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* i *

THE NORWEGIAN

NORTH POLAR EXPEDITION 1893-1896

SCIENTIFIC RESULTS

VOLUME V.

THE NORWEGIAN

NORTH

4

/If

S&.

POLAR EXPEDITION

1893—1896

SCIENTIFIC EESULTS

EDITED BY

FRIDTJOF NANSEN

VOLUME V

PUBLISHED BY THE FRIDTJOF NANSEN FUND
FOR THE ADVANCEMENT OF SCIENCE

LONDON,

CHRISTIANIA

NEW YORK, BOMBAY

LEIPZIG

JACOB DYBWAD

LONGMANS, GREEN, AND CO-
1906

F. A. BROCKHAUS

PRINTED BY A. W. BR0GGER. CHRISTIANIA 1906.

CONTENTS OF VOL. V.

XIV. O. B. BeGGiLD. On the Bottom Deposits of the North Polar Sea.
Pp. 1—52, with 3 Plates.

Appendix I. 0. N. Heidenreich and Charles J. J. Fox : Analyses
of the Bottom Deposits. Pp. 53 — 57.
Do. II. Hans Kler: Thalamophora of the Bottom Deposits
and the Mud from the Ice Surface. Pp. 58—62.
(Printed June 1904).

XV. V. Walfrid Ekman: On Dead- Water: Being a description of the so-
called phenomenon often hindering the headway and navigation of
ships in Norwegian Fjords and elsewhere, and an experimental investi-
gation of its causes etc. With a preface by Professor Vilhelm
Bjerknes. Pp. 1—152, with 17 Plates.
(Printed June 1904).

XVI. Fridtjof Nansen: Protozoa on the Ice-Floes of the North Polar Sea.
Pp. 1—22, with 8 Plates.
(Printed March 1906).

o t I 5 3

XIV.

ON THE BOTTOM DEPOSITS OF THE NORTH POLAR SEA

BY

0. B. BGGGILD.

WITH

APPENDIX I:
ANALYSES OF THE BOTTOM DEPOSITS

By 0. Heidenreich and Charles J. J. Fox.

APPENDIX II:

THALAMOPHORA OF THE BOTTOM DEPOSITS AND THE MUD
FROM THE ICE SURFACE

By Hans Ki^er.

H.

INTRODUCTION.

aving been entrusted with the mechanical and mineralogical examina-
tion of the bottom-samples of the Fram Expedition, I now publish the results
of this examination, in the hope that a tolerably clear idea will thereby be
obtained of the lithology of the bottom of the North Polar Sea, a sea which,
on account both of its geographical situation, and of most of the factors that
have to do with sedimentation, occupies a most exceptional position as com-
pared with all other seas.

Among the innumerable important scientific results obtained by the Fram
Expedition the proving of the existence of a large, deep, North Polar Basin
is by no means the least. Formerly, we generally believed that the North
Pole was surrounded by great tracts of land, and that the sea to the north
of the Old World was of comparatively small extent, and particularly, of in-
considerable depth compared with the large oceans of the world.

It was formerly, hardly possible to form a clear conception of the appea-
rance of the bottom-deposit of this ocean bed, but it was scarcely expected
that it would be of so consistently fine a character as these bottom samples
would seem to indicate. As long as nothing very definite was known about
the remarkable drift which nearly always prevails in the Polar Sea, it was
conceivable that a portion of the region at least, might be covered with ice-
bergs ; and even though it be conceded that their power of transporting gravel
and stone is of a very disputable character, yet it is certain that with the
lapse of long periods the bottom would obtain some coarse material from

this source.

l

4 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. POL. EXP.

As the Fram Expedition has made clear that there is nearly always
a drift over the Polar Sea from the Bering Strait to the Sea between Green-
land and Spilzhergen, and that there is no land anywhere in the neighbour-
hood of the Frams's drift, from which icebergs could originate, it is now to be
regarded as absolutely impossible that this sea bottom could be sprinkled
with coarse material in that way.

All the ice found must therefore consist of sea ice — which cannot possibly
contain any earthy matter — or to a much smaller extent, of coast or river-
ice from Siberia and N. America. At these places the bottom as far as is
known, chiefly consists of fine loose material such as sand and clay, and the
conveyance of stony material from these districts must therefore also be
extremely small.

Furthermore, other sources from which Ihe sea bottom very largely
derives coarse material such as the presence of solid rocks or moraines,
are in these regions entirely missing, and the combined result of all these
factors is therefore the quite surprising one that there has not been found
a single stone in any one of the samples brought home by the expedition;
the size of the largest particle observed, being little more than 2 nini. Most
of the samples, as I shall subsequently relate at greater length, are even
without any component larger than Va mm. Whenever we have any know-
ledge of the bottom-deposits in other arctic regions, we find that they, com-
pared with deposits from other parts of the Ocean, generally contain a greater
abundance of stones, including every possible transition from boulder clay
sediments — more especially in the region of the great sea-currents car-
rying ice-bergs — down to the finer sorts of clay that are found farther out
at the bounderies of the temperate seas, where ice-bergs play a less important
part. Now as this last condition was everywhere paramount in the field of
the Fram Expedition's researches, it has occasioned the above-mentioned
remarkable fineness of the particles in the samples, so that, mechanically
considered, these samples correspond almost exactly with those from warmer
seas.

On the other hand, there is another characteristic which the deposits
under discussion have in common with other true arctic deposits, namely,
the small amount of organic particles they contain. In other arctic regions
this may be ascribed to two altogether different reasons; on the one hand

NO. 14.] INTRODUCTION.

to the great quantity of deposit continually being formed, and on the other
hand to the small number of organisms that can exist at the surface of a
sea completely covered with ice for the greater part of the year, and which
only for a short time in the summer presents a small, open area in which
the microscopic organisms, as far as we can judge, are even then not found
in nearly such large numbers as in the warmer seas. In the Fram Expedition
deposits, only the latter of these two circumstances is of any importance,
and yet the result is almost the same. The deposits before us contain ex-
ceedingly few remains of organic origin; even in the deepest places, farthest
from land, their total amount scarcely ever exceeds 5% of the total deposit,
and in most places it is very considerably less.

Yet a third, very striking peculiarity of these deposits is the great uni-
formity of their mineralogical composition. So far as can be judged from
the bottom-samples, they originate exclusively from quartziferous locks, either
from granites, gneisses, and other similar rocks, or from the sediments ori-
ginating from them, such as sand and clay. There is here a complete ab-
sence of any volcanic region, such as for instance, in the North Atlantic,
contributes such great mineralogical variety to the bottom-samples; and older
basic rocks, such as gabbros, diorites. etc., seem, at any rate, to occupy a
very subordinate place. The consequence of this again, is, that in the whole
of the region here treated, it is extremely difficult, not to say impossible, to
make out the distribution in detail, a circumstance which, more than any
other, has produced the difficulty experienced in examining these deposits.

It will be apparent from the foregoing remarks that several important
circumstances conspire to give a particularly uniform character to the
bottom-samples of the Fram Expedition. Since there are neither stony
ingredients, as is mostly the case elsewhere in the polar regions, nor great
quantities of organisms such as are found in the temperate and warm seas,
nor yet any great variation in the mineralogical composition, it might easily
be imagined that there can only be comparatively slight differences between
the various samples. A closer examination will show, however, that a number
of properties can nevertheless be brought to light, which sufficiently charac-
terise the various localities in their relation to one another. It is here my
intention in the first place to give as complete a description as I possibly can

6 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

of these deposits, which, as already stated, occupy a peculiar position among
the various marine bottom-deposits.

Among the works that I have employed in the preparation of the present
treatise, I will here confine myself to a mention of the following : Report of
the Challenger Expedition on Deep-Sea Deposits, by F. Renard and Sir John
Murray, Report of the Norwegian North Atlantic Expedition, Part IX,
Chemistry, by Ludvig Schmelck, and Report of the Danish Ingolf Expedi-
tion on the Deposits of the Sea-Bottom, by 0. B. Boggild and of the Danish
Expedition to East- Greenland 1900 by the same author (Meddelelser om
Gronland. Vol. 28).

All local information concerning the hydrography of the regions here con-
cerned, is to be found in the very detailed treatise of Nansen: The Oceano-
graphy of the North Polar Basin; Vol. Ill, No. 9 of this work.

NO. U.] MECHANICAL COMPOSITION OF THE SAMPLES.

II.
MECHANICAL COMPOSITION OF THE SAMPLES.

The material submitted to me for examination consists of samples from
16 different localities, most of which are situated along the north coast of
Siberia, while the remainder of the samples have been taken from the bottom
of the deep North Polar Basin, more or less distant from land. From some
of the first-named localities, there are two or more samples, taken at different
hours on the same day, and they frequently present very great differences,
and give a very characteristic illustration of the rapidity with which the
nature of the bottom may change in the neighbourhood of land, even in ad-
jacent spots, according as the depth becomes greater or less. The distribution
of the samples may be seen from the accompanying chart, Table I, in which
the stations are numbered in chronological order, and to which constant
reference is made in these pages. The samples will be designated by their
numbers, and the addition of letters will indicate the various samples from
the same locality.

The samples were preserved either in alcohol, or in a dry condition.
We do not know at present whether this difference has any influence upon
the washing-results. It is possible that by being dried and kept for some
time, the clay may become rather more coherent than it originally was, so
that a wrong idea of the mechanical nature of the samples may be obtained.
As far as I am aware, nothing has yet been proved with regard to this circum-
stance; but when we consider how easily dried samples such as these, become
soft in water, it would seem as if the degree of coherency attained by the
clay in drying, can be only very small. Upon the whole, the mechanical

0. B. B0GGILD. BOTTOM DEPOSITS.

[nORW. POL. EXP.

No. of
Sample

Date

Lat.

E. Long.

Depth
in

Metres

Designation

1

1893. July 24, 10 p. m.

71° 17'

48°

22'

130

Shallow water deposit

2

- Aug. 17, 12 p. m.

75 10

80

31

46

-

3

- 18, 9 a. m.

74 38

80

15

26

- -

4

— — - , 12 noon

& 2 p. m.

74 29

80

32

40

-

5

— — - , 10 p. m.

73 51

80

44

39

- -

6

West of the Kjellman Is.

?

?

7

Near Taimur Sound

?

?

8

1893. Sept. 13, 12 noon

74 55

116

40

20

Shallow- water deposit

9

- - -,8,30 p.m.

74 37

114

44

40

- -

10 a

- Oct. 4

78 42

135

40

1460

Grey deep-sea clay

10 b

- - -

-

-

- - -

10 c

_ _

-

-

— — —

11

- 21

78 19

135

45

135

Shallow-water deposit

12

- 26

78 31

136

10

100

— —

13a

— May 1

80 46

131

18

3800

Grey deep-sea clay

13b

- - "

-

-

14

— Aug. 6

81 8

127

32

3850

Grey deep-sea clay

15

1895. Jan. 23

as 24

102

14

3450

_ _ _

16

- July 23

84 32

72

20

3700

— — —

consistency of the clay is one of the most complicated questions met with in a
mechanical examination of the deposits; but as it is of the highest importance,
and very greatly influences the results obtained, it will be necessary subse-
quently to enter into the question more fully.

The accompanying table gives the geographical situation of the several
stations, and the designation, general consistency, and colour of the samples.

As was already pointed out in the introduction, and as will also appear
from this table, the bottom-samples in most respects are remarkable for their
very slight variation. They can only be referred to two of the ordinary classes
of marine bottom-deposits, namely, (1) the Shallow-Water Deposits, and (2) the
Grey Deep-Sea Clay; and these two classes do not differ from one another
in any one decided character. The boundary is here placed, as usual, at
200 m.; and here, as elsewhere, it is apparent that on the whole this division
is fully justified. Where the depth is less than 200 m., the deposits consist

NO. 14.]

MECHANICAL COMPOSITION OF SAMPLES.

No. of
Sample

Colour
when dry

Consistency

Degree of
Coherence

Bemarks

1

Brownish grey

Very clayed sand

Slight

2

Brownish grey

Fine, slightly sandy clay

Great

3

Brownish grey

Clayey sand

None

4

Brownish grey

_ _

—

5

Brownish grey

Slightly sandy clay

Great

6

Brownish grey

Coarse sandy clay

Considerable

7

Brownish grey

Very sandy clay

Bather slight

8

Grey

Sandy clay

Great

9

Grey

Very clayey sand

Very slight

10 a

Brownish grey

Sandy clay

Great |

Taken at one time; 7a formed

10 b
10 c

Brownish grey
Greyish brown

— —

: 1

I the uppermost, 7 b the middle,
and 7 c the nethermost layer.

11

Brownish grey

Slightly clayey sand

None

12
13 a

13 b

14
15
16

Greyish brown
Brownish

Sandy clay

Fine, slightly sandy clay

Clay

Fine, slightly sandy clay

Slight
Great

Very great

1 Taken at one time; 10b formed
I the uppermost layer of the
sample. Very little of the
\ deposit obtained.

Light brown

Very fine clay

-

Very little of the deposit ob-
tained.

as a rule of gravel or sand; and only where special conditions exist, such as
the presence of more enclosed sea-basins, or where the coast consists mainly
of argillaceous rocks, or in places where the rivers carry great quantities of
clay, are they for the most part clayey, and therefore in no way different
from the grey deep-sea clay.

The above-mentioned clay does not differ essentially, in the region under
discussion, from the grey deep-sea clay found in other parts of the world.
It is always of a rather fine, clayey consistency, and becomes finer and finer
with increasing distance from the coast, and with greater depths, although it
never becomes so pure in this region that it is not possible to distinctly feel
the sandy particles in it, when rubbed between the fingers. Its colour, as a rule,
is a tolerably pure grey near the coast, while farther out in deep water it
acquires an increasingly brown tone, and in the deepest places is almost pure
brown. Taken separately, however, some exceptions are apparent, of which

10 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. Exp.

No. 10 must be specially noticed, its peculiarity being that it consists of several
layers, of which the uppermost is of a greyish colour, while the lowest is a
fairly decided brown. As the ocean-bed seems very generally to consist of
several layers of different colours, it will be necessary to investigate this some-
what more fully, although the facts obtainable are not sufficiently numerous
to permit of a clear understanding on this point.

The colour of each species of clay depends, as a rule, exclusively upon
the colour of the clayey matter itself. By washing, it will generally be
apparent that the finest substances composing the deposit have almost exactly
the same shade of colour as the entire sediment, while the sandy components
may have any other colour answering to their mineralogical composition,
although, the sandgrains are often provided with a very thin outer coating,
which makes their colour somewhat resemble that of the clay. This circum-
stance is of course particularly marked when the sand is made up mainly of
colourless minerals, especially quartz. If, for instance, we take a brown clay,
we shall see that the sand that is washed out of it, possesses a faint light-
brown colour, while this colour is altogether wanting in the sand that may
be washed out of the grey clay. It is easy to convince ourselves by chemical
means that this colour is due to hydrated peroxide of iron, which is deposited
in the form of a very thin coating round each separate grain of sand. It is
the same with the clay itself. Upon treating it with hydrochloric acid, the
brown colour completely disappears, and is replaced by the usual grey. Thus
here, too, this colour is produced by the precipitation of hydrated peroxide of
iron on the separate clay-particles. Schmelck has shown that the brown clay
in the bottom-samples is, on the whole, considerably richer in peroxide than
is the grey clay, for he has found that the proportion between peroxide and
protoxide varies as a rule between 1 and 2 in the grey clay, while in the
brown it is generally between 3 and 4.

We may suppose this change in the proportion between the oxides of
iron to have occurred in two different ways. Either the transformation has
taken place in the clay itself by the aid of the oxygen in the sea-water, or
the water has deposited hydrated peroxide upon the clay by the aid of the
iron compounds dissolved in the water itself. In the first case the chemical
analysis should show that the total quantity of iron remained unchanged after

NO. u.J MECHANICAL COMPOSITION OF SAMPLES. 11

the transformation ; in the second case, the amount of protoxide of iron should
be unaltered, while the peroxide should have increased. On looking at the
numerous iron analyses made by Schmelck, the first proves to be the case;
the average amount of iron is about the same in the brown and the grey
clays, when the percentage is calculated on what is left after the carbonate
of lime has been removed.

There is, however, much to indicate that sea-water can deposit oxide of
iron upon the bottom. As I have mentioned in the report on the Ingolf
Expedition, it is a phenomenon of very general occurrence, that the upper
surface of stones lying upon the sea-bottom becomes covered with a brownish
coating of oxides of iron and manganese, while this is not the case, or only
very slightly so, with the under surface. When the stone is of such a species
of rock as, for instance, quartzite, which does not contain the smallest quantity
of iron, this coating must necessarily be deposited by the sea-water itself.
It is difficult, however, to imagine that a deposition such as this can take
place upon the stones, without also at the same time taking place upon the
sediment between them ; and there thus appears to be good reason to assume
that this fact also plays a part in the production of the brown colour of the
clay, although it is perhaps not of quite so much importance as the chemical
transformation of the constituents of the clay.

In any case, it seems necessary to assume that the transformation of
the grey clay to brown can only take place in the very uppermost, exceedingly
thin layer, that is in immediate contact with the sea-water; for otherwise all
the mud upon the bottom could not but acquire the same brown colour, as
it is not possible to imagine the existence of differences in the sea-water itself,
that can cause the mud to be oxidised in one place, and not in another. The
only possible explanation appears to be that the grey clay is deposited so
much more rapidly than the brown, that the uppermost layer has not time
to be changed before it is covered with new sediment. We cannot, of course,
draw any positive conclusion from this, regarding the rapidity with which the
sediment is deposited, as long as we are althogether ignorant as to the length
of time required for the transformation; but on the other hand, this circumstance
is very important in estimating the relative rapidity with which the various
sea-bottom deposits are formed. Thus, where the conditions in the main are
uniform, and where there is no great variation in the composition of the

12 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

sediments that are carried out into the sea, we may assume that the rapidity
with which the deposition takes place is about proportional to the amount of
brown in the colour of the sample. It is not impossible, however, that several
different factors, such as temperature, currents, etc., may modify the condi-
tions to some extent. The amount of lime it contains does not seem to
influence the colour of the clay in any way, except in giving it a lighter shade.

With regard to the circumstance that in one part of the sea-bottom,
deposits may be found in which the upper and lower layers are of different
colours, it seems most natural to assume that it is due to changing rates of
sedimentation. It is also possible to imagine other reasons; for it appears
that on shaking a sample into a little water, the heavier parts are precipitated
first as a grey layer, and then above this the lighter, considerably browner
parts. We should imagine that this separation takes place when the sample
is taken, were not the apparatus constructed in such a manner as to make
this impossible; the bottom-deposits may possibly have been previously set
in motion by some large animal or other. The results of this would be that
the uppermost brown layer will be of a very fine, clayey consistency, while
the lower will be sandy clay. This is the case with several of the deposits
from the Indian Archipelago ' ; first there is a layer of brown clay of a pasty
consistency, wich attains a thickness of up to 15 cm., and below this there
is grey, green, or blue clay. This circumstance has not yet been very closely
investigated, however, and may possibly be due to other causes.

In the North Atlantic nearest the coasts of Norway, there is according
to Schmelck, grey clay, and beyond this brown clay. The latter, nearest to
the grey clay's territory, forms as a rule only a thin layer above it, getting
thinner with a nearer approach to land. Here the brown clay is expressly
designated as sandy clay, and cannot be separated by movement in the clay.
The probability thus is, that formerly, at the time when the grey clay was
deposited in these localities, there has been considerably greater sedimentation.
It has not been decided whether this can be traced back to the Glacial Period,
or only to the last, more humid period. The latter is the more probable, as
it is scarcely possible to imagine that the deposition takes place so slowly
that only a very thin layer of clay has been formed since the Ice Age in a

1 "Die niederliindische 'Siboga' Expedition, von Prof. Max Weber". Peterm. Mitt. 1900.
Heft VIII.

NO. U.] MECHANICAL COMPOSITION OF SAMPLES. 13

region where a comparatively large quantity of material is carried out from
the land. It has been proved that since the Glacial Period there have been
several alternate periods of drier and moister climate. The greater the
precipitation, the greater is the erosion and the consequent deposit upon the
sea-bottom, of terrigenous matter; and thus in a moister period, the grey clay
will extend farther out into the sea. If we had a vertical section of the
ocean-bed, we should see that wedges of the grey and the brown clay
alternate with one another just as many times as there have been climatic
periods.

Sample No. 10 of the Fram Expedition consists, unlike those from the
other localities, of clay greyish above, brownish underneath. Here the pos-
sibility of a separation brought about by movement seems to be excluded,
especially as the two kinds of clay have an equally large admixture of sand.
It may be imagined that there was temporarily a rather considerable de-
position of sediment at this particular spot as compared with what there had
previously been ; but as long as nothing is known of the climatic changes in
these regions, there is nothing on which to base a conclusion as to the reason
for this. On comparing the two kinds of clay, it appears that the sedimen-
tation must take place two or three times as rapidly now as formerly. Strange
to say, the chemical analysis of these two samples shows no corresponding
difference in the proportion between the quantities of protoxide and peroxide
of iron. The grey clay contains 2*40 and 530 per cent respectively, while
the brown clay has 2-95 and 5-25 per cent; but this must be due to chance
causes, possibly some difference in the mineral contents.

No chart of the distribution of the various kinds of bottom-samples ac-
companies the treatise, nor could one be drawn up with any great accuracy.
The boundary between the shallow water deposits and the Grey Deep-Sea
Clay, is placed, as already mentioned, at the 200 metres contour, and is thus
not directly connected with the nature of the bottom-sample. Throughout the
whole region, the only deep-sea deposit found is the Grey Deep-Sea Clay, a
name that is not altogether appropriate, as it also includes several rather
distinctly brown deposits. The boundary between this species of clay and
Globigerina Ooze is placed at 30 per cent carbonate of lime in the report of
the Challenger Expedition. If, following Schmelck, we make a special class
under the name Transition Clay, some of the most northerly samples might

14 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. poi.. EXP.

possibly come under that designation. As a rule, however, the Transition
Clay contains a larger quantity of carbonate of lime than is the case with
any of these samples. In the report of the Ingolf Expedition, I have put
the limit at 5 per cent, a limit which is rather arbitrary, but which lends
itself better to classification than the colour alone, which is generally very
difficult to determine. If this classification were adopted, none of the Fram
Expedition samples would come under the Transition Clay. Only one sample
— No. 12 — has about 4V2 per cent of carbonate of lime; all the others
have about 1 — 2 per cent or even less, and thus cannot possibly be said to
form any transition to Globigerina Ooze.

In order to obtain a more complete idea of the mechanical nature of the
samples, and thus possibly to find out the laws that govern their distribution
upon the sea-bottom, I have subjected some of them to washing. In the
case of the samples of this expedition, washing is of comparatively far greater
importance than it is generally. The proportion between the various sizes of
the particles here, is almost the only thing that causes any considerable diffe-
rence between the several samples, whereas in other cases the difference in
the quantity of organisms, especially the calcareous organisms, and in the
mineralogical components, are of equally great significance in unravelling the
complicated conditions that assert themselves in the distribution of the diffe-
rent kinds of bottom deposits.

The washings are accomplished by the aid of a Schoene washing appa-
ratus. In detail the same method is followed as in the case of the Ingolf
Expedition, with the one exception that the lowest limit for the size of the
grains is fixed at 001 mm. instead of at 0"02, principally because the first-
mentioned limit is most employed in geological researches, and is thus more
practical when it is a question of comparing bottom-samples with other depo-
sits. In other respects, if the mechanical nature of the samples be represented
graphically, the one of these limits may just as well be employed as the
other, and as that of 0-02 mm. is much quicker to work with, and certainly
also more accurate, it is very doubtful whether it is not to be preferred.

There is one very important circumstance in connection with the wash-
ing, to the clearing up of which my attention during the examination has
been very particularly directed, and that is, whether it is possible to make any
complete and reliable distinction between the various sized particles in which

NO. 14.] MECHANICAL COMPOSITION OF SAMPLES. 15

the Clay is found in the samples. In order to solve this question, it will be
necessary to subject it to a close investigation.

All clays or kaolins are originally possessed of so extraordinary a fine-
ness that in the process of washing a large quantity will come out among
the constituents that are less than O'Ol mm. It is for instance a well-known
fact that the clay can be held suspended in fresh water for a very long time,
so that in kaolin-pits and brick-fields it is necessary to have very shallow,
flat reservoirs in order to get it separated from the water. This circumstance,
however, is modified in many ways, and the transition to salt water in the
first place, plays a very important part. It is also a fact that has often been
observed, that clay sinks to the bottom far more rapidly in salt water than
in fresh, although the former is not so fluid as the latter, and moreover has
a higher density. Thoulet1 has pointed out that large particles sink at a
perceptibly slower rate in sea-water than in fresh, and that the proportion
between the velocities is about 0-955. The density of sea-water is about
T02652, and Thoulet, in his experiments, has employed a solution of NaCl
of this specific gravity. The proportion between the velocities of deposition
would be 0974, (the reciprocal of the above named 10265), if the density
alone determined the velocity of deposition. As the difference is, however,
greater, it shows that the smaller degree of fluidity in sea-water must be
of some consequence, and it would seem most natural to suppose that this
would be of still greater significance in the case of the finest particles. Here,
however, other circumstances assert themselves, and in order to come to a
clear understanding of them, I have made the following experiments.3

A sample of very fine clay was boiled thoroughly in distilled water, and
after being cooled down, an equal quantity of the liquid was poured into 3
glass cylinders of the same size and shape. One of these contained fresh
water, the second, water with 1 per mille NaCl, and the third water with 35
per mille NaCl, or about the same permillage as sea-water. I have not
investigated the question of the possible influence of the other salts in sea-
water, but they probably act in the same way as common salt, although in

1 Analyse niecanique des sols sous-marins. Annates des Mines, April, 1900.

2 Not in the Polar Sea, where it is 1-028. [F. N.]

3 For further particulars see Atterberg: Stutlier i Jordanalysen. Landtbrnks-Akade-
miens Handlingar och Tidsskrift, Stockholm, 1903, p. 217 etc.

16 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. EXP.

a different degree. I then, in the various experiments, poured different
quantities of the washed clay into the glasses, but exactly the same quantity
in each of the three glasses, each time. It then appears that if the quantity
of clay is so great as to make the water quite opaque in a glass with a diameter
of 1*5 cm., there is a marked difference in the rates of deposition in the 3
glasses. During the first few minutes, no difference is to be observed; but
at the expiration of half an hour, it will be seen that the water containing
the greatest amount of salt has become almost clear, the slightly saline water
is almost clear in the upper part and perceptibly clearer below, while in the
fresh water only the uppermost layer shows a slight indication of a decrease
in the quantity of clay, the greater part being apparently entirely unaltered.
After the expiration of twenty-four hours the water containing most salt is
quite clear, and the slightly saline water has only a very little clay floating
in it, while the fresh water still contains so much, that for the greater part
of its height it is quite thick, and it only becomes quite clear after several
weeks. If, however, we observe the clay in 3 glasses, both during deposition
and after, it will present a very different appearance in the different cases.
In the fresh water, it is always exceedingly finely and evenly distributed,
while in the salt water it coagulates, and after being deposited has an
uneven, gritty appearance. Thus the effect of the salt is to cause the separate
fine particles of clay to unite, and so in a manner alters the size of the grains.
This is confirmed still further by the phenomena exhibited when the clay is
in the form of a much diluted emulsion. It then appears that the differences
between the action of the several kinds of water are much smaller. If we put
into the glasses no more clay than is necessarv for a fairly clear observation of
the deposition, no noticeable difference is perceptible in the 3 glasses for the first
half-hour; indeed it almost appears as if the fresh water were a little clearer
at the very top than the salt. After the lapse of a few hours, however, we
shall nevertheless see that the salt water has become almost clear throughout,
while the fresh has scarcely made any progress in that direction. This seems
then to indicate that at first the particles of clay are at so great a distance
from one another that during the first part of the time they are unable to
unite to any great extent, and the fresh water's greater rapidity of depo-
sition can thus actually make itself apparent; but a union nevertheless

NO. W.] MECHANICAL COMPOSITION OF SAMPLES. 17

subsequently takes place, after which it is not long before the clay is deposited
in the salt water.

It might seem natural to assume that the mutual attraction between the
clay-particles was due to osmotic action between the salt water surrounding
them, and the fresh water enclosed in them from the boiling. For the purpose
of investigating this, I boiled clay in salt water of the same concentration
as sea-water, and poured the liquid into the various glasses. In connection
with this it must be remarked that it is quite impossible to work with
perfectly fresh water, as a certain amount of salt is conveyed by the clay;
no very marked results can therefore be expected. It appears, however, as
far as observation is possible, that the clay sinks with the same rapidity
in the various kinds of water, and moreover with the same rapidity with
which the clay boiled in fresh water, sinks in salt water. It also appears
that in the last experiment the clay always coagulates very much, and
that the above-mentioned osmotic action thus cannot be of any great con-
sequence. At present it is not possible for me to give any physical explanation
of the circumstance.

If we apply the result of these observations to conditions in nature, we
must assume that the clay sinks to the bottom at very different rates, according
as it originally comes out into the sea- water in larger or smaller quantities.
The clay in the sea generally originates either from the rivers or from coast-
erosion; but in the greater part of the polar regions, the glacial ice is an
additional important factor. This, however, as already mentioned, is not the
case in the region traversed by the Fram. The clay that is carried out by
the rivers may generally be assumed to be present in the water in a far
greater degree of concentration than that which is produced by coast-erosion.
The result of this must be that in the neighbourhood of the great river-
estuaries, deposits that are to no small extent argillaceous, must as a rule
be formed; and this, as will subsequently be shown, is the case here in a
marked degree. It must be assumed that the greater part of the clay-particles
the rivers bring with them, will unite when they come out into the sea, down
into the less disturbed water-strata, and will sink to the bottom very soon,
while only a small quantity will be carried farther out to sea. At other places,
on the contrary, a great part of the clay will be carried far away, while
only a comparatively small part will be deposited nearer the coast. The

18 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. Exp.

nature of the deposits in such places will thus, to a very great extent, depend
upon the nature of the coast rocks. As those, however, of the north coast
of Siberia, consist in great measure of clay deposits, morainic or stratified,
the sea-bottom north of Siberia will, on the whole, be covered with a parti-
cularly argillaceous deposit.

The aim of the washing is in the first place, to try to find out the laws
which have governed the distribution of the various deposits upon the sea-
bottom. This is in contrast to washings performed for agricultural purposes
where it is a question of the practical use of the clay, and where the aim
of the washing is to get it as fine as possible. Here the ideal to be aimed
at would be to get the clay washed out in exactly the degree of consi-
stency in which it was deposited in nature, so that whatever had sunk
in a coagulated condition could be retained in the same state, and
thus come among the coarser particles. In practice this is scarcely possible.
It is not unreasonable to suppose that the clay particles that fall upon the
sea-bed in a very finely distributed condition, acquire, upon coming into
contact with the other clay particles, exactly the same consistency as the
clay that has sunk to the bottom in a coagulated condition. It
should moreover be remembered that as time passes, the clay upon
the sea-bottom will scarcely remain in the condition in which it was originally
found. In all older deposits, the clay continues to become more compact,
chiefly owing to the percolating water, which probably endeavours to cement
it more and more together. As the extent of this operation is exceedingly
varied in the various parts of the sea-bottom, the result is that the clay taken
up in bottom-samples will be of a consistency that has little connection with
the conditions under which it was originally deposited. The chief result
obtained by the washing is thus to find out the proportion between the total
amount of clayey substance on the one hand, and of true mineral particles
on the other, and further the proportion between the various sizes of the
latter. It is clear, therefore that in order to attain this, special importance
must be attached to the measurement of the percentage of clay and sand of
each separate size of grain, with the greatest possible accuracy.

In the actual washing, the salinity of the water will now play a very
important part. As all the samples when taken are saturated with salt, this
will be capable of disturbing the rate of washing to quite an extraordinary

NO. 14.] MECHANICAL COMPOSITION OF THE SAMPLES. 19

degree as regards the clayey matter, if no attempt be made to get rid of it.
This is best done by filtration. The sample is first thoroughly boiled in
order to loosen the clay as much as possible and the liquid filtered,
until it is impossible to demonstrate the presence of salt in it. When the
boiling has been repeated, the clay will be ready for washing. It frequently
proves, however, that even after this treatment the very small particles of
the clay coagulate and fall rapidly to the bottom. In this respect there may
often be a striking difference between samples that are altogether similar in
appearance, and have been treated in exactly the same manner. In the one
the clay may be quite finely distributed, and come among the constituent par-
ticles'that are less than 0-01 mm.; in the other only a comparatively small
amount will remain suspended at this rate of washing, while a large quantity
will come among the coarser products. The rule in the main holds good
that in those samples containing the greatest amount of sandy particles, the
greater part of the clayey matter will also be thrown down, during washing,
among the coarser particles. This again is a natural consequence of the
circumstance that in places where sand is deposited, the wave-action, or the
currents, must have such force that they can remove the finest particles, so
that only such of the clay can be deposited as is more coherent than the
remainder, virtually only that which originates from older, compact clay de-
posits on land, and which have become so firmly cemented together in the
course of time, that they can no longer be disintegrated by natural force. A
portion may indeed be comminuted by boiling, and there is consequently
always, even in apparently, perfectly pure sand-samples, some small per-
centage of particles of less than O'Ol mm., especially as some of the sand
particles may have been disintegrated and comminuted during the time they
have lain upon the sea-bottom.

