p, in the equations

5; = K+ Cyn, log 73. = @,\— 1) log Ty]

S, = K + C,[n, log T,, — (nm, — 1) log T,]
Letus assume 1, = 1, = 0; let 0, be the temperature of the mass 1

at the altitude c, and 0, the temperature of the mass 2 at the alti
tude h — c, then we have

1 ais Wea SEC Oe
end 6, mele i. i Peele vi
C. C.
bg = a8 (Lo. — 91) es - (0, — Tr)
Hence for » = 2 and a vertical temperature gradient of about

0.5° per 100 meters and for h = 3000 meters T,, = 263°, T,.= 273°,
we find c, = 2154 meters and c, = 2090 meters.

In this case the greater part of the masses 1 and 2 remain unmixed,
the available kinetic energy will not be much smaller than if in the
final stage the whole of mass 1 lies below and the whole of 2 above.

Again, for h = 6000 meters T,, = 248°, Ty, = 258°, we find c, =
2390 meters and c, = 2096 meters.

ON THE ENERGY OF STORMS—MARGULES 575

In this case the descent of the mass 1, and the ascent of the other
mass 2, are much smaller than for the same values of h in the first
and second analyses §(24) and §(25); hence also the available
kinetic energy cannot be evaluated by using the equations there
deduced. ,

§(30) Two masses of air having constant temperatures. In order
to be able to express more accurately the influence of the formation
of three strata on — 0(P + JI) I have computed an example for
the case of constant T, and T,. In this case we have

- h—z

Sa wie AF G, log ake Salt iy

; ee

5; ha GC, log i 2 r,
gh g(h—<¢) G; 1
Es Ve a f = Cy log ie

In the final stage the temperature of the median layer isconstant,viz.,

co fone Bis Ce ead
For h=3000 meters, T, = 258°, T, =268°, we find ¢c, = 1099.5 meters
G = 1o25-9- meters, (7")' = 263.12°.

The available kinetic energy is to be found as in the first computa-
tion but by a much longer route. The velocity for the average
kinetic energy and for two chambers of equal volume isV = 9.5
meters per second or only half as much as for the more complete
overflow from 2 and underflow from’: as computed by equation
(I) of section 25.

FOURTH ANALYSIS. EQUALIZATION OF THE PRESSURES IN A HORI-
ZONTAL LAYER THAT RETAINS THE CONSTANT VOLUME

§(31) Computation of the available kinetic energy.

Initial stage. Assume a thin horizontal layer, bounded by rigid
walls, divided by a screen into two chambers having volumes k,
and k,, whose masses are under the pressures p, and p, respectively.
After removal of the dividing screen the pressure throughout the
whole volume k =k, +k, becomes p’; if the expansion of one mass

576 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

and the compression of the other takes place adiabatically then the
new volumes k’, and k’, will be

p, \/r Gale
ge ( 2) ki = ky
p’ p'

From the condition that k’, + k’, = k we find
as AoE ete
Ri Nica ae aes

The center of gravity of the whole massremains at the same altitude
wherefore 0P =
The available kinetic energy is therefore

=o) =) Si roadk = 3) p’) dk
1
= r—1 (ky Py + kp Py — Rp’)
If the difference p, — p, is small as compared with the pressure in
one of the chambers so that p, — p, = ep, then

Po = P, (1 — «)

(2 kik cea _
— i Ae p= sed. $
Pp p.( aa he = 5

Therefore if 7* is the average temperature of the whole mass, then the
average available kinetic energy for the unit mass = 2 is given by

[Va OP OR, REE

2 2 k? . 2
and when the other circumstances are the same this has its max-

imum when

1
k= y= 3k.

ON THE ENERGY OF STORMS——MARGULES Welk

If then the volumes of the chambers 1 and 2 are equal, we have

a. Cia Ween) «begin Garg alte Ee
(CH) pera 2 RES : = VIR Ee: <a)
2 \ Cs Deis \ Cy
If p, = 765 ™ mercury, p, = 755™™ mercury, T = 273° then this

equation gives (V) = 1.55 meters per second.

We will compare this value of (V) with the V that was deduced
previously in §(3) for two masses that initially lay in a deep trough
alongside of each other (see fig. 1). If h is the altitude [of the two
chambers] and 7,* T,* are the average temperatures and if the
greatest entropy in mass (1) issmaller than that of the lowest layer of
mass (2), then for chambers of equal volume the second analysis
gave the velocity V = } V ght (see the expression (T)-825).¢ This
may be brought into a form similar to that given above in (III)
if we put

a ia! Ae Bink, Por
RTY Ph RT¥ Ph
Fg <7
ght = gh t — ce = approximately RT* Por — Por
; ; Ol
whence
yee) (Bae arene ee her)
2 Po.

If for Po: Po. and T* we assume the same values as those just given
op) 705, P, = 755; 1 = 273° there results Vi '— 16 meters sper
second, ora velocity ten times larger than from equation (III), and
therefore a hundred times the kinetic energy per unit mass.

§(32) We can also add the following problem:

Let the chambers 1 and 2 of fig. 1 be limited above by a rigid
partition and contain masses of air that have equal entropies but
different pressures at the same altitudes, consequently there must
be a higher temperature on the side of the higher pressure. The
difference of pressure at any level is in the same direction at all
altitudes and is nearly proportional to the average pressure at
that level. The initial stages of 1 and 2 are respectively that of
stable equilibrium. After removing the separating vertical parti-
tion the adjacent layers on the same level unite. The altitude of

578 SMITHSONIAN .MISCELLANEOUS COLLECTIONS VOL. 51

the center of gravity remains unchanged. The resulting (V) has
the same form (eq. III) as for the thin horizontal layer considered
above, provided we now let J indicate the average temperature of
the whole mass and let p, and p, indicate the initial values of the
pressures at the base.

Again let there be resting in these chambers masses whose dis-
tribution of entropies is such as was assumed in the second
analysis, see section 25; this equation (I) or (I*) applies to their
overturning even in this present case of constant volume. For
the same differences of pressure at the base, and for smaller
differences above, and when #,, — Po. is a small fraction, as is the
case in our atmosphere, equation (I) gives a much larger value
of the living force than equation (III).

It seems now to have been abundantly demonstrated that the
available kinetic energy of such a system is not dependent materially
on the horizontal differences of pressure but on the distribution of
entropy and the buoyancy dependent thereon.

§(33) Appendix to the fourth analysis. Study of Joule’s expert-
ment relative to the mutual independence of the internal energy and .
the volume of a gas.

In the first chamber of fig. 1 let the horizontal layer of gas be
under the pressure p, but let the other chamber be empty or p,=0 ;
we now have the same arrangement as in Joule’s experiment, if
we put k, = $k.

For this case the first equations of our fourth analysis, § 31,
become

p= 27!" 2,
Ci, [R
= $f =o 7 eee )
p= % (tp -b.2%
Se Callas ah
R20

If T is the initial temperature in chamber one, then the mass of
the gas is

whence

ON THE ENERGY OF STORMS——MARGULES 579

In the case of motion without friction we have for air
Vy=V2CT (i — m4) = 0.70384 V CT.

For the temperature T = 273° this equation gives (V) = 307m. /sec.
If we assume that the kinetic energy is confined to that half of
the mass that flows out of the first chamber into the second, we
find the velocity 435 m./sec. These values are of the same magni-
tude as the molecular velocities. In small vessels the kinetic
energy is very soon converted (by friction) into heat and is added
to the internal energy of the system This added heat that we
fail to notice in our atmospheric movements is decisive for the
result of the laboratory experiment. Probably the experiment of
Joule would have given a very different conclusion if he could have
performed it in vessels of very large horizontal extent. In that
case one should have observed a diminution of the internal energy
at whose cost arose the kinetic energy of the systematic motion
appropriate to the extent of the vessel. The previous portion of
this article has been suggested by the relation of our problem to
Joule’s experiment but the following suggestion which has perhaps
already been made elsewhere may be added. In the case when the
volumes of the gas chamber and the vacuum chamber are unequal
and with the assumptions that the motion is frictionless and that
the change of condition is adiabatic and that at certain moments
the pressure p’ is uniform throughout the whole space, we have

ye Sc rl a2)

If the vacuum chamber is very large relatively to the gas chamber
so that k,/k =o approximately and since y—1>0 therefore this
equation gives

1
= (eae
al? »

On the other hand, from the kinetic theory of ‘gases, if (uw) is the
mean of the squares of the velocities of the molecules of gas in the
non-systematic free motions of molecules [or (u?) is the square of
the mean free path] we have

en ean
Cees)

580 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. §1

Hence if C, = $R ory = 3 we have (V) = (u). This is the value
of 7 that is found for non-atomic gases but for other gases 7 is less
than 3 and (V) is greater than (wu).

§(34) Comparison of the problem above treated with analogous analy-
ses for incompressible liquids.

We will now consider a system of liquids each of which retains
its constant density during its change of position. The available
kinetic energy is to be computed by the equation

aie: eR a

The potential energy of position for a unit column of a homo-
geneous body between the altitudes A, and A, is given by

ea

"a ar
Fl \ g2ndz = gu 5

(A) Let the chamber 1 (fig. 1) contain liquid of the constant density
4, the chamber 2 a liquid of smaller density »,. So longasthe screen

separates the two chambers there is neutral equilibrium on both —

sides of it. The volumes 1 and 2 are in this case assumed constant
and therefore equal to 1’ and 2’ respectively, B being the area of
either base. We now have for the initial and final stages

as B h? ans B h?
igs 9 Sli o> P,, = 9 Sta
be hy? ee 3h?
Pie Beng Poe = Bg ing

After the removal of the vertical screen the available kinetic energy
becomes

— MV? PY ae
= 9 P= 9 = gBh 8
and the mass is
a
M=x Bo bs
2
Let
a o
mM=H\ Its fo =p\1—>5
Por = ghity Por = gh ty Po = ghy

Te

ON THE ENERGY OF STORMS—MARGULES 581

then analogous to equation (I) see $25, or (1*) see $31, we have

ee ae or § v= 54 gh a Pa
0
(B) Following the initial condition assumed in the third analysis
we now assume that a parallelopipedon having the height h, length
! and breadth unity, is filled with liquid whose density is a func-
tion of the length x only. We also assume that the density dimin-
ishes continuously from + = co up to x = 1.
We thus have for the initial stage

rs ik i F a) F
i og oo CAR ee Ss 5 Wh Mam

In the final stage the liquid that was initially in a vertical column at
x above the elementary strip dx with density « becomes a horizontal
layer at the altitude ¢ with the thickness d¢.