It is stranger when in two samples that are otherwise quite uniform, the
clay is altogether different. We may here, for example, look at the curves
for the samples Nos. 14 and 15. Both contain more clay than anything else,
the clay in both being of the same brown colour, which gives the samples
externally the appearance of being exactly similar; but the maximum size of
the particles in the clay in No. 14 proves to be only a little less than 001 mm.,
so that a very large proportion of them are found among the coarser consti-
tuents, while the clay in No. 15 is extraordinarily fine, and almost entirely

20

0. B. B0GGILD. BOTTOM DEPOSITS. [norw. POL. EXP.

consists of immeasurably small grains. In this case, almost the only possible
explanation is, that even on the sea-bottom the clay must be subjected to
some influence or other, in consequence of which the clay in No. 14 has
been firmly cemented together, while that in No. 15 has been preserved
almost in the condition in which it was deposited. It is not possible at present
to give any reason for this phenomenon, which can probably only be ex-
plained by a large number of observations from many different localities.

Table of the quantity of the Particles of various Sizes in the

Bottom- Samples.

Percentage of Constituents

No. of

Depth in

Metres

Sample

Under

001-005 005-0-5

0-5-1

Above

001 mm.

mm.

mm.

mm.

1 mm.

1

130

19-42

9-89

69-26

1-21

0-22

2

46

79-18

9-73

1109

0

0

3

26

5-64

2-49

84-13

7-44

0-30

5

39

85-76

9-75

4-49

0

0

6

?

72-23

8-08

14-70

396

1-03

7

9

41.53

19-73

35-00

2-37

1-37

8

20

54-94

41-21

3-85

0

0

9

40

1910

5-63

73-31

1-93

0-03

10 c

1460

70-95

26-18

2-87

0

0

12

100

56-88

30-01

13-11

9

0

13 a

3800

56-16

37-84

6-00

0

0

14

3850

58-23

35-85

5-67

0-25

0

15

3450

80-50

9-92

9-58

0

0

On looking at the above table, we are especially struck by the small
quantities of the coarsest particles. It has previously been stated that these
bottom-samples were distinguished from the great majority of others that are
of purely terrigenous origin, by this peculiarity, and this is all the more
striking when they are compared with others from the polar regions, which
are generally strongly characterised by containing stony particles. On the
average, the samples contain 0*23 per cent of particles of more than 1 mm.,
and 1*32 per cent of particles between 0'5 and 1 mm., total 155 per cent
above 0*5 mm. If only the actual deep-water deposits, viz. Nos. 10 c and
13 — 15, be considered, the average of particles between 0'5 and 1 mm. is
0-06 per cent, while not one of these samples contains particles of more than

NO. 14.] MECHANICAL COMPOSITION OF SAMPLES. 21

1 mm. By way of comparison, the results from the Ingolf Expedition may
be given here, showing the particles of more than 0"5 mm. to have amounted
to 4"17 per cent in the case of the Grey Deep-Sea Clay, a value which is
about 69 times as large as in the case of the Fram Expedition samples;
while the number for the Transition Clay is 3'44, and for Globigerina Ooze
0"90. Even if a large proportion of these coarser particles in the Ingolf
Expedition samples are derived from localities where the deposits contain
a large quantity of stony particles from the rocks on the floor of the ocean
itself, it has also been proved that a very large proportion of the stony
particles must be carried thither by icebergs. In any case, the small per-
centages in the Fram Expedition samples show that both these factors are
virtually altogether absent.

It has already been mentioned in the introduction, that in the Polar Sea
north of Siberia, there are no icebergs to convey clay, sand, and gravel to
the sea-bottom. Siberia sends out no glaciers, and those that come from
Spitsbergen and other arctic lands, are not brought by the currents into this
region. The inference that may be drawn from the above figures is of
greater importance, namely, that in the whole region traversed by the Fram
north of Siberia, there are no projecting rocks upon the sea-bottom; for
these would always reveal their presence by a considerable quantity of stones
in the samples, and generally also by an alteration in the mineralogical com-
position of the samples from one locality to another, if the submarine rocks
varied in their nature. As will subsequently be related, it is not possible
to prove anything of the sort in this region.

Again, a very important conclusion may be drawn from the complete
absence of solid rocks on the floor of the ocean, namely, that this region
has been raised very little or not at all above the sea in any recent
geological period ; for wherever this has been the case, will always be apparent
from the great unevenness of the sea-bottom. The deposition of sediments
always takes place exceedingly slowly, and in the region under discussion
even more slowly than in most other places; and the very rough configura-
tion of the bottom, appearing near the coasts of the mainland, will only be
completely obliterated in the course of a very long time, by the gradual
filling up of the hollows with sediment. It may thus be assumed that this

22 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

region has scarcely been raised above the sea in the Quaternary Period, nor
probably in the Tertiary either.

As the particles of more than 0"5 mm. appear in such exceedingly small
quantities, it follows that the sandy particles on the whole must be consider-
ably in the minority as compared with the clayey particles. In the case of
the 4 samples of Grey Deep-Sea Clay, the average quantity of particles between
0'05 and 0*5 mm. is 6-03 per cent, while in the Ingolf Expedition it is 29-55
per cent — quite a striking difference. An increase in the quantity of the
finest particles will of course be found in the Fram samples in a correspond-
ing degree.

A number of quite important variations between the several samples, also
appear in the details. In order to obtain a better idea of these, and to give
as clear a picture as possible of the mechanical composition of the samples,
I have tried to represent this graphically, and have given the size of the
grains as abscissa and the percentage as ordinate. In practice, however,
this presents certain difficulties, and it becomes necessary to discuss more
fully the manner in which a representation such as this, may be made.

The marking of the figures on the ordinate presents no difficulty what-
ever. The percentages may be put down in an ordinary arithmetical series,
which will prove to be sufficient in all cases. This is by no means the case
with the abscissa figures. If we attempt in a similar manner to put down
the figures denoting the size of the particles in an arithmetical series, it will
be impossible in the great majority of cases to find a scale which will include
all the sizes of the particles in the sample, and at the same time give a cha-
racteristic representation of the most important constituents of it. This may
be best illustrated by one particular example. Sample No. 1 contains, as we
have seen, 0"22 per cent of particles of more than 1 mm.; the largest is 1"55
mm. If all the sizes of grain are to be included in one scale, this may be
divided, for instance, into 30 parts of 0'05 mm. each. The particles of more
than 1 mm. will extend over 10 divisions, and will thus average a height of
0'022, which it will be impossible to] show on a drawing unless the units of
the abscissa are very large, and this, as we shall presently see cannot be
done with the finer particles. The particles of sizes between 05 and 1 mm.
also extend over 10 divisions. As they are found to the amount of 1*21 °/o,
the curve will here be drawn at a height averaging 0*121 units, which at any

NO. H.] MECHANICAL COMPOSITION OF SAMPLES. 23

rate better admits of being represented. The particles between 0-05 and 0"5 mm.
extend over 9 divisions. They amount, in all, to 69-26 per cent, and thus the
height becomes 7*7 ; so that this size occasions no difficulty. The same may
be said of the particles between 0"01 and 0'05 mm. which occupy 0"8 of a
division; the percentage is 9"89, and the height consequently 12-36. But the
difficulty returns with the finest particles of less than 001 mm. As they oc-
cupy only 0*2 of a division, and are present to the amount of 19"42 per cent,
they would have to be marked at a height of 97'1, which is practically im-
possible, when a height of O022 has to be shown for the coarsest particles at
the same time. Even then we get no idea of the manner in which these
finest particles are distributed within the area they occupy. It is always
possible to see approximately in the microscope what is the size of the ma-
jority of the particles, and to observe that in this respect there is a consider-
able difference between the several samples. At some place or other the curve
must have a maximum, whence it descends regularly to both sides; and shades
of difference such as these cannot possibly be drawn in the space of 0-2 of a
division, when at the same time there are to be 30 divisions. It will thus be
seen that with this mode of representation it will be impossible to include
either the finest or the coarsest particles, and it is clear that the case will be
much worse when the particles of less than 001 mm. rise to 100 °/o, or there-
abouts or when, on the other hand, stony particles appear in the sample. A
graphic representation with the sizes of the particles in arithmetical progres-
sion can thus be employed only when the samples dealt with, are very homo-
genous practically only with pure sand or gravel deposits, and it can only
be employed for purposes of comparison with other samples, when the latter
are very nearly of a similar composition.

The case is altogether different when the figures for the sizes of the par-
ticles are given in a geometrical series. As will be seen from the tables, the
quotient 2 is here chosen as the unit. With 1 mm. as the starting-point, we
put Va, 1/4, etc. on the left, and 2, 4, etc. on the right. The abscissa can thus
be continued indefinitely on both sides, but will in no case acquire a length
that is not applicable. The advantages of the method are best seen by look-
ing at the curves themselves. The greater compression of the coarser particles
in relation to the finer, enables even the smaller percentages that are as a rule
found, to be very clearly shown, and the curve can easily be extended to in-

24 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. POL. EXP.

elude even very coarse, stony components, such as, for instance, diluvial gravel
and the "Till" contain. With regard to the finest particles of less than O'Ol
mm., it will here also be immediately evident that there is a very essential
advantage in their curve being extended over a greater space, as a consider-
able percentage of them is usually found in the samples. It also becomes
possible to give the differences in the size of the grains in the clay, that can
be observed under the microscope, by making the highest point of the curve
correspond to the size of grain found in the greatest quantity. But this
part of the curve cannot, of coarse, be very accurate in detail, while the area
enclosed by the curve must naturally give accurately, the value found for the
percentages of the particles under 0-01 mm. The only difficulty which cannot
in any way be surmounted in this mode of representation, is the impossibility
of determining how far to the left the curve is to extend, as there is no means
of finding out the size of the smallest clay-particles. That the sizes of the
particles do not decrease to an unlimited extent may be inferred from the fact
that all the clay does at last sink to the bottom in water, even though in
certain cases it may take weeks to do so. In none of the samples is the clay
of such fineness that 99 % of it will not have sunk to the bottom in the
course of 24 hours in a glass that is 20 cm. in height. I have always put
the lower limit at a size of about Vsooo mm. If it were in reality to be
a few units farther to the left, that part of the curve lying to the left of
001 mm. would be somewhat flatter as the total area must remain the
same; but in other respects the figure would not be altered in any essential
degree. By adopting the same mode of procedure everywhere, it will be
possible to make every difference between the various samples stand out sharply
and distinctly.

The reason for choosing geometrical progression for representing the sizes
of the grains, is not only that by its aid it is possible to represent quite other-
wise than with arithmetical progression, the mechanical composition of any
deposit whatever, and thus by the same system to delineate all kinds of rock,
from the finest clays to the coarsest gravel deposits; but it is also because
this mode of representation is quite in keeping with the natural forces that
operated in the formation of the rock. If we examine a tolerably uniformly
grained rock, such as stratified sand, we shall always find that when most of
the grains are, for instance, 1 mm. in size, the percentages of grains measur-

No. 14.] MECHANICAL COMPOSITION OF SAMPLES. 25

ing Va and 2 mm., Vi and 4 mm., etc., will be as nearly as possible equal.
A single operating force — in this case the velocity with which the water
moves at a particular place — will thus always make itself apparent in a
perfectly regular, symmetrical curve — the so-called curve of probability — ,
which will be more arched or flatter according to whether the force in question
has operated more or less regularly and exclusively. If we see that the curves
take another form, we may conclude that some factor or other has asserted
itself, which must be calculated separately in each case. If, for instance, the
right side of the curve is greater than the left, coarser particles must have
become mingled in the sample by some special natural agency; accidental
circumstances in the principal depositing force cannot by themselves have pro-
duced such irregularity.

As regards the bottom-samples, the curves that demonstrate their mecha-
nical nature, will have many varied and peculiar forms. This shows directly
that a number of different natural forces have asserted themselves at the time
of deposition. The bottom-samples on the whole, belong to the less regular
deposits; the numerous alternations in the sea, in wind, temperature, and
currents, the many different sources whence the constituents originate,
and further the previously mentioned, peculiar condition that clay presents in
salt water, all cooperate in making the deposits irregular. The curve for each
separate sample shows directly how great this irregularity is, and thus sup-
plies a means of finding out to some extent, to what degree the various forces
have asserted themselves in the deposition of the sample.

The curves were constructed in the following manner. First, on the axis
of the ordinate, figures are placed indicating the percentage of grains of each
separate size. The highest value that it has ever been necessary to employ
with these samples is somewhere about 30. In very homogenous rocks, it
will rise somewhat higher, though very seldom above 70 or 80. In the next
place, the values of the sizes of grains are placed on the axis of the abscissa,

1 mm. being taken as the starting-point, and the quotient 2 as the unit. The
area of the curve situated over each single unit indicates the quantity of the
corresponding size of grains. The scale is thus unlimited on both sides.
In these samples it has not been necessary to go to greater values than

2 mm., and the lowest value given is -rhj==^TT- Among the values
employed in washing, 0-05 and 001 mm. do not fit directly into this

26 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. POL. EXP.

scale; 005 lies between -^ and ^, and by calculation, its distance from ^
is found to be 032 of a unit; 0 01 lies between ^ and j^, and is found to
be at a distance of 0"64 of a unit from -fa. Among the parts into which the whole
sample is divided by washing, the particles measuring 1 — 2 mm. and 05 — 1 mm.
each occupy 1 unit, those measuring 005— 0"5 mm. 3'32 units, and those mea-
suring 0 01 — 0"05 mm. 2"32 units, while the finest particles, of less than 0-01 mm.,
extend over a number of units, which cannot be exactly determined. When
stVt is placed, as already stated, as the extreme limit of the scale to the left,
this gives 6'36 units for this part of the sample. If we now divide the per-
centages of the various sizes of particles found by washing, by these figures,
which give the number of units embraced by each size, we obtain the average
height attained by the curve in the space in question. By being content with
the horizontal lines only, we should have obtained a very poor representation
of the actual thing, where sudden leaps from one size to another are never
found. I have therefore always rounded off the curves, and two different
methods may be employed for getting at the correct form. The surest is of
course to examine the samples themselves under the microscope or with a
lens. If we place, for instance, a sample of the size 001 — 005 mm. under
the microscope, and examine the grains of these particular sizes, a fairly accurate
idea may be formed as to what are the intermediate sizes that are most abund-
antly represented in the sample, and thus as to where the highest point of
the curve will lie, and also to some extent how much higher it will be at this
spot than at other parts. A consideration of the adjacent sizes will also to a
great extent assist in the determination of the form of the curve. For in-
stance, it is evident that when we find a very small percentage of one size,
the curve for the size or sizes that lie next to it, falls down very rapidly to-
wards it. Both ways always lead to the same result.

It will be seen that there are always two curves drawn. The upper one
gives the quantity of all the constituents of the sample, the lower the quantity
of the true mineral particles. Two areas are thus obtained, one for the clayey
matter, the other for the mineral particles, here designated, for the sake of
brevity, respectively clay and sand. This division is made by counting under
the microscope a number of particles, and calculating the percentage of clay
and sand in each separate size. This admits of being accomplished with
tolerable accuracy so far as the coarser particles are concerned; but in the very

NO. 14.]

MECHANICAL COMPOSITION OF SAMPLES.

27

finest constituents it is impossible to distinguish the clay and the sand from
one another. For this reason, the part to the extreme left of the lower curve is
rather inaccurate; it is not drawn quite so far out as the upper one, as it
may be taken for granted that the mineral grains do not attain the same de-
gree of fineness as does the clay; but how small they can actually be, it is
impossible to say.

In the following table are given the values by the aid of which the curves
are constructed. For the three smallest sizes — less than 001 mm., 001— 0"05
mm., and 005 — 0'5 mm. — the percentages are given, and the average height
of the curve for these sizes calculated from the percentages, by dividing by
6'36, 2'32, and 3'32 respectively. With regard to the larger particles, which
each occupy 1 unit of the scale, the height of the curve is equal to the per-
centage found in the preceeding table. The percentage of clayey matter in
the four smallest sizes is also given : particles of more than 1 mm. never con-
tain clay.

Constituent Particles.

Less than 0.01

mm.

001

-0 05 mm.

0-05

—0.5 mm.

0-5-1

mm.

No. of
Sample

Percen-
tage

Height
of Curve

Per-
cent.
Clay

Percent-
age

Height
of Curve

Per-
cent.
Clay

Percent-
age

Height
of Curve

Per-
cent.
Clay

Per-

centage
of Clay.

1

19-42

305

80

989

4-31

40

6926

20-83

15

25

2

79-18

12-45

80

973

419

25

11-09

3-34

15

3

5-64

0-89

50

2-49

1.07

70

84-13

25-19

5

5

5

8576

1348

80

8-75

4-20

30

4-49

1-35

15

6

72-23

11-36

70

8-08

3-48

20

14-70

4-43

10

5

7

41-53

6-53

70

19-73

8-50

£0

3500

1054

35

20

8

54-94

8-64

60

41-21

17-76

25

3-85

116

10

9

1910

3-00

50

563

2-43

35

7331

22-08

8

10

10 c

70-95

1116

70

26-18

11-28

45

2-87

080

8

12

56-88

8-94

70

3001

12-93

15

1311

3.95

10

13 a

5616

8-83

80

3784

1631

50

600

1-81

30

14

58-23

902

80

35-85

15-46

50

567

1-71

10

0

15

80-50

1266

a5

9-92

4-28

5

9-58

289

5

As the samples throughout are rather varied in their mechanical com-
position, it is hardly possible to give any general opinion regarding the relation
between the forces that have aided in their deposition; they will therefore be
taken separately in the following pages.

28 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. EXP.

No. 1, which was taken on the 24th July, 1893, about 60 miles west of
Goose Land on Novaya Semlya, is a good example of a partially, uniformly
grained sample. The bulk of the particles, which lie between 005 and 0-5
mm., form a complete whole, which is due to a single factor. In this instance
it can only be the ocean currents, which flow in a north-westerly direction in
this region, coming from the Vaigach Straits (cf. Nansen, IX, p. 267). The
current must have just sufficient velocity to carry grains of this size from
Novaya Semlya and Vaigach to the station in question, while the larger par-
ticles fall to the bottom nearer these islands, and the finer particles are for
the most part carried farther away. The great expansion of the curve to the left,
however, shows that in this locality too, there must be some possibility of the
finer particles being deposited. This can only be the case when the water
near the bottom does not travel with any very great velocity, and this again
may possibly be caused by the fact that the locality is situated in a hollow
compared with its nearest surroundings. Other causes, however, may also be
imagined. The existence of two maxima in the curve for the clayey matter
is probably due to the fact that the clay in the sample is not of the same
consistency as when it was deposited. As the very great majority of the
sandy particles are of sizes between 0"05 and 0"5 mm., it is probable that the
greater part of the clayey particles had also corresponding sizes, when origi-
ginally deposited, they have thus been in a coherent condition, and they may
to some extent have been disintegrated by boiling. The fact that this is
not the case with the remainder shows that the clay must have had time to
become partially transformed since its deposition, which in this locality does
not take place with any very great rapidity, as the comparatively deep brown
colour of the clay also indicates. The extension of the curve to the right,
which is quite marked although very small, shows the influence of the ice.
Whether ice floes of shore ice, or possibly icebergs from Novaya Semlya,
there will easily be carried a small quantity of particles of all possible sizes,
of which only those of more than 05 mm. will be perceptible in the sample,
while the finer particles will be occluded among the other constituents.

Nos. 2—6 were all taken in the sea north of the mouths of the Obi
and the Yenisei. The three samples, Nos. 2, 5 and 6, resemble one an-
other greatly, and have a very characteristic appearance as compared with the
other samples taken near the coast. The river-water, as already mentioned,

NO. u.] MECHANICAL COMPOSITION OF SAMPLES. 29

brings with it much greater quantities of clay than can be produced by coast-
erosion, and in consequence of this clay being present in so comparatively
concentrated a degree, a considerably greater percentage of it than would
otherwise be the case will sink to the bottom as soon as it comes out into
salt water. The result of this is that these samples contain a greater quan-
tity of argillaceous matter than any of the others with the exception of No.
15, which was taken at a particularly great distance from land. As the process
of deposition in these localities must be assumed to be relatively very rapid,
the clay has not had time to undergo any appreciable transformation, and has
therefore almost all been washed out in a very fine condition. The colour of
the clay also leads to the conclusion that the deposition has taken place ra-
pidly, all three samples being described as brownish grey, about half-way
between grey and brown-grey.

The curve, however, for all three samples shows a very considerable
extension to the right, which must have its own peculiar origin. It cannot
be supposed that the rivers themselves have brought these coarser particles
with them, for in that case the curves would have had a far more regular
appearance, whereas Nos. 2 and 6, at any rate, have a separate maximum
at the particles between 005 and 05 mm. The reason of this extension is
to be found either in the river-ice or in the particles arising from coast-
erosion. The latter seems to be best suited to the form of the curves.

Nansen (These Reports Vol. Ill, No. 9, p. 294) mentions that the Fram
during nearly the whole of her voyage along the coast of Siberia, experienced
currents running almost exactly to the SW. in a direction opposite to her
course. These currents were related to the winds prevailing at that time,
which were likewise contrary. If such a current is at all usual in this
region the differences in these three samples just mentioned, can of course
be very easily and naturally explained. Material torn loose on the coasts
will be carried down by this stream towards the mouths of the Obi and
Jenisei and the two localities represented by samples 2 and 6 would in that
case be more exposed to the effects of the current than would No. 5, and
would in consequence contain much more sandy material. As No. 6 came
from a good deal nearer to the Siberian coast, it is naturally somewhat
coarser with quite a considerable quantity of particles over 05 mm., than

30 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

No. 2; particles of such a size could only be to a very small extent carried
to a locality as far out at sea as that from which the latter was taken.

Meanwhile, it is scarcely probable that the above mentioned current is
very constant in direction, and in that case other factors will also in time be
able to make their influence felt. No. 2 probably obtains a considerable
quantity of its sandy material from the near-lying Sverdrup's Island which
according to Nansen is certainly formed of rather sandy kinds of rocks;
Sample No. 5 lay rather farther away from this Island and the conveyance
of sand from the one to the other must consequently have been much less.
It would also appear to be likely that large amounts of material expelled
from the large rivers in this neighbourhood, could be scattered over the sea
bottom here; and this being so, No. 5 will owing to its closer proximity,
receive the largest amount of such material; which accounts for this particular
sample being of a more clayey character than the other two. As, however,
nothing is up to the present, known as to what sort of material the drift
ice which undoubtedly plays a very great part in the transportation of the
river material, actually does carry with it, there appears to be no possible
chance of saying exactly what influence the addition of materials derived
from this source can have had on the general texture of the samples.

Sample No. 3 has a quite different appearance; it is composed of
nearly clean sand. As it was taken in rather close proximity to Sverdrup's
Island it is reasonable to suppose that at least a large portion of the sanded
ingredients owe their origin to this source. Meanwhile, it is difficult to
imagine that an Island of such insignificant dimensions should be able to
supply such a large quantity of sand, as to many times outweigh the amount
of clay presumably brought down from the great rivers, were it not that
the sample was taken from such a small depth that wave motion, currents,
etc., may have had a very appreciable influence in determining the proportion
of admixture. Where the water near the sea bottom is either always, or
at least at frequent intervals in motion, clay particles could not possibly
be deposited, and even if they sink whenever the water happens to be still,
they will soon be carried away again. The comparatively insignificant
amounts of fine clayey material that appear on examination, appears to
make it probable that this sample was deposited entirely as clean sand; and
the small amount of material under 0-05 mm. must consequently be attributed

No. H.] MECHANICAL COMPOSITION OF SAMPLES. 31

to later changes that have possibly occurred to the sea bottom itself, owing
to which a proportion of the sand granules have fallen apart once more. The
subsequent boiling-out in the laboratory must also have been of influence
in this connection.

Sample No. 7 was taken west of Taimur Sound, in a little bay in the
Western Taimur Peninsula. The geographical conditions here are especially
complicated, as just off the land there is a large number of islands that have
not as yet been carefully surveyed, and these may give rise to a very com-
plicated condition of currents and deposits. The curve, too, presents a
rather irregular appearance with several maxima both for the clay and the
sand; and it is quite impossible to make out the details. The colour of the
clay is a rather decided grey, which makes it reasonable to assume that the
deposition has taken place very rapidly. A large portion of the clay, how-
ever, has not been capable of disintegration by boiling, but this may be be-
cause it orginates from older deposits on shore, which can often become so
hardened in the course of time, that the clay can no longer be disintegrated
by boiling. The comparatively large number of particles of more than 1 mm.
may possibly be due to conveyance by ice, but may also arise from the
close proximity of the sample to land.

Stations 8 and 9 are situated to the east of the Eastern Taimur Penin-
sula, outside the Khatanga Bay and north of the mouth of the Anabara. In
this region there are north-flowing currents of river water from the coast, so
that we may assume that a large proportion of the material originates from
the rivers. The two samples differ greatly from one another. The curve for
No. 8 is very regular in its course, as regards both the sand and the clay;
there are here very few particles of more than 005 mm. The maximum of
the curve for the sand is about -£$ mm. with an even descent to both sides;
and thus, whether the material originates from the rivers or from the coast,
the drift of the current must be such that most of the coarser particles have
been deposited already. The colour is a purer grey than that of any of the
other samples. It is scarcely probable, however, that this sample should have
been deposited more rapidly than those already mentioned off the mouth of
the Yenisei; features in its chemical nature may possibly also have asserted
themeselves here.

32 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. EXP.

No. 9 is very different from the foregoing sample. The right side of
its curve hears a great resemblance to No. 3, and, like it, indicates a regu-
larly assorted sand deposit. The sample as compared with No. 8, must thus
have been in a situation that was considerably exposed to the currents.
Probably it was taken from a place somewhere in the centre of one of the
currents carrying water from stony-bedded rivers; No. 8 on the other hand,
was taken farther out at sea and most probably, must be regarded as coming
from a locality at the edge of the current, where the water would be likely
to be almost always quite still. The curve for No. 9, however, has also a
fairly large left part, which is too large to have been formed by division
and disintegration of the sandy particles. It almost seems as if the whole
sample consists of two parts that are formed quite independently of one
another; and as it is not possible to imagine them formed simultaneously,
it must be assumed that the sample has been stratified in such a manner
that either two or several layers of clay and sand have alternated with one
another. It is true that no such stratification has been directly observed,
but it may easily have been obliterated when the sample was taken. That
portion of the sample that consists of clay, must have been formed in one
or several periods, during which the circumstances were identical with those
prevailing at the formation of No. 8 which happens when the prevailing
current changes its direction away from the locality of 9. The colour of
the clay in No. 9 is also a fairly pure grey, although not quite so grey
as No. 8. This colour may have been produced by a mingling of the
altogether grey clay in the finer portion of the sample with the browner clay
in the coarser particles.

The samples Nos. 10 and 13—15 all belong to the true deep-sea deposits,
and are formed far from land. All chance local circumstances such as in-
fluence the samples nearer the coast are consequently excluded, and more-
over these samples, all without exception, show quite a regular form of curve,
with only one maximum for both the sandy and the clayey particles. In
detail, however, there are certain differences between them. They have the
flat, broad form common to all deep-sea deposits, which are never indeed
made up of very much assorted material; but it must be noticed that
the curve draws more and more to the left the greater the distance from
land, and that in the greater depths of the great oceans the coarser particles

no. 14.] MECHANICAL COMPOSITION OF SAMPLES. 33

altogether disappear. This stage is not reached by any of the deposits of
the Fram Expedition; No. 15 alone shows a slight indication of it. Most
of the deep-sea deposits have shades of brown deeper than any of those formed
in the vicinity of the coast, a fact which is immediately connected with
their slower formation.

As already stated, sample No. 10 consists of various layers, of which the
uppermost, No. 10 a is of a greyer hue, and the lowest, No. 10 c, more
brownish, an order which differs from that generally prevailing wherever the
ocean-floor consists of deposits of various colours. In other respects, the
different samples exhibit very much the same consistency; the greyish layer
being at most a trifle more sandy. Only the lowest layer, No. 10 c has been
washed. As the curve shows, the maximum for the sandy particles is found
at about 001 mm., and only a trifling proportion is greater than 005 mm.
The current, which here flows north from the New Siberian Islands and
the Siberian coast east of the mouth of the Lena, has thus not sufficient
force to enable it to convey the still coarser particles so far1; and the small
quantity of these also shows that the transport by ice can only play an
insignificant part in these regions. It is impossible to say anything decided
regarding the reason of the greyer colour of the uppermost layer as compared
with the nethermost. It may, as usual, be assumed that this colour denotes
that the layer has been deposited more rapidly than the lowest layer; and
this change may possibly arise from the increased velocity of the currents
in these regions.

The fact that raised beaches with shells, etc., are found on the New
Siberian Islands2 indicates that the surrounding region once stood at a lower
level than it does now. It is very likely that the brown layer was formed
at this time; the higher water level must have lessened the velocity of the
currents going north from the Siberian rivers, and the transport of material
must consequently have taken place on a smaller scale and at a slower rate.
This would all seem to indicate that deposition in this region must be an
extremely slow process; and in confirmation of this, it may be pointed out

1 Especially as Nansen proved that the stream which here runs towards the North,
only has a range of ca. 200 m.; underneath it Ihere is a current in the opposite
direction.

2 See James Geikie: "The great Ice age," 1894. p. 700.

5

34 0. B. B0GG1LD. BOTTOM SAMPLES. [norvv. pol. EXP.

that a not very powerful current such as this north-going stream, can hardly
be expected to carry great quantities of material very far from land, before
they will fall into the cross-current lying below it. Neither can the material
originating from the ice be very considerable as there can hardly be much
opportunity of melting in these districts.

Samples Nos. 11 and 12 are from just east of the preceding one, and
thus rather nearer to the New Siberian Islands. The samples are taken
from a far smaller depth, 135 and 100 m., while No. 10 is from about 1460 m.
These samples are quite different, No. 11 being more sandy, and No. 12 more
clayey. So little of the deposit was obtained in the first, No. 11, that it was not
examined more especially. The reason for its more sandy consistency in
comparison with No. 12 may be the same as was given in the cases of
samples 8 and 9, namely that No. 11 is situated in a stronger current, while
No. 12 is in comparatively quiet water; but possibly also other unknown
reasons can have prevailed during the formation of these samples.

The two samples, Nos. 13 a and 14 were taken rather close to one
another, in very deep water; it is not therefore to be expected that there
would be any appreciable difference between them. The curves are also
almost exactly alike, and are both exceedingly regular, with few particles of
more than 0"05 mm., and with the maximum for the sandy particles at
about ^T mm., and that for the clay particles about 0'01. The clay has
thus only partially been disintegrated by boiling, but still in far greater
quantities than might be expected from the circumstance that these samples
have been deposited so slowly; the rule already mentioned holds good here,
that in very deep water the cementing together of the clay takes place only
in a very slight degree. The colour of both samples is given as greyish
brown, and in reality is not very far from pure brown. Sample No. 13 b
is designated as the upper layer; unfortunately there was so little of it that
not even the colour could be determined; otherwise it would have been
extremely interesting to see whether the difference between the upper and
lower layer was in the same direction as in No. 10.

Sample No. 15 was taken at a great distance from land, almost due
north of Cape Chelyuskin. It has the most pronounced deep-water character
of all the samples examined, with a greatly preponderating quantity of clayey
matter, and among the mineral particles the finest are especially predominant.

NO. u.] MECHANICAL COMPOSITION OF SAMPLES. 35

This last attribute is not immediately apparent from the curve, which shows
quite a large number of more than 0-05 mm. ; but in reality the greater part
of this area consists of Foraminifera, which with the increased coarseness of
the particles, make up a continually increasing percentage in the sample. As
the size of the Foraminifera in the sample have nothing whatever to do with
the laws that determine the inorganic particles, they ought in reality to be
either altogether omitted, or drawn as an independent part of the curve,
e. g. under the axis of the abscissa. As, however, No. 15 is the only sample
in which the Foraminifera play any appreciable part, I did not wish to in-
troduce a new principle for this one curve. The colour of this sample is
quite a pure brown; it has probably been deposited very slowly. Most of
the clay, and the finer sandy particles may be assumed to have been carried
to the locality by currents; while the coarser sandy particles and a corre-
sponding portion of the clay have probably originated from the ice. Almost
all the clay has been brought out in the washing among the very finest
particles; and thus, at this great distance from land, special conditions must
prevail, which prevent the coagulation of the clay. Several samples would be
necessary, however, for a closer investigation of this matter.

III.

MINERALOGICAL COMPOSITION OF THE SAMPLES.

After treating of the mechanical nature of the samples, and the results
that could be obtained by washing, it still remains to look at the samples from
the other side, and examine their composition from a mineralogical point of
view. One circumstance belonging to this side of the question has already
been discussed in the preceeding section, namely the amount of clayey matter
in the various sizes of grains; for this plays a very important part in the
composition of the samples, which cannot be lost sight of in treating of this
composition. In the following pages, the relation between the remaining minerals
will be as far as possible determined.

For practical reasons, the treatment of each size of grains has been taken
separately, so that the particles of more than 0"5 mm. are examined directly
with a lens, while the particles between 0'05 and 05 mm. are axamined as
microscopic preparations. The still finer particles are not considered here, as
the separate minerals in them cannot be accurately distinguished from one
another, and the proportion between them may be assumed to correspond fairly
well with the proportions of the coarser particles. The particles of more than
0'5 mm. on the other hand, may sometimes give valuable information
especially regarding the mineral combinations, or rocks present, which
cannot be obtained from the finer particles. In this particular, however, the
bottom-samples of this expedition are rather unsatisfactory, as few of them
contain these coarser particles, which, moreover, in no case attain a greater
size than 2"5 mm. Thus one of the most important means of determining the
species of rock that have furnished the material of the samples is wanting here.

NO. 14.] MINERALOGICAL COMPOSITION OF THE SAMPLES. 37

1. Particles of more than 0 5 mm.
No. 1. L63 per cent. Largest grain 1*5 mm., quartz.
Almost exclusively quartz in rounded particles; a few grains of felspar,
magnetite, biotite, and a single grain of muscovite.

No. 3 a. 7'74 per cent. Largest grain 1"4 mm., quartz.

A great majority of quartz-grains, which were found in very large num-
bers, most of them only a little larger than 0.5 mm. Some felspar and
magnetite were also found, and a few grains of garnet, olivine, and hornblende.

No. 6. 4'99 per cent. Largest grain 2"5 mm., fine-grained, grey, quartz-
itic sandstone.

Quartz predominated in the remainder, but there were also a great many
concretions of iron, consisting for the most part of sandstone, cemented to-
gether with limonite; and there were also some clay concretions. Further,
there were found a few grains of felspar, magnetite, augite, chlorite, and
biotite.

No. 7. 3*74 per cent. Largest grain 2*2 mm., quartz.

Quartz predominated, but here, too, there were a number of iron con-
cretions. A number of small fragments of quartziferous, fine-grained rocks
were also found, which could not be very accurately distinguished from one
another, possibly quartzite, quartz-porphyry, granulite, or something similar;
also a few grains of felspar and magnetite.

No. 9. 1"96 per cent. Largest grain 1'2 mm., graphite.

The remainder was almost exclusively grains of quartz, with a few par-
ticles of felspar, magnetite, and similar fine-grained rocks as in the preceed-
ing sample, a single piece of sandstone.

No. 14. 025 per cent. Largest grain 0"7 mm., concretion.
The only things found in this sample were 19 brown or black iron con-
retions, 9 grains of quartz, and 1 piece of graphite.

As will be seen from the above, these coarser particles reveal, on the
whole, very little as to the nature of the rocks that have yielded material to
the bottom-samples. The proportion between the various minerals may indeed

38 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

declare something concerning the composition of the original rocks ; but this can
be found out much better from the finer particles, as their number is always
far greater.

As far as we know, the whole of the coast of Siberia along which the
Fram sailed, consists of very quartziferous rocks. On the Western Taimur
Peninsula, granite is found, and crystalline schists ; on the Chelyuskin Penin-
sula, quartzite has been observed. The coarser-grained rocks were not to be
found as such in the bottom-samples, which contain only very small particles;
the fine-grained are met with in a few of them, but on account of their minute-
ness are always in a rather unrecognisable condition. It is impossible to say
whether the quartzite found in samples Nos. 6, 7, and 9 comes from the
quartzite in situ on the Chelyuskin Peninsula. There are still such great
stretches of the coast that are quite unkown, and moreover the material is
quite as likely to have originated from the loose materials on the coast, which,
over long distances, have been observed to form plains outside the solid rocks,
and, as such, will be more likely to be carried away by the shore-ice and the
waves than the solid rocks. As these looser deposits consist largely of mo-
rainic formations, and may have their origin in rocks that are in situ at a
considerable distance, it would be quite impossible to say anything about the
first origin of the by no means many kinds of rock, found in the samples.

With regard to the concretions of iron that are found in certain of
the samples in quite considerable numbers, there may be some doubt about
their primary or secondary origin. It has long been a well-known fact
that on the floor of the ocean concretionary formations of iron and
manganese are often formed. Concretions of iron are of course also found
in the rocks on land whence the material of the bottom-samples originates;
but it is not probable that they would come thence in quantities so large
in proportion to other constituents — especially quartz — found in certain
of the samples. In such cases then, we must assume that the greater
number are formed on the floor of the ocean itself. This is quite certain,
notably in sample No. 14, where the concretions of iron considerably
outnumber the grains of quartz. They must then be looked upon as formed
outside some very ferruginous mineral grains, that have been very easily de-
composable. Their degree of firmness is very varied. They sometimes form
well-defined, hard bodies; but most of them are of a considerably looser

NO. 14.] MINERALOGICAL COMPOSITION OF THE SAMPLES. 39

character, so that they can be partly disintegrated by boiling, and thus cannot
be distinctly seen. The formation of iron concretions is not very closely
connected with the other chemical processes that take place in the samples,
and this confirms the assumption that they must owe their formation to some
ferruginous mineral particle or other. They are found, for instance, in great
quantities both in some of the samples that are of the darkest brown colour,
e. g. No. 14, and in some of the greyest, e. g. Nos. 6 and 7. The appearance
of a brown colour in the clay must also be due to a formation of
ferric oxide, but this has nothing to do with the process by which the
concretions in the clay are formed. The former consists, as already stated,
in a deposit on the surface of the clay, precipitated by the sea-water itself;
and is therefore most abundant in the most slowly formed samples, which
on that account are the brownest. On the other hand, the concretions in
the clay are certainly connected with the formation of the concretions described
in the "Challenger" Report, from the very deepest oceans. Here the deposition
of sedimentary matter takes place so slowly, that the iron and the manganese
of which the concretions are composed, have time to be formed in great,
coherent masses.

Nor can there be said to be much connection between the formation of
iron concretions, and that other, not very well known, chemical process, which
causes the clay to acquire a firmer, more undecomposable consistency. The
formation of concretions will naturally bind the clay together as far as it
extends; but that it is very local may be seen from the fact that in a few
of the samples that contain most concretions of iron, such as Nos. 6 and 14,
the clay otherwise is very incoherent, this being the case particularly with
No. 6.

2. Particles measuring 0 05—0 5 mm.

In order to form an idea of the nature of the rocks that have yielded
material to the samples, it has been necessary to subject the sandy particles
in the samples, to a close examination. On a direct inspection of the sand,
it appeared that by far the greater part of it in all the samples, consisted of
quartz. To make microscopic preparations of the sand as a whole could thus
lead to no result, for in such preparations the other minerals would be pre-

40 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

sent in only very small quantities, so that the differences that possibly existed
between the several samples, could not be clearly brought out. It was there-
fore necessary to separate the quartz from the other minerals, and for this
purpose acetylene bromide mixed with ether until the specific gravity was
2*85, was used. By this means the quartz and the felspar on the one side
were separated from the great majority of minerals on the other. In the
case of the particles that consist of a single mineral, the separation can be
made very complete; but there are of course always a certain number of par-
ticles that consist of a very fine-grained mixture of several different minerals.
There is no definite specific gravity for these, and they may therefore enter
both sections. The same may be said of the iron concretions, which may
have a very different specific gravity, according to their greater or slighter
impregnation with ferric oxide. On the other hand, all the conglomerated
clay that is found between the grains of sand, will come among the
lighter constituents. The percentage of the two parts of sand was directly
determined by weighing. As there was only a very small quantity of sand
in some of the samples, it was impossible in their case to make any separa-
tion; and as an examination in any other way can give no result where it
is a question of pointing out such small differences as those under discussion,
the examination of these samples has been altogether omitted.

a. The Heavier Particles. The mode of treatment here was to count
100 grains of each sample on a slide, and the percentage of the several mi-
nerals is then directly given. The percentage in numbers must correspond
fairly accurately with the percentage in weight. It is true that certain of the
minerals, especially magnetite, have a considerably higher specific gravity
than the others; but in a like degree the size of the particles will be less.
The sizes of grains that were indicated as obtained by washing, are only
applicable accurately to rounded quartz-grains; considerably smaller grains of
the heavier minerals will continually be washed out among them.

The table below gives first the percentage of minerals with a higher
specific gravity than 2-85, and next, the proportion among these of the
various minerals. A cross under any of them indicates that it is not found
among the 100 minerals counted, but on searching in the remainder of the
preparation. It is thus highly probable that such a mineral is present in a
percentage of less than 1.

NO. U.]

MINERALOGICAL COMPOSITION OF THE SAMPLES.

41

in

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blende

Augite

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1

As almost all the samples have, as we have said, a rather marked local
character, there is here, as in most other respects, scarcely any common
feature that binds them together except that they all contain rather small
quantities of the heavier minerals. If, for instance, we compare these samples
with corresponding samples from the west coast of Greenland, we shall see
that the latter nearly always contain considerably greater quantities; even the
one that contains the smallest quantity (No. 38 of the Ingolf Expedition) has
45 per cent of heavier minerals, and the others have 10 per cent or more.
And yet the West Greenland samples also originate solely from very quartzi-
ferous rocks, especially gneiss and other crystalline schists, besides a certain
amount of granite. The cause of the difference must thus be sought else-
where. As Scroeder van der Kolk i has pointed out, the percentage of
heavier minerals is largely dependent upon the amount of alteration to which
the material has been subjected. Of all the minerals in the sand, quartz
is the least liable to alteration, and the longer, therefore, the latter operates,
the larger will be the quantities of quartz found. From this again, it follows
that the greater the number of transportations the material has undergone,
before it has reached the bottom of the sea, the richer will it be in quartz,
as most of the geological processes upon the earth's surface, expose the
material very considerably to the action of the atmosphere.

The difference between the Siberian and the West Greenland samples is
explained quite naturally in accordance with the different geological conditions

1 Bijdrage tot de karteering onzer zandgronden (I), 1895. Verh. der Koninklijke Akad.
van Wetens. te Amsterdam (tweede sectie), deel IV, No. 4.

6

42 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

in the two places. In Greenland the loose deposits play a very small part.
The coast almost everywhere consists of solid rocks, and nearly all the rivers
flow upon rocky ground. In consequence of this, all the constituents come
out into the ocean as nearly in their original condition as possible. Some of
the heavier minerals will probably be altered, but their percentage in the
sand of the sea-bottom will still be not much less than in the original rocks.
A great part of Siberia, on the other hand, consists of sedimentary material,
of which probably a large proportion has its origin at a great distance, and
has undergone numerous transportations before reaching the ocean.

A comparison of these percentages with those known from other places
is also extremely interesting. Schroeder van der Kolk gives a very large
number of measurements of sand-samples from Central Europe, and shows
that in diluvial sand of Scandinavian origin there are percentages of heavier
minerals that as a rule are higher than 0'5, while sand-deposits of more
southern origin as a rule have smaller quantities. Thus the deposits at the
north of Siberia answer with tolerable exactness to the first kind of diluvial
sand, of which samples from Denmark, England, North Germany, and North
Holland have been examined. As the deposits on shore from which the
material of the ocean-floor comes, cannot have a smaller percentage of heavier
minerals than this material itself, we thus have a means of comprehending
the great extent to which the Silurian loose rocks have undergone transpor-
tation and subsequent deposition.

The differences between the percentages for the several samples are due
in a great measure to purely local causes; the various localities obtain their
material from widely different parts of the coast. The large percentage in
No. 3 is characteristic, that sample being taken from a locality not very far
from that of No. 6, which would lead us to expect that their sandy particles
would be of a similar nature. The difference can arise from the fact that
while the greater part of the constituents of No. 6 emanates from the coast
of Siberia or from the neighbouring Kjellmanns Island, No. 3 has obtained
its materials, at least partly, from Sverdrups Island. Different current condi-
tions can also have played their part in the separation of the materials. The
comparatively large percentage (2'45) in No. 15 is more immediately connected
with the circumstance that this sample gets its material from the most eastern
part of Siberia, where the country is rather rich in solid rocks; and it is there-

NO. U.j MINERALOGICAL COMPOSITION OF THE SAMPLES. 43

fore reasonable to suppose that a large proportion of the minerals are of
primary origin.

The proportion between the various heavier minerals exhibits rather
great variations in the various samples. The opaque particles are made up
for the most part of magnetite, but some of them may also consist of the
previously mentioned iron concretions. This is true also of the greater num-
ber of the class named "Aggregates, Concretions, etc." by which is meant grains
that are only very slightly transparent, but which obviously do not consist
of a single crystal. If the latter be the case, the particle is classed with the
mineral in question. The iron concretions, as we have already said, are for
the most part formed upon the sea-bottom itself, round some one or other very
ferruginous mineral, most frequently magnetite ; and thus the sum of the figures
in the first two columns gives the approximate quantity of magnetite deposited
in the sample. The various remaining samples do not differ much in this
respect.

But the proportion of garnets is remarkable. Particularly large quan-
tities are found in samples 7 and 9, which indicates that Asia's most
northern peninsula consists very largely of garnetiferous rocks, (especially
crystalline schists), some of which, in certain places, are found in situ.
According to Nansen the strand on Reno Isle one of the Kjellman group,
was red with garnets, and the micaceous clay at the same place also con-
tained them in abundance. As it appears impossible that samples 7 and 9
can have obtained their materials from such a source we must assume
that there are also garnet-bearing rocks at other places farther east-
wards. The strikingly small quantity of garnet in No. 15 can only imply
that this mineral must be exceedingly poorly represented in eastern Siberia
whence the sample in question obtained the greater part of its material.

The percentage of hornblende in the samples is very characteristic.
No. 1 has quite a considerable quantity, but all the other samples along the
Siberian coast have an infinitesimally small amount. As hornblende is generally
one of the commonest minerals in quartz sand, and as it is also very charac-
teristic and easily recognised in the preparations, it is difficult to imagine any
other reason for this circumstance than that the great majority of rocks in
northern Siberia must be almost destitute of hornblende, but on the other hand
particularly rich in augite, as may be gathered from the generally considerable

44 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

quantity of this mineral found. Sample No. 15 again, contains rather more
hornblende than the samples along the Siberian coast, and it may therefore
be assumed that the rocks containing hornblende occur in rather greater quan-
tities in east Siberia.

b. The Lighter Particles. The same method of treatment has been
employed for these as for the heavier minerals, namely, that of counting 100
grains in a preparation, whereby the percentage of the various minerals is
given directly. As the separation of quartz from felspar in sand preparations
is exceedingly difficult, in some cases even impossible, I first attempted to
separate these minerals by treating the sand with hydrofluoric acid. This
acts upon both minerals, but in such a manner that the surface of the felspar
becomes coated with a layer of insoluble fluoride, while the surface of the quartz
particles remains quite clean. This difference only becomes visible when, after the
sand has been washed, it is placed in a solution of fuchsine or some other
strong dye. The surface of the grains of felspar then becomes coloured,
and their number can be determined by counting. The advantage of this
method is that all the different felspar minerals are separated from the
quartz; but it is not particularly adaptable in practice, as in spite of all
possible variations in the process of the experiment, it appeared that some
of the grains became very imperfectly coloured, so that all possible transitions
were found, and the number per cent could not be counted with very great
exactitude.

I have consequently employed the difference in refraction to determine
the quantity of felspar and quartz. While orthoclase, microcline, albite, and
the plagioclases rich in soda, have a weaker refraction than Canada balsam,
that of quartz, anorthite, and the plagioclases rich in lime, is stronger. By
this means only, some of the felspars can be separated; but the last named
plagioclases will certainly occur in very small quantities in materials originating
from very quartziferous rocks. In most of the grains they will also be
recognised by the oscillatory twinning, as there is a greater probability of their
lying vertically than horizontally on the slides. I have not found, however,
in any one of the samples, a striated grain that had not a weaker refraction
than Canada balsam; and we may therefore conclude from this that these
plagioclases must be exceedingly rare.

NO. 14.]

MINERALOGICAL COMPOSITION OF THE SAMPLES.

45

The actual difference in refraction is observed with extreme ease and
distinctness by the method recently described by Schroeder van der Kolk1,
namely, the employment of oblique transmitted light. If a shade be pushed
under the slide until it reaches the middle of the grain of sand, the latter
appears to have a bright edge on the side turned towards the shade, and a
dark edge on the opposite side if the refraction of the grain is greater than
that of the surrounding medium; if it is less, the two sides are reversed. In
practice this kind of illumination is effected most simply by inserting a ruler in
the space between the mirror and the slide, and at the same time endeavouring
to hold the ruler as near to the latter as possible, or otherwise the opposite
condition of light in the grains may supervene. In this manner a considerable area
of the preparation may be rapidly inspected, and the separate grains of felspar
are then easily recognisable at the moment they come in contact with the
edge of the shadowed part. If the grains are then examined between crossed
nicols, a large proportion of them will show distinct oscillatory twinning, while
the remainder will not show the slightest difference from the quartz grains,
and will here be designated orthoclase. Under this heading, however, are
classed all albite and oligoclase particles that have the twin lamellae lying
horizontally, and also grains of these minerals, that only contain a single
individual. They will certainly not occur, however, in any very great
quantity.

Table of the Percentage of Minerals in the Lighter Parts of the Sand
(specific gravity less than 285).

No. of
Sample.

Concretions,
etc.

Quartz.

Feldspar.

Orthoclase.

Microcline.

Plagioclase.

1
3
6
7
9
15

18

6

15

39

9

9

72
82
77
51
71
75

5
6
7
5
14
7

4
5
1
3
6
6

1
1

2

3

1 "Bijdrage tot de mineraaldeterminatie", Handelingen van het 7" Natuur- en Genees-
kundig Congres.

46 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. POL. EXP.

In the first column are placed all the grains that did not consist of one
or a few recognisable individuals. Under this head come a number of
different minerals and rocks that cannot be very clearly distinguished from
one another. The greater part of the whole class is made up of iron con-
cretions, which, unlike those found among the heavier particles, cannot be
very strongly impregnated with iron. There is also every possible transition
to particles that consist exclusively of coagulated, hardened clay. The grains
in this column are to a smaller extent made up of fine-grained rocks such
as sandstone, porphery, etc. In the samples that contain particularly large
quantities in this column, by far the greater number are grey clayey particles,
e. g. No. 7, where the quantity is so great that the sand acquires a peculiarly
impure appearance. The proportion between the clayey matter and the other
mineral particles has been previously discussed as regards each separate
sample, and will not be further commented on.

Respecting the proportion between felspar and quartz, the various
samples exhibit certain differences which may arise partly from the kind of
rock from which the sample had its origin, and partly from disintegration,
which will always greatly affect the felspar, and thus lower the percentage
in proportion to that of the quartz. The proportion of felspar is smallest
in No. 46, where the quantity is about ^ that of the quartz, and rises with
every possible transition to No. 9 where the proportion is 2 : 7. For the
rest it is impossible to say anything more definite as to the causes of these
variations, as long as nothing more definite is known about the geological
conditions in the places whence the samples come.

The same may be said of the proportion between the various kinds of
felspar. On an average, about half of them are orthoclase. No. 6, however,
shows a remarkable exception to this, 7 out of 8 particles being orthoclase.
This sample must thus have originated from rocks that are essentially different
from the remainder. The quantity of plagioclase is always far below that
of the other kinds of feldspar, which corresponds with the general proportion
in granites and crystalline schists.

IV.
ORGANIC CONSTITUENTS OF THE SAMPLES.

We still have to mention the organic particles in the samples. The
exceedingly unimportant part which these play has already been pointed out
in the introduction. In the samples taken nearest the coasts, there is hardly
any trace of organisms, and even in the deep-sea deposits there are strikingly
few, as compared with corresponding deposits from other oceans. The
reason of this is of course, that the greater part of the sea to the north of
Siberia is covered with ice all the year round, and therefore the conditions
for the development of plants or animals at the surface, are as bad as they
possibly can be1. This will appear more clearly in the following pages, in
which the quantities of the various organisms in the samples, will be briefly
reviewed. There is no question of the determination of the various species,
as that is beyond the scope of this paper. All that can be done here is to
establish the importance of the organisms as rock-forming constituents, in
order to have a basis of comparison between these deposits and other
corresponding deposits from early and late periods.

Remains of Algce are found in certain of the samples, always in
extremely small and indeterminable fragments. They can only be found in
the rapidly-formed deposits nearest land, as in others they would be destroyed
in the course of time. As a rule they are found in very small quantities, a
single piece, or a very few pieces, being found among the coarser constituents
of most of the shore deposits; the greatest quantity is found in No. 1, in
which, however, they can only be estimated at 10 per cent of the coarser

1 For the reasons of this, see Nansen's account in the 3rd vol. of the present work.

48 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. pol. exp.

constituents, or 0*14 per cent of the whole sample. As will be pointed
out below, the contents of a part of the samples taken from the surface of
the ice, include appreciable quantities of Algae; but even on the assumption
that a portion of this material will be able during the summer to thaw out
and settle on the bottom, it is nevertheless probable as before mentioned, that
all organic matter will be soon decomposed in the more slowly formed
samples, and algae are therefore not found in any one of them.

Siliceous Organisms have not been observed in any of the bottom-
samples of the Fram Expedition. This is very remarkable, as sponge
spicules and diatoms in particular, are generally found in very great quantities,
and are scarcely ever absent, even from the samples formed nearest land.
If found at all, it must be in exceedingly small quantities, as a considerable
number of all sizes of particles have been examined under the microscope,
and these organisms are always very conspicuous. Even in the small area
of open water found in these regions, diatoms must be very feebly represented;
and the entire ocean-floor where the samples were taken must be nearly
wholly destitute of siliceous sponges.

Fragments of Mollusc Shells are found in several of the samples among
the coarser particles, but never more than 1 or 2 very insignificant pieces,
except in No. 6, where they occur in somewhat greater numbers, though
only in indeterminable fragments.

Foraminifera, which are generally particularly characteristic of bottom-
deposits, play a very unimportant part in these samples, although they occur
in considerably greater quantities than any of the other organisms. There
are only 2 specimens of the larger forms — more than 0*5 mm. — in the
samples, viz. a rotaliform foraminifer in No. 6, and a Haplophragmium in
No. 6. As usual, by far the most numerous of the smaller forms are
Globigerinae, with a very few rotaliform foraminifera; it is only in the samples
from near the shore — and this is also the case elsewhere — that the last
named may be in the majority, or even the sole occupants. The smaller
forms of Foraminifera were found in the following samples:

No. 2, a few rotaliform Foraminifera

No. 7, a single Globigerina

No. 9, some Foraminifera, chiefly Globigerinae

No. 13 a, a few Foraminifera, exclusively Globigerina?

NO. H.] ORGANIC CONSTITUENTS OF THE SAMPLES. 49

No. 14, about 10 per cent of the sand (0'57 per cent of the entire
sample) was made up of Foraminifera, almost exclusively Globigerinae. The
difference of their quantity in this and the preceding sample is not easy
to account for, as they were taken in the immediate vicinity of one another,
and are very similar in all other respects.

No. 15, about 40 per cent of the sand (383 per cent of the entire sample)
was made up of Foraminifera, almost exclusively Globigerinse. This is the
largest amount that has been found in any of the samples. There was too
little of No. 16, which lay considerably farther to the NW, for examination;
but the chemical analysis shows that this sample can contain only very few
Formanifera. The reason of this is probably to be found in its situation in
rather close proximity to Franz Josef Land, of which the consequence is a
large deposit of terrigenous matter. If there is any part of the sea north of
Siberia where one might expect to find samples even richer in Foraminifera,
it must be the still unknown regions north-east of No. 15. It can hardly
be expected, however, that a percentage will be found anywhere so relatively
large, as to permit of the sample being designated Globigerina Ooze.

Coccoliths were found only in No. 15, and then only after a very long
search, and in very small numbers. They are so unbroken, however, that
it is not probable that they originate from early deposits in Siberia. As they
occur in such small numbers, it is not certain that they come from cocco-
spheres that have lived in the Arctic Ocean itself; but they may possibly
have been brought all the way from the Atlantic Ocean by the previously
mentioned, warm undercurrent. In size and shape they exactly correspond with
the species found in the North Atlantic, described by Ostenfeld1 under the
name Coccosphaera atlantlca.

It will be sufficiently evident from the above, that the samples here
discussed contain, as has been already pointed out, exceedingly few organic
constituents, and therefore, in this way, occupy a somewhat unique position
among sea-bottom deposits. When the organisms are not found in larger
quantities in bottom-samples, the deeper of which at least must be assumed

1 'Ueber Coccosphaera und einige neue Tintinniden im Plankton des nOrdlichen Atlant-
ischen Oceans.' Zool. Anzeiger, Vol. XXII, No. 601, 1899; and 'Ueber Coccosphaera.'
Ibid, Vol. XXIII, No. 612, 1900.

7

50 O. B. B0GGILD. BOTTOM DEPOSITS. [noRw. POL. EXP.

to have been formed exceedingly slowly, the animal and plant life in the
sea in question must have reached a minimum as regards the siliceous and
calcareous shell organisms. It has also already been shown that this accords
well with the physical conditions in these regions, especially with their
being covered so extensively with ice.

SAMPLES TAKEN FROM THE SURFACE OF THE ICE.

It is convenient to give an account here of 5 samples taken from the
surface of the Ice between April and June 1894, in a region NW of the New
Siberian Islands about 80—83 N by 120—135 E. In most respects they show
close resemblance with one another as also with the finer bottom samples.

An investigation of these surface samples promised, it might be expected,
less of interest than the bottom samples themselves; the constitution of the
latter is in every case intimately related to the physical conditions prevailing
round about the district concerned. And indeed since the composition and
constitution of the bottom is very largely a direct result of the co-operation
of influences of this kind, it is from a suitable investigation of samples, pos-
sible to draw many valuable conclusions as to these influences. On the other
hand, a sample taken from the Ice might conceivably have originated entirely
from one locality or have come, indeed, direct from land; in any case its
origin and destination is very largely a matter of mere accident. The samples
here under consideration probably came from the coast, broken loose by wave
action from the shore ; or material may have fallen from the land out on to the
ice or have been brought down by rivers, already occluded in the frozen sur-
face. The constitution of a sample depends upon the nature of the rocks in
the neighbourhood from which it came; it may evidently be very variable.
The fact that all the samples here described show a very markedly similar
composition can only be explained on the basis that all have the same origin.
It is true they were taken at places far apart, but it must at the same time

NO. 14.

SAMPLES TAKEN FROM THE SURFACE OF THE ICE.

51

be borne in mind that the ice in this region was travelling in the same
direction as the Fram and at about the same rate, which would make it pos-
sible that all the samples were taken from a relatively limited area of ice,
and it may well have been, from one and the same locality. In this district
one must always remember there is a strong probability that earthy matter
once in the ice, may be carried a great distance from land.

The importance of such samples as evidence bearing on the agencies at
work in forming the sea bottom may in other cases be very great indeed;
but in connection with the bottom-samples of this expedition they are of only
very insignificant, or no importance. For practically the whole year the ice is one
continuous, massive sheet all the while growing in thickness through the
freezing going on at its lower surface; there seems small likelihood that the
ocean bottom can receive appreciable increment from this source. In some
places however, notably in the Atlantic ocean where the ice is continually
melting, this factor may become of importance, and an investigation of
samples bearing on this fact might be of great interest.

The 5 samples are rather fine, as will be seen from the analyses here
given. In all cases the colour is practically pure grey, as would be expected,
since a brown colour is, as already mentioned, only developed after the
lapse of some considerable time on the sea bottom. They are rather friable;
most of the particles seem to wash out with the fine constituents, but it is
difficult to draw definite conclusions from this kind of circumstance because
as already stated, it may have happened that all have come from the same
place.

The following table gives the results of a mechanical analysis of the
samples.

No. of
sample

Date
1894

Constituents

Less than
0-01 mm.

0-01-0-05
mm.

0-05-0-5
mm.

More than
0'5 mm.

I
II
III
IV

V

April

May 24th
June 2nd
June 4th
June 17th

57-5
62-3
573
599
523

33-9
34-6
41-3

34-8
469

8-5
3-1
1-4
5-3

08

01

0

0

0

0

52 0. B. B0GGILD. BOTTOM DEPOSITS. [norw. POL. EXP.

A comparison of these numbers with those of the bottom samples shows
that these are on the whole finer than the four samples of grey deep water
deposits, which on an average contained 6"03 % between 005 and 05 mm. and
06 % between 05 and 1/0 mm. The finest of these samples (Nrs. Ill and
V) are markedly finer than the finest of those from the bottom (No. 10 c);
it contains on the whole extremely little sandy material among the clay
particles, which fact places it in this respect, nearest to the plastic clays of
the tertiary period. It is however scarcely legitimate to infer that it has
actually originated from a formation of that age, since it would probably
not be difficult to find among alluvial clays some of similar character. In
any case it seems unlikely that there can have been any washing out of the
clay, during the time it was being transported from its original starting point
out on to the ice.

The mineralogical composition was not investigated in detail; the small
proportion of particles over 0-5 mm. in Nr. I was found to consist almost
always of Algae in fragments, and in some cases of Foraminifera which were
very probably occluded by the ice during a period when open water
conditions obtained. There were a few particles of conglomerated clay and
very few quartz grains. The sandy constituents were almost always
wholly quartz ; the quantity is however so small that it is not possible to say
whether a separation of the constituents could be accomplished by treatment
with fluids of different densities.

APPENDIX I

to Memoir No. XIV.

ANALYSES OF THE BOTTOM DEPOSITS FROM THE NORTH POLAR BASIN.

By Dr. 0. N. Heidenreich and Dr. Charles J. J. Fox.

ANALYSES OF BOTTOM DEPOSITS FROM NORTH POLAR BASIN.

By Dr. 0. N. Heidenreich.

Number of Sample

10 a.

10 c.

11.

12.

13 a.

14.

15.

16.

17.

Date

Oct. 4.
1893
78° 42'
135° 40'
1460 m.

Oct. 4,
1893
78° 42'
135° 40'
1460 m.

Oct. 21,

1893
78° 19'
135° 45'
135 m.

Oct. 26,

1893
78° 31'
136° 10'
100 m.

May 1,

1894
80° 46'
131° 18'
3800 m.

Aug. 6,

1894

81° 8'

127° 32'

3850 m.

Jan. 23,

1895
83° 24'
102° 14'
3450 m.

July 23,

1895
84° 32'
72° 20'
3700 m.

July 8,

1896 '

83° 2'

12° 52'

3400 m.

N. Lat

Depth

Loss on Ignil

Si03 s

Ti09

A1203

Fe303

FeO

MnO ,
Mn02
CaO

MgO

K20

Na,0 ....

C02

p2o8 J

Si03 .

Al2Oa

F1203 ....

FeO

CaO
MgO

Ka0

Na3

ion

w

o_

ef
er

r^

5'

ta

1 ©

o
o

Er"

O

X

Q

=T

00

o
c"
er

re*

5'

ta

©

o
a

a

6-41 °/„
0-07 -

o-oo -

401 -

5-30 -

2-40 -

0-30 -

043 -

079 -

1-62 -

0-65 -

0-38 -

0-41 -

0-21 -

22-98 -

57-97 -

1254 -

1-87 -

o-io -

050 -
0-64 -
253 -
1-59 -

77.74 -

640 %
0-11 -
000 •
4-68 -
5-25 -
2-95 -
0-40 -
0-74 -
0-74 -
2-17 -
0-75 -
026 -
037 -
0-29 -
25-17 -
56-11 -
1207 -
150 -
0-17 -
055 -
0-88 -
2-48 -
1-47 -
75-23 -

4-75 %
0-11 -
000 -
448 -
3-52 -
2-98 -

| 011 -

0-35 -

1-69 -

0-59 -

0-35 -

0-26 -

0-22 -

1941 -

6308 -

1116 -

1-45 -

0-20 -

0-56 -

021 -

2-42 -

1-93 -

81-01 ■

5-43 o/D
011 -
000 -
4-25 -
336 -
2-76 -
0-12 -
0 10 -
0-64 -
1-77 -
041 -
0 39 -
0-51 -
0-07 -
19-92 -
62-27 -
10-96 -
1-53 -
013 -
0-18 -

o-io -

2-73 -

2-42 -
8032 -

5-81 »/„

0-18 -

not det.

530 -

> 7-12 -

| 0-39 -

073 -

1-78 -

1 not de-
termined

60-50 -
12-14 -

J 1-53 -

105 -

036 -
) not de-
Jtermined

5-81 %
060 -
000 -
4-74 -
4-71 -
1-97 -
064 -
011 -
0-85 -
1-21 -
0-38 -
0-31 -
077 -
005 -
22-15 -
59-35 -
11-99 -
1-29 -
009 -
0-43 -
0-58 -
2-35 -
1-92 -
7800 -

5-03%
010 -

o-oo -

4-50 -
327 -
4-06 -
0-58 -
005 -
2-61 -
1-40 -
0-26 -
089 -
2-20 -
0-26 -
2511 -
57-11 -
1114 -
1-78 -
019 -
095 -
029 -
2-48 -
107 -
7661 -

8-24 »/„

010 -

not det.

5-08 -

} 8-87 -

\ 0-49 -

1-12 -

2-61 -

0-41 -

0-22 -

not det.

0-17 -

27-32 -

5241 -

14-05 -

} 2-07 -

076 -
0-61 -

2'42 -

1-34 -

73-66 -

5-58 •/„
011 -
000 -
4-65 -
5-69 -
1-92 -

0-47 -

1-61 -

1-87 -

0-65 -

0-28 -

1-31 -

0-22 -

24-36 -

57-47 -

12-35 -

1-27 -

011 -

041 -

0-27 -

2-09 -

1-45 -

75-72 -

100-72 °/o

100-40 °/0

100-42 °/0

100-24 °/„

100-15 °/0

100-71 »/o

10097 %

100-08 %

1 The Date and Locality was not indicated on the label of this sample, but there is
but little doubt that the above date is the correct one. F. N.

ANALYSES OF BOTTOM DEPOSIT.

By Dr. Charles J. J. Fox.

Prof. Nansen brought me what was left over of Samples 10, 10a, 10c,
with the request that 1 would carry out a few analyses just to obtain some
idea of the order of accuracy of the methods as employed above by Dr.
Heidenreich. Sample No. 10 was in three portions, one being distinctly
brownish another brownish grey and the third one grey. They are referred
to here as 101 102 103 respectively. The samples as brought to me were
from 6—8 gms. each, and therefore really too small to allow of as complete
an investigation of this obviously important point, as would have been desirable.

After due consideration it was decided to estimate in each sample, the
Ferrous and Ferric Oxides and in addition, in the cases of samples Nos. 10a
and 10 c the Lime and Carbonic Acid. These seemed to be the most important
constituents and after a short preliminary investigation, it also appeared likely
that they could be estimated even on such small samples, with very fair
accuracy.