Since hdx = ldg and hx = l¢ therefore for the final stage we

have
a h gh?
ca IY eucde = ap [vv

x
= fs, (1-07

M=Ihyp, (1 — 4.0)

If now we put

there results

Pages eel : go MYA
=o PS Ban Peo he a 9

and when a is a small fraction then, and in agreement with (II)

($27) we have 2
z gho
V oe qe

6

(C) Let us now arrange the liquid in the trough in parallel inclined
layers of equal density and assume for the initial stage

x ra
n= (1 — 27 ~ % 7) = Mo (1 — 9).

582 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The computation of the available kinetic energy for this case
supplements the computation for air whose entropy is a function
of length and altitude. The angular inclination to the horizon of
the layers of equal density is

fate Tanti aa
a l

z

If ¢,>0, then the layer that starts from the edge where x = o and
z = h will intersect the bottom of the trough.
The analysis must be executed separately for the three re-

; , , % a
gions in which g = o, i + 6; j is between o and o,; or between

o, and o,; or between o, and o, + a, The first and last of these
regions are triangles in the xz plane, the second is a parallelogram.
The evaluation of P, and P, for the separate regions is rather
tedious. Eventually we find

\ 2
ia 0 Oo, — oO Leo, ( ] Ay
72 nat EL eae: = = ; : : oat =
1 (1 9 ri gh} 6 Spey” 1 Baers f

If o, <o, then the above described layer (that starts from the edge
for which x = u, =h) will intersect the opposite vertical wall of
the trough. For this case we have

ie ee gee (1-5 =)
| > aye oo. Tee 5 eee
In this case also the available kinetic energy is independent of the
length of the trough.

If o, =o [then a = go° and the layers are vertical columns as in
case B and] the former of these two equations becomes

ve ( 1 — =) = ph = which is identical with the value of V com-

puted in case B when a, is a small fraction.
If o, =, then the layers are parallel to the diagonal surface of
the trough. For this case the two equations agree in giving

; gho
1 ea —o) = aa
therefore, if o is a small fraction, the available kinetic energy is
about one-fourth of that which we found for the same value of a
in case (A) or two-fifths of the analogous quantity in case (B).

ON THE ENERGY OF STORMS—MARGULES 583

(D) Finally, in order to imitate with incompressible liquid the case
treated in the fourth analysis we return to the two chambers; we
assume their basal areas to be equal; the chamber 1 to be filled with

liquid with density mw to the height h + 3 and the chamber 2
-

filled with the same liquid to the height h — 2 so that in the final

~

stage the fluid extends to the altitude h throughout the whole
trough. We now have

This last expression is the analogue of equation (III) of the fourth
analysis, §31. For equal values of ~,, and ~,. and when their dif-
ference is small relative to p, then in this'case D, the velocity (V), is
much smaller than the V in case (A).

CHAPTER IV

THE EQUATION OF ENERGY FOR MOIST AIR IN WHICH CONDENSATION
OCCURS IN CONNECTION WITH THE CHANGE OF LOCATION

In order to investigate the influence of the latent heat of condensa-
tion on the available kinetic energy a fictitious gas 1s introduced.

§(35) We may consider the equation (6*) deduced previously for
an ideal gas of constant composition as applicable to any closed
system. The significance of I depends on the nature of the system.
We will apply the equation of energy to an atmospherecomposed of
air, water, and vapor, assuming thereby that the vapor is an ideal
gas up to its point of condensation. In this case we can deduce
the equation of energy by a special method if we change the equa-
tion of continuity so as to include the processes of condensation
and evaporation.

We adopt the equation (6*) of §11 as an axiom

Q)=d8K+P4+D+R)

584 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

Of the many processes that occur in moist air we will base our
analysis on those only that we consider important for our problem,
which is to determine the available kinetic energy of any initial
stage; all other considerations we temporarily omit.

The condensation of vapor into small drops causes the capillary
energy to be included in J, and the pressure of the saturated vapor
to depend on the size of the drops, and the water floating in the air
to contribute slightly by its weight to the pressure of the strata
beneath. We free ourselves from these influences which are of
minor importance in our present problem, by assuming that in our
system the condensed water immediately falls to the ground [or at
least separates from the air under consideration].

Let a, 3,7 be the subscript indices referring to the air, vapor, and
water, respectively, so that the mass (m) of moist air is composed
of three portions: mq; mg; m,y respectively; the specific heats are

Cya Coe Coy : Coa Cpe Cpr : Moreover Ce — Cig = Re, etc.

L = latent heat of evaporation of a kilogram of water at the
temperature T; and L’ at the temperature T’.

L—RgT = internal latent heat of evaporation.

C = specific heat of water, assumed to be constant.

CT = internal energy of a kilogram of water.

CT + L — RegT = internal energy of a kilogram of vapor.

Assuming that aqueous vapor follows the laws of ideal gases we

have

L= Loy c= (C- Cy) Ak
Fate 9 8 at treed (Sie Oo.) ee
L, = Constant

For the temperature T the internal energy dl of the elementary
mass dm which is composed of dmg, dmg and dm, is given by the
expression

dT = Cyy Tdma + CT (dmg + dm,) + (L — RgT) dmg
= Coa T dmg + Cog T dmg+C T.dm, + L, dmg

We will first assume that during any change in the system the con-
stituents of any elementary mass remain the same, so that in the
final stage all have again a common temperature as in the initial
stage; therefore dmg remains unchanged and dm’g + dm’, = dmg
+dm, where the superscript primes refer to the final stage.

othe hd a

—

ON THE ENERGY OF STORMS——MARGULES 585

§(35a) Let usconsider a system that in its initial stage contains
no liquid water. Its internal energy will be

T, = Cra | Td ma eeu: dmg +L, {dmg

For the final stage this becomes .
i= eke d My + Cop \T' dm'g + Gt dm’, + L, fd m’ 3
Since we assume dm, = 0 therefore dm’g = dmg — dm’, and
i= Cae d My + Cup $ T'dmg + Ld mg —
— {{L, — (C — Gig) Tam’.

The excess of the internal energy in the initial stage over that in
the final stage is

ST = tT. ha) i — T') dma + Conf SE ae, +
ey — ReT’)dm',. .

We assume further that the density of the water is infinitely great
in comparison with the density of the air (or that the volume of
the water is zero). Under this assumption ], and dJ retain their
values when the condensed water falls to the ground.

If the system is, as before in figure 1, composed of a lower por-
tion of the mass of atmosphere, extending up to the altitude h, and
an upper portion that acts only as a piston of constant weight Bp,
where B is the area of the base; if also the air is at rest in both its
initial and its final stages, then for the potential energy of position
we have the following expressions, in which the volume and mass
integrals are to be extended over the lower portion only. This
latter is true also for the mass-integrals in J. The partial pressures
are Pq and pz.

h
P.= faB pdz + Constant = io (Pa + bg) dk+ Constant
0
= al Tdm,g + Rg \ Tdmg + Constant
P, = Ry eee: Ma + Re ( T’dm, + Constant

== ihe i T’dmg + Rp J Tams — Rp ii T’dm, + Constant

586 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The water that in the final stage is lying on the ground contributes
nothing to the P,. The excess of the potential energy of the
initial stage over the final stage is

—dP =P, —P, = Raf (T— 1’) dig + Rof (T — 1) d mgt
+ Ry | Tidm',

If we assume that each portion of the system passes adiabatically
over to its final stage, then we have (Q) = o and the available
kinetic energy is

0K + R)=—I@P +1) =Cyaf (T — T) dmg +
+ Cog f(T — T) dmg + JL'dm', (F)

For moist air the final stage of stable equilibrium must be deter-
mined under conditions similar to those required for a gas of con-
stant composition, i. e., that the strata be so arranged that the
entropy increases upward. Assuming that we know the final loca-
tion of each mass, then we can determine the pressure p’ that the
element dm’ experiences in its final stage: since we also know the
pressure p and temperature T for this element dmin its initial stage,
therefore 7’ and thence L’ and dm’; are to be computed from the
well-known equations for the change of condition of moist air.

§(35b) We will now substitute a mixture of dry gases a and f
whose composition has a local variability in place of the moist air
[whose composition was uniform]. Assume that for each element

of the mass the ratio ite remains unchanged during the overturn-
dmg
ing.
The specific heat is determined by the relation
Cpdm = Cpa dmg + Cpgdmg :

The change of the total potential energy due to the overturning
process under constant pressure is

—o(P +1) =fco,(7-T)am

z= oe s| (T — T')dmg + aera! (fT = T’) dmg

For the element dm the values of (I. — T’) are the same as before

ON THE ENERGY OF STORMS——-MARGULES 587

for moist air. But in order that this be possible, we must add
heat during the overturning and the total quantity for the whole
mass will be (Q). Hence according to (6*) the available kinetic
energy will be

dK + (R)=(Q)+ Coa f(T eT) ding A Cop f(T ~ T’) dmg
and the flow of heat is determined by the equation (F)
(Q) = { Lidm, (F*)

It_is to be noted that L’dm’, is not exactly the latent heat of
condensation that the element dm receives during its whole path,
but the quantity of heat evolved by the condensation of dm’, at
the temperature of the final stage of dm. ‘This is in accordance
with the assumption that was made in the computation of I, where
it was assumed that condensed water is carried along with the air
to its final stage.

We will therefore now investigate the influence of the latent heat
of condensation on the available kinetic energy, by means of
another system that is more perspicacious than moist air. Since
the local difference of composition is of slight influence in this
problem we will replace the moist air by a homogenous gas that
can expand with increase of heat.

§(36) Equations for a fictitious gas that receives increase of heat
by tts own expansion.

The fictitious gas that we will introduce instead of moist air
behaves when it is compressed, like dry air and obeys in general the
equation of elasticity p = RTyp. But with every diminution of
pressure there is connected an addition of heat so that for expansion

ai dp

RCs ae ee

where A differs from the x that holds good during compression.
The quantity of heat imparted by this law of expansion is
dp

RE
d0= CdT = Op im (R= AG) Po aa)

588 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

We assume that dQ is positive when dp is negative

therefore R—AC, is positive

and also that Fs txlcet ea Co eee ee
and that cooling accompanies expansion as A is ee =. (4)
and finally assume that Ais constant. .... 1 Se Sse

If T, and p, belong to the initial stage of a mass then by the
expansion or transition to a smaller pressure p we have

\A
teen ee

=A
(Te Pc Ar ere ome

Consider a vertical column filled with this gas at rest: Let p and
T at the altitude z have the same values that a particle would have
when ascending [adiabatically] from the base (p, and T,) to this
altitude.

The distribution of temperature in this column is now given by
the above equation (1) by the condition of equilibrium (a) [$13],
and by the equation of condition for elastic gases p = RT uy.
Combining these we obtain

lap plete ie eu g
pie RL ae 1 Oe
whence
OL shal he Mae
— 35> ROE 6)
z DO RA

With this fictitious gas, and for any given distribution of tempera-
ture in the vertical column, we can carry through a process similar
to that considered in our preceding second chapter (§§ 13-22)
and find that for ascending particles (or diminishing pressure) the
diminution of temperature just given in equation (6) belongs to
the condition of neutral equilibrium, and that a more rapid diminu-
tion of temperature corresponds to unstable equilibrium. In the
first case the vertical temperature gradient is smaller than that
for neutral equilibrium of dry air.

ON THE ENERGY OF STORMS——MARGULES 589

§(37) We now pass to the computation of the available kinetic
energy of an extended horizontal system (fig. 1).

First analysis. Initial stage. Chamber 1 contains dry air,
chamber 2 the fictitious gas; both of these are in neutral equilibrium,
and both umder the same pressure p, at the altitude h. The tem-
peratures are to be so chosen that, after the overturn, in the final
stage, 2’ lies wholly above 1’ and p, remains unchanged. Therefore
if the serial sequence of the elementary layers be unchanged, every
layer of chamber 2 expands except the highest one which retains
its original pressure. The layers of 1’ and 2’ are individually in
the condition of neutral equilibrium. As regards 2’ this result
follows from the application of equation (1a), $36.

Let (Q) be the quantity of heat added to the mass 2 by its expan-
sion, then for the available kinetic energy of the whole system we

have OK +R= (Q) — o(P +1 =m S

O16, | b= Ty am | ide,

The given data are h, p,, Tj4, Ty, 4, and 8; whence for the initial
stage we find

1
Oo = Tia (1 tr yes ss) Por pa ( a KP =
iG Tyo(1 +A gt a ge: - ) :
U2 he Rite Bo Sony eee fy i
For the final stage we have
Locality Pressure Temperature
At the upper bound-
ema OL 2 v5: sade site Ph Typ
At the boundary 7 zh Pi: \?
between the masses tia = Tis Ph
Lg a I ee Pi = 4 (Poo + Pr) :
; P; ’
| aN Ae ee
Al hi Pr,
ONE
Ate the Ase cin. P, = 4 (Por + Poo) tas 2 (2:)
h

590 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

By reason of equation (2a) we have

K—A :
(2) ee Sere | (T, — T.) dm,
whence .

eK +(R) = eu Wee —T’)dm, + Sa, —T') dm,

In equation (5) in chapter II, $20, for a, the vertical gradient
of temperature, substitute the values g/C,, for the masses 1 and 1’
and Ag/(KC,) (see eq. 6 $36) for the masses 2 and 2’ and we obtain

B 1
T,dm, =>3-- ieee KPa Low = Pali
Sane a, ony
J) Tam, == AP, Tote Tap
4
B it
T,dm, = 5=— oars (Poo I ia tn as)

es ei
Lots = 5 4g - (Pi Tix — Pn Tra)

§(38) Example. In order to make the fictitious gas similar to
moist air we compute the values for the initial condition in a dif-
ferent order of succession than that above given.

Initial stage. For mass 2: assume Ty, = 303°, Pop = 760, Pp =
soo™™ mercury and seek first the value of T),, for saturated moist
air, that is to say, the temperature that such air attains when it
expands from 303° and 760™™ to 500™™ mercury. This value lies
between 289° and 290°.

We adopt T,, = 290° and with it by equation (1a) compute 4 =
0.1047307 and further the vertical gradient of temperature in

A
mass 2 of a, = 7 = = 0.0035780 degree Centigrade per meter ~

which is nearly 3.6° per 1000 meters.
Finally we compute

ie The
h = ———— = 3635.29 meters

a,

Initial stage. For mass 1 we adopt the same temperature at

ON THE ENERGY OF STORMS—MARGULES 591

the base T,, as for mass 2, i.e., 303°, whence for the same altitude
h = 3633.29 meters we find Ty, and po, as follows:

ey ES

h = 3633.99 } Me telat on ye sobay uk tee Pee

Final stage. For the final stage we compute the following values

p; = 630™™ Tg = 297.1047° Ty, = 285.4593°
P. = 766.70o11™™ EF = 302.2342°
h, = 1688.60 meters. h;, = 1985.65 meters.

From these we now obtain
P B
ger — T) dm, = — 2.2312 py

B
J (1, —T) dm, = + 2.3323 Pa

Vy?

M ~~

Il

B
Cy 0.1011 p . =

B
‘M = 0.5334 p, —
g

V = 19.3 meters per second.

The true average temperatures of the masses 1 and 2 in the
initial stage are T*, = 285.9° and 7*, = 296.9°.

If instead of the fictitious gas we had assumed dry air of the
same average temperature in chamber 2 and if its entropy had been
such that in the final stage 2’ it lay uppermost spread over 1’ then
we should have computed the corresponding V = 18.5 meters per
second from the approximate formula (I) §(25). Therefore the
available energy is not much larger for the fictitious gas in chamber
2 than for dry air of the same temperature.

With the above given equation for (Q) (see 2a, §36), we compute
the quantity of heat communicated, per unit area of the base of
the whole trough, to the mass 2 during its expansion

(Q) Calories
Bo 2409 ie

592 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52

If this is due to precipitation of aqueous vapor then it corresponds
to the condensation of 4 kilograms of water per square meter or to
a depth of rainfall of 4™™ over the whole area.

If instead of the fictitious gas in chamber 2 we had assumed
saturated moist air then we could have found the approximate
quantity of water condensed and falling away from it as follows:

By the overturning the lowest layer of 2 changes from T,, = 303°
and p,.. = 760™™ to 7’;, = 297 and p’; = 630™™. In this lowest
layer there is initially 0.02696 kg. vapor associated with each kilo-
gram of dry air but in the final stage this is reduced to 0.02271;
therefore in this layer there condenses 0.00425 kg. water out of
every 1.027 kg. of mixed air and saturated vapor. The highest
layer of mass 2 does not expand and contributes no water; we may
assume that the whole mass 2 contributes on the average 0.0021
kg. water per kg. of its own mass so that the unit column gives up

)

~

wg X 10833.0 x 0.0021 = 7.4 kg. of water

Because of the spread of the mass 2 over the whole trough this
water is distributed over double the original base giving 3.7™™
depth rainfall in close agreement with the value above given.

§(39) Second analysis. Approximate method for the computation
of the available kinetic energy when the chamber 1 is filled with dry
air and chamber 2 with the fictitious gas. |

In this case all the considerations that were made in the analogous
second analysis, $25, chapter III, are to be repeated excepting only
that A is used instead of x in chamber 2.

Initially the masses 1 and 2 are each in stable equilibrium within
itself; the succession of layers within each mass remains unchanged
in the overturning. Hence we obtain p. and p, and, assuming
equal volumes for the two chambers, we find the following approxi-
mate values:

ON THE ENERGY OF STORMS—MARGULES 593
Fee S ¢a.— roa i:
K+ B= y J ( Lk 7 my +" f (1, — Ty) dm,
=C 4g , Ei (Pos a Pr) ai T, (Pos am Pr) — = (os + Pp) b

This is the same value as before, and now the same considerations
as in §25 lead to the approximate formula (I) of that article for the
velocity V. We arrive at the same result as if instead of the
fictitious gas in chamber 2 we had used dry air of the same average
temperature. The reason why this happens is shown by the course
of the analysis. The change of P + J for the unit mass remains the
same no matter whether chamber 2 is filled with dry airor with the
gas; the amount that the mass 1 contributes to the available kinetic
energy remains unchanged.

The contribution of mass 2 by simple change of location only. or
the change of P +] for this mass, (which is C,{ (T.- ee) dm,),
is in the new case (for the fictitious gas) smaller than for dry air
since the gas cools less by expansion and therefore T”, is larger.

But on account of the development of heat associated with the
expansion (which we have introduced as equivalent to the latent
heat of condensation) there is (Q) to be added to the expression
0K +(R) and for the fictitious gas the expression

(Q) + C, f(T: — T)) dm,

is as large as the second term alone would be for dry air.

Thus it is that the addition of heat by virtue of the expansion
causes no increase in the available kinetic energy, but serves only
to warm the expanding mass or to diminish its cooling.

§(40) The difference between the fictitious gas and the motst atr.

In order to simplify the analysis and investigate separately
the influence of the latent heat of condensation we have given the
fictitious gas that has replaced moist air the properties of dry air
and have only introduced the condition that it shall expand when
heat is added. In order that it might more nearly resemble moist
air we should have also assumed its density smaller and its R to be
variable with its condition.

594 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The fictitious gas cannot replace moist air in everyrespect. The
proof that the condensation has no influence on the available kinetic
energy, does not exclude the possibility that the proximity of
masses of relatively dry air and moist air should favor the origina-
tion of a storm.

Since the available kinetic energy of the system,is derived from
the buoyancy, therefore any diminution of density by reason of
the vapor content of a mass of air operates like an increase of tem-
perature. A particle of the fictitious gas remains in stable equilib-
rium in dry air, if it has the same temperature as the surrounding
air and if the vertical temperature gradient in that air is smaller
than Ag/R. A particle of saturated moist air, having the same
exponential factor 4 [would not be in stable or neutral equilibrium
but unstable and] would rise because of its smaller density.

In the example of the first analysis §38,if instead of the fictitious
gas we had used saturated moist air of the same temperature and
pressure, then for the altitudes o and h its densities would have
been respectively equal to that of dry air at [,,=307.8° and py =
760™™ mercury and that of dry air at T,,= 293.2° and p,,=5co"™™
mercury. This 307.8° corresponds to a difference of Ty, — T9,= 1.8°
from the value T,, = 303.0° as there adopted and a difference of
3.2° fromthe value T;,,,=290° there computed for the altitude h or a
difference of 4.0° from the average temperature of the whole mass
of 2 [when it is composed of saturated air instead of the fictitous
gas]. Therefore for these two cases the available kinetic energy
is in the ratio 15/11 and the velocities V are larger than in the
fictitious gas in the ratio 1.17/1. Or, if we require the velocity V
to be the same as before, then we need a smaller difference of tem-
perature between dry and moist air, viz., about 8° instead of 11°.
All this relates to the unusual high temperatures of our examples;
for lower temperatures the influence of the moisture on the density
will be still smaller.