Some of the samples were in alcohol and some were dry; all were
powdered finely and dried in a dessicator for a few days. It then appeared
that they were slightly hygroscopic and the weighings had to be done from
a closed weighing bottle. Of each sample two quantities of about 2 gms.
each were weighed out; the one sample was used for a determination of the
Iron (ferrous and ferric) and the Lime, and the other for the Carbonic Acid.
The former sample was boiled for some time in an air-free flask with 30 cc.
of 20% HCI. After allowing to settle, the liquid was rapidly decanted, the
residue washed thoroughly and the washings added to the bulk of the liquid.
The whole was much diluted and then titrated with Potassium Permanganate
to get the amount of Ferrous iron; pure zinc was added and the whole

56 0. B. B0GGILD. BOTTOM DEPOSITS. APPENDIX I. [norw. pol. exp.

of the iron reduced to the Ferrous state and again determined by the same
method. These titrations furnished the data for calculating both the Ferrous
and the Ferric Oxides. To the solution obtained after these operations
Ammonium Chloride, Ammonia and a slight excess of Ammonium sulphide
were added. The precipitated Fe., Mn. etc., was then filterred off, the filtrate
warmed and an excess of solid Ammonium Oxalate added to precipitate the
Calcium. The Calcium Oxalate was filtered off, dissolved in HC1 and repre-
cipitated with Ammonia, to remove traces of Magnesium possibly carried down
with it. Finally it was transferred to a Berlin porcelain crucible, carefully
heated and weighed as Carbonate; it was then treated with a drop of
Ammonium Carbonate solution, gently warmed and reweighed, the operation
being repeated until a constant weight was obtained. In this way it was
made quite certain that the Calcium was quantitatively in the form of
Carbonate.

It was feared that the determination of the Iron might not be quite exact
by this method, owing to partial oxidation of the HC1, even though rather
dilute, by the Permanganate1. To make quite sure of this, a similar quantity
of the original sample was treated in the same way as before but with 30 %
Sulphuric Acid, instead of Hydrochloric Acid, and the estimation of the Iron
repeated as a control. It will be seen that the agreement of the two methods
is satisfactory; though a lack of agreement might possibly not be regarded as
unsatisfactory, inasmuch as there is no reason to suppose that the two
methods would furnish the same results in the case of every clay.

The Carbonic Acid was determined gasometrically; the apparatus
used, which has been specially designed for determining the gases dissolved
in sea water2, allowed the clay to be introduced, boiled with acid and the
volume of the Carbonic acid evolved, to be estimated with an accuracy of a
few hundredths of a cc. — an order of accuracy higher than here required.

1 This is the method as used by Tornoe and subsequently by almost all who have
carried out thiskind of analysis. It appears to be rather reliable as the analyses
here recorded also appear to show, but according to my experience it is better to do
the titration with Permanganate after adding a solution of Manganese Sulphate and
Phosphoric acid to the Iron solution. The end point is then much more permanent
as well as sharper. (See Classen, AusgewShlte Methoden der Analytischen Chemie.
Braunschweig 1901. Vol. 1. p. 455).

1 See Charles J. J. Fox, On the Determination of the Atmospheric Gases dissolved in
sea-water. Publications de Circonstance No. 21 du Conseil permanent international
pour l'exploration de la mer, Copenhague 1905.

NO. 14.]

C. J. J. FOX. ANALYSES OF BOTTOM DEPOSIT.

57

FeO

FeaOa

CaO

co2

HC1 sol.

H2S04
sol.

HC1 sol.

H2S04
sol.

10'

263

2-55

5-68

553

-

-

102

3-20

306

566

549

-

-

103

349

3-58

511

515

-

—

10a

321

Heidenreich 2'40

306

5-60
Heidenreich 5'30

511

•82
Heidenreich -78

•40

■41

10 c

2-88
Heidenreich 295

2-79

535

Heidenreich 5'25

550

•79

■74

•40
■37

The results of these few analyses appear to agree very well under the
circumstances with those obtained by Heidenreich, except in the case of one
Iron estimation ; and it may be assumed that the methods adopted give quite
reliable results. It is commonly believed that in a clay deposit graduating
from brown to grey through grey-brown and brown-grey, the ratio of Ferrous
to Ferric oxide found, should alter simultaneously with the change of colour
— the Ferrous oxide giving to the clay its grey-green and the Ferric oxide
its brown colouration. And this may on the whole be said to hold in the
case of the samples here under consideration, with possibly just one exception.
This exception however, happens to coincide with the above mentioned
discrepancy in the two Iron estimations of Heidenreich and myself. As will
be seen from Heidenreich's analysis, a greyish sample appears to have a
higher percentage of Ferric iron than a brown layer of the same clay; my
analysis on the other hand seems to indicate the exact contrary. In view of
the fact that the samples have been all used up, it is now impossible to
decide which is right for certain, but inasmuch as the former result appears
unlikely and the latter what might be expected, it seems at all events safe to
say that so for as is known a brown layer probably does contain more
Ferric iron than a grey layer of the same clay.

Kristiania, May 27tb 1905.

APPENDIX II

to Memoir No. XIV.

THALAMOPHORA FROM THE BOTTOM SAMPLES AND THE MUD FROM THE
SURFACE OF THE ICE IN THE NORTH POLAR SEA.

By Hans Kler.

In the following account of the Thalamophora from Prof. Nansens
bottom samples, r — indicates rare, c — common, v. c. — very common.

No. 1.

Juli 24, 1893. 10 p. ra. 130 m.
71° 17' N. Lat.; 48° 22' E. Long.

Truncatulina ungeriana (r).

No. 2.

Aug. 17, 1893. 12 midnight. 46 m.
75° 10' N. Lat.; 80° 31' E. Long.

Polystomella sp. (r).

No. 3.

Aug. 18, 1893. 9 a. m., 26 m.
74° 38' N. Lat.; 80° 15' E. Long.

No Thalamophora.

No. 4.

Aug. 18, 1893. 12 noon and 2 p. m., 40 m.

74° 29' N. Lat.; 80° 32' E. Long.

No Thalamophora.

No. 5.

Aug. 18, 1893. 10 p. m. 39 m.

73° 51' N. Lat. ; 80° 44' E. Long.

Polystomella sp. (r).
Haplophsagmium nanum (r).

No. 6.

West of the Kjelman Islands.

Polystomella artica (r).

No. 7.
West of Taymyrsound.

Polystomella artica (r).
Spiropleda biformis (r).
Pulvinulina Karstenii (r).

No. 8.

Sept. 13, 1893. 12 noon. 20 m.

74° 55' N. Lat.; 116° 40' E. Long.

Polystomella ardica (r).

„ subnodosa (r).

„ striatopunctata.

var. incerta (r).

No.9.

Sept. 13, 1893. 8-30 p. in.
Off. Anabara. 40 m.

No Thalamophora.

NO. 14-]

HANS KLER. THALAMOPHORA.

59

No. 10.

Oct. 4, 1893. 1460 m.
28° 42' N. Lat.; 135° 40' E. Iang.

The upper layer (No. 10a).

No Thalamophora.

Between upper and under
layer (No. 10b).

No Thalamophora.

The under layer (No. 10c).

Reophax difflugii formis (r).
Nodulina sp., young specimens (r).

No. 11.

Oct. 21, 1893. 135 m.
78° 19' N. Lat. ; 135° 45' E. Long.

No Thalamophora.

No. 14.

Aug. 6, 1894. 3850 m.

81° 8' N. Lat. ; 127° 32' E. Long.

The upper layer.
Gloligerina bulloides (v. c).

„ pachyderma (v. c).

Reophax difflugii formes (r).
Discorbina arancana (r).
Pullenia quinqueloba (r).

No. 15.

Aug. 7, 1894. 3850 m.

81° 7-6' N. Lat.; 127° 27' E. Long.

The upper layer.
Globigerina bulloides (v. c).

„ pachyderma (v. c).

Quinqueloculina seminulum (r).
Polystomella arctica (r).

No. 16.

Jan. 23, 1895. 3450 m.

83° 24' N. Lat.; 102" 14' E. Long.

Globigerina btdloides (v. c).

„ pachyderma (v. c).

Pullenia sphaeroides (c).
„ quinqueloba (c).
Lagena orbignyana (r).
Botivina punctata (r).
Spiroplecta biformis (r).
Discorlina berthelothiana (r).

„ arancana (r).

Quinqueloculina seminulum (c).

Sample from the surface of the ice.
Nodulina scorpiura (r).
Cassidulina crassa (r).
Polymorphina lactea (r).
Nonionina scapha var. labrado-
rica (r).

Globigerina bulloides.

Exists in great quantities and varying size in the great depths of the
Polar sea. The larger specimens are always thick-shelled, while the smaller
have generally thinner shells. The size of the shells is variable, from
0-1—0-3 mm. Only a few small 2—4 chambered shells were found (size:
0-03-006 mm.).

Globigerina pachyderma.

Very common, as in the case of the preceding species. Size: 0-l — 0-38 mm.
There also occur some small, starved, thick-shelled specimens.

60 O.B.B0GGILD. BOTTOM DEPOSITS. APPENDIX II. [NORW. POL. EXP.

Between bulloides and pachyderma numerous transition forms were
observed.

The Globigerina shells seem to have been dead for a long time. They
are either empty or filled with a brown granular mass, which absorbs dye-
stuffs badly1. This mass is certainly mud. The thickness of the shell-wall
is 0012— 0-035 mm.

The other Thalamophora, from the brown clay are true bottom forms.
The most of them are small, starved deep water forms, only three species,
Bolivina punctata, Spiroplecta biformis and Polystomella arctica are as a
rule distributed in comparatively shallow water.

The size of Pullenia sphaeroides is 007 mm.

„ „ „ „ quinqueloba „ 0-07— 0-16 mm.

„ „ „ Lagena orbignyana „ 02 mm.

„ „ „ Bolivina punctata „ 01 „

„ „ „ Spiropleda biformis „ 0-14 „

„ „ „ Discorbina berthelothiana „ 0-042— 0072 mm.
„ „ „ „ arancana „ 0-14 mm.

„ „ „ Quinqueloculina seminulum „ 03 „

With respect to the occurrence of Thalamophora it may be said that
the mud from the depths of the North Polar Basin is very much like
the Biloculina clay in the Norwegian Sea, although it lacks the Biloculina
shells. But the other Thalamophora occur in like number and appearence
just as in the Biloculina clay. This is aspecially true of Globigerina as also
of the true bottom forms such as Quinqueloculina seminulum, Pullenia
and Discorbina spp. etc.

The bottom forms are proportionally rare and they probably originate
from mud, which the ice constantly carries from the coasts of the Polar Sea.
The occurrence of salt water Thalamophora in the mud from the surface of
the polar ice, shows that the mud belongs to recent or post-tertiary marine
deposits.

The mud from 1600 metres lacks Thalamophora. Only in the under
layer were some small arenaceous shells found, of which one specimen,
Reophax difflugii formis, is distributed in deep water deposits from Franz

1 The majority of the bottom samples were preserved in spirit.

NO. 14-] HANS KI^R. THALAMOPHORA. 61

Josephs land to the Antarctic Ocean. The Thalamophora from the shallow
water along the Siberian coast are pure arctic and are only mixed with a
few boreal forms.

In the brown clay from 3850 metres one fragment of a Radiolaria was seen
and in the grey clay from the surface of the ice and from a depth of 39
metres at the Siberian coast, some Diatoms (Coscinodiscus sp.). In the
mud from the ice were also found some badly preserved and indeterminable
vegetable substances, probably grains or fragments of moss. Prof. Wille and
cand. Holmboe have assisted me with the examination of the vegetable
fragments and Diatoms, for which ready assistance I would here express
my thanks.

Empty shells of shallow-water molluscs were found scattered over the
deep parts of the Arctic Ocean by the Norwegian North Atlantic Expedition
1876—1878.

Dr. A. S. Jensen has attempted to explain this phenomenon as connected
with a subsidence of the sea-bottom1. The remains of shallow-water animals
found there, would thus be fossil remains.

Friele and Grieg on the other hand think, that the shell-fragments must
have been carried out into deep water by the ice2.

Certainly it would be interesting, in order to obtain a satisfactory
explanation of the phenomenon, to examine the distribution of Thalamophora
in the nothern oceans.

Rhabdammina abyssorum is very common in the Arctic Ocean between
Norway, Spitsbergen and Novaja Zemlja, and also in many of the Norwegian
Fjords of depths of 100—600 metres (in the Sogne Fjord to 1200 metres).
Only in the eastern portions of the Bilocidina mud were some few fragments
found to a depth of 2000 metres.

On the other hand Rhabdammina abyssorum does not exist in shallaw-
water, but the occurrence of the species as sub-fossil in some parts of our
Fjords especially the Kristiania Fjord3 proves its comparatively great age.

Operculina ammonoides is very common along the coast of Norway to
Vadso, and is never found at greater depths than 624 metres, except in one

1 Om levninger af grundtvandsdyr .... Vidensk. Meddel., 1900, p. 229.

5 The Norwegian North Atlantic Expedition 1876-1878, vol. XXVIII, p. VIII.

3 H. KiJEn, Synopsis Norw. Mar. Thai. p. 55.

62 0. B. B0GGILD. BOTTOM DEPOSITS. APPENDIX II.

locality, the Sogne Fjord, where it was found at a depth of 1036 metres.
The species occurs in the post-tertiary deposits of Norway.

Uvigerina pygmaea and Biloculina simplex have similar distribution.

Operculina ammonoides is not found north of Norway.

Not a specimen nor a fragment of these three Thalamophora were
found in the Norwegian North Atlantic Ocean.

If this Ocean was shallow in Quarternary times, we should now expect
Rhabdammina abyssorum and the three other species to be common there.

On the other hand Thalamophora occurs in mud taken from the ice
by Nansen's North Polar Expedition and also in mud from the ice in the
Denmark Strait, collected by Nansen in 1882.

In the mud from the surface of the ice from Denmark Strait, kindly
sent me for examination by Prof. Nansen, very few Thalamophora were
to be seen, in fact only three specimens of Trochammina inflata. The
other sample of mud from the ice contained proportionally1 many more
Thalamophora-organisms and altogether it seems probable that an examina-
tion of mud from different parts of the drifting ice would show the presence
of a great many Thalamophora.

1 Of the mud from the ice from Denmark Strait Prof. Nansen sent me V4 of a 'itre-
which was treated by Dr. Madsen's method (V. Madsen, Istidens Foraminiferer i Dan-
mark og Holsten. Copenhagen 1895). The other sample was not very large.

ERRATA.

Page 8. Table, 2nd column, line 17, read 189*. May 1.

Page 9. Table, last column, for 7 a, 7b, and 7c read 10a, 10b, and 10 c,

for 10 b read 13 b.
Page 14, line 8 for No. 12 read No. 15.

EXPLANATION OF THE PLATES.

PI. I. The map of the North Polar Sea gives the position of Stations where bottom-
samples were taken during the Expedition.

Pis. II & III. The Curves illustrate the quantities and different sizes of the grains in the
samples of bottom-deposits. The area delimited by the upper Curve represents the
whole of the sample. The lower curve represents the actual mineral grains (mostly
Quartz). The area between the two curves therefore represents the Clay.
For further explanation see also pp. 22—27.

The Norwegian North Polar Expedition 1893-96 No I**

Map of the North Polar Sea, shaming Stations <•> where Bottom- Samples have Veen taken.
The figures (2) at the stations indicate t/ie numbers of the Bottom.- Samples (sec/Table p.8)

fc.ii-nll.iio.jr Wwitt.Oir-a

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XV.

ON DEAD-WATER:

being a description of the so-called phenomenon often hindering the head-
way and navigation of ships in Norwegian Fjords and elsewhere, and an
experimental investigation of its causes etc.

BY

V. WALFRID EKMAN

WITH A PREFACE BY

PROFESSOR VILHELM BJERKNES.

PREFACE.

J. he present investigation of "Dead-water" was occasioned by a letter in
November 1898 from Prof. Nansen asking my opinion on the subject. In my
reply to Prof. Nansen I remarked that in the case of a layer of fresh water
resting on the top of salt water, a ship will not only produce the ordinary
visible waves at the boundary between the water and the air, but will also
generate invisible waves in the salt-water fresh- water boundary below; I
suggested that the great resistance experienced by the ship was due to the
work done in generating these invisible waves. In addition to some inaccur-
acies — at that time I was not intimately acquainted with the theory of water
waves — my letter further suggested a plausible explanation of the suddeness
with which the resistance ceased: when the ship's speed has become so great
that the waves in the boundary below cannot follow her, the work done in
sustaining them will be saved.

The matter was subsequently discussed once or twice when Prof. Nansen
and I occasionally met, and it was finally decided that I should have the sub-
ject rigorously examined by experiment. In December 1899 I consequently
suggested to a pupil of mine at the Stockholm's Hogskola, Dr. V. Walfrid Ek-
man, now assistant in the Central Laboratory for the International Study of the
Sea, Kristiania, that he should do some simple preliminary experiments. From
the very beginning they were successful and furnished results confirmatory of
the above mentioned assumptions.

IV

Mr. Ekman has since the beginning of the following year been carrying
out the systematic investigation of the phenomenon, and the present paper
embodies the results obtained independently by him since then, without any
intervention from me.

Stockholm, 1903.

V. BJERKNES.

INTRODUCTION.

Norwegian seamen often speak of a strange phenomenon which they call
"dodvand" or dead-water, and which without any visible cause makes the
vessel lose her speed and refuse to answer her helm. Their only definite
knowledge of its origin is that it exists solely at places where the sea is co-
vered by fresh or brackish water. The same phenomenon is known by sea-
men in other countries although to a much smaller extent; but most people
have certainly never heard of it. The tales of dead-water have often been
regarded as mere fictions of the imagination.

When the From made her way along the Siberian coast in the autumn
of 1903, she three times met with dead-water off Taimur Island. This occur-
ence made Prof. Nansen very desirous of having the causes of the pheno-
menon cleared up, and it led, as mentioned in the Preface, to Prof. V. Bjerk-
nes' explanation of the phenomenon and to the present investigation. If the
objective reality of dead-water may now he acknowledged as an undeniable
fact and if its causes are, in the main, known, they may certainly be reckoned
among the scientific results of the first Fraw-expedition.

In addition to the collective description of the dead-water, which intro-
duces Chapter I, the original accounts are frequently inserted in detail, and
for two reasons:

1) The narratives are not in every detail quite in accordance with one-
another, and it was not possible always to decide in what degree the features
of the phenomenon itself, are variable, or what descriptions are the most cor-
rect. They ought therefore to be accessible to the reader's criticism.

VI

2) It was thought that the original accounts would best give a clear and
complete picture of the phenomenon in its different aspects. Parts of Accounts
Nos. 1, 5, 6, 8, 9, 10, 13 may be specially referred to in this respect.

In some of the accounts desirable rearrangements and alterations in form,
have been made, but in every case, I have endeavoured to render the sub-
stance as exactly as possible. Statements, apparently having no particular
import have been omitted. Of the narrators' own explanations of the phe-
nomenon, their means of getting rid of it, etc, only a summary is given in
the collective description. A mile, when the contrary is not expressly stated,
always denotes an English nautical mile (= 1852 m.); all other measurements
are reduced to the metric system.

Some parts of Chapter II on matters bearing on the subject, are merely
a summary from other books and are inserted only for the convenience of
the reader. A brief account of Sir John Scott Russell's experiments on
phenomena in canal navigation, which are remarkably analogous to "dead-
water", is found in this chapter. It is interesting to notice here, that from these
phenomena and Lord Kelvin's and Sir G. G. Stokes' mathematical treatment
of them and of waves in the boundary between two liquids (see p. 139 and
p. 41), it would be but a short step to anticipate that waves in the salt-water
fresh-water boundary should cause effects quite similar to those here recorded
of "dead-water". It would, however, owing to the small difference of specific
gravity between the two water-layers, be rather difficult to believe a priori,
that the effect should prove so powerful as it actually is.

The experiments, although simple typical conditions were selected so as
to allow of a simple discussion, were so carried out as to imitate as closely
as possible on a small scale, real cases. A model of the Fram and some
other boats, were towed in a glass-tank filled with homogeneous water or
having water-layers of different specific gravities. The towing force and the
velocity of the boat-model, were registered; and one of the water-layers being
coloured, the wave-motion at their common boundary could be observed and
photographed.

The experiments thoroughly confirmed Prof. V. Bjerknes' opinion: the
vessel when moving at low speeds generated large waves at the salt-water
fresh-water boundary, and the resistance at these speeds was anomalously
increased. At higher speeds, however, the waves disappeared and the resi-

VII

stance was not affected by the fresh-water layer. These facts and another in-
teresting phenomenon observed during the experiments, form the subject matter
of Section B, Chap. III.

In Section E of Chap. Ill, I have tried to show that all other phenomena
connected with the dead-water — the appearance of the sea-surface, the loss of
steering, etc., may be explained from these boundary-waves. Owing to the
small size of the tank in which the experiments had to be made, the ex-
planation of all these points could not be experimentally confirmed, and some
details will possibly be subjected to modifications in the future. It is hoped
that the Article "How to get free of dead-water" (p. 110) will not only be
found to be an explanation of the seamen's experiences, but that it will in
the light of our present enlarged knowledge of the phenomenon, be found to
contain valuable suggestions as to the best means of getting free from this
very inconvenient occurrence.

To make sure of the correctness of the explanation given, it must be
proved that the boundary-waves, created, were the essential cause of the in-
creased resistance in the experiments; and further that this increased resistance
is large enough to explain the effects of the dead-water. The proof of these
points is one of the chief objects of the last section of Chapter III.

The experimental work was performed during the time from the beginning
of 1900 to July 1901; the first half of the time was, however, occupied with
experiments which now may be regarded as only preliminary.

The expense of apparatus has been defrayed by the Fridtjof Nansen
Fund for the Advancement of Science. The Council of the Stockholm s
Hogskola made me a grant for the year 1901, from the Fund to the Memory
of the Civil engineer August E. W. Smitt and renewed it for the year 1902;
I am glad of here having the opportunity of expressing my warmest appre-
ciation of this help.

Also I desire to place on record my sincere thanks to my revered teacher
Professor V. Bjerknes, who has with the greatest interest followed my work,
and has on many occasions given me the most important advice.

Professor Fridtjof Nansen, by an appeal published in several Norwegian
newspapers, has rendered me most effective assistance in collecting accounts
on dead-water. Dr. S. Almquist, Rector of the Hogre realldroverket i

VIII

Stockholm, was kind enough to have a most excellent room placed at my
disposal, in which to conduct the experiments. Some instruments were lent
by Stockholms Hogskola. H. M. Foreign Office were so good as to publish
in the autumn of 1901 an appeal by the author in a great number of foreign
newspapers with the object of collecting accounts on dead-water. Dr. Charles
J. J. Fox kindly read the whole manuscript as well as the proofs, and with
great advantage improved the English. To all those who have in these and
other ways assisted, and last but not least to seamen and others interested,
who have left valuable communications on dead-water, I here desire to present
my sincere thanks.

Kristiania, June, 1904.

V. WALFRID EKMAN.

CONTENTS.

Page

Preface by Professor Vilhelm Bjerknes HI

Introduction V

Chapter 1. Descriptive.

A. Collective description 1

B. Original accounts 9

Effect of dead-water on steamers and ships in tow (Accounts Nos. 1—4) p. 9. —
Effect of dead-water on sailing vessels (Accounts Nos. 5-12) p. 15. - Effects
of dead-water and surface-currents combined (Accounts Nos. 13— 15) p. 22. —
Collection of various accounts of dead-water in Scandinavia (Nos. 16—32)
p. 25. - Collection of accounts of dead-water beyond Scandinavia (Nos.
33—42) p. 27. — Accounts from ancient authors (Nos. 43—45) p. 31.

Chapter II. Preliminaries.

A. The resistance to vessels under ordinary circumstances 33

B. Resistance to vessels in shallow water 38

C. Waves in the boundary between salt and fresh water 41

D. The effect of a light surface-layer on the resistance of a vessel . . 45

E. On the application of small scale experiments 49

Chapter III. Experimental investigation.

A. Apparatus and methods 54

B. Qualitative results 60

The connection between resistance and velocity, p. 60. — The waves generated
by the vessel, p. 62. - The oscillations in the velocity of the boat; con-
clusions regarding the wave-making resistance, p. 67.

C. Numerical results '5

D. Experimental errors and corrections 87

Page

E. Explanation of the various effects of the dead-water phenomenon . 93

The loss of speed; the sudden appearance and disappearance of the dead-water,
its apparent capriciousness, p. 94-. — The appearance of the sea-surface,
p. 97. — The motion of the water around the vessel, p. 102. — The loss of
steering, p. 105. — The sudden effect produced by the stopping of the en-
gine, p. 107. — How to get free of dead-water, p. 110. — The occurrence
of dead-water, p. 112.

F. Empirical laws of resistance 115

Influence of the difference of spec, gravity between the water-layers ; the dif-
ferent causes of resistance, p. 115. — The influence of the depth of the
fresh-water layer, p. 121. — The influence of the sharpness of the bound-
ary, p. 123. — Application of the experimental results to the case of full-
sized ships, p. 124. — The influence of the shape of the boat-model, p. 128.
— Application of the experimental results to the case of the Fram at Tai-
mur, p. 133.

Appendix (Mathematical treatment) 139

Supplement. (Accounts of dead-water) 146

Explanation of the plates 148

CORRECTIONS.

Page 57, line 13, for Aderman read Adermax.

Plate XI, Fig. 3, for wave-resistance read dead-water-resistance.

Plate XIII, in the figure below Fig. 1, for quadrate read square.

I.

DESCRIPTIVE.
A. COLLECTIVE DESCRIPTION.

The following description is based entirely upon verbal and written ac-
counts which I have received from a great number of sailors having experience
on the subject. Special weight is laid on such statements as have been un-
animously given by several authorities, or as may, for other reasons, be con-
sidered trustworthy.

Dead-water only appears near to coasts, in those places where a suit-
able layer of fresh or brackish water rests upon the heavier sea-water. A
vessel, moving in such a place at slight or moderate speed, may happen to
feel the influence of this phenomenon; it is then said that the vessel "has
taken dead-water" or "got into dead-water". It is a very troublesome
matter indeed. A sailing-vessel in this plight, generally refuses to answer
her helm and becomes unmanageable; steamers, at times sailing-vessels also,
keep their steerage, but nevertheless the dead-water is a great hindrance,
causing the ship to lose her speed almost entirely. The Fram, for instance,
though generally capable of making 4"5 knots, along the Siberian coast when
heavily loaded, had her speed reduced to about 1 knot in dead-water; and a
similar reduction of speed seems to be a common effect of this phenomenon.
If, in addition, the vessel has to move up a river or against even a moderate
current, her progress may be altogether stopped.

When dead-water is present, the sea-surface around the vessel presents a
peculiar appearance, varying under different conditions. When the phenomenon
takes place regularly, a set of stripes will be observed astern crossing the wake,

2 EKMAN. ON DEAD-WATER. |norw. pol. exp.

or a couple of stripes stretch obliquely aft from the sides of the ship. They
are described as "rips" or whirling "current backs"1; also as stripes of hop-
ping wavelets. These stripes often stretch far away from the ship. They may
be seen in the various sketches Figs. 6—13 of PL IV, which are copied from
original drawings, appended to some of the mariners' accounts. An indication
of similar stripes may be seen in Fig 5. Fig. 1, PL V — illustrating the
same case as the schematic sketch Fig. 10, PL IV — gives a more objective
representation of the phenomenon. Prof. Nansen himself does not speak of
any such rips or stripes but he observed very long and low waves, stretch-
ing across the wake of the Fram; the crest-lines of these waves are shown
on the rough sketch, Fig. 1, PL IV.

Round the ship's stern a wake is formed of unrippled, eddying water,
which is said to follow the ship and even to advance towards her, so that
a boat in tow will be carried in close up under her stern. The stripes is-
suing from the sides of the vessel seem to form the boundary line between
the water following the vessel and the water outside. It is commonly believed
that a bulk of water is clinging to the vessel; and this proceeds through the
water outside, with a roar. It draws off from the vessel with increase of wind,
and vice versa. Likewise the stripes crossing the wake are said to come
nearer to the stern, the more the wind slackens.

It is a peculiarity of dead-water, that it always appears quite suddenly.
Its influence upon the steering of a ship, or the appearance of the sea-surface
may, in some cases, be subject to gradual modifications; its effect upon the
speed of the ship always takes place, however, quite suddenly, the speed be-
ing at once reduced from its ordinary magnitude to a small fraction thereof.
It very often happens, moreover, that the ship has dead-water at the very
outset. Just as suddenly does the ship recover her ordinary speed when she
gets rid of the dead-water — "as if cut away from a mooring astern". Some-
times she soon gets free, but on particular occasions vessels may remain
helpless in the dead-water for a whole clay or even longer.

Usually it is only vessels in tow and sailing vessels in a light breeze
(vessels with comparatively small motive power), that are influenced by dead-

Smooth or agitated streaks often seen on the sea, denoting the boundary between two
currents with different motions.

NO. 15.] COLLECTIVE DESCRIPTION.

water. It has happened, however, that steamers have been caught by it. It
is said that vessels do not run the risk of falling into dead-water when mov-
ing at above a certain speed, e. g. 3, 4, or 5 knots, according to conditions
prevailing.

The phenomenon shows its simplest phase, when a steamer or a ship
in tow takes dead-water. There is, however, a difference in steering, between
screw-steamers and ships in tow; thanks to the influence of the screw the for-
mer are able to maintain their course; towed ships on the other hand, do not
answer their helm at all, and often in narrow waterways, the tow-rope must
be shortened, to prevent the ship from sheering off, with the consequent risk
of running ashore.

If the engine be stopped, a ship in dead-water does not lose her motion
gradually, as under ordinary circumstances, but she stops short, and may
perhaps be sucked astern. In navigating the mouth of the river Glommen
similar and still more remarkable effects of dead-water have been observed.
As illustrated by Fig. 6, PI. IV, the vessel is followed by a long train of the
dead-water stripes described above. When the tug-boat is stopped and the
towed ship in consequence stops short, the dead-water stripes overtake her,
and, as they pass, the ship swings backwards and forwards, once for
each stripe that passes. In the same way, vessels made fast to the shore,
will be pushed up and down the river when a ship in dead-water has been
towed past them ; the power of the stripes being at times so violent as to tear
a vessel away from her moorings.

Sailing-vessels, when caught by dead-water, usually do not answer their
helm and, in spite of the rudder and various manoeuvres with the sails, take
a certain course depending on the direction of the wind; often they run up
in the wind with sails shivering. Therefore, the loss of steerage is generally
the most troublesome effect of the dead-water on sailing-vessels, although in
particular cases, the vessel may be kept to her course with more or less
effort. Owing to the wind the aspect of the sea is often asymmetrical, the
stripe issuing from the windward side being best developed (see Fig. 12, PI. IV).
When the sea is rippled by the breeze the stripe on the windward side may
be invisible, whereas on the leeward side where the sea is smoother, it may
may still be seen. Often, however, the dead-water appears in its regular
aspect.

4 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

In the Kattegat the phenomenon is sometimes less regular (see accounts
Nos. 13 and 14 as well as Fig. 14, PI. IV). As long as the ship's course
is between two certain points she may answer her helm quite willingly, but
she cannot be made to head a course beyond either of these two limits.
The wake and the "dead-water stripes" have often an assymetric direction.
The cause of this is, no doubt, to be ascribed to the lighter brackish wa-
ter running as a narrow surface-current on the top of the heavier sea-water,
so that the upper and the lower parts of the ship's body move in water of
different velocities. Such surface-currents were directly observed in two
cases mentioned below. It is evident that the two currents — especially if
the ship draws more water aft than forward — tend to turn her head in a
certain direction. To both sides of this direction she may be made to head,
though within certain limits, depending on the strength and direction of the
surface and under-currents, and of the wind. Thus the currents in the sea
are able to considerably modify the effects of the dead-water. It is very
probable that particular accidents mentioned by the mariners as "dead-water"
are mainly caused by such surface- and under-currents. Some Scandinavian
mariners apparently give the name of dead-water to various effects upon
their vessels, which cause them to lose their steerage. Thus, for instance,
when a vessel in a light wind, is affected by a whirl-pool or when she is
brought out of her course by the influence of currents of different directions,
she is sometimes said to have got into "dead-water" although the cause of
the mishap has nothing in common with this peculiar phenomenon.

It was mentioned above (p. 3) that vessels run the risk of getting into
dead-water if moving at below a certain speed depending on the conditions
prevailing, but not when proceeding at higher speeds. In particular cases
even steamers have "taken dead-water", whereas, in certain places, only
sailing-vessels, in a very faint breeze, are exposed to it. It is therefore evi-
dent that dead-water may be of varying strength in different places and
under different conditions. Without further defining this notion, I will give
a summary of the experiences of several Scandinavian mariners as to
the strength of dead-water under different conditions. The explanation of
the different statements will be reserved for Chap. III.

First of all, dead-water seems less effective the smaller be the difference
of density between the surface layer and the sea-water below, or the more

NO. is.] COLLECTIVE DESCRIPTION.

the former has mingled with the latter. In one of the strongest cases of
dead-water that we know of — the experience of the Fram at Taimur —
this difference of density was about as great as possible (fresh drinking water
on the sea-surface, and pure sea-water on a" level with the bottom-cock of
the engine-room). In the Norwegian fjords, where the conditions are unusually
good for river-water spreading almost unmixed over pure sea-water, most
marked cases of dead-water are quite general. In the Kattegat, the density
of the sea-water is not so great, and the river-water, before flowing out over
the sea, becomes much mixed with sea-water. Dead-water appears there only
with a light breeze, after some days of fine weather, and not at all when the
water-layers are stirred by previous storms. (In the neighbourhood of the
mouth of the G5ta River, however, strong dead-water has been experienced).
In the Baltic, where the specific gravity is less than 1'006 or 1'007, dead-
water is only exceptionally observed, and then only with very feeble wind.