§(41) The kinetic energy of a mass of air is derived from its
internal energy and from the work done by the force of gravity.
In the case of a continuous distribution of density the importance
of gravity in the production of great velocities can be concealed,
whence we derive the very common belief that the horizontal
gradient of pressure produces the storm. But it is now demon-
strated that, even when the distribution of pressure at the base is
as observed in storms still the horizontal movements of the masses

ON THE ENERGY OF STORMS—MARGULES 59r

have a potential energy that is only a small fraction of the observed
kinetic energy. So far as I can see the source of storms is to be
sought only in the potential energy of position. A system in which
the masses are disturbed vertically from equilibrium can contain
the necessary Potential energy. Hence, therefore, the storm winds
develop by reason of the velocity due to descent and that due to
buoyancy, notwithstanding the fact that these evade attention
because of the large horizontal and small vertical dimensions of
the storm area. The horizontal distribution of pressure appears
as a translation of the driving power of the storm; by means of
it a portion of the mass can attain greater velocity than by simple
ascent in the coldest or descent in the warmest portion of the
storm area. Here we come into the presence of problems that
cannot be solved by a simple consideration of the energy alone.

XXV

THE THEORY OF THE MOVEMENT OF THE AIR IN
STATIONARY ANTICYCLONES WITH CONCENTRIC
CIRCULAR ISOBARS

By Dr. F. Pockets

[Translated from the Meteorologische Zeitschrift, January, 1893. Vol. X, pp. 9-19]

The solution of the hydrodynamic differential equations for
the movement of the air in stationary cyclones with circular iso-
bars as attained by Oberbeck under certain simplifying assumptions’
does not allow of application to the case of the analogous anti-
cyclone. This circumstance led Oberbeck to the conclusion that
there is really an important difference between anticyclones and
cyclones, in that the former must be a phenomenon dependent on
the latter and must originally cover ring-like regions adjoining the
cyclones. But on the other hand the synoptic weather charts show
us that quite frequently well rounded anticyclones continue to exist
for a long period of time although no well defined cyclones are
present; consequently a mathematical presentation of the move-
ment of the air in such anticyclones founded on the principles of
hydrodynamics must be possible, quite independent of the reason
for the existence of these anticyclones. In the following memoir
I will attempt to give such a presentation of this problem as may
be of interest as a supplement to Oberbeck’s investigation, not-
withstanding the fact that it is based on certain special assumptions.

The hypotheses under which I shall treat this problem are the
same as those that were adopted by Oberbeck, viz..

(1) That the system of winds is a stationary system, that is to
say, the movement at any place is independent of the time.

(2) That the air is an incompressible fluid (this is allowable
because of the insignificance of the ordinary differences of pressure)
and that the temperature is constant.

(3) That the portion of the earth’s surface under consideration
is a plane surface and that the geographic latitude has a constant

1A, Oherbeck: Annalen der Physik und Chemie, 1882, N. F., XVII,
pp. ro8—148,

596

MOVEMENT OF AIR IN ANTICYCLONES—POCKELS 597

average value: (this is all the more allowable in proportion as the
average latitude is nearer the pole).

(4) We shall study only the movement over the earth’s surface,
of,a layer of air of moderate depth assuming that it experiences
a frictional resistance opposed to the direction of its movement
and proportional to the velocity of the current.

(5) That a descending current of air prevails over a surface
bounded by a circle of radius R and that its descending velocity is
directly proportional to the altitude above the earth’s surface and
is the same, for any given altitude, over the whole of this region.

(6) That purely horizontal motions prevail outside the circle
whose radius is R.

From this last assumption combined with the second and third it
follows at once, that the atmospheric pressure, the velocity of the
current and the angle that the current makes with the radius-vector
depend only on the distance, 7, from the center of the descending
current. Designate by V, the radial component of the velocity V
positive inward; by V, the velocity component tangential to the
isobar counted positive in case the rotation is directed contrary
to the movement of the hands of a watch; let p be the atmospheric
pressure expressed in absolute units of force, o the average density
of the air, k the coefficient of friction, and 4 the product of the
angular velocity of rotation of the earth multiplied by the sine
of the geographic latitude; then in the case under consideration
of concentric circular isobars, the hydrodynamic equations of
motion can be written?

Bee 2 a Mane ace tsb Ve aes Yea eae os)
p dr dt r
= £0 Ni Ns _1V, + BY, ee are

which equations moreover can be deduced directly from very simple
considerations. Because of the assumption of a stationary condi-
tion, the total acceleration is identical with the acceleration depend-
ing on a change of location, that is to say, a change in the distance
from the center of the whole system of winds, consequently in our

problem we have
GV (dV. ar OV, EV ee OF
ee a Pe rite | ee :

dt dr dt dt dr dt

42 See Sprung’s Lehrbuch der Meteorologie, Hamburg, 1885, p. 135.

598 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL.= 51

dr
Further, if we consider that a is nothing else but the negative of

the velocity component V,, then the equations of motion take the
form

bet seen Te ov, +e bay, + BVS ton Re
p dr dr-
gS SOM gy 2 eS yee ee
dr r

To this we add the condition of continuity [as to mass] which
requires that [if the density is to remain constant then] as much air
flows out of any elementary volume in a unit of time by reason of
the horizontal current as flows into it [in the same unit of time]
by reason of the vertical current. Now the mass of the horizontal
outflow of air for an elementary prism whose altitude is unity, whose
base is bounded by two circular arcs of the length dg and by the
radii y and r + dr, is equal to

_ der)

. drdg.
dr S

uu tne other hand by reason of a descending current whose velocity
increases by the quantity w within a unit distance, or is itself
equal to w at the unit altitude (compare assumption No. 5) the
mass of air that flows into the unit volume is equal to pwrdrdg.
Therefore we must have

or if o is considered to be constant then

ais

Soe ee arpa |
is rw (Ic)

4 wus CYUALIUN W Mgnt be considered as a known function of r
but as already stated in assumption (5), we will make a special
hypothesis, i. e., that this quantity has a constant valuety within
the region for which r< RK but that outside of this region it has the

MOVEMENT OF AIR IN ANTICYCLONES—POCKELS 599

value zero so that the condition (Ic) consists of two, one for each
region, 1. e.,

d (rV,) = ry Rote <e Ko ay hide. oo eas ae Le)
dr
, 4
GOVE bet ae ie FOS: es aes)
dr

The continuity condition (Ic) alone determines V,, as a function of
r; if then we substitute this function in (Ib’) we shall obtain a
differential equation for V,; finally the equation (Ia’) serves for
the determination of the distribution of pressure after we have
substituted therein the functions found for V, and V,. The com-
plete solution therefore demands the integration of three ordinary
linear differential equations of the first order for the inner region and
three others for the outer region; in this solution the integration con-
stants are to be so determined that both V, and V, as also p are con-
tinuous at the boundary between the two regions, i. e., for r=R,
since at the passage from the inner to the outer region both the
velocity and direction of the current of air, as also the pressure of
the air, must change continuously.
In the manner thus indicated we first find

Va -Zrrforr<R er Se ag |)

where the constant of integration must be zero because other-
wise V,, in the center of the system of winds would become infinite;
furthermore
am constant . tee > je

Yr
and the constant of integration is — 47k? so that V, shall remain
continuous when r = Rk, hence

2

R
=47 porn

In the case of a cyclone the sign of 7 is to be taken oppositely from
that in this equation for the anticyclone. Now the differential
equation (Ib’) becomes

forr< R 0= pA ee (IIa)

forr >kR pRe(sh +) aay +3 +. eras ~ (Lb)

600 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51
The first of these equations is satisfied by the function

wegleee T0018
2(k +7)

the second equation is satisfied by

Re a 5

re ante
as is easily seen without further comment. In order to obtain the
general integral, we have still to add the integral, multiplied by an
arbitrary constant, of the differential equation that arises fromthe

omission of the terms that do not contain V, in equations (IIa) or
(IIb) ; this homogenous differential equation reads

Nae, Gy VR mate ae
dr ry r

whose integral is

and again

d(rV,)_ 2k
dr ri

rol V = Ofer 7 Sd

whose integral is
ual
rV;, =iG%e (-; =)

Hence the complete solution for V, reads as follows:

PRT
Ve A ae for ¥ SR Ee
2(k +7)
eee aS
2 * R2
viel TA Ree ie ener
a. cake r i 2

The integration constants C’ and C” are now to be determined
in harmony with the conditions of continuity. In the case of a
cyclone for which we have negative values of 7 (that is to say, an
ascending current in the interior region) we must put C” = o,
since otherwise V, would become infinitely large at an infinite dis-

/
MOVEMENT OF AIR IN ANTICYCLONES—POCKELS 601

tance; we thus arrive at Oberbeck’s solution.* In the case to be
considered by us ofan anticyclone, or a positive 7, C’ is to be put
zero in order that V, be not infinite when 7 = 0; on the other hand
the exponential function in the expression (2’) is to be retained
since its exponent is negative and it therefore disappears when
r =a. It is because he omitted the exponential function in his
general solution that Oberbeck could not apply his solution to the
anticyclones.

In order that the expressions for V, namely (2) with C’ = o and
(2’) may be equal to each other when r = R, as is required by the
continuity of the velocity, we must have

ee ATs eo LAT pe oe k/7

: 2(b +7) 2k R

whence the following value results
ron eS Tay
Zi le (e-Ey)
Finally, as the complete solution for the velocity components we
obtain

1
|e ak
n 97
forir < Rn pe par ete)
Vee fet r
2 ke ay
ie ade4
Ve ee
¥ a!
a Baier for7r > KK (39
Vag 's LED he ke @ = (i ‘)
: FB e VS ORES

The exponent
k ( r i )
i oA:

8 Oberbeck (Annalen, 1882, XVII, p. 143) subjects the quantity — 7 =c
to the condition c <k in order to obtain an infinitely large value of the
velocity at the center and a deflection of the direction of the wind to the
left instead of to the right of the gradient. But this is attained by the con-
dition c <2k; for the velocity (logarithmic) becomes infinitely large when
c = 2k and the angular deviation remains in general always between the
limits + tg—14/k and + 2/2, which latter value is attained at the center
as soon as ¢ > k.

602 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL: ht

is negative throughout the whole exterior region and the factor
in brackets in the expression for V, in (3’) is therefore positive;
hence V, is everywhere finite and negative whatever may be
the absolute value of 7 and therefore the intensity of the descending
current in the inner region of the anticyclone need not be subject
to any limitation whatever. Hence from the expressions (3) and
(3’) there result at once the following values of the absolute wind
velocity, V = V V2 + V? and of the tangent of the angle of
deviation, tand = V,/V, namely,

in the inner region (r<k)

RP
Var leg Spade geen ae eee
A
eS ae otk vat\ Sula eke eee
in the outer region (r>R)
| k (vr
bf T > \pe — 2 2
Ves he 1+ 41 MEER g 7 ( Be

J r pr) he ee

Hence the velocity of the wind in the inner regions is proportional
to the distance r from the center, but in the outer region at a suffi-
ciently great distance from the boundary circle it is inversely pro-
portional to that distance. The maximum wind occurs in the
outer region in the neighborhood of the boundary between it and
the inner region or even at this boundary itself depending on the
values of A, k and ;¢.

In accord with the expression (5) the angle of deviation is con-
stant in the interior region and smaller than the “‘normal”’ value

which is given by iggy = :

On the other hand in the outer region in accord with equation (5’)
the angle increases with distance and rapidly approaches this
“normal” value. (It should be remarked that conversely, for
cyclones there is in the outer region a constant angle of deviation,

MOVEMENT OF AIR IN ANTICYCLONES—POCKELS 603

i.e., the ‘“‘normal’* while in the inner ascending region the angle
of deflection from the gradient increasesas we proceed inward.)
Hence in the interior region of an anticyclone of the special struc-
ture here assumed the paths of the winds are logarithmic spirals.

The distribution of barometric pressure remains now to be deter-
mined by substituting the value of V, and V, above determined
in the equation (Ia’). This latter equation is thus transformed
into the following:

for r < R~
0
ld 2k +
wpe ee eh 6)
pd) 1 Ue eae)
for *7 o> KR
lap -~R 1G
re ee oa
pdr r
| a fa
re w{1- r lf lc
Ly A Zks k+y
k [rr
— = (> =1
ie r Bat LN ae
k+y j

These expressions need only to be multiplied by a constant factor

: in order to obtain the gradient G or the change of barometric

pressure per 111 kilometers in the direction of the radius vector r:
10 333 X 9.81
760 X III 000
= 0.0012 and a has the value 1.293 where the units are a kilogram
of mass, meter of length and second of mean solar time.
Equation (6) shows that in the interior region of the anticyclone
the gradient is simply proportional to r as we found to be also the
case with the velocity of the wind. Inthe exterior region of the anti-
cyclone according to equation (6’) the law is much more complex

to this end the constant yw has the numerical value

4This term was introduced by Guldberg and Mohn in 1876. See No.
XI of this present volume, pp. 143—-146.—C. A.

604 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

but at a moderate distance from the boundary circle it assumes
the following simpler very approximate form

yi ( elie ay
Ben Vere yale Gr ur

where the second negative term is the important one as it ought
to be since the atmospheric pressure diminishes outwardly. This
last given law for the gradients differs only by the sign of 7 from
that which was deduced by Oberbeck for the outer region of a
cyclone.

Finally, in order to express the barometric pressure as a function
of the distance r from the center we have to integrate the differential
equations (6) and (6’) which only requires simple quadrature. If
P represents the pressure on the boundary circle whose radius is R
we obtain
forr<R

a ee Bees <oe
PE pe Lapa) ee eae

On the other hand for the exterior region, we find the following
complex expression

for ri RK

A

La re a)! ;
— 05 + 72 Se eres

nomen
Bi a Ta aie Pes
2

-(sees) ale l{a-#) r
Diba a) oe — 3: Shes Huet peti)
where
e—2t|t=kr/yR kr/yR? —2x
tek E | mee \ eax
x z= k/y k/y *%
e —2 | 2=2kP/7R? 2kr/yR? —2
Eps E | Br { es ax
x = 2k/7 2k/r x

The integral

(ieee
x

MOVEMENT OF AIR IN ANTICYCLONES—POCKELS 605

that occurs in equation (7’) cannot be presented in definite form
except as the converging series _

which series is, however, for large values of « rather inconvenient
for computing*. In such cases and when great accuracy is not
important we compute only the gradients G, and G for RK and r
and G,,G,. . G, for a series of intermediate values 7,.. . 7, and
then from these compute the pressure in millimeters of mercury
for the given 7 according to the formula

+G
pa = on oe
~ 2 Tan)... “8 ¢ Hn)... ®

where B represents the barometric reading at the distance r = RK
and the values of r are expressed in units of 111/km [or degrees of a
great circle].

The objection might be urged that according to equation (7)
the difference (P — p) becomes infinite for an infinitely large value
of r (logarithm of r). But it must be noted that for very large
distances the assumptions made by us become in part inapplicable
(for example the geographic latitude can no longer be considered
as constant) and this too quite independent of the fact that in the
actual atmosphere the neighboring cyclones or other anticyclones
affect the distribution of wind and barometric pressure. There-
fore we need only expect that our results will apply up to moderate
distances from the center of the anticyclone, which may perhaps be
slightly larger than the radius of the inner region.

In order to show that within these limits the theoretical results
as concerns wind-force and _ pressure-difference correspond to
those actually occuring, I have computed in detail the following
example:

The constants A and k are considered as given previously for that
portion of the earth’s surface over which the anticyclonal system
of winds prevail; on the other hand the parameters 7 and Kk which
also occur in our final formule remain adjustable in order to repre-

*Smithsonian Mathematical Tables. Washington, 1909. Table IV, pp.
225-262.—C. A.

606 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

sent anticyclones of different intensity and extent. In the suc-
ceeding example we shall adopt the following values:

4 = 0.00012, which value applies exactly to the geographic lati-
tude 554°.

k = 0.00008, a value of the coefficient of friction that has been
deduced from the average angle of deflection as determined for
North America and approximately for Norway.

7 = 0.00004.

R = 400,000.

The meter, second, and kilogram, are adopted as units. The
assumed value of 7 is such that for r R the formula (4) gives
a velocity of about 11 meters per second corresponding nearly to a
wind of force 5 on the Beaufort Scale.

Since the velocity of the descending current of air acccrding to
our hypothesis is equal to 7 multiplied by the elevation above the
earth’s surface, therefore the assumption that 7 = 0.00004 is equiva-
lent to the statement that this velocity is 4 centimeters per second
at the altitude 1000 meters, or 12 centimeters per second at the
altitude 3000 meters, at least in so far as that hypothesis is appli-
cable to such a great altitude. Therefore we have to deal with
very small vertical velocities that are not at all improbable. In
his numerical example for a cyclone Oberbeck assumes that the
vertical component of the velocity is 2.4 times as large as this.

Under the above given assumptions our theory gives the follow-
ing results for the wind velocity V (in meters per second), the
angle of deflection ¢, gradient G and difference of pressure (b — B)
in millimeters of mercury, for a series of different distances r
expressed in kilometers from the center.

Interior region.

Tsdicvetard Wine te arsvetatensie ° 100 200 300 400 kilometers
Vicious dave cc Gi aete ° 2.82 | 5.65 8.47 re ee meters
db Sree! Sie re cece auch cleueneie @ oF (45°) 45° 45° 40° 45°
Gare woreicie6 be eceterar ies ° 0.43 0.86 1.29 1.72 millimeters
Gi Be eee ntoe sete s 3.0 2.9 2.32 1.36 ° millimeters
Exterior region
ne | |
oth otis 1400 |450 | 500 |600 700 | 800 900 I000 kilometers
Veet. TZ «| \it.Te | 10.67 9.57 8.22 7.20 6.42 5.78 meters
Wass | 45° 50° 21’) 53° 14’ | 55° 36’ | 56°r0! | 56° 18’| 56° 19’| 56° 19/
(Gace rclefel ek<a8 | 1.425 | 1.413 1.305 1.17 1.05 0.95 0.86 millimeters
B—b.| o 0.63 1.27 2.49 3-61 4.61 S05 6.32 millimeters
| |

MOVEMENT OF AIR IN ANTICYCLONES—POCKELS 607

Therefore at tooo kilometers from the center the barometric
pressure is 3.1+6.32= 9.42™™ lower than at the center.

At the boundary between the inner and outer regions the gradient
is discontinuous, since it falls suddenly from 1.72 to 1.38; but that
this must be*so is evident from equations (Ia’) since

ave
dr

has different values when r = R outward and inward because of
the conditions as to continuity.

In the exterior region and as thedistance from the boundary circle
increases, the angle of deflection rapidly approximates to the normal
value which in our case is 58° 19’ = tg! 3/2.

In general the winds and pressures computed in our example
correspond very well to those that are actually observed in baro-
metric maxima especially in those of the warmer season of the year
and where the lowest stratum of air does not play too prominent
a part.

Perhaps we should have come still nearer to the actual conditions
of nature if we had assumed the intensity of the descending current
ef air in the interior region of the anticyclone, not constant, but
diminishing toward the boundary so that at the boundary between the
inner and outer regions a continuous transition exists for the verti-
cal velocity component and consequently for the gradient. A
simple assumption of this kind for the vertical velocity at the alti-
tude unity above the earth’s surface is

e-rti-(3)"}

where 7 may be any positive number, for in accord with this theorem
w attains its greatest value 7 at the center of the anticyclone but
disappears at the boundary circle whose radius is R.

For this value of w the equation of continuity (Ic’) becomes

and by integration

where again the constant of integration is unnecessary.®

5 It is zero as in equation (1).—C.. A.

608 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The differential equation (Ib’) for the tangential component
V, for the inner region now becomes

sa gl a rV, F
fee wee ere eats
(ie + 2) R* 22

The general integral of this equationis the sum of a function that
satisfies the complete differential equation, added to the product of
an arbitrary constant multiplied by a second function (V’,) that
satisfies the same differential equation after omitting the term 2.
For this latter function we find

2k/
tyme 2S :

Y 2 r

Since this expression becomes infinite when 7 is positive and r = o
therefore we must have C = o. On the other hand this constant
must be retained in the case of the cyclone where 7 has a negative
value whose absolute value however can not exceed 2k.

Hence our solution for V, is only attained through the integral
‘cf the complete differential equation for which the following expres-
sion is found

eae omens A He din 2 cL.
a7 Ble (sey
2

which does not allow of presentation in definitive terms for all

k
values of - A simplification is possible when — is a simple rational
r

fraction. I give the following result for the special case when

yr =k.
9 R
eee see ey

2r 2 r

x G + MOE log nat f 1 = cane’ : oe \ y
2 tk n+2 J
The last factor in this expression (and therefore also V, itself) is
negative and for r = o becomes infinitely small in such a way that
V, also itself becomes zero.
The preceding relatively simple result was attained without
special limitation as to the exponent in the law for the vertical

MOVEMENT OF AIR IN ANTICYCLONES—POCKELS 609

velocity, and no further difficulties arise in computing’ from it the
distribution of pressure in the inner region of the anticyclone
and in so determining the constants of our previous solution for
the exterior region whose form remains the same that V,,

, d
V, and p and now also 7? pass continuously over at the boundary

circle.