Furthermore, the relation between the thickness of the surface-layer
and the draught of the vessel is of great importance as regards the effect
of dead-water. At the mouth of the Glommen, for instance, small craft
experience dead-water farther out at sea, where the surface-layer has less
thickness, than large vessels, by which it is again felt higher up the river (see
Account No. 3). According as the outflow of fresh water increases, the region
where dead-water appears withdraws from the river mouths seawards, and vice
versa. In winter, when there is little water in the Glommen, dead-water prin-
cipally appears in the river proper, between the town and the Sarp rapids
(see the maps, PI. Ill); but in summer its region is below the town and ex-
tends as far as the outermost rocks of the Kristiania Fjord.

Another fact, probably connected with the one stated above, is that dead-
water is generally stronger in a moderate sea-breeze, than when a land-
breeze is blowing. For, as a result of the sea-breeze, the fresh water is
retained at the coast and its depth becomes in concequence greater, while
the land-breeze carries most of it out to sea. On the Glommen the dead-
water is said to be stronger at flood-tide, than at ebb — possibly owing to
the tidal currents or to variations in the depth of the fresh-water layer.

Some of the narrators attribute importance to the shape of the vessel:
it is said that a sharp built vessel is more exposed to dead-water than one

EKMAN. ON DEAD-WATER. Inorw. pol. EXP.

of bluff design. One of my authorities has stated the contrary. Those that
are laden or of deep draught are always more liable than are light ones.

Even after taking into account all the above circumstances, there is never-
theless something highly capricious about the appearance of dead-water; and
it is often impossible to understand why, in a certain case, a vessel has not
"taken dead-water", and in another case, why she did not escape its in-
fluence. A ship may, for instance, be towed without difficulty from one
place to another, but another similar or smaller ship being shortly after
towed the same way, will be so forcibly held by dead-water as scarcely to
be moveable from the spot. On another occasion a sailing-vessel or a vessel
in tow may be held by the dead-water, while other similar vessels, with less
or equal moving power, may pass quite near to her without being in the
least troubled by the phenomenon.

Vessels apparently often "take dead-water" on account of the wind slacke-
ning or as a result of the vessel entering water-layers of a different character;
sometimes the cause of gelting free may likewise be put down to a similar
influence. But often the change cannot be explained by any perceivable
external cause. Often a vessel gets into dead-water while tacking, or on
account of bad steering, or when her speed is from any cause temporarily
slackened. If a sailing-vessel takes dead-water on account of the wind
slackening to below a certain strength, the wind, as a rule, must freshen to
above this strength to free the ship again. In general, when a vessels speed
is temporarily slackened and she gets into dead-water, she may be unable
to recover her head-way for some shorter or longer time, even when the
conditions for full speed are present again.

Mariner's opinions of dead-water and its causes vary somewhat, and
to judge from their explanations of the phenomenon they generally acknow-
ledge they do not understand it. Most of my authorities, nevertheless agree
in the observation, that it depends on the existence of a surface layer of
fresh or brackish water. It is a general opinion, that "the fresh water sticks
to the vessel" and is dragged along with it on the top of the salt water,
thus impeding the speed — the fresh water on account of its forward motion,
has no influence upon the rudder. Other narrators declare that the phenomenon
is owing to the fresh water running as a surface-current above the salt
water; if a ship moves at a slow speed, the rudder becomes too much

NO. 15.] COLLECTIVE DESCRIPTION.

influenced by the currents, so that the vessel loses her steerage. Another of
my correspondents has advanced an explanation somewhat more correct. (See
the end of Account No. 12). Mr. M. Leegaard, harbour engineer, explains the
phenomenon as owing to the turning effect of currents on the ship's body
itself, and, as already mentioned, this is sometimes the case. (See further
account No. 15).

With a view to removing the dead-water, seamen have ' made use of
all sorts of odd means, which they believed would "loosen" or "rub away"
the "dead-water crust", that is, the fresh water. Such means are:

Sheering off from the course,

Running the whole crew forward and aft on deck,

Pumping violently,

Scooping up a quantity of water on deck,

Pouring out petroleum ahead of the ship,

Dragging a hawser under the ship's bottom from stem to stern,

Working the rudder rapidly,

Firing guns into the water (on men of war),

Cutting and beating the water alongside with oars or handspikes etc.,

Dragging a seine along the ship's side, and so on.

Sometimes the two last mentioned methods are said to have been success-
ful, but in most cases all of them are by the narrators themselves, declared
to have been of no use. I may mention now, that on account of the ex-
planation of the phenomenon which will be given later they must be expected
to be of no appreciable effect, although several of them are not quite un-
reasonable.

Tug-boats, when their vessels in tow get into dead-water, have more
effective means of getting them loose again, and these are said to often
succeed (see Accounts Nos. 3 and 26). The simplest method is to let the
tug stop for a while, until the dead-water stripes have passed by, and then
to go full speed ahead again. Another effective way is said to be, to
have the tow-rope as short as possible so that the screw violently stirs up
the water around the towed vessel: or for the tug-boat to go to and fro
along the sides of the ship and then to make full speed again. It is a sin-
gular experience, recorded by several observers, that a ship in dead-water may
get free if passed by a steamer, even at a distance of several ship's lengths.

8 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

It is a difficult thing to state anything certain concerning the frequency
of " dead- water" ; the accounts are much too scanty and incomplete. The
map PI. II is an attempt in this direction, as far as Scandinavia is con-
cerned. The places where dead-water has been observed, or is said to
occur, are represented by different signs explained on the map. It must of
course, be expected a priori that the greatest numbers of accounts should be
received from those fjords and other waters that are most frequented, and that
accounts should be altogether wanting from several small places with very little
traffic, or where Prof. Nansen's request in the newspapers did not become known
Taking these circumstances into account, it seems probable, from the results
illustrated by the map, that dead-water occurs in all Norwegian fjords into
which any considerable quantity of fresh water flows and, although with less
strength, in the Kattegat as well. As a general rule the phenomenon seems to
appear in particular cases, only when circumstances are favourable, but yet
not so very infrequently. In the environs of the mouth of the Glommen it
is constantly feared; the towing masters must lake it into account and not
take too great a load at the risk of sticking in dead-water. It must be noted
that the figures on the map give a too low estimate of the frequency of
dead-water. For several narrators declare they have been out in dead-water
on many occasions that they do not think it necessary to mention specially.
All these cases, not specially described, are left out of account.

Still more difficult would it be to draw any reliable conclusions as to
the occurrence of dead-water beyond Scandinavia. To my appeal published
in at least 36 foreign newspapers,1 I have not received more than 18
answers, of which number half are of decidedly negative import. Only two
narrators have certainly experienced dead-water themselves, one in the
Kristiania Fjord and the other inside Vancouver Island (Canada). It is
not probable, therefore, that dead-water is at all as decided or as common
on other seas as in Scandinavia; for one cannot assume that a phenomenon
so troublesome and so characteristic should escape the attention of seamen.
On the other hand, four of my Scandinavian authorities mention dead-water

1 6 British, 1 German, 2 Dutch, 1 Belgian, 1 1 French, 2 Italian, 2 Chinese, 2 Brazilian,
1 in Argentina, 4 in United States of America and 4 Canadian.

NO. 15.] COLLECTIVE DESCRIPTION.

in the Mediterranean and off the great river-mouths of North and South
America. Some old stories also tell us about certain strange adventures on
the Mediterranean which doubtless were cases of dead-water, although owing
to the narrators' modes of explanation, they would rather seem to be myths.
Vessels propelled by oars or running before a fair wind were suddenly stopped
in their course by a strong, unknown force. It was commonly believed that
this was caused by a small fish the Remora, sucking itself fast to the ship's
body, and it was said that but one of these fishes was required to hold a
ship immovably. The belief in this power of the Remora seems to have
survived far into later times, and for that reason it seems probable that the
phenomena in question have appeared occasionally.

From all these circumstances I conclude that dead-water may occur at
every place where fresh-water flows out over the sea, but that from some
reason or other it is comparatively seldom met with beyond Scandinavia or
appears in a less decided manner than in the Norwegian fjords. The causes
of this circumstance will be discussed below.

B. ORIGINAL ACCOUNTS.

Effect of dead-water on steamers and ships in tow.

No. 1. The series of narrations may well begin with an account of those
famous cases of dead-water which happened to the Fram in the autumn of
1893 North of Siberia, and which gave rise to the investigation of the matter.
The following representation of these cases is extracted from the narrative to
be found in Dr. Nansen's book "Fartherst North", pp. 172—175 and 177 and
from a letter of his to Professor V. Bjerknes, which also contains extracts
from parts of Dr. Nansen's own journal. In arranging this material the ori-
ginal form of the different statements is maintained, and in its present state,
the whole has been revised by Prof. Nansen himself.

"On Tuesday, August 29th 1893 the Fram got into the open water in the sound
between the isle of Taimur and Almqvist Islands and steamed in calm weather through
the sound to the north-east. At G ' in the afternoon I saw from the crow's-nest thick ice

1 In "Fartherst North" stands five, which is incorrect.

10 EKMAN. ON DEAD-WATER. [norw. pol. Exp.

ahead, which blocked further progress. It stretched from near Cape Laptev right across to
the islands north ' thereof. We approached the ice to make fast to it, but the Fram had
got into dead-water, and made hardly any way, in spite of the engine going at full pressure.
It was such slow work that I thought I would row ahead to shoot seal. In the meantime
the Fram advanced slowly to the edge of the ice with her engines still going at full
speed, and there was made fast at half past ten in the evening. The engine stopped hut
one half a ship's-length from the edge of the ice (according to Scott-Hansen0, it was one
whole ship's-length), but it looked as if the ship was drawn back, at the same moment the
engine stopped, and she barely struck the ice.

"The edge of the plain ice, when seen for the first time, at all events, was not more
than 8 naut. miles off, and hardly that, because it was quite low and could not have been
seen from a greater distance with the naked eye. According to the unanimous calculations
of myself, of Svebdrup in the log, and of Scott-Hansen, the speed must have been reduced
to 1"5 or 1 knot in the dead-water. About 6 o'clock the dead-water was still not fully
developed.

"The Fram had at that time a draught of 5 m. or more. Her common speed in
smooth water, and at full steam pressure, was at that time, fully 4'5 knots. Perhaps it was
5 knots at top pressure. I may add, that I convinced myself that there was really full
steam pressure and that the engine was being worked at full power.

"There was but a very slight current to be observed at this time — from 6 in the
afternoon to about midnight — as likewise next morning.

"The ice that covered the sound north of Taimur Island was in a state of dissolution
and apparently melting very rapidly, and this was probably the main cause of the sea in
the sound being covered with a layer of fresh water. Unfortunately, I have no measure-
ments of the thickness of the fresh-water layer. I only say in the journal that the water
at the surface was almost fresh (drinking-water), whereas through the bottom-cock of the
engine-room we got perfectly salt water3. I suppose that the bottom-cock at that time
was about 4 m. or more, below the surface of the water, and accordingly the Fram
struck the salt water.

"Aug. 30th, in the morning, we went on to anchor in a bay at Cape Laptev. We
now wanted to thoroughly clean the boiler, a very necessary operation. I say in the jour-
nal that the bay lay a few miles farther south, and I am sure that it might have been at
most 3 nautical miles. But we took 4 hours and more, to steam that little distance.

"I dare not affirm that the steam was at top pressure during the whole time on this
occasion. The distance being so short, it might be conceivable that the engineer did not
think it necessary to fire up very heavily, but there cannot have been very much wanting
on that score, and at any rate the speed under ordinary circumstances (i. e. with no dead-
water) would have been 4 knots.

"We could hardly get on at all for the dead-water, and we swept the whole sea along
with us. It is a peculiar phenomenon this dead-water. We had at that time a better
opportunity of studying it than we desired. It occurs where a surface layer of fresh water
rests upon the salt water of the sea, and this fresh-water is carried along with the ship,
gliding on the heavier sea beneath as if on a fixed foundation. Dead-water manifests itself
in the form of larger or smaller ripples or waves stretching across the wake, the one be-

1 In "Fartherst North" north should evidently be read for south.

2 Scott-Hansen, who was at that time in command, says: "When we went in to moor
at the ice, I had the engine going at full-speed until we were about 30 or 50 m.
from the edge of the ice. I then stopped, and the ship lost her speed altogether while
going just this slight distance."

3 On special inquiry Prof. Nansen informed me that this latter observation was made
while the ship mas in motion. As will be seen later, this circumstance is of im-
portance.

no. ib.] ORIGINAL ACCOUNTS. 11

hind the other, arising sometimes as far forward as almost amidships1. We made loops
in our course, turned sometimes right round, tried all sorts of antics to get clear of it, but
to very little purpose. The moment the engine stopped, it seemed as if the ship were
sucked back. In spite of the Fram's weight, and the momentum she usually has, we could
in the present instance, go at full speed till within a fathom or two of the edge of the
ice, and hardly feel a shock when she touched.

"On September 2nd, at last, the boiler was ready. We steamed south in the evening,
but were still followed by the dead-water during the whole night. According to Norden-
skiold's map, it was only about 20 miles to Taimur Strait but we were the whole night
doing this distance. In two watches (8 hours) we hardly advanced 8 miles, the engine
constantly working at full speed. Now, the boiler had been cleaned out and filled with
fresh water from the surface of the sea, so that the conditions for good speed were very
favourable. It may therefore be supposed that the speed was reduced to about a fifth of
what it would otherwise have been.

"At 6 a. m. September 3rd, we got into a thin layer of new sludgy ice, that scraped
the dead-water off us. The change was noticeable at once (according to the account of
Sverdrdp, who had the watch at that time). As the Fram cut into the ice she gave a
sort of spring forward, and after this, went on at her ordinary speed; and henceforth we
had very little more trouble with dead-water2. The cause of the last fact evidently was
that later there was a much stronger current and wind, so that the fresh-water layer at
the surface was swept away. During August 30th and the night between 2nd and 3rd
September, the speed was rated as 1 knot, in the dead-water."

No. 2. Even on her way north, the Fram met with dead-water; it was
on the By Fjord on going in to Bergen. The Fram on this occasion also,
was under steam, but prams and row-boats easily passed by her. Captain
S. Scott-Hansen, who had the command at that time, writes about this
episode:

"On the By Fjord at Bergen the Fram got into dead-water about one nautical mile
off the mole of the "Vaagen". The speed was considerably reduced. Of exterior, visible
phenomena the most remarkable was a stripe, resembling the boundary between a current
and still water, and stretching from the bow obliquely aft, as indicated in the sketch Fig.
13, PI. IV. We also had an impression of the surface-water round the stern, and in the
immediate proximity of the ship's side, being dragged along with the ship. The wake of
the ship also varied from its customary appearance, being broader and not showing the
regular central line of defined whirls. It looked as if the water set in motion by the
propeller, was spread over a much broader space than it is wont to be, and the whole
mass of the surface-water in the wake to a distance of 10 or 20 m. from the stern, gave
the impression of having a tendency to hang on to the vessel.

1 For the purpose of illustration Prof. Nansen has drawn a sketch shown by Fig. 1,
PI. IV. The lines stretching to the sides of and aft of the vessel represent the crest-
lines of long, low waves.

2 Nansen adds in a note: "It is probable that the fresh surface-layer has been rather
thin just where the ice occurred. I have found that ice often is formed on the under
side of a fresh surface-layer by the cooling effect of the cold water-layers below (see
No. 9 of this report: "The Oceanography of the North Polar Basin" pp. 308-309 as
well as the footnote on p. 300). In open water this ice floats up as delicate ice-
needles, which melt in the warmer surface-layer; but if the latter be thin enough,
they will reach the surface before they have had time to melt, and may even form
a crust."

12 EKMAN. ON DEAD-WATER. [norw. pol. exp.

"When passing the mole-head, the engine still worked at full-speed; and I only stop-
ped it when the ship was a little way (100 or 150 m.) from the buoy to which we
should make fast. It was remarkable how quickly the ship lost her speed, and if my me-
mory does not deceive me, I was obliged to start the engine again in order to reach
the buoy.

"Finally I will not omit remarking, that the description given above has been written
several years after the occurence, but according to my best recollection of the facts cited."

No. 3. Mr. G. A. Larsen of Fredrikstad has during many years' experi-
ence of towing, struggled with the dead-water on the river Glommen and the
fjord off it, and he has most kindly, by letters and word of mouth, com-
municated to the author the result of his practical experience in these waters.
His communications are very inslructive, based as they are on long experience
of an extensive district where dead-water seems to be more common and
stronger, than in any other place. The different statements have been ar-
ranged below in a consecutive account, and this has been revised by Mr.
Larsen himself.

"As is seen on the maps (PI. Ill), the river Glommen branches at Fredrikstad into
two outlets — the East Arm and the West Arm — girding Krager Island. Most of the
water flows out the straight way through the East Arm, but a considerable quantity flows
through the channel north of Krager Island and further on to the West Arm. In both
outlets, especially in the East Arm, the current is sometimes very strong, but they are
both navigable, as is also the main river all the way up to the Sarp Bapids.

"On these waters and the surrounding parts of the Kristiania Fjord I have towed
ships and lighters with a tug of 200 H. P., and drawing nearly 3 m. The ships and
lighters in tow generally have a draught of 3 or 6 m., and on them the dead-water has
principally taken effect. The tug-boat may also take dead-water but — on account of her
smaller size — very slightly and to no hindrance. The following statements principally
concern the effect of dead-water on towed vessels.

"Dead-water only occurs where there is a layer of fresh or brackish water above
the salt water. Its effect depends on the thickness offthe fresh-water layer. If this
be great, it is hard to advance; but if it be only small so that the screw throws dark
sea-water up to the surface, we never fear dead-water, it has then very little influence ex-
cept on very small vessels. At flood-tide, dead-water is always stronger than at ebb. A
sharp and fast-sailing ship is always at a much greater disadvantage in brackish water,
than a bluff one of bad design.

"The strength of dead-water in different places changes with the season. In winter,
when there is little water in the Glommen1, the worst district for dead-water is on the
river beyond Fredrikstad, and there it reaches right up to the Sarp Rapids. In winter
there is also dead-water in the Fredrikshald Fjord. In spring, as the water rises, the
dead-water moves farther off, and in summer it does not exist beyond Vaterland on the

From the data given in "Hydrologiske meddelelser for Kougeriget Norge, Vandstands-
observationer, B. 1", Kristiania 1900, 1 have calculated the average quantity of water
carried by the Glommen during the different months. The mean averages for the dif-
ferent months during the years 1881 — 1893 are in cubic metres per second: Jan. 180,
Febr. 165, March 162, April 265, May 1055, June 1525, July 1045, Aug. 900, Sept. 805,
Oct. 740, Nov. 500, and Dec. 260. I am much indebted for these data to Kanaldirector
G. SiETBEN, who was kind enough to bring them under my notice.

NO. 15.] ORIGINAL ACCOUNTS. 13

East Arm1. Then, it generally occurs below Vaterland, on the Single Fjord, Sceken,
Leret, and all the way to Torbjbrnskjcer and Fcerder (see the map, Fig. 1, PI. III). The
smaller the vessel so much the farther out, will it run the risk of being caught by dead-
water. On the other hand, only deep vessels stick very fast in it. In sea-water we are
able to draw at least four times as much as in brackish water (dead-water).

"On both outlets of the Glommen it may be very prevalent, and if I cannot tow the
ship at 5 knots or more, I run the risk of falling into dead-water. On the river and its
outlets, however, we do not fear dead-water except when going up-stream; for when going
down-stream we are always carried along with the current. Near Krosnats on the West
Arm, it once happened that a 200-ton pilot-steamer got into dead-water; she was of about
GO H. P. and was able to steam at about 4 knots. On the East Arm the dead-water is
still stronger than on the West Arm, and sometimes sailing-vessels may there be seen
stuck fast in spite of a breeze brisk enough to keep the sails firmly strained. The worst
place in this respect, is the sound between Krager Island and Kjogo.

"Sometimes it happens that one vessel gets into dead-water and another not, though
it is impossible to discover any reason for it. Once, for example, — it was flood-tide — I
had to move a vessel of 400 tons from one place to another in the channel between the
East and the West Arms. The vessel took dead-water, and 3 hours were spent in going
a distance of 3 cables' length (600 m.)2. Immediately after, I towed a vessel of 800
tons the same way without any similar difficulty or trouble. Another time, in the Fre-
drikshald Fjord, I towed a lighter of 120 tons and drawing 4-5 m. The lighter took dead-
water, and the tug of 12 H. P. could not get it loose. Nevertheless a ship of 400 tons
drawing about 5 or 6 m. and towed only by three men in a boat had no experience
of the dead-water and easily passed us. There was no wind to be seen on the water, and
the stream was with the ships. Twice, when I have towed a lighter in dead-water and have
not been able to get her loose, it has happened that she has run aground and then she
has got free from the dead-water and has been towed further without any difficulty.

"It is an easy matter to perceive if a vessel has got into dead-water. From the stems
and sterns of the tug and the ship in tow, there are then formed 4 pairs of streaks or
"dead-ivater waves"3 (see Fig. 7, PI. IV) indicated by very small and short wavelets. They
stretch far away to the sides and, when the distance is not too great, even reach the
shores. In the Lrammen Fjord beyond Svelvig I have seen such streaks, extending half
a naut. mile on each side. There are not always "dead-water waves" formed from the tug.
And if there are, they may fall astern and disappear, and then, a while afterwards, new
streaks may be formed. It often happens that the streaks issuing from the stem of a ship
in tow are missing, or that they first disappear, and then recur again. The streaks from
the stem always remain the longest, especially the streak on the side opposite to that to
which the tow-rope is directed. The ship is also followed by a train of similar streaks
moving on at the same speed as the ship4.

"Around and aft the stern the water follows or even overtakes the ship, so that a
boat which is following in tow is drawn close to the ship's side and cannot be kept clear
of it. The water is likewise pushed before the stem, but along the sides it runs astern at
great speed — faster than if there were no dead-water. For example a cutter of about 70
tons lay in dead-water on Leret in spite of a SW. wind which under ordinary circum-
stances would have probably given her a speed of 3 knots. The cutter could not be

1 According to Mr. Larsen, dead-water has been observed beyond Vaterland, during the
summer of 1901, which was very dry with little water in the river.

2 It may be remarked that this does not give the velocity through water, because the
vessel was tugged upstream.

* The sign of quotation is due to the present writer.

4 At the author's request Mr. Labsen has made a sketch (Fig. 6, PI. IV) illustrating this

matter. This figure upon the whole, gives a better idea of the streaks than Fig. 7.

The two horizontal lines denote the banks.

14 EKMAN. ON DEAD-WATER. [norw. pol. exp.

steered before the wind, but she luffed and steered N. or E. A pilot boat of about 10 tons,
which she had in tow, was sucked in to the stern and could not be kept clear of it. As-
sistance was requested from a passing tug, which steered to the bow of the cutter to re-
ceive a hawser, but the two vessels were pushed from each other; the attempt was repeated,
in vain, and in order to come near enough to get the hawser aboard, the tug was obliged
to back astern to the bow of the cutter.

"A vessel which is towed in dead-water does not answer her helm at all, and on the
river it is necessary to shorten the tow-rope, lest she should run aground or ashore; she
always strives to steer to the side, away from the course of the tug. Nor is it possible
to put the "wash" of the tug against the stem of the vessel in tow; it is pushed to the
side as shown by the figures. In dead-water it is better to use two tugs attached to the
vessel by short tow-ropes. Then a separate "wash" may be projected to each side of the
vessel and so "cut away or destroy the dead-water layer, so that it cannot cling to the
ship's side"1. In this manner two boats of 10 H. P. more easily drag a ship of 400 tons
than one boat of 20 H. P.

"When the streaks or "dead-water waves"1, following the shores of the river, en-
counter a vessel at her moorings, they prove very powerful. When the first streak issuing
from the tug reaches the vessel, she is pushed forward (sucked back)2 until the streak has
passed half the length or more of the ship; then she is drawn back (pushed on)2 until
she is reached by the next streak when she is pushed forward (sucked back)2 again and
so on. This is repeated with still greater force by the streaks issuing from the ship in
tow; and it has happened that vessels, moored for the winter, have broken their moorings
when a large ship has been towed down the river (in this case the force of the streaks is
greatest). When the tug and the ship have passed, the vessels on the banks continue to
swing to and fro, owing to the force of the successive streaks. The motion gradually
slackens, being perceivable for half an hour after the ship in tow has passed.

"In the same manner, if the engine be stopped, the towed vessel herself stops short
and is then pushed backwards and forwards as she is reached by the successive dead-water
streaks. The streaks having passed by, the vessel may, in many cases, be got free from
dead-water, by making full speed ahead.

"On the contrary, if, towing with a rather powerful tug, you wished to make a ship
fast in dead-water, you must begin to go at slow speed and then increase the pace very
gradually. In this manner it is possible to get so firmly fast that the ship cannot be got
free by the full pressure of the engine, without first stopping and letting the dead-water
streaks pass3."

No. 4. Mr. A. E. Tonnessen, Instructor at Grimstad, has kindly communi-
cated the following facts:

"On the West port of Kristiansand (see the map on the upper left corner of PI. Ill)
dead-water often occurs in the summer, in calm weather or with easterly wind. Between
the town and Odder Island there is a channel, 3 or 4 m. in depth, through which the
water (river-water and salt water from the East port) almost continually flows out over the
West port. The ships, when leaving the town, must pass this stream of river-water and
there, athwart the channel, they often in calm weather get into dead-water. Among several
cases I have observed, the two following are the most remarkable.

The sign of quotation is due to the present writer.

In two separate letters these two different successions of the motions were stated. With

regard to this order the account is therefore not quite reliable.

When the author in May 1901 was at Fredrikstad to see the dead-water, Mr. Larsen

on account of unfavourable circumstances did not succeed in getting fast in dead-water.

Only a couple of very feeble dead-water streaks appeared and disappeared again.

NO. 15.] ORIGINAL ACCOUNTS. 15

"On Sept. 20th 1884, Wind slight SW., I left Kristiansand with a laden barque,
"Carla", 502 tons and drawing about 4'9 m. We had a steamer attached to the bow,
and we already had good speed, when all at once, the ship took dead-water off Odder
Island. She did not answer her helm, and the water followed at the stern, as if it were
clinging to the ship. On account of her great inertia she moved right through it, but her
velocity was almost entirely gone when we finally got rid of the dead-water.

"One day in the summer of 1890 (or 1889?) I saw a barque of about 600 tons go out
light, towed by a powerful tug. The wind was gentle SE. breeze. Though previously go-
ing at a good speed, the barque took dead-water at the same place as the "Carla", and
she stopped so quickly that it looked as if she had dropped anchor again. Both the ships
were new-coppered, so that the friction must have been a minimum."

Effect of dead-water on sailing vessels.

No. 5. Mr. Colin Archer of Larvik, sent me a letter, from which, by
kind permission of the writer, I make the following extract.

"It has often occurred to me that it would be an extremely interesting problem to
investigate that very peculiar phenomenon which we call "dead-water", and which has not
yet, as far as I know, been made the subject of systematic investigation.

"We have here on our fjord a very good opportunity of observing the phenomenon.
Two rivers fall into the fjord; and it often happens, when out for a sail, that the boat
suddenly loses her way and is held fast, almost as in a vice, in spite of a fair breeze
which, in the open sea, would give her a speed of two or three knots. The boat seems
to drag after her a broad belt of water which follows in her wake. At the same time
a system of sharply defined but small waves is generated on each side. These may be
compared to the side waves set up by a steamer at full speed but, of course, on a di-
minutive scale. I enclose a sketch (Fig. 11, PI. IV) showing approximately the shape of
this wave-system. The waves are small and short, and resemble, in some degree, the
ripples caused by a gentle breeze; but they form a simple succession, as shown by the
sketch.

"All this is no doubt caused by the layer of fresh water — which is spread over the
salt sea — having a motion of its own independent of the underlying water; but the con-
nection between this cause and the singular effect it produces, is not very evident. The
dead-water often appears in quite still water, as in closed basins of ports (though in com-
munication with the sea), where no considerable currents can be supposed.

"Whether the shape of the vessels cross section has any marked influence on the for-
mation of dead-water I am not able to say; but I have observed that the drag (i. e. the
difference of draught forward and aft) plays an important part, more particularly as regards
steering. If the drag be great, the salt water gets a hold on the deepest part of the ves-
sel's keel, and the surface current will carry her head round in its own direction. The
rudder loses all, or nearly all, influence on the steering."

No. 6. Admiral C. Sparre of the Norwegian Navy, often experienced

dead-water in the Kristiania Fjord1 during cruises in his own yacht. He

told my the following and kindly revised it, when written. The sketch (Fig.
12, PI. IV) is made by Admiral Sparre himself.

See the map Fig. 1, PI. HI.

16 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

"In the Moss Sound, in which a rather full river empties itself, dead-water very com-
monly occurs, especially in spring and summer time. Skippers of small craft relate that
they are often obliged to tow their vessels through nearly the whole sound (about 3 or 4
miles) by a rope from shore, even with a nice little breeze of lair wind. Sailing while
the dead-water lasts is impossible, if the wind be not fairly strong.

"Often the phenomenon appears in the manner described below:

"A small vessel sails free (the wind on her quarter) on the starboard tack for instance,
as in Fig. 12, PI. IV. Suddenly a stripe begins to form on the water, issuing from some-
where on the windward side of the vessel and stretching obliquely astern (see the figure).
Outside (forward of) this stripe the water, as usual, runs aft by the vessel, but inside it
the water forms a kind of wake in which the water seems to follow the ship. This has
been observed in wind, sufficient to give the vessel about 2 knots' speed. On the whole
the phenomenon presents itself to the sailor, as if part of the water separated from the
rest, attached itself to the ship, and was dragged by it through the sea '. When the stripe
is developed, the vessel runs up into the wind in spite of the helm and lies quite power-
less with her sails shivering. By rowing with an oar on the windward side she may be
brought off again, and sailing is possible for a short time, but soon a new stripe begins
to form and the vessel runs into the wind again. The masters of quite small craft often
try to free their vessels from the dead-water by stirring the water with an oar, and it is
said they sometimes succeed.

"Several years ago, while at gun practice in the Kristiania Fjord the narrator, then
a lieutenant, was ordered with a gun-boat to tow away two small vessels, which lay be-
calmed near each other in the line of firing. One of them was towed away without any
difficulty, while the other, though of similar size, got into dead-water, and an extraordinary
amount of work was required to get this vessel from the spot."

No. 7. Mr. G. 0. Nilsen of Bestum near Kristiania has been kind
enough to ask several sailing masters for information on dead-water and to
send me a summary of the result obtained. From this summary the follow-
ing may be cited.

"If a vessel, sailing with an even breeze at a rate of 3 or 4 knots, enters a zone
of dead-water, her speed will be immediately slackened, as if she had struck a reef of
mud. The water is seen to follow to a distance of several metres from both sides of
the vessel, just as if she had suddenly been enclosed by a large ice-floe. As long as the
vessel makes head-way, a number of small whirl-pools (eddies) are seen in the boundary
between the "ice-floe" and the water outside it. The eddies produce a bubbling sound.
The vessel gradually has her speed stopped and then no longer answers her helm, drifting
helpless sometimes even against the wind.

"If the wind increases, the vessel slowly begins to make head-way, constantly dragg-
ing the surrounding water with her. This body of water, reaching 3 or 4 m. before
the stem, drops slowly astern, until the vessel has the bow clear of it. Then she begins
to get more speed, and the "dead-water" constantly moves aft clinging, at last, to the
stern of the vessel and dragged along with it as a float of as much as 20 m. in length.
If the wind now decreases, the whole mass of water may rush forward and enclose the
vessel once more. If not, the vessel now answers her helm, and after some manoeuvres,
all of a sudden, breaks free.

These details are given with reservation, owing to the uncertainty naturally connected
with such an observation when not made carefully, with a conscious and definite in-
tention.

NO. 15.] ORIGINAL ACCOUNTS. 17

Sailing vessels often lie in dead-water for several days; towing with a boat is of no
purpose; at most the vessel may he turned a little, but as soon as rowing ceases, she
resumes her own way.

"Sharp and deep-drawing vessels are more apt to take dead-water than those that are
bluff, or flatbottomed; likewise laden vessels are more subject to it than are light ones.

"Dead-water occurs mainly in the neighbourhood of river mouths, especially at floodtime
in spring and summer. In this respect the following places are specially to be mentioned ' :

"The Langesund Fjord; the Dramtnen Fjord below Svelvig, aud in the neighbourhood
of this fjord; the waters SW. and SE. of Fredrikstad ; the Single Fjord all the way to
the Sceken.

"Furthermore the Moss Sound and several other places in the Kristiania Fjord, count-
ing from the port of Kristiania and the cove at Lysaker and as far outwards as beyond
Fcerder.

"Two special cases have been brought to my notice: —

1) A ship-master sailing from Rodtangen for Drammen in March 1901, there being
little water in the river, felt dead-water only beyond Svelirig. (It was at this time uncom-
monly high water). Somewhat later, when he made the same journey, the river had increased
considerably, and this time, dead-water was experienced below Svelvig and not beyond it.

2) On May 13th 1901 a sharp-built cutter, sailing for Kristiania, took dead-water on
the Single Fjord. A yacht of the same size, but of bluff design and sailing somewhat more
slowly, came after her at a speed of about 4 knots. The yacht made an attempt to tow the
cutter out of the dead-water, but the result was that both vessels became fast in it. They
were lying in dead-water from 10 a. m. the first day to 4 p. m. the next, and during this
time drifted four miles back again with the current, against the direction of the steady,
fresh breeze, although they had all sails set."