I will not now go more precisely into this computation but will
only communicate some results for the special case of nm = 2. In
this case the velocity of the descending air is

Since now we put y =k therefore, by retaining the values of k and
R adopted in the previous example we obtain for the center, r = 0,
a descending velocity twice as large as then; on the other hand the
total mass of the descending air for the whole interior region

f : R
remains the same and is proportional to f wrdr. We have also
0

2
V, = -Er(1 A)
2 Die
rae
Vim A (2h 1) {242 Re log nat (1 —
27 r? Pj ee

\
f
igg = -24/8) (142(2) tog nat (1 — }

Therefore in the interior region also the angle of deflection is no
longer constant: let the “‘normal”’ angle of deflection be

a =ig"h/k

then for our two special values of r we have
1
for r = 0 US retire

forr=R tg Jp = 0.7726 tga

whence by introducing the numerical values above given (i. e., A
= 0.00012 and k = 0.00008) we find the angles ¢, = 36° 32’ and ,
Yr = 49° 13’ respectively.

610 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51

The wind-velocity at the boundary of the interior region is

R

Vaal
- 4 cos 9

= 12.16 meter per second

which is rather larger than for the preceding solution as tabulated
above.

In case 7 = k and m = 2 the equation (Ia’) becomes
2 2
de 28 p(t 1) a Maratea
o dr t Pitas 2 fe

a 2 Jae 2 2
x[1+2 tg (1-75) |e+2 tog (1-5 7) |
r 2 R? 2. # 2 R?

and for r = R this gives the special value of the gradient at that
distance

per r11 kilometers or one degree of a great circle which now holds
good for both sides of the boundary circle. In the «terior region
the gradient now diminishes with distance from the center more
slowly than in the previous case when w is constant; therefore in
spite of the above given smaller value of G the total difference of
pressure between the center and the boundary circle still remains
about as large as before. In the exterior region the distribution
of pressure and wind remains very similar to that of the example
previously computed, it is indeed plausible that this depends prin-
cipally on the total intensities of the descending currents (which
are the same in our two examples) and only slightly on Sis horizontal
distribution of the descending velocities.

Perhaps it would be of interest to compare the solutions that
we have obtained in the manner above explained for cyclones
under various special assumptions as to y and n, with cases actually
observed, in order to ascertain what law as to the ascending cur-
rent best corresponds with the facts. In the case of anticyclones
thedata presented in thedaily synoptic weather chart is not so well
adapted to such a comparison with theory because the differences
of pressure and the wind force are generally too slight to be obtained
from them with sufficient accuracy.

A.
PAGE
AbbperCleveland: introductiomibyzs sia. e-) seve gh aceite aisle eve avelone ss skeeupleneye orstelenaie 1-3
Adiabatic changes of moist air, determination of (Neuhoff)................ 430-494
TAO MATIN P SMM ees Wee a senanctiocs, Qrebatads Baie eine rah ere ane aiote, saa ctr there ee catenin REG 479
Expansion Ol ASCENdiNg Alriat.. stoi ee «Ae dane os out, ved aseseuaks, Sie eter aeiomiee teens 462
{ISON SS 52, Piao ier in STIS TR SLSR CI LNA Gien NERSGE Peta ores Bona odin 469, 480-494
ANG@iabatsor moistair, ceneral equation for.......2..2.0.-.e8+ece dene. Gaertner 452
PSCUGO MOL MOIS Aliso 5.5 aw orsususlons crey-tolcie Svelersiorevoyatejcleiapeis aishl na: ec chee 454
Aeronautics, scientific results of balloon ascensions (von Bezold).......... 285-333
Air, see also atmosphere.

ASCENGING AGIA WALIC EXPANSION Olja. « s ciais_arevaveiis aie » cer ttotey stein a) 0 </erspa tones ee 462
SoMGin GVEELNIDING OF SLTALA ID... © 6's, 0. ocala avon 2s" aie «wis Slow. daaeala oe SE 549
currents, ascending and descending, condition of.....................00.. 166
change in temperature of (von Bezold) 6.6 a2 a6.c 2 is cress whe ees 334
Olaniatmosphene whitls asc .cs.- «cee seettm dead aous ott seneenr 158
Ppexminnent and. borizontal.... 26 vcs aitsoierek oth Uae s 139
PEEMAMENE VELUGAl - ssc x a loleten'e 4 dies wis ahs Wks ee woo) 6 neat 163
MORAT Van tet etvetei els) <iiel\ ch oie) aictta, sirels) ©) =) sjcin ev eh sles urie tate Peekete ststenotels Oeil e geetamee tele Igo
verincal horizontal Velocity Of <<. vcjn)2 beens 2.018 Lee olen ojala vale shore 170
expansion and contraction of (Guldberg and Mohn)...................-. 129
RAOISE. eta DAtIC CHANGES OL. e< 5 ad. 5.5 6 so tis hdd vie cade ah oloinlays ocgn et we AGO —AO#
ACTA MAE SROUS, Sete cia ae cis cere choos seal a astngiena Fale enw ovoys se oft edits ict} cho} ie eo 452, 454
movement of, in anticyclones, (Pockels). .. <2)... nee cst eee sce eee 596-610
movements of (Guldberg and: Mohn)... 0.0 2-:. 0.54. t6+ 06 cote 122-248
SAPURALECSO CLOW, ZELO! vavercrcce ncaus) vlcietnicte-s.efbct-}urt sis lace ales /retsveie <lorora ai recerton ners 137
RENEE ELOUNISONTE: GES Gin Gis sath week ee d's acter iraratve meet A Gee Om Bee eee eer 436
STN ESL EI Se Gres. ch ayer ara ii esto Sia, 6) siete) AM alae kin uct aia = fcal ots, Shot oat meen eee 449
Aitiudesmaxtni tm OL Initial sVeLOGIEY:- con iin acre oraieielerelelete acres « <1 ietee Pele iia ia 165
one thousand meters, wind velocity at (Gold)...................005 113-121
PETA PIT ORCI OCIGY EO Sie vis, 6)c\a.n'0 sve ice oars nates aiaperoiaNee®, screenees rene nie 87
PEM EMR IEe VATICS WIth (icine. yewie noe nies vee a siete = Glsimipine soe 96, 311, 432, 470
WATISEIQTUEELCSSULE WICH. os 5 soe co ais'e Oro w6 oo wie Claisinusselerey aie Cel steclo eae 127
Anticyclones, stationary, movement of air in (Pockels).............-..-00055 596-610
PREM CONIC WaHOS. SYS OF. 6 622.0% d bys ioe ace as octet wee eninin oo ele a pions eh ae dey 2
Meaueous vapor transtormed tO ice.) 6.65. koe oa os oldies wai elim ce ce wees 133
Ascensions, balloon, scientific data from (von Bezold)..................0+005- 326
PESMMEMOE GOO IBEZANG) 3 o)c% 0.x. uld » --acieraiens papers e's emiatnais mee e}eleeto aap 285-325

Atmosphere, see also air.
BACAR ES CONGIUON, OF 6.26.5. + eee ee ole bina win Siac Sal ee Oye mine ee © wieteiee hehe nace 31
BARU MOUNES Oli: cha.2 ai sas, + 5 on bib foie wm aio a Siele my araieh ston aye © et aan tee 43
Gaia OTIO) & aeka es Meee eRe eee Te eco sa SOR mada Soom e 506
Peres DER ah Sf he ered sie s n0.c 2 sides ee eins © eG eae Oe eee re 47, 125
imterenanee of ‘heat-in (von Bezold),,../....-0-2'<.@ vane wat om eee sete 376, 415

(611)

612 INDEX

Atmosphere—Continued

irant of (MGtBbRE) oe occ Soar nae Aico went tet poe eee eee 43-56
movements of (Guldgercaned Wotin).; it... oe cd as cote ee eee eee 122-248
steady circulation ti Gry. < Ssinc Me dog ps eee cs Hen ee 520
steady motions of (Guldbers and fol) yee ene ete ere eee eee 31-42
SYMMELHIC POMS OL. aA eA neo ye lone se kee Tee ete are 51
temperature of, causes or VArItiGm: 2) 15s S.c e one cee eee 126
thermodynanucs of (wor, Bezald). 05 s.o nck sos pa tee eee 249-284
Atmospheric. disturbances: (Gorodensky) i... 02 y),.0¢ ray ke ds esa eae eee 105
pressure, representation of distribution of(von Bezold) ............... 366-375
pressure, mechanical equivalent of (Margules)....................3.. 501-532
Winirl, WmitenloruOktic3. scthateee- oe Se etetas shales) Wo cer aes thee ae 158
Averages, climatolopicall (von Bezold));...... peek ae een ene eee 416-429
B.
PANOMMELTIC. TMARMMANIS Sie 2 Says sae: ont che tale tenses Rtroa Rhee aed ene are 156-162
POGUE cic-c-sic's ita ne He Genie Calis Sead hn Mae ER eee 152, 161, 162
Balloon ascensions, scientific results of (von Bezold)...................... 285-325
himidity. data. from. (von Bezald)s...;.<...cch vl say Ree ee 326-333
sounding ..... ‘Sis Weeacsti mee tek da teeta rig aA Oe rake Rc ee 2, 285, 326
Bauer, L. A., potential temperature and ‘entropy. .../5...5.0..).c6seo. 495-500
Berlin) pballoon:ascensions .(yomyBezold)i. «+... .<t.. sk new on Se ee ee 285
Besselion Jengthiot seconds pendulumy,.., 4244-2 er as ee eae 9
Bezold, Wm. von (See von Bezold).
meclow, f. H.,0n formation of cyclones. 0.7 6, sis sos. Pauls vo eR 541
Braschmann, N., influence of diurnal rotation on horizontal motions.......... 23-30
IGE
Clmatological'ayeraces (von Bezold)) gun -c.anbu sence oe sone ee eee 416-429
importance of “air currents’ (von ‘Bezold)m.™ 2242-2 os ee erie 280-289
Contractioniof air (Guldbere and) Mohn) Maen sae «cee one ie ees ae 124
Currents, air, ascending and descending (von Bezold)..................... 280, 334
POVIZON CANT AM cee cette Brae yale td SOMA Te Ree eee ee 148, 152, 156, 185, 188
HoOMZontal and mermanent. 5 --..5 ales cera ete eh Cae ete eae et eee eae 130
With, "CANCULAr, ISODAES » <2 cute nasaeseetnce.steeiono oe nae ene eee 152, 156
TEctilMear ISGWAES oaks eco oa. hh be Se eva niet ace PRC Lay ee ene 146
Paternal) ECE IMI ..5, srcachsns Soto A Rear b sotto voeh oc CEERI Sot ee Roper ee Aceaa 529
POLAR Y. 5 ivrctreyfawe, vrai ete, Sve = pa otis dc aacsetheFa,"e gicciPatnyale (Orek 8 ben ak Seaman tol hee eae I4I
WeLticalind. Neier Gacy atte izs ees mie ys ela Saket Ee een eee 243
Vertical and permanente. 5.5. or ag epee eee eae ee hae ree ete 163
(CyGlone@s: CAUSGIOE sro: 2 ss sce ance ies Foe ee ete os goa CC eee 541
distribution! of pressure Wn 4. wisn sere ee bom pee eee 507
TsObaws OL <5) Aeon Ses Becta ee Oe nus ole cede > ole a ae reg 221
ISOChETIMS OF. 6 ots Alas ox setae Dee Rae Rpm ee ee vc 225
PrOpasation LOL ver oa. Fetes ceases set es Gee ae ke ne ee 227
SVSCEIIIOL 5.0.5.5 -5.5:') 3 zcvevsnegerct Epa. ahdhorMate Qi nk se Cite «ORCS SERIE tenance Aces ea 199
theory ‘of (von Beézald)).. 3. isc fe eecn Me ae een ees eee te 344-365
VelocityiGls:... Kaveh oe ae auaslace Cae ele entre SSE ere 206, 217

yclouic. winds, system ‘Of... .. <0. .< 1. J+escekeiebac i eee ae ee 134

INDEX 613

Db;

Density diminution withvaltitudes ssa.) vate sete cities «sr oid Gs eee iene tena 81

Determination of adiabatic changes (Neuhoffy..........-..--- fe e- toe tone 430

Diurnal rotation, influence on atmospheric disturbances (Gorodensky)..... . 105-110
influence on horizontal Motions: (Brascimanm) |e... eye oe eee ers 23-30

E.

Earth, influence of diurnal rotation on atmospheric disturbances (Gorodensky) ro5—r110
influence of diurnal rotation on horizontal motions (Braschmann) ........ 23-30
interchange of heat with atmosphere (von Bezold) .................-..05 376
Lelaah overezT bid eee perciae ee aaa Ee cme Ie nCioe ty Old GDOIRO Giclgtuicay ad Cad. oat 3.6 Hidons,c 415

ET OVARECMA TIONS (Oli. cisco |, Mel ens arses eattomatenens ss the yoeks cesta Ly, SA4s, 540, 593
Kinetiewcomputatlomols sa. cetisiemnts Serres s een eaten Ge hier iL 561
LOSSMITRIMIO MIN SC air sata ope feat enact alates micieiaee a snes eye a caaeravake ehecental racreaes 501-529
cMmestorms, (MAreWIES)) face. ssa nte aes ose Sa ice ial ati toa an = 533-595
thermal stranstorma tions: Ofe.) 4+ yealacsse = BSE ears faa er ee on Se eter 3

Entropy and potential temperature (Bau@r).....7.................055- 495-500

Bran Adolphs steady, mouons Of atmosphere... 4... ese ele er 31-42
abstract ofpbraschmann! MeMOIl 4s acon] yee ection iar le ieee 23

BIS pivege Vine ON kaTINOVEMICMES - eeticitrac ccissis ces utero da day anes donee 18

Expansion andicontraction Of alta... .2-)/oee- 5 ss ee CRLa aN ail See See 129

F.

Ferrel, William, on motions of atmosphere..........5...00 60sec eset eee etees 23

ROE CO RG Ose. Opener ie eo Were yy ee a tl aatavely o trevnls alae rena long sean thonene eel yates) eee ees 3

Eorcestactine- unin exalt MO LON ccc: yee tes clei onls ceric wae sthersloie oe re eye 141

Formation of precipitation on mountain slopes (Pockels).............---++55 80-104
Giecumed erstorms (vor) BEZOld) ih cece evctycscra tals +e cue) vuretcie. ot, =screue clepeieli 249

BricuOnM Internals einealt CURTEMES! ac yal). eck esis eile ope ie ace eens 529

G.

Gold, E., wind velocity and surface pressure............--.-2.e eee eesee> 113-121

Gorodensky, M., diurnal rotation and atmospheric disturbances............ TO5—I12

RACEMIC AVEDEICAN 2 cur ewe HV Hgis Sinaide ciciosly Seis NL ies Ale eka alerts “cra aet ea 175

(Sahaticiesy patel greclopich aes esa eme sudo emonDeneEp boson bogda oon oct coraces 139
GIDE CELTS O fe acetone ceri nu te aot ore aeieaoh ta os akc hak es Bana ohn ok ee ceg ee MOI a oe 149

Guldberg, C. M., and H. Mohn, movements of atmosphere..............---- 122-248

18h

Hadley, Geo., cause of general trade winds ..............----eeeeeee eee eee 5-7

Heat, addition of, to vary pressure(Margules)............ 0.0.00 e eset ee eee 520
interchange of: (von Bezold)< oh . 2. feces eso wiales apie oie Sear 376-415
quantities lost by radiation... 2... .2 00d. eee cee be ees ee eee 385
quantities lost from outer atmosphere............-.-- 2200s seer eccrine 396
quantities received by insolation.............0--- essen eee cence eee ee 385
thermallexchange ta STOUNGE = laciscterneade sicl= <ahare crete oo Sele eyegsie ls sheet ayer 402

Height of atmosphere (Kerber)... 5... 00.0. etn eee eee ie ee ete cee ee teE 43-56
WALIALION (OF PLESSULE WATE: 6: oc ees ie me tens apa oie! +) ala at ntale ot donate wae alee 125

temperature With). se. 6 oc eke sey. eee eee se 96, 3EL, 439255470

614 INDEX

Humidity data from balloon ascensions (von Bezold) ................... 326-333
FMUIMMIGAM ES ICAUSE OLA A eie:5.c.c08 sec aig me eine foie Menge Ca CE Ree 21
it:

Ice, aqueous vapor turned to (Guldberg and Mohn)...................000005- 133
Insolition and sada hon, VATietlOUs Wolscie + e/shai tears eaters ale cient emiees 399, 427
Interchange of heat between earth and atmosphere (von Bezold)........... 376-415
Derrerngl action in. AIG COPECTIES | oa rern p Giarie es hin ha aie es mid Ripa ode emaegaianai 185
Ba REO SUEEACES Ey Ui Ses untae tarnhe tins son a Cainer pas Riayen acho toe oer aire akan 175
Wsabars. and: coradion tet. cc: 0.4 syne deena ans cue, che tate sue cai eee cae on eee 139

CIE CULAT Py OR eee nyse tttcaie ha fos eahaeene he rene NA on area oA oT ne 152,156
RONCeM Ute KARCUIAT Sons 0.5 x eatiicrics wy > sm 0d5-k Fe ee oleh eae eee 596
distribution Of pressure iDYyis. vtec shes ce eat ee ee te ae OR eee 366
Ofta vatiablecy clone. so. ket seco paleo tae ete Sees, eRe Ue een 221
MECUUMMCAT SAS iatre ste eescae ok aera siecthanere ears nae LNT eh OEE ee eae 146,148
WSOMIESLIGISUIELACES icy eerie. chs, Cletaua ere Sais eave cto akere tees et ouch tee EER et ae ana ene 175
Hsothermsvolowindksy Stems... s.yeaec eric: cogent oe rane ental ae i eae 225
K.
Kerber, A, limit of the atmosphere i <.555%.0+,c15-< 2s seis + ae he oe ee 43-56
L.
Latitude, climatological averages for complete circles of ................... 416, 429
infiuence onvhomzontal currents ..../.1. nv: series siete eterers ee terre te eee 148
Dimit of atmosphere (Rerber) 0052.5 \o.aon a0 wo ae Boe cole ares epee 43-56
M.
Margules, Max, mechanical equivalent of pressure................e.0eee0e 501-532
oni the enereysohstorms’ 2c. aw sas cine ance otters ee one suena reyes eae atte 533-595
Mechanical equivalent of atmospheric pressure (Margules)................ 501-532
Meteorological elements, mean vertical distribution of.....................45. 308
significance of moving partticlés (Sprung reir. ve eos hoch oe eee ae a
Mohn, H., and C. M. Guldberg, movements of the atmosphere............. 122-248
Moist-aw adiabaticehangesvat ((Neuboth) cass. ieee a icine Memeerteetieere es 430-404
Moisture “variation with albitudescncd. cies. oe eee etree mie renee 288, 318, 323, 326
Motion, equationsior atmospherics Jou. . os cence coe nnee Teh ee ee een eee 178
horizontal, influence of. diurnal rotationon.....2e =. 0s ses hee eee ee eines 23
horizontal rectilineariand uniform: ..s.0.ss0 eee ee eee nee en eee 142
Of atmosphere generale. 60.5: asc Aveta sare tears ols Seo eee See ee D7
of projectiles and earth’s rotation (Poisson),............2.0sccceeesseees 8-15
of the atmosphere (Erman) .....:2% «-...a8%,0. 2 eee So eee eee 31
relative; due to-inertia. 2s. 4.c.. sic 0 shinee once, ees ea kee 65
Mountain slopes, formation of precipitation on (Pockels).................045 80-104
Movement ‘of air in.stationary anticyclones 0! uciwiid ines an Sete eee 596-610
OL SwiNd SYStEMS sos. <:c.is%-o.aye- 0 w/a mie aoe eioonis oe ere era er 234
Movements of the atmosphere (Guldberg and Mohn)...................... 122-248
CAUSES Oli). 5 i5s0 cis. § chore bisa « eete a eiale outer abel. oe Gv HORROR TCI ae 137,
Moving particles, paths:of (Sprung)... <5 cos. ..c nd saan ee ae ee 57-79