No. 8. Mr. H. B. Eriksen, shipmaster of Fredrikstad has favoured me
with the following very instructive and interesting account. The sketches
Figs. 8 and 9, PL IV, are made by Mr. Eriksen himself.

"During a series of years I sailed between Finland and England — I have made about
50 voyages between Kolka and London — and in the Kattegat and Skagerack have been
much exposed to dead-water. On this trade I sailed the barque "Martha", 515 reg. tons,
about 47 m. in length, 10 m. in breadth and with a draught of about 5'7 m. when laden
and 3"8 m. when empty.

"In my opinion dead-water may be met with at any hour of the day and independent
of the direction of the wind, and it only occurs while the wind is decreasing in a light
breeze, when the ship has but a low speed. When there has previously been a fresh breeze
from W. or NW., the dead-water is less felt, whereas, after a long spell of fine weather,
it is much stronger. For this reason dead-water is worst in June and July, and becomes
more feeble in the autumn with its heavy westerly storms. If her speed were so small as
3 knots, and she were laden, my ship easily got into dead-water, and then her speed was
considerably slowed.

"When the ship takes dead-water, as a rule (not always) three "rips"2 are seen,
stretching across the wake aft of the stern (Fig. 8, PL IV); the steering becomes bad. If
the wind decreases, the speed of the ship gets slower, and then the rips come nearer and
nearer, and finally come right up to the ship and then disappear. In their place one rip
appears on each side of the ship forming with the latter an acute angle and moving farther
forward to the bow (Fig. 9, PI. IV). With a very slight wind from due aft both rips are
visible, but if the wind blows from the side, the phenomenon is commonly disturbed on

1 See the map Fig. 1, PI. III.

■ See the note at the bottom of p. 2.

18 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

the windward side, where the water is rippled by the breeze. The surface of the water
between the rip and the ship's side is smooth and unrippled. The steering is now entirely
lost, and the ship turns her stem in the direction of the surface current. It feels as if
something were fastened to the ship and holding it back.

"If the wind freshens again, the phenomenon reoccurs in the same manner, but of
course, the order is reversed. First, the single rip (Fig. 9) is seen; it moves aft, and when
it leaves the stern, the three rips (Fig. 8) are formed. As the speed of the ship increases,
these rips draw farther and farther off, and when they are IV2 or 2 ship's lenght from
the stern, the ship gets rid of the dead-water. The rips however remain, and as the ship
sails away, they disappear in the distance to the great satisfaction of the seamen.

"That the vessel may get free, a stronger wind than that which prevailed when it
got into dead-water, is generally required. A sudden freshening more easily frees the
vessel, than a gradual increase of the wind, so that in the latter case a greater increase
is necessary than in the former.

"When empty, my ship less often took dead-water; the breeze then had to be very
feeble and even with the least increase of wind she was free again. This, no doubt, de-
pends on the smaller draught of the ship. I also observed that vessels of smaller draught
were less liable to dead-water; deeper vessels, on the contrary, more so. A good sailer
sooner gets free than a worse ship of the same draught.

"Both when taking dead-water and in getting free, the change seemed to take place
suddenly, although, certainly, the influence of the dead-water (or of the current) made itself
felt on the steering, even if the ship kept her ordinary speed.

"In the Sound, by beating against a fresh, northerly breeze, and with the current
going strongly northward, the ship took dead-water every time she tacked, and then
kept it during some minutes until she got up her speed again. In a more feeble breeze
and with the same current, the ship could not go about, whereas, by veering, one could
get her round. In some cases, I have also seen vessels incapable of going round either
way, beat back again with backed sails and stern ahead.

"When sailing out of the Baltic, dead-water is not encountered before past Falsterbo,
and it then gradually grows stronger until out in the Kattegat. There, it is probably
strongest between Lceso and Skagen where it then again diminishes, in some degree, in
getting out into the Skagerrack. During feeble easterly winds dead-water can be perceived
over the whole Skagerrack, and stretches as far as the westgoing current along the Nor-
wegian coast; but farther in the North Sea and off England I never observed it. In the
Gulf of Finland I have perceived dead-water in the months of June and July, but very

feebly.

"I have observed that dead-water always occurs in connection with more or less of
a current and that this has been strongest at the surface, whereas, below, there has been
either no motion at all or the current has taken an opposite direction. Probably the light
water from the Baltic has moved upon the Salter North Sea water.

"If sailing out through the Kattegat before a decreasing SW. breeze, the ship, when los-
ing her steering, commonly turns her stem towards NE.; and as the current commonly has
the same direction, the ship is soon brought into critical proximity to the Swedish coast,
and often we have been forced to drop anchor on this account so as not to drift ashore.
I cannot say whether the vessels everywhere turn their stems in the direction of the cur-
rent, but I have observed it off the Norwegian coast.

"Several methods have been tried to get rid of the dead-water. Thus I have poured
oil before the stem, have had a hawser laid under the bottom of the ship and drawn it
from stem aft, have worked the rudder, but everything was of no avail. Twice it has
happened in the Kattegat that a steamer has crossed our wake just astern, and curiously
enough, the ship both times got free from dead-water, without my perceiving any increase
of wind."

NO. 15.] ORIGINAL ACCOUNTS. 19

No. 9. A letter from Mr. A. Aanonsen, shipmaster of Bergen, contains
the following statements, as well as the sketches Figs. 2 — 5, PI. IV.

"Although, during twenty years practical experience as a sailing-master, 1 have often
had occasion to observe dead-water, I am sorry to say I can offer but scattered and in-
complete information.

"I have never experienced dead-water in the open sea, but have done so several times
in the Baltic, the Sound, the Kattegat, and the Skagerrack. I have experienced it only in
spring and summer, and then only in smooth sea and calm weather, or immediately after
a calm. The dead-water seems to be limited to scattered areas of rather small extent and
with greater intermediate spaces of "living water"1. I have observed this especially in the
Kattegat, when after some days of calm weather, several sailers were steering in company
before a gentle westerly breeze. In such cases, one or more vessels might suddenly lose
their steering and remain on the spot, while the others passed freely through the midst of
them at a distance as short as two or three ship's length. After a while it was the turn
of other vessels to get into dead-water.

"A good sailer is as much exposed to it as the worst tub.

"On the surface, a line of distinction can often be observed between the dead-water
round the ship and the "living water" ' outside. It forms a line, more or less curved, one
or two metres from the ship's side. (Fig. 5, PI. IV). There is however no difference in
the colour of the water. The direction of the wake is quite incalculable; sometimes it
points to windward, and sometimes to leeward, and sometimes it seems to lead off simul-
taneously in both directions. The sketches, Figs. 2-5, PI. IV, are intended to illustrate
the appearance of the phenomenon; the wind is supposed to be the same — alight breeze
— in the case of all the sketches.

"Fig. 2: The appearance of the wake under ordinary circumstances; speed of the vessel
about 5 knots.

"Figs. 3-4: The vessel is influenced by dead-water, she answers her helm, but with
difficulty ; speed about 1 knot.

"Fig. 5: The vessel lies in dead-water. Agitated spots on the sea, separated by inter-
mediate smooth areas; broken lines of distinction appear and disappear; the direction of
the wake undeterminable; speed about 1 knot.

"The worst case of dead-water which I have experienced happened when sailing in to
Bergen, in the last days of June 1882. My ship was about 40 m. in length and drew
33/4 m. After previous calm weather and calm sea off the coast, we went in on the fair-
way. The sea-breeze was fairly up, and we made good speed. At Kvarven (see the map
of Bergen at left hand upper corner of Fig. 1, PI. Ill) we were caught by dead-water,
and it held us, all the way to Nordnces. We scarcely glided along and were forced to
have all sails set, until we were quite near our anchorage. Then the dead-water suddenly
let go its hold. Believe me, they were both in a hurry, the ship and the pilot. Braces
and falls ran a race together, and we only just got the anchor dropped without any mis-
fortune."

No. 10. Kommandorkaptein Joh. Kroepelien, late of the Norwegian Navy,

gives the following account of a case of uncommonly strong dead-water:

"1 have several times sailed in ships exposed to dead-water both in Norwegian and
foreign seas, but only on one occasion did the dead-water so powerfully affect the handling
of the ship, that she became almost unmanageable. I remember that at the time both my-
self and my fellow-officers were quite taken aback at this phenomenon, and the chief, an

The sign of quotation is due to the present writer.

20 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

old sailor of great experience did not remember any other similar occasion. Our teacher
of Navigation — the late Admiral v. Krogh — always told us that a ship sailing at a rate
of 5 knots was sure not to take dead-water, and on this occasion we were making even
more speed.

"In the summer of 1857 I was a young officer on board H. M. Schooner Sleipner. She
was a large, finely modelled, sailing schooner with an uncommonly large sail-area (610 m.-)
and famed for her capability of beating to windward. Her principal dimensions etc. at
the time were:

Length on water line 28 m. j Draught aft 415 m.

Breadth moulded 81 m. - forward 2'95 -

Displacement 280 m.3 Drag . . 1"2 -

"On the morning of the 3rd of July we were lying at anchor in South Varanger in
the Bog Fjord (see map at right hand upper corner of Fig. 1, PI. Ill), at the outlet of the
Pasvik River, south of Reno; the place is indicated on the map by an anchor. At 6-30 a.m.
we weighed anchor. From 4 a. m. to 2 p. m. the wind was blowing from the north (strength
= 2, perhaps a little more). The log for the preceding day states gentle breezes, (strength
= 1) southwesterly in the forenoon, veering to north in the evening. So far as I remember
there was no indication of dead-water before we weighed anchor ' ; had that been the case
we should scarcely have sailed at all, because with the wind dead against you, it is rather
a difficult task to beat out of the Bog Fjord. To accomplish this a strong breeze and other
favourable circumstances are needed.

"We had main, top, top-gallant sail and jib set, and we soon made quite a good speed,
to the WNW., sailing close to the wind towards Skoger Island. The sails bellied out in
the fresh breeze, and I remember for certain that the ship, though rather stiff, heeled some-
what. A little after starting, however, the ship all of a sudden, lost her headway without
any perceptible external cause, and the turning power of the rudder became nil.

"We then perceived that the ship had taken dead-wakr. From about amidships, and
outwards to boLh sides and to a considerable distance aft, she was surrounded by a mass
of dead-water, smooth as glass, as if the surface were covered with oil. The line between
this smooth surface and the water farther out, looked like boiling "rips"2 and, was quite
distinct, the outer surface being strongly rippled by the breeze 3. The roar caused by
the dead mass of water which, clinging to the ship, was dragged along through the
water outside, was so loud that it might well have been deemed we were in the vicinity
of a rapid. I do not remember the appearance of the wake, nor I believe, was there
anything remarkable about it. The rudder was of no use; we were forced to handle the
ship by means of the sails and our two boats towing from the bow, and thus we proceeded
at a speed of one or two knots.

"In this manner we went on for a couple of hours. All of a sudden, without any
known cause, we were set free from the dead-water. The wind had been very steady the
whole time, and we had constantly endeavoured to keep the ship in the same course. After
being freed from the dead-water the ship got headway, and after a while we logged 7 knots,
going close to the wind.

1 At the author's request, Mr. Kboepelien explains the meaning of this statement in the
following manner: "As far as could be seen from the ship, the surface oftheseawas
evenly rippled by the breeze, without being broken at different spots by smooth, oily
areas; as far as I know, seamen have no other indication of dead-water."

2 See the note at the bottom of p. 2.

3 This is illustrated by two free-hand sketches made by Mr. Kroepelien. The position
of the lines of distinction was, according to the remembrance of the narrator, something
like that on Fig. 10, PI. IV. The appearance of the whole phenomenon would be best
illustrated by Fig. 1, PI. V.

no. 15.] ORIGINAL ACCOUNTS. 21

"The only reason I can give for the change is that neither at our harbour at Reno
nor west of the point at Ellinghavn had we been so strongly exposed to the fresh-water
stream from the Pasvik River as in the middle of the channel. As after leaving Ren5 we
did not keep our reckoning, I cannot verify in the log, the speed given, but I am not far
wrong in what I have stated above, for the matter was thoroughly discussed at the time
and therefore became fixed in my memory.

"Going towards Skoger Island we went about, but in tacking we got into dead-water
again; we, however, succeeded in going about, but the dead-water stuck to the ship even
after this. In the same manner as before, we were forced to work our way back again by
the help of the sails and the boats towing. We proceeded at a snail's pace and after
much struggling we dropped anchor at our last harbour at noon, while a steady fresh breeze
seemed to scoff at our helplessness.

"The next day a southerly wind was blowing, and we got safely out of the BOg Fjord
and across Varanger Fjord to VadsO without any more trouble from dead-water."

No. 11. Mr. G. Pedersen, shipmaster of Arendal, writes:

"The Brig "Trio", 309 reg. tons and drawing 4'9 m., was on April 12th 1901 at ."»
p.m. about 4 miles north of Lappegrunden's lightship (Helsingor). Headed SSE. V2E. at
a speed of 4 knots through the water, for a westerly, uniform wind. The current in the
Sound ran northward.

"The brig got into dead-water — I am unable to say whether it happened suddenly
or by degrees. The speed was lost, and the ship was as if nailed to the spot, but she
still answered her helm. She did not leave any wake farther aft than about 8 m. from
the stern, and the water round the ship was somewhat stripey. A barque sailed past us,
without being influenced by the dead-water. To get free, I poured half a gallon of pe-
troleum over the stem — but with no effect. Then I laid the helm hard a port and let
the ship get a good swing, and then laid hard starboard, and continued in that manner
for a while — with no effect.

"At 8'45 p. m. the ship refused to answer her helm and headed about SE. for half
an hour. After that she suddenly went through east to north. I then braced round ; the
ship steered again, and I veered round through east and headed for the light-ship with no
feeling of the dead-water.

"During the whole time from 5 to 9 p. m. we had a fresh westerly breeze, which,
under ordinary circumstances, and with all sails set, would have given the ship a speed of
4 or 5 knots.

"The day before, we had dead-water for awhile off Kullen, but on this occasion there
was only a very light wind.

"The worst regions of dead-water in which I have sailed, are the Kattegat, the Sound,
and the St. Lawrence River."

No. 12. Mr. 0. Olsen, late shipmaster, of Kristiania, in the following
manner describes a case of dead-water, which he experienced in the spring,
several years ago.

"I entered the Drammen Fjord with a laden schooner, 140 reg. tons and drawing
4 m. or a little more. The vessel was short, broad, and bluff, but generally steered well.

"We passed Rodtangen in the forenoon with a fine breeze from about due aft; the
mainsail to port, veered off right up to the shrouds; bonnets starboard. Athwart Hohnsbo
she refused to answer her helm. We tried to manoeuvre with braces and sails, but to no
purpose. Then I let brace hard a port, had the bonnets hauled in, laid the helm hard a
port; and the ship went up in the wind on the starboard tack. As the whole area of the
sails could then work, it all at once appeared as if the vessel had been cut loose from a
mooring aft; and, after some manoeuvres, we sailed up to Svelvig at a rate of about 5 knots

22 EKMAN. ON DEAD-WATER. [norw. pol. exp.

(the vessel was capable of making 8 knots). The force of the wind was constant during
the whole time." — — — — — — — — — — — — — __ — _.—

"When the ship is moving ahead, leaving a void space astern, the fresh-water on the
surface rushes in from aft to fill the wake, thus tending to reverse the action of the rudder;
the steering of the ship is, in consequence, destroyed. In fact the fresh-water can be seen
rushing after the ship and it makes a great noise."

Effects of dead-tvater and surface-currents combined.

No. 13. I am indebted to Kommendorkapten F. W. L. Sidner of the
Swedish Navy, for a verbal account, which he has been good enough to revise,
of the following interesting accident.

"In July 1899 I was on my way with the corvette Freja from Carlscrona to Leith.
The Freja is a ship of 2000 tons' displacement, 66 m. in length, 12 m. in breadth and draw-
ing 6 m. Besides sails she is furnished with engine and screw-propulsion, hut this was not
used in the case mentioned here below.

"On July 11th in the evening, the Freja was running before a southerly breeze from
Lceso towards Skagen.

"The breeze, being rather light, was dying down but still gave a speed of 3 or
4- knots. At 7 p.m. — the ship was then probably about 7 miles SE. of Skagen — she got
into dead-water, which at first mainly manifested itself by bad steering. At midnight the
dead-water became more decided, and the speed was reduced. The ship, then about 5 miles
east of Skagen, was heading northward before the wind, and her course had to be changed
to west. She answered her helm and turned through two points, heading NNW., but she
could not be brought further westward. An attempt was made to turn her round the other
way through north, east, and south to west. She answered till she got two points from
the wind — SSE. — , but then the sheer stopped, and she fell off in spite of the action of
sails and rudder. These attempts were repeated several times, with just the same result;
within the semicircle NNW.~E.-SSE. the ship could be steered, but not beyond these
limits. She could not be brought to head westward, and we got farther and farther from
Skagen.

"During this involuntary northward sailing, peculiarities were observed in the sur-
rounding water (see Fig. 14, PI. IV)1. Before the bow on the port side, a low hillock or
bank of water was formed at a short distance from the ship's side. Inside this bank and
along the whole port side of the ship, the water was "boiling". All the way starboard of
the ship the water had the appearance of an eddying current. Furthermore, the ship was
followed by two sharply defined wakes, the one slightly curved to the port side and the
other more strongly bent to starboard; between them the water was agitated.

"At half past two next morning, a steam- trawler was seen, heading straight for the
Freja, which lay still helpless, though the wind had increased. As sailors believe that a
steamer can shake another vessel free from the dead-water, we waited with interest to see
whether the trawler would come near enough to do us this service. She had the trawl
in tow and, therefore, could not have made more than about 3 knots. She advanced to a
distance of about l'/2 cable's length (300 m.) and then turned round and went back again;
and actually, when she was closest to us, the Freja suddenly got rid of the dead-water
and sailed at a good speed, which after a while was logged as 6"2 knots."

1 The sketch was made by the present writer and afterwards corrected by Kommendfir-
kapten Sidneh.

NO. 15.]

ORIGINAL ACCOUNTS.

The Nautico-meteorological journal of the Freja gives the following data, for the time
during which the above mentioned accidents occurred.

Date
July

Hour

Position of the ship

Wind

Surface-water

Lat. N.

Long. E.

Direction

(Subject to compass

error 11° W.)

Force

Spec,
gravity

Temp.C.c

11
12

4 a. m.
8 a. m.
Noon
4 p. m.
8 p. m.
Mid t.
4 a. m.
8 a. in.

O /

56 46-7

57 5-0
57 17
57 21-2
57 43-2
57 46-8

57 51-7

0 /

12 0
11 457
11 291
11 8-0
10 500
10 515

10 27-3

SSW.

SW.bS.

South

S.bE.
SE.

3
3
3
3

1
1
3

2

1

009
011
008
009
010
010
020
022

190

200
200
20-5
200
200
190
20-0

The data in the 7th column are of special interest. They show that the surface-water
had a spec, gravity 1'010 in the Kattegat and 1'020 and more in the Skagerack. To judge
from the usual conditions prevailing in the Kattegat and Skagerrack, it is probable that the
water of spec, gravity 1'010 had formed a shallow surface layer in the Kattegat, reaching
out as a shallow tongue north of Skagen, upon water of spec, gravity 1'020. As the transi-
tion of spec, gravity at the surface seems to have been rather sharp, the tongue of
light surface-water might also have been distinctly separated from the heavier water below;
and near the end of the tongue the Freja might have sailed in a sharply defined surface-
layer of no greater depth than she drew. The surface-layer apparently has had a motion
of its own (to the east) upon the water below; this is quite clear from the description of
the appearance of the sea round the ship.

An officer on the corvette, Lieutenant O. Wallahder, has made a somewhat different
sketch of the phenomenon (Fig. 15, PL IV). This sketch shows no asymmetry, which, how-
ever, need not depend on negligence; for when the ship during her manoeuvres headed in
the direction of the surface-current, the asymmetry must have been lost, and on such an
occasion the appearance illustrated by Fig. 15 might have been observed.

No. 14. Count M. Hamilton, Kommendorkapten in the Swedish Navy,
has communicated to me the following experience, in which a strong surface-
current was proved to have played an important part.

"On May 28th 1895 at 2'30 p. m. H. M. Brig Gladan' was about 3 or 4 miles NE. of
Skagen, heading WNW., at a speed of about 2 knots; wind ESE. At the hour mentioned
sail-drill began, and simultaneously with the shortening of sail, the ship suddenly sheered
two points to port. Believing that it depended on the sails being shortened, I intended
to bring the ship back to her course after they had been set again. However, the ship
could not, by any means be brought to starboard. I then tried to go round to port and
in this way get into the desired course. The ship, also, answered willingly; she went
round by the wind and fell] off on the starboard tack — but only north, and there she
stayed. I tried to turn her the first way again, and as before she went by the wind will-
ingly and fell off to leeward to the west, but no further. She could not be brougth into
the quadrant between W. and N., while within the 3 other quadrants she could be man-
oeuvred, and could make about 2 knots. A schooner in the neighbourhood seemed to have

24

EKMAN. ON DEAD-WATER.

[NORW. POL. EXP.

fallen into the same mishap as we. During an hour and a half I endeavoured to get the
ship into her course, but to no purpose ; then, it became calm.

"In the evening a sounding was taken, and I then found that a strong under-current
was running just below the keel of the ship or else that she was carried away by a sur-
face-current of considerable velocity. As soon as the lead was about half a meter below
the keel, it was forced under the ship, and the line pressed against the ship's side. Although
it was calm during the whole night, the brig next morning was close to the Pater Noster
light; thus she had been carried by the current across the Kattegat from Skagen.

"In the morning (May 29th) a gentle SW. breeze sprang up, strong enough to enable
the fishing boats to sail past and around us, at a good speed; but the brig could by no
means be brought out of her course straight towards Pater Noster. It was only at about
half past five that we, all at once, felt as if the ship had broken loose, and from that
moment we had her in our power. We headed without difficulty close to the wind and
thus beat southwards at 3 knots, which speed was increased in the course of the day to
4 or 5 knots.

"Several vessels were seen during the day, most of which seemed to feel the dead-
water. In such cases they lay with the wind athwart or on the quarter, with head-sails
shortened and usually the rudder made fast. A ship could be seen making good bead-way;
she suddenly fell two or three points to leeward, the steerman worked the rudder to and
fro — to no purpose — , then the head-sails were shortened, and we knew that the vessel
had got into dead-water.

"Several times the Gladan got into dead-water during the day, especially in the
neighbourhood of other vessels that lay in dead-water, but she always soon got rid of it
again."

No. 15. Mr. Michael Leegaard, engineer to the Norwegian Harbour
Administration, has kindly communicated to me the following facts with the
idea of giving an explanation of the phenomenon of dead-water.

"At Eaersund the river-current and the
tidal current from Nysund sometimes en-
counter one another as in Fig. 1. Along
the line of encounter there is formed a "rip"
or "current-back" A B, where the water is
"boiling". This rip has the form of a cur-
ved line, and remains stationary as long as
the conditions are unaltered. If a boat be
steered for some distance on either side of
the rip and then be left to herself, she will
be carried in towards the rip and will lay
herself along it. Then she will be carried
downwards along the rip, following even
its smallest windings, all the while being
followed by a "boiling" wake aft. The boat
cannot be made to turn across the rip with-
out some considerable effort, and she im-
mediately turns back into her former direc-
tion along the rip." — — — — — — —

Fig. 1.

"That a sailing vessel with slight wind is inclined to take "dead-water" might be ex-
plained with the aid of the facts mentioned. The vessel will be carried by the current
into the "rip", there — by the effect of the current impelling her from both aides — she will
take her own course along the rip and be slowly carried down stream."

NO. 16.] ORIGINAL ACCOUNTS. 25

Collection of various accounts of dead-water in Scandinavia.

No. 16. Mr. J. P. Posti, of Hammerfest, who has navigated the Arctic
Sea for 40 years with small sailing vessels of about 30 reg. tons, has favoured
me with the following information:

"Dead-water occurs in the arctic regions in places where there is fresh water, off
river-mouths, or where the snow is thawing on land and ice. It may influence vessels in
a slight wind or calm weather. In the Kara Sea and Kara Bay I have been most ex-
posed to it. — In the Kara Bay it has happened that 8 men in two boats could not tow
the vessel loose, before we got help from the wind.

"In the Alien Fjord I have also experienced it; inside Alten-ncesset it is very bad,
and it has happened that 4 men could not tow the vessel free, in calm weather."

No. 17. Mr. J. Ellingsen, of Kristiania, informs me that dead-water occurs in Banen
Fjord, Vefsen Fjord, Vel Fjord, Namsen Fjord, North of Kristiansund, Romsdal Fjord,
on the north entrance to Bergen, and generally off the mouths of great rivers. It occurs
in the months of May, June, July, and August.

No. 18. KommendOrkapten J. A. Ekelof, late of the Swedish navy has told me that
once, several years ago, he experienced dead-water in the Trondhjem Fjord, when sailing
in to Trondhjem with a corvette.

No. 19. The narrative No. 2 (by Captain S. Scott-Hansen) had the
following supplement:

"Our pilot told me that he had several times been exposed to dead-water; he spe-
cially mentioned one occasion on the Pudde Fjord at Bergen, when the ship — an 8 knot
cargo-steamer — according to the pilot's own phrase, hardly moved from the spot."

No. 20. Mr. M. Leegaard, in addition to account No. 15, sends me the
following:

"Since the year 1885, I have each summer navigated the coast between Fredrikstad
and Bergen with a cutter, 12 m. long and drawing 23 m.

"During these cruisings the vessel has often got into dead-water and almost always
at the same spots, mainly at places where there is fresh water, such as off Larvik and
Arendal, off Kristiansand (near Odder Island) and in the port of Egersund. The dead-
water is especially felt when setting sail at such places.

"I have heard, that off the town of Bergen dead-water is often met with between
Kvarven and Stangen (about 3 miles south-west of Kvarven); between Kvarven and Stan-
gen there is often strong current."

No. 21. Mr. Bernt Larsson of Fede, navigation Instructor in Haugesund,

has reported the following:

"There is often very strong dead-water in the Fede Fjord, especially where the fjord
becomes narrow at Avaren. It receives water from two rivers, and this fresh water, ac-
cording to my measurements, forms a surface-layer of half a metre or a little more, in
thickness.

26 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

"The dead-water is more severe in the first part of the year — till Midsummer — than
later. It is mostly met with in westerly or south-westerly winds (sea-wind), probably be-
cause a greater quantity of fresh water is then heaped up in the fjord. At all events,
dead-water does not appear in the Fede Fjord during a land-wind.

"A sharp-built and deep-drawing, laden vessel is more exposed to dead-water than one
flat-bottomed and drawing little water. Often, galeases of about 50 reg. tons, drawing laden,
3 or 4 m. of water and sailing at a speed of 6 or 8 knots, take dead-water and run
straight towards the shore; while at the same time modern, flat-bottomed vessels of 80
reg. tons drawing only 2 or 2'5 m. are not influenced by it. A vessel most easily takes
dead-water through bad steering, or on changing her course."

No. 22. The account No. 38 below (by Mr. Olsen Rod) had the follow-
ing supplement:

"I have several times, before and afterwards, experienced dead-water, though in a
moderate degree. Thus I have met with it in the Kristiania Fjord, especially between
Fulehuk and Bcidtangen and in the Frier Fjord. On the North Sea, in the Channel, or
on the Atlantic, I have never observed it, and only slightly in the Baltic."

No. 23, A Dutch naval officer, Lieutenant G. van Hulstyn, has reported

a case of dead-water in the Kristiania Fjord:

"In the month of July 1888 H. M. "Nautilus" sailed northward past Fcerder for Kri-
stiania. In the fjord we had fair wind of strength 6 (Beaufort) and made 5 or 6 knots.
At a certain moment the ship lost her head-way, although the sails stood filled. The Nor-
wegian pilot called the phenomenon by the name of "dead-water". After some time the
ship again recovered her head-way."

No. 24. According to Mr. L. H. Larssen, of Drammen, they are much troubled by
dead-water there, in spring and autumn. In summer and winter there is dead-water only
after strong SW.-winds.

No. 25. Mr. H. Halvorsen, ofj Kristiania, writes:

"In the month of July, probably in the year 1887, I was towing a 600 tons' lighter
up the East Arm of the Glommen. The wind blew astern, and the lighter was being
towed at 5 or 6 knots, when off Futerod, she fell into dead-water and did not progress as
much as one cable's length (200 m.) during fully three hours. She could not be kept on
her course, either by rudder or by help of the towing-rope. This was also the case with
another lighter in the same situation. The dead-water let go its hold suddenly."

No. 26. From a letter from Captain A. Macfie, of Falkenberg, the fol-
lowing may be extracted:

"On the west coast of Sweden dead-water is often experienced in feeble wind or calm
weather. Very often it occurs off the two mouths of the Gota River, but also in other
places, where no river disembogues. Among several cases, I have experienced, the follow-
ing may be mentioned:

"1) With a cargo-steamer of feeble engine power, off Elfsborg on the mouth of the
Gota Biver. Head-way almost lost.

NO. 16.] ORIGINAL ACCOUNTS. 27

"2) When towing a large vessel near Kattan (inside Marstrand). Made no head-way
but drifted back with the current. Got free through stirring up the water before the vessel
with the screw-propeller, and after that, made 7 knots.

"3) Also when towing a large vessel. Head-way almost lost. Got free through shor-
tening the tow-rope."

No. 27. Captain S. Scott-Hansen has reported a case of dead-water in
the Kattegat, about 16 miles SE. of Skagen.

"It happened to the Norwegian corvette the "Nordstjernen" in the night between May
21st and 22nd 1897. During the time the ship had dead-water, she turned right against
the rudder, although the sails stood filled. Aft in the wake there was a splashing sound,
as when the wavelets strike a shore — a peculiar sound, which is not heard when the
ship makes head-way."

No. 28. Admiral H. Koch, of Kjobenhavn, relates:

"The corvette "Valkyrien", probably in the summer of 1853, met with a case of dead-
water off Fornces, in Jutland. The wind was southerly — a light breeze; current southerly.
For several hours we could not advance by beating, but drifted to leeward with the dead-
water to windward."

No. 29. Lieutenant 0. Wallander relates, that the Swedish frigate "Wanadis" got
into dead-water north of Anholt in the Kattegat on May 13th 1889. Slight, north-easterly
winds. After some manoeuvres — all to no purpose — the screw-propeller was set in mo-
tion, and then the dead-water disappeared."

No. 30. On Aug. 4th 1899 the corvette "Freja" (see Account No. 13) met with dead-
water in the Kattegat between Anholt and Kullen. The wind was very slight, but the
ship soon got free again.

In the same summer H. M. brig "Gladan" is said to have met with a case of dead-
water in the Kattegat.

No. 31. An old sailor, Captain Isaksen, of Fredrikstad, has told me that even in
the North Sea he has observed dead-water ; but only under feeble "Catspaws" which, under
ordinary circumstances, would have given the ship a slight motion.

No. 32. Mr. Sandstrom, of Sundsvall (on the Bothnian coast of northern
Sweden) has mentioned the following event that happened there, several years

ago:

"A vessel was to be towed away from her haven in the Sound inside Alno; but the
tug could hardly move the vessel from the spot; it was as if she were stuck in the mud.
Only when they came farther out from the haven did the speed increase, and the towing
became easy. Many people had seen the struggle of the tug and were much astonished.
Possibly this case may have been owing to dead-water. At the ends of Alno Sound two
rivers empty themselves into the sea."

Collection of accounts of dead-rvater beyond Scandinavia.

No. 33. According to Kommandorkaptein Joh. Kroepelien, the late Rear Admiral G.
von Krogh, formerly instructor of seamanship, used to speak of dead-water and its causes,
in his lectures. He often dwelt on the troublesome dead-water off the great river mouths
of South America.

28 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

No. 34. Admiral H. Koch, to whom I am indebted for account No. 28,

also writes:

"In the autumn of 1859 I was mate on a little merchant barque the "Emma Arvigne".
When we had got out a little way to sea, off the mouth of the Orinocco, sailing for St.
Thomas, we met with dead-water. The wind was easterly, weather fine. The ship drifted
almost crosswise to leeward with the dead-water to windward. She could not go about,
but we succeeded two or three times by help of manoeuvres with the sails, in tacking.
At last we were obliged to anchor. Some hours afterwards we weighed anchor again and
were prepared for the necessity of going west of Trinidad, although we had no chart of
this water; but we were now free, and so we sailed to the east of Trinidad."

No. 35. Mr. H. Hansen, shipmaster, of Kristiania, mentions the Gulf of Mexico among
the waters in which he has been out in dead-water.

No. 36. Mr. G. Pedersen, the narrator of Account No. 11, mentions the St. Lawrence
River as among the worst regions of dead-water which he has navigated.

No. 37. Mr. P. M. Land, of Nanaimo (inside Vancouver Island, Bri-
tish Columbia) writes as follows:

"My only experience of the phenomenon occured at the entrance of this harbour, in
the light draught twin screw steamer "Mermaid", of which I am master, and under the
following circumstances.

"During the winter or rainy season, of 1900—01, while entering the harbour, my
steamer, which was drawing 2 m. aft and 1 m. forward, entered a belt of water in which
she became almost unmanageable, though she is capable of a speed of 8 knots, and is under
ordinary conditions, remarkably easily handled. The best description I can give of the effect
produced on the "Mermaid" is, that it was as if a long floating spar were lying fair across
her stem, causing her to lose her headway almost completely and making her answer her
helm with difficulty.

"Owing to unusually heavy rains, the Nanaimo and Cliase Rivers were discharging a
great volume of muddy fresh water, which lay upon the sea water to a depth of half a
metre or more. The region of dead-water was about 200 m. across, and I was about 10
minutes in passing through it. The phenomenon is known here by the name you give it,
"dead-water". It is frequently met with in the Straits of Georgia, off the mouth of the
Fraser River, and I have heard accounts of it from at least two of the Nanaimo pilots,
who experienced delay and annoyance from it while bringing large steamers past that place."

No. 38. Mr. A. Olsen Rod, late shipmaster, of Kristiania, has informed

me of a case of dead-water to which he was exposed on the Mediterranean.

From his letter the following is extracted:

"Late in the autumn of 1857 I arrived in the Gibraltar Straits with the brig "Elise"
(29 m. long and drawing 3 m.) and sailed eastward for the Black Sea. After having had
much rain of late1, we arrived in the neighbourhood of Cape Matapan with fine weather
for several days.

1 According to a statement in "Beitr&ge zur Physicalishen Geographie von Griechenland"
von J. F. Julius Schmidt, Band I, Athen 1861, it rained during Nov. 1857, 62 French
lines (= 140 mm.). For Dec. 1857 no data are given.

Mr. Olsen Rod writes in a second letter: One or two weeks before Christmas we
got rainy weather, very welcome because our store of fresh water was quite rotten.
It rained almost every day for about a fortnight, sometimes very hard, and we col-
lected 3 large barrels of rain-water.

NO. IB.] ORIGINAL ACCOUNTS. 29

"On January 2nd 1858 we were between Cape Matapan and Cerigo and sailed east-
ward for the Archipelago. The wind was WNW. a gentle breeze, and water quite smooth.
We had all sails set and made about 3'/2 knots. At 10 a. m., when we were about 12
nmit. miles SW. of Cerigo, the brig no longer answered her helm and began to go up north-
ward to the wind. We worked the helm but to no avail. We backed the yards and shi-
vered the braces and made all conceivable manoeuvres, but the ship only turned a little
and went back again. The little wind that we had, seemed to be the same as before, and
there were many ships in company both to port and starboard of us, which sailed away,
whilst we were lying as if at anchor. Yet there was one sail about 3 miles to port of us,
in the same predicament.

"In this manner we lay for l3/4 hours, when the ship began to glide and fall to lee-
ward a little. We then got the head-sails filled and had the aftersails shivering, and with-
out any command of the helm the vessel got down into its course. The most remarkable
thing was, however, that when I stood, afore, I saw a long stripe stretching from the bow
far over the water on each side dividing the water into two parts. The water aro undthe
ship was light gray, but ahead of the stripe it was wholly dark. These stripes seemed
by and by to move aft — of course it was the ship that began to glide slowly onward —
and after 5 or 6 minutes, when the stripes had passed along the ship and had left the
stern and the rudder, then, at that same moment, the ship again answered her helm and
made head-way. The wind was about the same — WNW. by W. a gentle breeze. We
made 3 knots, but no more, in the afternoon.

"When we approached Cerigo, the ship was about to get into dead-water again, but
by working the rudder to and fro, we steered again, and after that, we did not feel the
dead-water any more.

"The ship, during its long voyage had become very dirty and overgrown with bar-
nacles of 10 or 15 cm. in length, which may have had some effect."

I have received information of several other cases of annoyance expe-
rienced by vessels at the mouths of rivers in America, Africa, Europe, and
Asia. I cannot decide, however, whether "dead-water" or currents and whirl-
pools have been the main cause of these accidents, as they are too scantily
described. In general it is mentioned that the vessels have lost their steering,
but as a rule nothing is said about changes in the speed. The phenomena
in question are possibly the combined effect of several causes; for it is obvious
that a vessel in dead-water, being deprived of her head-way and steering-
power, should become more easily influenced by the disturbing effects of cur-
rents and whirlpools.

Four of these cases only, will be inserted below; the others are too in-
completely described to be of any value.

No. 39. Captain H. E. Purey-Cust, R. N., York (England), has kindly

sent me the following information:

"It is a common complaint, the difficulty of steering at the mouth of the Congo River.
The captain of one of the steamers trading there, told me that he always experienced
that difficulty after being at anchor there, when on weighing he endeavoured to turn down
river, and that it was an utter impossibility to do so when going ahead from anchoring,

30 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

the only way being to reverse the engine and go astern. I found, myself, great difficulty
in steering when going slow and at all across the current. With the ship stopped across
the current, the water would be seen making past the bow and stern down river at a con-
siderable rate, giving the appearance of the ship drifting headside on against the current.
On making some rather detailed observations, the reason of this became apparent. The
fresh water of the Congo running at 3 or 4 knots, on meeting the salt water of the sea
some miles inside the actual mouth, passes over it with increased velocity — 5 or 6 knots

— and diminished depth, in some cases only a few feet, the salt water below having only
a faint tidal motion, so that a vessel's keel may be in still water and her water line in a
current ot 5 or 6 knots, which amply accounts for the difficulty experienced."

No. 40. M. Dechaille, "directeur des signaux de sauvetage", Havre, has

— in "Journal de Havre" — given the following particulars of a phenomenon,
known at the mouth of the Loire, by the name of "les bournes".

"When a vessel is influenced by this phenomenon, it is said that "le navire est em-
bourne"; she then does not answer her helm until she has got out of the region of the
phenomenon.

"Once, I was in command of a 600 ton sailing-ship and had left Nantes with a good
easterly breeze, able to give the ship a speed of 6 knots. At the mouth of the Loire the
ship became "embourne" and turned all round two or three times. I succeded in coming
out of the "bourne", and then my ship again answered her helm and sailed without any
further accident. I do not believe that the "bourne" would have had any effect on a big-
ger ship, and not at all on a steamer."

An old pilot says about this phenomenon, that it effects vessels at even a velocity of
5 or 6 knots, and even large steamers. He has not observed it except after heavy rains,
or when the snow has been melting, or when the Loire rises above its banks after a series
of storms.

No. 41. Mr. F. Picamilh, Bordeaux, has kindly sent me the following
information respecting the river Garonne, in the neighbourhood of Bordeaux.

"The river is always very muddy, so that objects left on the shore during one high
tide may become covered with several millimetres of mud. In the summer, which is the
dry season, the water in the river is considerably reduced, and its level sinks. Then the
rising tide stirs up enormous quantities of the deposits from the bottom, giving to the
river the appearance of a river of mud.

"Seamen then say: "les eaux sont lourdes". Vessels steer with difficulty; but more
particularly lighters cannot navigate the river in the usual way by the help ot the current.

"For navigating the river, these lighters, having an anchor dragging at the bottom,
are left to drift with the current. If the vessel should be moved in a direction different
to that of the current, she is made to swing out by the help of the rudder, as indicated
by Fig. 2. But when "les eaux sont lourdes" it is, sometimes, impossible to perform this
manoeuvre: The lighter does not answer her helm, and in spite of a strong current im-
pelling the rudder, she remains immovable in the direction of the cable (Fig. 3)."

No. 42. Mr. Picamilh has told me of another peculiarity experienced in
the basin at Arcachon west of Bordeaux.

"This basin is filled with sand-banks, which during the high tide under water, are at
low tide above the water-level, and are separated by deep, navigable channels. The water
in the basin is pure Atlantic water, and the rivers disemboguing there, carry but little water.

NO. 15.J

ORIGINAL ACCOUNTS.

31

ffUdcL

e»*

Fig. 2.

^

"In this basin it sometimes happens that sailing-vessels in a slight breeze, cease for
some minutes to answer their helm. This phenomenon is in particular observed by yachts-
men, during the summer-regattas in the basin. Then, in slight wind and smooth water,
they fear the places, "where the yachts do not answer their helm". These places are,
however, of very small extent, and the phenomenon is rather rare."

Accounts from ancient authors.

No. 43. Several old Roman authors especially Pliny the Naturalist,
tell us of events when ships have been suddenly stopped and deprived of
their head-way.

In his Historia naturalis, Book IX, Chapt. 41, Pliny narrates that a ship, carrying
the boys of noble families, who by the order of Periander the despot should be castrated,
was checked on her way, though she had all sails set. The cause was attributed to a
species of Mollusc (Murex), which by affixing itself to the vessel, stopped her speed and
thus saved the boys.

Commonly the checking power was attributed to a fish, Echeneis Remora. This fish
has on its back a haustellum by means of which it can affix itself to the rocks or to float-
ing bodies as for instance, to vessels. Pliny says that but one of these fish kept back a
vessel even in the strongest wind; and to produce this effect it only needed to affix itself
to the body of the vessel. Thus in the naval battle of Actium it held Antonius' own ship
fast, so that he was obliged to board another vessel. (Pliny. Historia Naturalis, Book XXXI,
Chapt. 1).

At the same place Pliny mentions another event which happened in his own time:
Caligula the emperor, on his way from Astura to Antiam, was detained, because one single
vessel of his whole fleet was stopped and could not move from the spot. The vessel — a
quinquereme — was overhauled, and a Remora was found sticking to the rudder. When
the fish was loosened and brought before the emperor, to the emperor's great astonishment,
its power was gone, and the ship could be rowed again.

No. 44. A similar story is narrated by Bartolomeo Crescentio Romano
in his "Nautica Mediterranea, printed in Rome in the year 1607. This

32 EKMAN. ON DEAD-WATER. [norw. pol. exp.

narrative, which has been kindly sent me by Mr. Salvatore Raineri, secre-
tary of the journal "Lega Navale Italiana", Genoa, when somewhat abridged,
runs as follows:

"_ _ _ _ and I must tell you about another deed of the devil, because you must
know in how many ways this enemy of mankind works against poor seamen. — —

"On a voyage from Gaeta to Napoli, the Galley "S. Lucia", when sailing before a
fresh wind and being two miles from Port, stopped quite immovable in spite of her sail
being strained. The steerman examined the rudder to see whether there was some rope
or net fastened to it, and as nothing was found, he commanded the oars to be got out
and the galley-slaves to be forced on with hard blows. But the galley did not move from
the spot, and when she had been lying motionless for a quarter of an hour and more, the
other galleys, which had sailed on, shortened sails, waiting. Then a man named Catelano,

told the captain to have three monks removed from the deck of the galley and averred

that the galley would then immediately begin to move; and when the captain had had them
removed, the galley certainly did begin to speed like an arrow.

"Then all the men were about to throw these three poor fellows into the sea, saying
that they were excommunicated; but the same man Catelano helped them saying, that this
was a stratagem of the devil to the detriment of the monks; and he obtained permission
that they should only be taken from the vessel.

"This occurrence would have caused scientists to suppose that a very small fish, resist-
ing the progress of the vessel, had got the better of the force of sails and oars and made
the vessel stop. — "

No. 45. In Tacitus, "Agricola", Chapt. 10 (treating on the geography of
Britain), it is said:

"Thule ' was also seen, previously hidden by snow and winter; but the sea is said
to be tough and hard for the rowers (sed mare pignum et grave remigontibus) and to be
little stirred by the winds. — — — "

If search were made all through ancient literature, there is no doubt that
a more ample collection of tales would be obtained similar to the few here
inserted. There are moreover, stories about submarine, magnetic rocks, or
supernatural forces fettering the vessels in certain places on the sea, and
possibly, some of these have their real basis in cases of dead-water.

Probably Norway.

II.

PRELIMINARIES.

A. THE RESISTANCE TO VESSELS UNDER ORDINARY

CIRCUMSTANCES1.

Imagine a vessel towed on a hawser. When her speed has become uni-
form, the resistance is evidently equal to the stress in the tow-rope; its im-
mediate cause is the sternward resultant of the water pressure, against the
vessel. In this pressure is then included, the "tangential pressure" or friction
of the water against the sides of the vessel. Further, the resistance is equal
to the work done in towing or propelling the vessel a unit of distance; this
work is heaped up as energy (heat and vis viva), communicated by the vessel
to the surrounding water. The resistance may consequently be regarded from
two points of view : either, as the resultant of pressure (and friction) of the
mater against the vessel or, as equal to the energy communicated to the
water per unit of distance covered by the vessel. One must, of course, be
careful, not to use these two views simultaneously, so that the resistance, or
part of it, be not taken into account twice.

If the water were frictionless, and if its surface could be held plane
as under a sheet of ice, vessels would, according to a well known hydro-
dynamical theorem of Kirchhoff2, experience no resistance, when moving

1 Part of the substance of this section is drawn from Chapter XI of Sir W. H. White's
very interesting "Manual of Naval Architecture", London 1900, and from Chapter IX
of the excellent "Hydrodynamics" of Prof. Horace Lamb, Cambridge 1895- To these
books reference may also be made for further information on the subject.

- Vorlesungen ilber Mathematische Physik, von G. Kirchhoff. Mechanik. Neunzehnte
Vorlesung § 2.

5

34 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

at a uniform rate in open water. The physical reason for this is, shortly ex-
pressed, that under these suppositions the motion of the water depends only
on the actual velocity of the vessel; the vis viva of the water consequently
remains unchangeable, and as mechanical energy cannot, in a frictionless fluid,
be transformed into heat, no energy at all is communicated to the water by
the vessel.

In actual practice the water has a free surface. The pressure of the
vessel against the water then causes a disturbance of level, which persists in
the form of waves. These gradually spread over all the sea behind the
vessel, and the vis viva of the water thereby continually increases. The work
necessary to generate this vis viva must be spent by the vessel and causes
a certain "wave-making resistance".

Further, water is a viscous fluid, and this circumstance will in a twofold
way cause an alteration of the motion, and the addition of new causes of re-
sistance. Firstly, the water, flowing past the ship's sides, exerts on them a
sternward tangential stress — "frictional resistance". Secondly, the motion
which, though unstable, would theoretically take place in a perfect fluid, is
disturbed by the viscosity; the wake, which would otherwise be smooth and
even, becomes irregular and eddying, and the steady supply of energy required
for creating new eddies is a cause of resistance — "eddy making resistance".

Elaborate experiments have been made for determining the relative im-
portance of each of these factors in contributing towards the sum-total of
resistance. The frictional resistance is found to be quite preponderant at low-
speeds, and even for fast vessels going at full speed, it amounts to nearly a
half of the whole. The eddy-making resistance is rated at about 10 per cent
of the former (in well-formed vessels), and the rest is wave-making resistance.
These numbers are under the supposition that the water is not shallow (see
the next section of this chapter). The frictional resistance is approximately
proportional to the square of the vessel's velocity.

Tlie wave-making resistance is of special interest to us, because it is
the chief cause of the speed-reduction in "dead-water"; the following general
remarks, though referring particularly to wave-making resistance under ordi-
nary circumstances, are, with some modifications, applicable to the case of
a vessel moving in dead-water.

NO. 15.1 RESISTANCE OF VESSELS. 35

The waves following a vessel in rapid motion consist, as we are accus-
tomed to seeing, of two different systems, which are both easily seen in the
photographic illustration Fig. 3, PI. XII. One set of waves, the transverse
waves (best seen on the left-hand side of the figure), stretch right across the
wake, bending slightly aftwards; the other, the diverging waves (best seen
on the right-hand side) stretch out from the stem as wedges each one more
extensive than the preceding one.

The shape of these waves has been calculated mathematically under the
simplifying supposition that the vessel producing them is infinitely small1.
The error caused by this simplification is, as far as interests us at present,
without appreciable influence on the shape of the waves at a distance from
the vessel. Fig. 3, PI. V shows the crest-lines of both systems of waves cal-
culated in this way, in the case of deep water. The vessel must be imagined
to be at the point at the extreme left of the figure. Theoretically the diverg-
ing waves should fill the whole space to both sides of the middle line, but in
the proximity of this middle line there would be an infinite number of infinitely
short waves which cannot be drawn on the figure. As a matter of fact, the
diverging waves are never perceptible in the middle of the wake.

Really, the stem and the stern of a vessel each produces both these sy-
stems of waves; but owing to the shape of the vessel, the transverse bow-
waves and the diverging stern-waves are very low and are easily overlooked.

The wave-length depends upon the velocity v, of the vessel and upon the
direction of the crest-line of the wave considered : in order that ship and wave-
system may keep the same position relative to one another, the velocity c of
a wave must be in a fixed ratio to v. — The transverse waves, for instance
(or more properly the central part of them) must have the same velocity v as
the vessel; the diverging waves, because moving in different directions to the
vessel, must have smaller velocities. If a be the angle between the wave-
crest and the course of the vessel, the velocity of the wave must evidently
be c = v sin a (see Fig. 3, PI. V). — On the other hand, c is a function of
the wave-length, varying, as the square root of the latter, in deep water. The
transverse waves are consequently longer than the diverging waves (longer,
the greater is a), and the lengths of all the waves increase if the velocity of

See Lamb, Hydrodynamics, Art. 228.

36 EKMAN. ON DEAD.WATER. [norw. pol. exp.

the vessel be increased. If the waves were shorter than indicated by the
above rules, they would move more slowly than the vessel, and would gra-
dually move away from her; whereby the wave-length and the velocity of the
head-most wave would increase until the wave be long enough to follow the
vessel. Similarly, the next waves, one after the other, would have their wave-
length and velocity increased.

In calculating the work done by the vessel in maintaining the above de-
scribed wave-system, it must be observed, that part of the energy wanted,
is constantly transmitted from behind, by the waves already created; but
another part of the energy of the latter is always left behind, and a cor-
responding quantity of energy must constantly be procured by the vessel.
This may be illustrated by a very common phenomenon. If a stone be
thrown into smooth water, there is initially formed one circular wave which
quickly expands; but one will very soon observe that there are two waves,
one in the place of the original wave and one outside it. Both these waves
are lower than the original one. This partition of the waves proceeds inces-
santly; the wave-rings become larger and larger in number and smaller and
smaller in height, the middlemost wave being always the highest. But if the
motion of the original wave-ring be carefully followed, one will find that it
always remains the outermost one. Thus, the average velocity of transmis-
sion of the wave-energy, is smaller than the velocity of the waves themselves

— really, the ratio is exactly one half in water of infinite depth1. This ratio

— i. e. the ratio of the energy really transmitted across an imagined vertical
plane in the water, to the energy which would be transmitted if the waves
propagated themselves undivided with their actual velocity — may be called
the ratio of transmission of wave-energy2. The ratio of transmission of wave-
energy is consequently 0'5 in water of infinite depth.

From the waves following a vessel in uniform motion, the wave-making
resistance may then be estimated for the case of deep water, in the following
simple way. Imagine two straight lines AA' and BB' (Fig. 3 PL V) stretching
in the water-surface at a distance I from each other across the wake of the

1 See Lamb, Hydrodynamics, Art. 221; see also a highly interesting paper on the subject
by Prof. 0. Reynolds, "Nature", XVI p. 343 (1877).

- Not to be confounded with "the rate of transmission of wave-energy", which is an-
other notion.

NO. IB.] RESISTANCE OF VESSELS. 37

vessel, and fixed in space; for simplicity let I be a multiple of the wave-length
of the transverse waves. The energy of the transverse waves between AA'
and BB' may be I X Ex • As the height of the waves and their position relative to
the vessel are invariably the same, the energy of transverse waves ahead of BB'
is increased by I X -E\> when the vessel has moved a length = I. In the
same time nearly half this energy1 is carried by transverse waves across BB',
and consequently the rest or about PX^i must be supplied by the vessel.
Secondly consider the diverging waves. The energy of them between the
lines A A' and BB' may be I X E2. The average velocity c of the diverging
waves is c = v sin a, and its component in the direction of the vessel's keel-
line is v sin2 «, v being the velocity of the vessel, and a some mean value
of the angle between the diverging wave-ridges and the keel-line of the
vessel. When the vessel moves forward I units of length (= AB), the energy
\ E2 X & sm2 a is therefore carried across BB' by diverging waves; the energy
of diverging waves ahead of BB' is increased by I X E2, because the motion is
steady, and consequently the energy £ I X E2 (2— sin2«) must be supplied by Ihe
vessel. Thus, when the vessel moves a distance I, the wave-energy to be cre-
ated by her is, in all, about £ I X Et -\-\l\E2 (2— sin2a), and the value of the
wave-making resistance consequently approximates to | Ex -\- \ E2 (2 — sin2 a).
Greater accuracy could be obtained by further dividing the wave systems into
smaller parts, so that within each of them,1 the extreme values of a differ less
from each other. The analysis above, gives, however, an idea of the degree
in which the waves contribute to the resistance of a vessel ; it shows that diver-
ging waves cause comparatively more resistance than transverse waves, because
the energy of the former is in a smaller degree propagated with the vessel.

It is well known that a vessel moving at slow speed, creates but very low
waves, and as the energy of waves varies as the square of their heights, the
wave-making resistance is in this case inconsiderable. At moderate speeds the
wave-making resistance increases, in deep water, approximately as the square
of the velocity, but at higher speeds it increases as the cube — or even ac-
cording to an higher power.

It would be exactly one half, if the transverse waves were perpendicular to the keel-
line of the vessel throughout their whole length.

38

EKMAN. ON DEAD-WATER.

NORW. POL. EXP.

B. RESISTANCE TO VESSELS IN SHALLOW WATER.

The general principles explained in the preceding section are quite in-
dependent of whether the vessel is moving in deep water or in shallow water;
hut nevertheless the law connecting velocity and resistance is essentially dif-
ferent in the two cases.

This subject, investigated more than 60 years ago in a number of canals
in Scotland, is of great interest to us, because it offers a remarkable analogy
to the laws of resistance in "dead-water". Scott Russell describes in the
following manner the discovery of the peculiar fact which induced further in-
vestigations upon the matter. 1

"As far as I am able to learn the isolated fact was discovered accidentally on the
Glasgow and Ardrossan Canal of small dimensions. A spirited horse in the boat of William
Houston, Esq., one of the proprietors of the works, took fright and ran off, dragging the
boat with it; and it was then observed, to Mr. Housron's astonishment, that the foaming
stern surge which used to devastate the banks had ceased, and the vessel was carried on
through water compaiatively smooth, with a resistance very greatly diminished. Mr. Hou-
ston had the tact to perceive the mercantile value of this fact to the Canal Company, with
which he was connected, and devoted himself to introducing on that canal vessels moving
with this high velocity. The result of this improvement was so valuable from a mercantile
point of view, as to bring, from the conveyance of passengers at high velocity, a large in-
crease of revenue to the Canal proprietors. The passengers and luggage are conveyed
in light boats, about sixty feet long and 6 feet wide, made of thin sheet-iron, and drawn by
a pair of horses. The boat starts at a slow velocity behind the wave, and at a given signal
it is by a sudden jerk of the horses drawn up on the top of the wave, where it moves
with diminished resistance, at a rate of 7, 8 or 9 miles an hour."

Scott Russell was appointed
to investigate the matter and ar-
ranged great experiments1 with
vessels 10—20 m. in length and
weighing 600—9000 kgr. Fig. 4,
reproduced from Scott Russell's
paper, represents the resistance
at different velocities according to
these experiments. The velocities
are plotted along the horizontal Y-
axis in statute miles2 an hour, and

3 8 4367891011 12 13 14 \i IS 7 13 1

Fig. 4.

1 John Scott Russell, "Experimental Researches into the Laws of Certain Hydrodyna-
mical Phenomena that accompany the Motion of Floating Bodies, and have not pre-
viously been reduced into conformity with the known Laws of the Resistance of Fluids".
Trans, of the Roy. Soc. of Edinburgh. Vol. XIV, 1810.

2 One statute mile is 1609 m.

NO. 16.

EFFECT OF SHALLOW WATER.

39

the resistance (against 6 different vessels) vertically with an arbitrary unit. As
shown by these curves, the resistance was a maximum at a certain critical
speed, which Scott Russell found to depend upon the depth of the canal.
If the speed was further increased, the resistance rapidly fell down to a
minimum and then again increased1.

The decrease of resistance at the critical velocity was accompanied by
remarkable changes in the general features of the motion, illustrated by Figs.
5 — 7 below, which are reproduced from Scott Russell's paper. Fig. 5 repre-
sents the vessel at rest or with a slow motion. When the vessel was forced

E=7-~-

Fig. 5.

Fig. 6.

Fig. 7.

up towards the critical velocity (see Fig. 6), the waves aft of the stem, in-
creased strongly, and the vessel pushed before her stem a large wave of
the type called by Scott Russell "Solitary wave", a single elevation of
water travelling along the canal. When the critical velocity was exceeded,
the breaking stern-waves disappeared, and the vessel moved on the top of the
"solitary wave" (Fig. 7); at the same time her stern, which was before sucked
downwards, was now raised so that the vessel drew considerably less water
than when at rest.

The above described, peculiar facts depend on the laws of motion of waves
in shallow water. As was discovered by Scott Russell, waves of any length

Scott Russell believed the existence of a second maximum and of a second minimum
of resistance at certain speeds, to be greater than could actually be produced by ex-
periments; but the theoretical speculations from which these conclusions are drawn are,
as far I can see, entirely erroneous.

40 EKMAN. ON DEAD-WATER. [noew. pol. EXP.

cannot move spontaneously at more than a certain speed igd, d being the
depth of the canal and g the acceleration due to gravity1. This maximum
velocity of waves is just the critical velocity at which the resistance of a vessel
began to diminish; when moving at a greater velocity, the vessel cannot be
followed by any transverse waves (compare p. 35), and as the work required
for creating these waves is then saved, tbere must be a corresponding decrease
of resistance2. If resistance were not caused by friction and by the diverging
waves, the vessel would move without resistance, at velocities above the cri-
tical one. It will be made clear, in the next chapter, that it is just the trans-
verse waves, which are of preponderant influence on the resistance in shallow
water, as well as in "dead-water".

The influence of shallowness is practically insensible, as long as the depth
of the water is more than half the length of any wave actually created by
the vessel. The velocities of the waves are, in this case, in practically the
same ratio as the square roots of their wave-lengths, and the ratio of trans-
mission of wave-energy is Va — just as in deep water. But when the
velocity of the vessel is increased, the wave-velocity and the wave-lengths
correspondingly increase; when the wave-length becomes more than twice
the depth of the water, the laws of motion of the waves are sensibly
altered: the wave-velocity increases more and more slowly, approaching as-
symptotically its maximum value \gd, when the wave-length increases. At the
same time the ratio of transmission of wave-energy gradually increases from
05 to 1; i.e.: the longer be a wave, the smaller part of its energy will be
left behind, and the more slowly will it diminish in height while travelling.
Very long waves consequently may travel long distances spontaneously without
diminishing very much in height and without leaving waves behind them; in
this respect Scott Russell's "solitary waves" comport themselves as very
long waves. If the velocity of the vessel be a little below the critical velo-

1 Scott Russell particularly studied a peculiar sort of wave which he called "solitary
wave". It consists of a single elevation travelling spontaneously without altering its
shape. If the depth of the canal be d and the height of the elevation be h, the velo-
city of such a wave is \g {d + h), that is, somewhat more than the critical velocity

igd.

- This is more rigorously established by a mathematical investigation of Lord Kelvin
"On Stationary Waves in Flowing Water", Phil. Mag., Oct., Nov., and Dec. 1880.

NO. 16.] EFFECT OF SHALLOW WATER. 41

city, the transverse waves, in order to follow the vessel, must be very long,
and a comparatively small part of the wave-energy, is therefore left behind.
In consequence, the transverse waves, at this velocity, cause a comparatively
smaller resistance than equally high but shorter waves at a smaller velocity,
would do. On the other hand, as they follow the vessel spontaneously to a
greater extent, they will, by accumulation, reach a greater height, than they
would at the smaller velocity. The result of these two circumstances, acting
in opposition, is, as mentioned on p. 39, that the resistance increases to a
maximum at the critical velocity \gd, and then suddenly falls off to a lower
value. Lord Kelvin's mathematical investigation (I. c. p. 40) gives substantially
the same result, as will be mentioned below.

C. WAVES IN THE BOUNDARY BETWEEN SALT AND FRESH WATER.

When a layer of light fluid rests on the top of a heavier one, waves
can be created in the boundary between the two fluids, as well as in the free
surface. The mathematical theory of such waves has been developed by Sir
G. G. Stokes1. The chief properties of them, as well as a few simple approx-
imate formulae for which we shall have use later, are collected here below;
the analysis not inserted here, may be found in Stokes' paper or in Lamb's
"Hydrodynamics" Art. 223. All the formulae are founded on the supposition
that the waves are of small or moderate heights, so as to be approximately
conformable to linear dynamical equations.

Such "boundary waves" may easily be demonstrated as follows: half fill
a tumbler (or better, a square glass-vessel) with a salt solution, and lay on the
surface a thin disc of cork. Then, by help of a glass rod or a lead-pencil,
pour fresh water in a fine stream on to the disc, and, with a little care,
there may be obtained a quite sharp boundary between the two water layers.
If now the glass be given a suitably slow oscillatory movement to the right
and to the left, the boundary between the two water-layers is put into great
uninodal oscillations while the upper surface remains almost still. The less the
difference of specific gravity between the two water layers, the slower are the

1 On the Theory of oscillatory waves, Math, and Phys. papers, vol. I, pp. 212—219.

6

42 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

oscillations; and if the salt-water has a specific gravity of only l-02 or l-03,
one can produce even binodal and trinodal oscillations in the boundary, with-
out disturbing the upper surface.

In a basin of larger dimensions, progressive waves, moving in the same
manner as ordinary surface waves, may be created in the boundary1. The
waves in the boundary produce a similar wave-motion in the surface, although
of considerably diminished amplitude; the surface has elevations immediately
above the depressions in the boundary and vice versa, as is illustrated by
Fig. 4, PI. VI. The former places, where the fresh-water layer is thickest,
may be called wave-crests, and the latter wave-hollows. The motion of
the water particles at the wave-crests and the wave-hollows, is represented
in the figure by small arrows, the large arrow denoting the direction of the
wave-motion.

The relative height of the surface waves depends on the difference of
density between the two water-strata. If

q = the density of the fresh-water,

q -f- Aq = - - - - salt-water,

I = the wave-length (from crest to crest),

d = the depth of the fresh-water layer,

D = - - - - salt-water layer,

and if D is great compared with d, the ratio of the amplitudes, h and H, of
the surface-waves and of the boundary- waves is

F = f •>-- «

If the depth of the surface-layer is very small compared with the wave-length,
the ratio of the amplitudes is approximately

H ~q~ (2}

i. e., there is statical pressure-equilibrium in the salt water. If the depth of the
surface-layer is considerable, compared with the wave-length, the ratio h : JET is,
according to (1), smaller than Jq : q.

For the sake of brevity, I shall call the upper water-layer fresh water, and the heavier
water below salt water, although, in reality, the two water-layers may consist of salt
water of different densities. Likewise by the surface we may always understand the
upper, free surface, and by the boundary, the common boundary of salt and fresh
water.

NO. IB.] ON WAVES BETWEEN SALT AND FRESH WATER. 43

In all cases actually concerning us, the difference Jq between the den-
sities of the two water-layers, is very small, the specific gravity of sea-water
being always less than 103. In what follows this should always be assumed
to be the case. Tlie surface-waves are then, according to equations (1) and
(2), very low, compared with the boundary-waves by which they are caused.
In Fig. 4, PI. VI, the vertical scale of the surface-waves is exaggerated about
30 times, if we assume the water-layers to be made up of fresh-water and
pure sea-water of spec, gravity 103.

The most peculiar property of the boundary-waves, in contradistinction
to ordinary waves on the surface of homogenous water, is their very slow
velocity (Jq assumed to be small). With moderate wave-lengths it varies as
the square root of Jq and stands to the velocity of equally long waves in
homogenous water, as ]/jq : ^2q \ As the wave-length increases, the velo-
city approaches the value

--1%

q VcZ+VD'

which is its maximum value ; or, if D be great compared to d,

Vm = igd, X l/jq/q1 (4)

This formula shows an obvious analogy between boundary-waves and waves
in shallow homogenous water, the maximum velocity of the latter being
yfgd. There are indeed several such analogies, as will be shown below.

The average energy per unit area of the wave-systems considered, is
also small, being proportional to the difference of density Jq, in cases in
which the heights of the waves are the same. It is exactly twice the potential
energy of the waves and consequently varies, as in the case of ordinary
surface-waves, as the square of the wave-amplitude.

Just as in the case of waves in shallow water, the ratio of transmis-
sion of wave-energy (see p. 36) is Va for short waves and increases asymp-
totically to 1, when the wave-length increases. In Fig. 1, PI. VI, it is repre-
sented as a function of the ratio v/vm of the wave-velocity v and the maxi-
mum velocity Vm of long waves in the same water. The ratio of transmis-

1 This formula, as well as (3) and (4), are exact under the supposition that Jq is infi-
nitely small; if Jqjq is small, they are approximately true.

44 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

sion of energy is plotted vertically. The faint curve is valid for waves in
shallow water, as well as for boundary-waves when the two water-layers
have the same thickness. If the two water-layers are of different thickness,
the ratio of transmission of energy becomes somewhat altered, and is repre-
sented by the heavy curve, if one of the water-layers — say the salt water —
is by comparison, infinitely deep. In either case the curves show that for
waves moving with not more than half the maximum wave-velocity, the ratio
of transmission of energy is almost exactly V2, just as in deep water. Only
when the velocity of the waves is further increased, do their laws of motion
begin to be influenced by the shallowness of the water-layers.

The pressure in the water is, of course, altered by the wave-motion, but
differently in the salt and in the fresh water-layer, p may be the pressure
when the water-layers are at rest, and p -\- dp when there are waves. Then
Jp is positive at the wave-crests and negative at the wave-hollows, in the
fresh-water layer, and vice versa in the salt-water (see Fig 4, PI. VI). In
the fresh-water layer

/ 2%-d) _ 2My-d)\

4p = %gh'q [el + e l J ,

and in the salt water, when D is infinite,

dp = — \ gli {q + Jq) el y e 1 — e l J ,

where y is the height of the particular point considered, above the mean level
of the boundary {y negative in the salt water), and h' is the height of the
water-surface above its mean level, in the same vertical as the considered
point. The other symbols have the same signification as before.