significance Inimeteorolopy a. <2. <1). am 2 aot tans ene ete ee 57

INDEX 615

N.
Neuhotiz'@tto, adiabatic changes of moist air -....5...-+.0.+--+ secu eae 430-494
O.
Optics: optical:syssem: of atmosplere....4..2..c00ccseee ieee ncese se -dmean Dhetostels 46
124.
Paths of moving particles (Sprung) ........... aise sod atles aaneyy aha lavesaretaneMersroreers 57-79
Pendiulimemo tions, air, resistance tOnm acces sieicie cioteicie nell tiersicialoleciecisieie clare 9
Pockels F., formation of precipitation on mountain slopes ................-. 80-104
movement of air in stationary anticyclones.........6.:2+.00c0ce+ Hs asian 596-610
Poisson. Ss. motion: of projectilesiin the aim. ...a2% = © wedieiee oelleiaaeeee 8-15
Polar limits ofutrade winds; pressure'atas....0. «sos oe ciisine serneare oe cies 31
Poles North direction ofjain currentsiatee-..> ames se)sicl ciacieye aie aers roe eer ciate 67
Potegjial temperature and entropy (Bauer). ..25....2. 06 .+ + oe oe core ectenic 495-500
Precipitation on montamyslopes) (be OckKels))s ve a qe cite ire cierisielacieis orernenare 80-104
Pressures atpolanlimits oftrade winds) 4.2.15. se erie «ici see Welticiso steerer 33
Gitterenceotmaimtenance by, heat. 2.2... eset ose nie crerere e steavetcetclete icine nae 520
GIS EET ENGLO MO Lice teserystaiecc rosteevet 5st eal ovals uate cls eiecote-e: trast ease lew ohare ate Re 366, 502
TNE 2, 3.0 4: bh BENE AUIS In ee eRe IC a en an ees AEE nat cio. tc 125
mechanicalsequivalent ot (Miargules)ja.uc.eosciees oetercs seit een ere 501-532
PEL AMELOMELOMWOL KG a sars's wi eiaeote siete foto a1 ap8 w srnlgiave e Guaveyb)n Oa. e ereetnaee a eRe 514
Sunfacerdistrbucion iol (Gold)... deen oes cee ome << iatioees Co eee II3-I21
VATTA CIO Me Wal tlIe EAE It sc: «ic ciefevs crocs lorclin,s © wusbe apeievave e oncrone cob evo cis atte aeereheeea a 125
VIL CUAIteMpPerature: an Gees ceils cis lorcie.cicese © = weiss als sia ehantielohe ts © evehels loins fevers 123
Projectilesamotion Ola(POissOm) ens coins wie, s vee. « 3. tuele «iste eis oi he Safer se hehe teres 8-15
IPseudo-adiabats Ol mOISty ait <...00): eine assess eieace eo aile a tieeuss sists Sugeenernemee ot 454
R.
ead MaOn ANG WHSOlatlOnNs VALLA tLlOMS) IM. sjetetyeciteie sree) ori fava el tens era) oreleue eee rae 309
hain: formation on mountain slopes (Pockels)) i... 66.0.2. ccs oc nel ewe nnns 80-104
Rags enmity poimvt ol, (RETDEr)): «coco cic teas ae eths oa single scam o.0\6 aia teneaegets 51
Resistance of aim influence Of On projectiles\ ccc aee oe. seesics ence os selec 8
ipatauvedecion Os SCOlMS CLLACY) wi... p< bce sd Pawels tes cisiedele pieitle Seale aE SR 16-22
Rotation ofearth> diurnal, imfuence Of .. 1... +» iss + iclele s+ cle tone 23-30, IO5-II0
influence on atmospheric disturbances (Braschmann)......,.....-...++-+++ 23
InsueNneean PEOjectiies (POISSON) ..<.<,:vcieie bs:s\eloie's/ wins « wisyata dae Mem eal eral 8
INMMUEHCETONEYehtI Gal CUITENTS sacs ryeic) «1-1 iste el oie loses «clan felerelersie lolelnelNexate terete 243
S
SOUT LTe A UAE FOUN UGNG EURIG 13). aon pois wis, oles s/mvepanelieno. ave. oles a /asuee Sih al tlare Ratatat ela tee 436
Snowsrormation On MOUNtaIn SlOMESss 2 0c lereier« «gets ei ore ele hei eneje etd eet eterer =e 80-104
SOUMCin ge alloousweemetatiere sieyae cies patna a eend eels ole eieheha estan eehar=iteeenels 2, 285, 326
Sprimes Aj, paths:of moving patticles...... 0.0. .000 6 oUt a de ee owelee em seen 57-79
Steady motions of earth’s atmosphere (Erman)..............00cseeceeeeeeees 31-42
EGertP CHETISY Ol CMATOULES) | oc. 0. < otia« sist oce So cvele Adal ble bier Mus tata 'ete te Stele esaliaba 533-595
ESTER Eo ie dion ccos aerate wince ales sense ePtia a: Glare syupenth Dene UALR a's AA SNe nee oe 541
PARMAR ELTON OL CLTACY aie os care 5 + 0 «(devs es spies ste me sie ete ITE Re ae 16-22

(Wiiiaa ae, Seine NS ONO wee BO Me Oem M OOOO MODS SUDOtOe ic. dom odes cacti: 249, 262

616 INDEX

Subcooling and supersaturation (von Bezold)...........0...0ccceeeeceeeeees 249
Suupaenon Of, CAUSE Gl tiade WINGS) «ii cos asses nnn elas sve yeade seamen iE 5
Sumface1sObaviC re. aeteeicine eiatehe bcd adapes etn eee ape ish gO ee toe arlene oo Tepe ete r75
Ob earth, INHUEHCE ON WINES i, 0.006. s4 gaiew woke es aica.t2 colo cease elem 232
interchanre ob heat ataadscsis-c test urine 96 serene | ha eee 376
ea eye UME ES 255th tatnte eh otk salve! Whe swine cree fv aren tac oe ore 366
feces yew cic) e |) 61 1 eee RA ARR Re ey TEAS ricen rats see 113-121
TOLACING OLEATE. <jos5/.tc gestae rerevere See as ietele rm. TMeie Goa atolc foteu shave elancrensta/ne ene fF
Siriace tecistance (Margules) oo. 5.6 nck clninn acer Shairbtte Po ee 3 Oe Bia eee 531
¥:
Temperature, changes in ascending and descending currents (von Bezold)... .334-343
Giculation of air of, unequale <0). jen. ac wnrincr Ps ay Aa ce emer 501
ob PRREAIOS PNR ai. 5 on a wie Seco, nieersrniaioisie wre sae hg Pe mip cichs tea ea Pree 126
PEO PRR os we aco Sw cca -vom wi Wy & Soe tN OR ag Ce RET te 415
LNA rs ool aecin oi 00 has ev mop 8 oadomynh pc Mea ay AE a 405, 554
Warlesnwith) lAtuMEsicc cia melee, o.< eyecare er stanvainie oaeakateees 96, 311, 432, 470
VEGEICAN IStiD UETO IN Ole <raisrarats is nce Slaves tiene’ Meet Case Cee byaerers erin ee 288, 323, 326
RODE ERT sch aes Hess sy ce Spey eI age dn Jetevcand vata aud ata 7ay Sleuststeieha ae)is dale ence eee 123
Thermodynamics of atmosphere (von Bezold)..............0.eeeeeeeeeeeee 249-284
PRbwMGETSLOLINS , LOLIMALION, GLH... i: <)cyay re 1cvaretate talers mratereravsl abel shateve ora oie betray eee 249, 262
Heat and Cy Clone 3). ahis.ciaszite ses ese olapararele Sata layne alate ele meacken mere ree eee 262
"Fomedees and typhoons, rotary character of. .).1i.:0 sis oi ofS abun bikie ote the alata 19
Rieey, Charles, ratary action of Sams. 1005660. ina taig 2 ancie eeiennea eee ee 16-22
rade swans; Cavise Of (HAGE) \<a:i-c-are aie serevotere.ai clare olore one erhener er tere tr rekars any 5-7
:
Upper atmosphere, balloon observations Iie: cscs ie as siete» dee malin 285-333
¥:
Wapnr aqueous f 22 79505. 2r ees FUE ee cba are een ars Rae ee er 133
OLCWALEES Ys ate ee T sces kore Sameera Be le age oc hous Itoh a ahaa tater oteN sh ate epee 130-134
Welacity- initial andraltitwde: | aces rf hese b-cyofelents tara eeepc ener verh 165
GAR ees, ch Ee EE hh Ged Cee he arden ee eg ee 217
Cig palhl hy cha\ol: pee eee tar Hen hae MU eerie ia.a GSC tye Bacar OO tae xe 154-156
GE winds (Gold) se vos eee Nae where te is tee Oe I ER peeve eter I13-121
Vertical currents, influence of rotation of earth on..................2-----ee- 243
PERMA EN 0h a,c cle es crn) wie aie bs Gan obese avengre ts Sacvetetoatied scercel oh cHopel oy ional anaars Mereeeaays 163
Vertical distribution of meteorological elements..............202.000+-++--0 308
Westrcal motion; deviation from: ss: «2.42 ss004s yadda sree ees eerie II
you Bezold; Wilhelm, climatological averages... 5.8010 oe od eet er 416-429
distributionsof atmospheric pressure.% . 37 «ales ieee eee 366-375
interchange of heat between earth and atmosphere.................... 370-415
reduction of humidity data from balloon ascensions.................... 326-323
scientincresults of balloon ascensions. 4.): «62°. 5": «<< </telersteelelerse) ste betel 285-325
temperature of ascending and descending currents ................... 334-343
theory et cyclones. 27 oi Fe. 6 Sos vs Sosa ee eee eee ee 344-365

thermodynamics of the atmospheres: . aj sees eer eee 249-284

INDEX 617

W.
Wihinishinetheatmosphere! (Margules). 4...) ssc) sce sin she a eee ei 5090-514
Whirkwand, about a barometric minimum +. o... 00... 006s oc. cctet see tanan 157, 161
barometricanaximumj4s- eee een eee eee 158, 162
cause of..... PR 20
LO PLESSLY CPINO CIO Of. .'y ctor eee crete auoe eiosele Rie arash ciel SAO a She eee 112
VELOCE MOL sey sa there n! wet Xeis ARO OREO tee SOT Rene I Nee ier ae ee EEE 154-162
WiiridmimenSURGIOENts, s nconicteeke ssi eatsrons acti ee Che eee eae 104
WAGs SUEMIS ps cs, cee ard ays aves tito etme deine! ethete Sues Sh cis ewes 181, 192, 212, 232
Windswascendino: parallel! system of ss. a. cs =o le eicie cata wie Sle ieecioaie 182, 198
Maen ce OL CAtth’s SUTLACE ONL. .5. sein denict-ss vin Saetne gen oie eed ae 232
Gceankanduland:systems| Of LA sec syste crievo mies ottate Aimer eerie eee ieee 212
Mele OMSLO AM PECSSULEC',. sire istetye acess sie Ueele a.gucie OO lc era tye CimeronsPaees, she rsane terranes 58
Mela One lon VeLtl Cal Currents) ..y.)ayts sere eemeies avon ects ye aye On eee 122

trademeusesiol.(FHadley )i.,..2% oa saere c.cisit Gost levels oOo rises ced nc cet ete 5

} a ar ony

Ma noes _ 2 ae
i ‘ emery ¢ rm
My elhpar ih a ; aha
Riese 7 i ’

i ay J
..

ay

vy

A if) iL

4
i]

Drs

3 9088 01421 4423