If the wave-length is very great compared with the depth of the surface-
layer and with the distance between the boundary and the considered points

in the water-layers, — =- and — p are small quantities. Then the formulae

above take the following simple forms; in the fresh-water layer,

jp = gh'q (5)

and in the salt-water

Jp=-gh'(q + Jq)^£ (6)

NO. IB.] ON WAVES BETWEEN FRESH AND SALT WATER. 45

From equation (1) p. 387 in Lamb (I. c. p. 33), the velocity of a water-
particle in its orbital motion, may be calculated. It follows that it is pro-
portional to the wave-height, and is always less than the velocity of propag-
ation of the waves, i. e. the wave-velocity. The velocity of a fresh-water par-
ticle in a wave-crest would, in the case of very long waves, be equal to the
wave-velocity, only if the wave-height H (from the mean level of the boundary,
to its highest level) be equal to the mean depth d, of the surface-layer. As
this is impossible, it only shows that in the case of long waves, the velocity
of the water-particles is always less than the wave-velocity, as long as the
wave-height is moderate enough for the waves to be approximately conform-
able to linear dynamical equations. In the case of short waves (wave-length
less than two or three times the depth of the water-layers) the greatest hori-
zontal velocity of the water near the boundary, should be equal to the wave-
velocity, only if the wave-height H be Ve (or Vaw exactly) of the wave-length;
and the velocity of the water near the surface is then considerably smaller.
This wave-height — Ve of the wave-length — is about the extreme limit of the
height of waves, if they are not breaking.

It is very easily proved that, when restricting us to two-dimensional waves of a per-
manent type, the orbital velocity of the water-particles can be as great as the wave-velocity,
only when the waves have their extreme height; or in other words, the orbital velocity can
never be greater than the wave-velocity, as long as the waves do not break. For when
in the contrary case, the wave-motion is reduced to steady motion by superposing a velo-
city equal and opposite to the wave-velocity, the fresh-water at the very wave-crests, would
have a velocity opposite to the general flow of water ; and this is inconsistent with the repre-
sentation of the steady motion by means of stream-lines. In the extreme case in which the
velocity of the fresh-water (in the imagined steady motion) vanishes at the crests, these
must be infinitely curved so as to form sharp angles. This extreme case, however, cannot
be attained by boundary-waves. For, as can be immediately seen by drawing the stream-
lines in the immediate proximity of a wave-crest; the velocity of the salt-water would
then be infinite there. The velocity of the water-particles in the boundary-waves, is there-
fore always slower than the wave-velocity.

D. THE EFFECT OF A LIGHT SURFACE-LAYER, ON THE RESISTANCE

OF A VESSEL.

As long as we confine ourselves to a merely qualitative examination, it
is not difficult to see in what manner a lighter surface layer resting upon the
salt water, may influence the resistance of a ship.

46 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

First consider a simple case, which can be treated by mere statics. The
vessel may be supposed to be dragged slowly in a narrow square-sectioned
channel, and her bottom to reach into the salt water. She may be quite flat-
bottomed and with vertical sides, fitting to the walls of the channel, so as
to allow no water to pass except than under her bottom. When the vessel
begins to move, the fresh-water must then be heaped up ahead of the vessel
and become thinner aft of her (see Fig. 6, PI. VI), and as there must be sta-
tical equilibrium in the salt water below the vessel, the upper surface rises
ahead and sinks aft. The vessel is in consequence, resisted by a sternward
pressure easily calculated. The depth of the fresh water, fore and aft, may
be fej and h2 respectively, and the densities of fresh and salt water q and
q-\- Jq respectively. In consequence of the statical equilibrium, the differ-
ence of level of the salt water, fore and aft, is then found to be

]h = (ft, _ }h) X q/(q + Jq) ,
and the difference of level of the upper surface

hl—hi — h3 = {hx - h2) X ^2% + ^2) •

The breadth of the channel being 6 and the acceleration due to gravity g,
the resultant of pressure against the vessel is when Jqlq is small, then
found to be approximately

gbJq 'h % *' (7)

As the vessel moves along, the difference of levels — and the resist-
ance — grows larger, until the fresh water ahead of the vessel reaches a
little below the bottom of her. It then runs aft below the vessel, also resist-
ing her by friction. If the speed of the vessel be not too small, the fresh
water will not come to rest when buoying up aft of the stern, but, on account
of its inertia, continue to swing above and below its level of equilibrium
thus giving rise to a series of waves in the boundary (Fig. 7, PI. VI). As
energy is needed for the creation of these waves, they contribute to the resi-
stance (by increasing the sternward pressure-resultant).

Now suppose that the vessel does not reach, although nearly, the salt
water, and that the vessel begins to move slowly. Then, the fresh water
passes freely by the vessel, and the latter cannot be resisted by any statical
pressure as in the former case. But the passage for the fresh water below

NO. IB.] EFFECT OF A SURFACE-LAYER. 47

the vessel being narrow, its velocity there becomes increased, and consequently
the friction against the bottom of the vessel becomes increased, by the effect
of the surface-layer. Further, because the fresh-water is hinderd in its aft-
ward motion, the surface rises a little — and the boundary is lowered —
ahead of the vessel. Thus the vessel becomes influenced by a sternward-
pressure, which may be calculated approximately by formula (7). When the
vessel is moving at some greater speed, and the inertia of the water conse-
quently becomes of greater importance, the difference of density of the two
water-layers is insufficient to hold their common boundary nearly plane.
The fresh-water displaced by the vessel, presses down the salt-water below,
and the resulting disturbance of boundary level, persists as waves giving
rise to wave-making resistance. Finally, when the vessel moves at velo-
cities higher than the maximum velocity of the boundary-waves, she cannot
be followed by any train of boundary-waves, and the corresponding part
of the resistance accordingly disappears. The vessel when moving at such
high velocities, may leave only a very small disturbance, in the boundary
behind. For the water-particles, on account of their inertia, then move in
nearly the same paths as if the water were homogenous; the gravity has not
time to appreciably alter the motion of a particle, before it has already passed
by and is at rest behind, in the same level as it had ahead of the vessel.
As the water-particles move past the vessel in nearly the same paths as if
the water were homogenous, the increase of frictional resistance will, of course,
also vanish at these high velocities.

If the vessel does not move in a narrow channel but in open water, the
influence of the surface-layer may be discussed in a similar manner. Whether
the vessel reaches the salt-water or not, the fresh water has free passage past
her. If the vessel is moving slowly, the boundary between the two water-
layers will therefore remain nearly horizontal, and the frictional resistance will
be increased just as if the vessel moved in shallow homogenous water of the
same depth as the actual surface-layer. Really, it may be increased even more
than in shallow water, for the depth of the latter, down to the bottom, must
be greater than the draught of the vessel, which on the other hand, can proceed
in an even shallower water-layer resting on the top of heavier water. At greater
velocities the inertia of the water becomes of more importance, and waves will
consequently be created in the boundary between the fresh-water and the salt-

48 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

water, and will give rise to wave-making resistance. In the present case, the
vessel may be followed, not only by transverse waves but also by diverging
waves, and as these move with a smaller velocity than the vessel herself, the
wave-making resistance will not completely disappear at the before mentioned
critical velocity. But the influence of the stratification of the water, on the
fridional resistance, may be expected to diminish and disappear at these high
velocities, for the same reason as was mentioned in the former case (p. 47).
Figs. 2—5, PI. V, illustrate the different forms of the wave-systems corre-
sponding to different ratios between the vessel's velocity and the maximum
wave-velocity1. The lines represent the wave-ridges seen from above, and the
vessel must be imagined to be at the point at the left end of the figure. In
Fig. 3 the vessel is moving at a considerably slower velocity than the maxi-
mum velocity of the waves (slower than at half this velocity). In Fig. 4 the
velocity of the vessel is nearly as great as (l-2 times smaller than) the maxi-
mum wave-velocity ; in this case the wave-length of the transverse and diverg-
ing waves, is greater, and the waves stretch farther out to the sides, than at
a slower speed. In Fig. 5 the vessel moves at twice the maximum wave-
velocity, in this case the transverse waves cannot exist and have en-
tirely disappeared, but the diverging waves still exist and form a certain
angle with the course of the vessel. Fig. 2 gives on a larger scale, and for
several different velocities, the wave which is nearest to the vessel. In this
figure, d denotes the ratio of the maximum wave-velocity to the velocity of
the vessel, the latter velocity being the same in the case of all the curves.
The dotted curve inside the curve for d = 2, corresponds to d = <x>. If the
heights of the waves be known, the resistance caused by them may be cal-
culated in a similar way as on pp. 36—37, except that the "ratio of trans-
mission of the wave-energy" is not the same in both cases.

The curves are drawn according to calculations, quite similar to those found in Lamb's
Hydrodynamics, p. 402, for ordinary ship-wares.

NO. 15.] APPLICATION OF SMALL SCALE EXPERIMENTS. 49

E. ON THE APPLICATION OF SMALL SCALE EXPERIMENTS.

It is obvious that experimental investigations of the phenomenon of dead-
water cannot be made except on a considerably diminished scale. It is of
importance, therefore to see under what circumstances we may draw trust-
worthy conclusions from such small-scale experiments.

The possibility of answering a question in hydrodynamics by means of
experiments on a reduced scale, depends upon the possibility of so arranging
the circumstances that the motion in the two cases — the real, full scale case,
and the small scale experiment — become "geometrically similar"; that is to
say, that all linear dimensions in the one case have a constant ratio to the
corresponding lengths in the other case, that the velocities in corresponding
points are in a constant ratio to one another, and similarly for the other
quantities concerned. The conditions for such "geometrically similar motions"
may — by a simple method given by Helmholtz — be found directly from
the general hydrodynamical equations1.

Let the ratio of the linear dimensions in the two cases, be I

— » — velocities — » — v

— » — densities of the fluids — » — 6

— » — fluid pressures — » — n

— » — extraneous forces, e. g. gravity — » — y

— » — coefficients of viscosity — » — x

Then the ratio of the time-intervals — » — is l/v

The dynamical equations to be satisfied in water, which may be regarded as
incompressible, are three, of the type

du dp . „ , . / d2u , d*u . 3% \

(8)

where q is the density, k the (dynamic) coefficient of friction (not the kine-
matic coefficient, used by Helmholtz), u, v, w the components of velocity

1 H. v. Helmholtz. Wissenschaftliche Abhandlungen, Vol. I, p. 158. "Ueber ein Theorem,
geometrisch fihnliche Bewegungen flussiger Korper betreffend, nebst Anwendung auf das
Problem, Luftballons zu lenken".

7

50 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

along the axis of coordinates x, y, z, and X, Y, Z, the components along the
same axis, of the extraneous forces. In addition, u, v, w, must satisfy the
"equation of continuity"

9u to 2w _

dx ~ ty ~ iz v

as well as the initial- and boundary-conditions, which may be of different forms.
If the linear dimensions be multiplied by X, the velocities by v, and so on,
the four terms in (8) are multiplied by

(5w2 7C , j v
"T ' X ' 7 ' * ¥

respectively. To satisfy (8) for both cases, it is therefore necessary that these
four quantities be equal, and the quantities X, v, S, it, y, and x must then
satisfy the equations

n = v2d , (a)

yX=v\ (6)

x = dvl , (c)

Equation (9), does not involve any restriction in the choice of I, v, 6, it, y, x,
but the initial- and boundary-conditions must accord with the choice of A, v,
and n. The boundary-conditions, are always fullfilled, if the boundaries con-
sist of: (1) perfectly welted, rigid bodies; either immovable and satisfying the
ratio X, or moving so as to satisfy the ratios X and v; (2) free surfaces, in-
fluenced by extraneous pressures satisfying the ratio it. The initial conditions
in the fluid are in accordance with any choice of X, v, it, if the motion be
steady, or if the water be initially at rest, in both cases.

If all the above conditions be satisfied, the motion will be geometrically
similar in the two cases, and the ratio of the resultants of pressure upon cor-
responding surfaces is then

p= lin = Pv'-d (d)

In the case specially interesting us, the boundary-conditions are then
practically satisfied if: (1) the linear dimensions of the two vessels are in the
constant ratio X; (2) the linear dimensions of the basins, in which they move,
are in the same ratio X; or the basins are so wide and deep that their
boundaries have no influence upon the motion of the vessel; (3) the veloci-
ties of the two vessels are in the ratio v to oneanother. It is not necessary,

NO. 15.] APPLICATION OF SMALL SCALE EXPERIENTS. 51

that the condition concerning the pressure on the free surfaces be satisfied.
For, as the water is practically incompressible, the motion is, in both cases,
unaltered, if the pressure in the water be diminished by a constant quantity
(for instance, the atmospheric pressure), so that the pressure be nil in the free
surface. It is then obviously necessary to leave the air-pressure consistently
out of account. Equations (b) and (c) give

23 — x
A ~ yd* •

As the possible variations of the density, of the gravity, and of the coef-
ficient of friction, are very limited, the right hand side of this equation cannot
be made many times greater or smaller than unity; and it is consequently
impossible to reproduce exactly similar motions on very different scales, if
gravity and viscosity have both to be taken into account. The gravity is of
essential importance, in cases where there is wave-motion. We must therefore
at first neglect the viscosity, and afterwards consider its influence as best
we can; equation (c) is consequently left out of consideration for the present.

Gravity is furthermore practically constant, and so y = 1. If the densi-
ties of the water-layers are also the same in the two cases, d = 1 ; and (a),
(6), and (d) take the form

n = Vi; A = u2; P= in* = A3.
That is: If the linear dimensions be increased in the proportion X, and
the velocity of the vessel be increased in the proportion |T, the motion of
the water, on the larger scale and on the smaller scale, will be geometrically
similar to oneanother, and the resultant of pressure against the vessel
(the wave making resistance) will increase in the proportion I2. This is
the well-known rule which was used by Froude for his experiments with
ship-models, and which still bears his name.

By an artifice, the equations (a), (b), (d) may be made to allow an impor-
tant variation of the experiment, other than that which is indicated by Froude's
rule. At the slow speeds which come under consideration, the waves in the
surface are quite insignificant, and the surface-disturbances caused by boundary-
waves, are also very small, because the difference of density between the
different water-layers, is small. The motion in the water will therefore not
be appreciably altered, if, by some means, the water-surface be held rigidly

52 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

plane; the pressure in the surface will, of course, no longer be uniform, but
the differences of pressure in a horizontal plane will be almost exactly un-
altered. We may therefore, with very small error, assume the water-surface
to be held rigidly plane by suitable extraneous pressures. The gravity would
then have no influence upon the motion, provided the density of the water
were uniform ; and in the case of a fresh-water layer of density q resting on
the top of salt-water of density q + Jq, the motion will take place just as
if the gravity did not act at all in the fresh-water, and in the salt-water only
upon its excess of density Jq. The small difference between the inertia of
fresh- and salt-water is of very little influence on the motion. We may there-
fore assume the density to be the same (= q) in the whole fluid, but, as-
sume instead, that the gravity varies, being nil in the fresh water and
dQ./q X 9 i}l the sa^ water1. In this way we are virtually able to change
the gravity to a considerable degree, by just varying the specific gravity of
the lower water-layer. We then obtain, by putting 1=1 in equations (b)
and (d) p. 50, the following rule, which — as far as the pressure exerted by
simple harmonic boundary-waves is concerned — is a consequence of Stokes'
theory of these waves, namely:

If the difference of density Jq of the two water-layers (Jq always
supposed to be small) be increased in the proportion y, and if the velocity
of the vessel be increased in the proportion V y , the geometrical similarity
of the motion will be kept, and the resultant of pressure experienced by
the vessel (the wave-making resistance) will increase in the proportion y.

The two rules above were deduced on the assumption that the viscosity
of the water could be neglected. We may therefore — in the same way as W.
Froude2 — determine the frictional resistance separately, and add it on to
the pressure-resultant deduced according to the above rules. Rigorously the
wave-making resistance, the eddy-making resistance and the frictional resi-
stance cannot be quite independent of each other, and the method should
consequently not be allowed ; but the experiments seem to show — as might
be expected a priori — that it is practically correct.

1 This artifice may often be of use in solving problems concerning the motion of the
water-layers in the sea.

2 See White's 'Manual', p. 479 seq.

NO- 15.] APPLICATION OF SMALL SCALE EXPFRIMENTS. 53

It may be pointed out that the two rules above, hold approximately even
if the whole resistance be considered. For the frictional resistance varies
approximately as the wetted area of the vessel and as the square of the
velocity, so that it is obvious it will vary approximately according to the two
rules given. The eddy-making resistance is of smaller importance; the same
rules hold true for it, provided the motions are really "similar", because it
is a resultant of pressure. It could not, however, be taken into account when
deducing the rules, because it should not exist at all in a frictionless fluid.

Besides the viscosity, we must also take account of the capillary forces,
which influence the small scale experiments more strongly than those on a full
scale, and thus disturb the similarity. On the one hand, these forces prevent
the creation of ordinary surface waves in the experiments; on account of
capillarity these waves cannot move with a velocity slower than 20 or 23 cm.
per second, and the boat-models were towed at still smaller velocities. This
effect of capillarity is, however, of no importance, because, at the slow speeds
at which dead-water occurs, even full-sized ships do not produce any appreci-
able surface-waves. The secondary waves in the surface which are produced
by the boundary-waves, are — on account of their greater length — not ap-
preciably influenced by the capillarity.

On the other hand the surface-tension directly impels the vessel. If it
were the same on all sides of the vessel it should have no effect; if, however,
the water is even very little contaminated with grease, its surface-tension is
reduced, but in a smaller degree in the wake of the vessel, where the cont-
aminated surface film becomes ruptured by the eddies. A superficial resi-
stance then arises, which although quite insignificant in the case of full-sized
ships, might be of considerable importance in experiments on a small scale.
It will be shown later, that even this effect of capillarity is of no essential
influence on the experimental results.

III.

EXPERIMENTAL INVESTIGATION.
A. APPARATUS AND METHODS.

The first series of experiments was made with a model of the Fram on
the scale of 1 : 200 in a glass tank 120 cm. long, 25 cm. deep, and 15 cm.
broad. The results, however, seemed to show that on such a small scale the
influence of viscosity was rather too great, and especially that the length of
the tank was too small to allow the velocity of the model to become uniform.
In the summer of 1900 a new tank, 350 cm. long, was therefore made, and
in it, it was possible to experiment with a model of the Fram on the scale
of 1 : 100. From this time all experiments were made in this large tank. As
its construction required considerable forethought and care, and it has since
proved very suitable, I think it is well to begin the account of the experi-
mental arrangements with a description of this tank.

The tank (Figs. 1—3, PI. I) is built up of five panes of plateglass (Fig. 1, g),
forming its bottom and four sides, which are mounted in a wooden frame
(Figs. 1 and 2). Its inside dimensions are 350 cm. in length and 40 cm. in
breadth and height. Owing to the considerable length, care was required to
prevent the long panes from breaking. To prevent warping, the beams of the
frame were therefore made up of well-seasoned spruce-fir, sawed into boards
and glued together in such a way that the structure of the whole was the
most symmetrical possible. To reduce the give of the tank under the weight
of the water, as much as possible, it was on Prof. V. Bjerknes' advice sup-
ported at eight points, the ends of four wooden springs, instead of at four
points only. Two of these springs ss', ss are seen in Fig. 2; the position of

NO. 16.] APPARATUS AND METHODS. 55

the 4 points of support s, s, s, s' are so chosen that the greatest deflection
at any point of the beam should be the least possible. Two horizontal iron
screw bolts (b, b, Figs. 1 and 2) join the bottom beams together and receive
the pressure against the sides; similarly an iron cramp c holds the upper
beams together. By these arrangements it was calculated, that the deflection
of any part of the beams to which the panes are cemented, does not exceed
O'l mm. The wooden springs (ss) also protect the tank from too great twist-
ing forces; if the two tables which support the tank be not exactly in one
plane, two of the springs would bend a little more than the two other one's
and would sustain only a few kilogrammes more pressure.

The panes are so put in that, when broken, one may easily be taken
away and replaced by a new, without disturbing the others. They were laid,
one at a time, in spacious channels of tin-plate1 (t, Figs. 1 and 3) filled with
"marine glue" (m, Fig. 3). The glass having been left for some hours to sink
down into the pitch, the wooden laths I were laid directly on the glass and
screwed to the beams. The elastic "marine-glue" allows the panes to expand
freely by heat. Other details and dimensions are shown by the figures.

The wooden frame was made by Mr. E. G. Ekstrand in Stockholm, and
is of excellent workmanship. The tank has now been in use for 3V2 years,
and as far as can be seen, the frame has not warped the very least.

The towing-apparatus, attached to one end of the tank, is arranged for
towing with constant force, not at constant speed. It is shown in Fig. 4, PI. I.
The towing-thread — a cocoon thread weighing about 3 mgr. per meter — is
laid over the wheel wx, which also serves to record the distance covered by
the boat-model and therefore has a circumference of exactly 10 cm. Further,
the thread is brought under the aluminium wheel w2, on which towing- weights
t are hung, and its end is fixed to the hook h. Thus, the boat-model is
dragged twice the distance descended by the wheel w2.

An additional "starting weight" s can be hung directly on the axis of
ws, to bring the boat-model more quickly to its uniform speed. This starting
weight is lifted off on reaching the platform p, which is movable by soft
friction along the rail r and can be placed at different heights according as a
greater or lower initial speed is desired.

Copper channels, being much more durable, would have been far preferable.

56 EKMAN. ON DEAD-WATER. [norw. pol. exp.

The wheel w2 alone, weighs 1-68 gr. To get towing forces less than
half this (0-84 gr.), counter-weights c were used in the manner shown by the
figure (actually, the cocoon thread of the counter-weights was always un-
hooked, when — as in the figure — the boat was being towed by more than
the aluminium-wheel's own weight). The weights and counter-weights were
made so as to produce towing forces of even decigrammes, attention being
paid to the friction in the wheels.

Hie registration of the velocities of the boat-model was effected on a
telegraphic tape, which received two sets of marks side by side — one set of
"time-pricks" at equal intervals of time, and one set of "way-pricks" at equal
intervals of distance covered by the boat-model. The apparatus employed for
this purpose is represented by Fig. 5, PI. I. The current from an electrical
battery o of 4 volt passes through anyone of the two induction-coils ix and i2,
when the concerning circuit is closed. The circuit (1) is closed each 0.435 of
a second, through the point of a pendulum px touching a mercury meniscus mx.
The circuit (2) passes through the spindle of the registering-wheel (w1( Fig. 4)
and is closed when a steel point p2 on the wheel, touches the mercury menis-
cus m2. Except when the boat-model moved at very high speeds, two such
points were used, placed on the wheel, diametrically opposite to oneanother. As
the circumference of the wheel was 10 cm., the circuit was then closed once
for each fifth cm. covered by the boat-model. The telegraphic tape t moves
between the secondary poles s,, s2, ss of the induction-coils (the cylindrical pole
s3 is common to both the coils) and is pierced by the sparks. The spark-length
is considerably diminished, and the effect of the sparks increased, by a con-
denser c of three metal discs, connected with the poles s1? s2, s3. If the
meniscus m is not too extensive, the interruptor of the induction-coil has time
enough to break the circuit but not enough to close it again, before the point
p has left the mercury. With this arrangement the current is never broken
at the meniscus, which remains clean and in working order very long. By
friction against a short piece of India Rubber tubing, the vibrations of the
hammer-interruptor was each time stifled, before the primary circuit was closed
the next time. The pieces of tape belonging to the separate experiments, were
registered and were read off at convenience. The punctures were easily seen
when the tape was held before an illuminated mirror. The "time-pricks" —
or usually each fifth one — were read off on the scale formed by the "way-

NO. 15.] APPARATUS AND METHODS. 57

pricks"; in this way the distances covered by the boat-model in equal inter-
vals of time, were directly obtained.

For getting a sharply defined layer of fresh water above salt water,
the following simple method was used (Fig. 6, PI. I). A plane disc d of tin-
plate, cleaned with acid, is suspended horizontally from one end of a lever I;
the other end of the lever is properly loaded, so that the disc, when lowered
on to the surface, adheres to the water which is raised a little above its free
level. The fresh water, running from a siphon s upon the disc, flows softly
out over the salt-water, and the disc is maintained on the upper surface by
the lever. With two such discs, 25 cm. in diameter, a sharply defined fresh-
water layer of 5 cm. thickness could be formed in less than one hour, even
if the salt water had a specific gravity of 1*01 only.

The specific gravity of the water layers was measured with an Aderman
hydrometer. These determinations were not made with as much care as they
might have been; in particular I did not pay much attention to the changes
of temperature of the surface-water. The differences of density of salt- and
fresh water are for this reason, in most cases smaller than the values actu-
ally given (see section D of this chapter).

It was necessary to have the surface of the water freed from dust. If
this was not done, the dust was gathered up in front of the stem of the boat
and caused resistance. The dust was skimmed off by a strip of thick blotting-
paper, supported by a metal plate and reaching over the whole breadth of
the tank (Fig. 7, PI. I). It was moved slowly from one end of the tank to the
other, by means of a sort of sleigh, and as the paper protruded only one or
two mm. into the water, it had no disturbing effect upon the surface of sepa-
ration of the water-layers. After the dust was skimmed off and collected on
the blotting-paper, this was washed under the water-tap and moved once more
from one end of the tank to the other; there it was left standing, while the
experiments were being made.

To make the different water-layers visible, two methods were employed.
In most of the experiments, the salt-water (or the fresh-water) was blackened
with liquid Chinese ink1, before the water-layers were prepared. In salt-water
of 4 % salinity or less, good Chinese ink keeps floating for several days; in

Fuchsine would be very good if it did not diffuse so quickly from one water-layer
into another. Chinese ink, of course,, does not diffuse at all.

8

58 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

water of 10 °/o salinity it settles out in streaks and sinks a good deal in the
course of two or three hours. About 20 cm.3 of it, make an area of one m.2
of water almost impenetrably dark. A white screen s, illuminated by a lamp
I, was placed behind the tank (Fig. 9, PI. I), and against this screen even
very small waves could be observed at the boundary between the blackened
and the clear water.

In this way, only a silhouette of the waves is obtained. To get a better
idea of their true shape, they must be observed from above or from below
by reflected light, so as to appear in relief. For this purpose, the salt water
was carefully filtered free from all solid particles, and the fresh-water was
made milk white. After several trials the most convenient substance for this
purpose was found to be silver chloride as precipitated from a solution of 3
gr. silver nitrate in 20 liters of water1. When this fluid was spread out in
a layer upon the salt water, the boundary, observed from below, appeared
quite opaque and of a pure milk-white colour, and so it remained tolerably
sharp for one or two hours. The greater the salinity of the water below, the
longer the boundary remained sharp. Fig. 10, PI. I, shows how the experi-
ments were arranged; no screen was used, and the boundary was lighted
directly by the lamp. As there was some difficulty in obtaining good "relief-
photographs", and the necessary preparations required a good deal of time,
as a rule only "silhouette-photographs" were taken.

In photographing the waves — in either of the two above ways — a
flash-lamp (f, Fig. 10, PI. 1) burning a mixture of 3 parts magnesium powder,
2 parts potassium chlorate, and 1 part antimony sulphide, was employed.

When an experiment was to be begun, the boat was kept at its starting
place by a hook h (Fig. 2, PI. I), the towing weights and starting weight (if
such was being used) were hung on, and the platform p Fig. 4 was placed
in an appropriate position. The Grenet's elements were connected up, the
pendulum and the telegraphic tape were put in motion, and when everything
was in order, the boat was unhooked by the action of the electromagnet e

Milk, or milk and water, does not float very long above salt water. The salt diffuses
into the milk; and milk being heavier than fresh water, salt milk is heavier than salt
water and consequently sinks. New quantities of milk come into contact with the
water, become salt, and sink in their turn; and after a little while, the milk is seen
to fall through the salt water as a shower of small vortex-rings. The same thing takes
place in the case of all precipitates in fresh water, but at different velocities.

NO. 16.] APPARATUS AND METHODS. 59

Fig. 2. When it arrived at the other end of the tank, the hoat glided into
a sort of slip to avoid thrusts and agitations in the water-layers.

The boat-models were made of solid wood and loaded to the weight stated
for each of them. The screw-propeller and rudder-post (but not the rudder)
were omitted, as well as most of the vessels body above the water-line. The
small Fram-model (1 : 200) used in the small tank, was of painted fir ; the small
Fram-model (1 : 200) as well as all the other models used in the large tank,
were of polished mahogany. The shape of each of them is described below in
section F of this chapter. The towing-thread was fixed to the boat, to a sort
of bow-sprit, so as always to be nearly horizontal. If the boat moved freely,
it made greater and greater sheers and finally struck the side of the tank.
To avoid this inconvenience, a little fork fixed to the stem of the boat was
made to glide along a fine silvered copper-wire, stretched tight along the mid-
line of the tank. The friction against the wire increased with the velocity of
the boat and was between 5 and 20 cgr.

When the boat-model was in motion, it created small oscillations in the
water-level, and these were measured by particular experiments. As level-
gauge a disc, 5 cm. in diameter, was used. It was suspended from the shorter
end of a light balance, so as to adhere to the water-surface, which it lifted a
little above its free level; by means of levers, the vertical motion of the disc
was communicated 50-fold to a pointer which allowed the variations of level
to be recorded with an accuracy of 0*02 mm. The apparatus was fastened in
a suitable place to the upper beam of the tank. The disc was very insensible
to the horizontal motions in the water, provoked by the boat passing — prob-
ably because it was raised above the free level of the surface. Horizontally
it never moved so much as half a mm., which would have caused an error of
0001 mm., only, in the observation of the level. When all waves in the water
had disappeared and the level-gauge was adjusted with its pointer at zero, the
boat-model was unhooked. As the boat was moving along the tank, a free-
hand curve on squared paper representing the subsequent indications of the
level-gauge as ordinates with the corresponding positions of the boat as ab-
scissae was drawn by me. By a second experiment the curve was completed
and, if necessary, corrected. Provided the motion can be considered as sta-
tionary, these curves, drawn on a suitable scale, as well represent the profile
of water-level following in an invariable position relative to the boat.

60 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

B. QUALITATIVE RESULTS.
Tlie connection between resistance and velocity.

The influence of the fresh-water layer upon the speed of the vessel ap-
peared distinctly even in the first preliminary experiments in the small tank.
The results of some of these are represented graphically in Fig. 8, PI. VI.
The velocities of the boat-model in cm. per second, are plotted as abscissae
and the corresponding resistances in grammes, as ordinates.

The curve (1) relates to the case in which the boat moves in homogenous
water (salt or fresh) of the full depth of the tank. The resistance varies
approximately as the square of the velocity. The dotted curves (2) and (3)
relate to the cases of homogenous water of smaller depths, 5 and 2-5 cm.
respectively. As might be expected, the resistance is greater in the cases in
which the depth is small; but it seems to increase with the velocity according
to an exactly similar law as when the water is deep1.

When there is a layer of fresh water on the top of the salt-water, the
result is quite different. Curve (4) is characteristic for such a case, the spec,
gravity of the salt water being l-030 and the depth of the fresh water 2 cm.
In this case the resistance is, at velocities below 6 cm. per second, more than
twice as great as in homogenous water of 2"5 cm. depth. At about this velo-
city, however, the resistance becomes a maximum, and when]' the velocity
is further increased, the resistance decreases and becomes smaller than in
homogenous shallow water. At great velocities the resistance seems to be
approximately the same as in homogenous deep water.

There is, of course, no stable motion possible, corresponding to a point
on that part of the curve (4) which slopes to the right (at velocities between
7 and 11 cm. per second); for if the velocity be increased a little, the resi-
stance decreases, and the velocity continues to accelerate still faster. If the

' The actual velocities in these experiments were too small (below 16 cm. per second)
for the peculiar phenomena discovered by Scott Russell (see pp. 38—39) to take place.
Indeed, the maximum resistance discovered by him, should appear at a velocity of
50 cm. per second, when the water is 2"5 cm. deep ; at half this velocity, i. e. 25 cm.
per second, the shallowness has no sensible influence upon the waves and wave-making
resistance (see p. 44).

NO. 15-1 QUALITATIVE RESULTS. 61

towing force is increased a little above the maximum resistance 0*29 grammes1,
the boat begins to be slowly accelerated ; it is accelerated faster and faster as
the velocity increases right up to 11 cm. per second, and continues to accelerate
as long as the resistance is below 029 grammes, i. e. up to 15-5 cm. per second.
Thus, if the towing-force be gradually increased, an almost sudden change
of velocity from 6 to nearly 16 cm. per second, will at a certain moment
occur. Similarly when the towing-force is again being gradually diminished,
a sudden decrease of velocity will take place, from 11 or 12 to about 4 cm.
per second. From this point of view the curve of resistance ought to consist
of two curves connected, by a horizontal straight line representing, in the case
of increasing towing-forces, 0.29 grammes1, and, in the case of decreasing
towing-forces, 0-21 grammes. It may be here mentioned that the peculiar
shape of the curve (4) thus affords the explanation of the sudden decrease
or increase of velocity, which characterizes respectively the appearance and
the disappearance of the dead-water phenomenon.

There is an apparent similarity between curve (4) and the curves in
Fig. 4, p. 38, representing the law of resistance in shallow water, discovered
by Scott Russell.

A glance at curves (1) and (4) leaves the impression that the resi-
stance in salt-water covered with a layer of fresh-water, is made up of two
parts of different origins. One part is independent of the fresh surface-layer
and is identical with the resistance in homogenous deep water. The other
part, which must depend on the difference of density between the two water-
layers and may be called "dead-water resistance" , is practically restricted to
a certain range of velocities — below 12 or 14 cm. per second, say. We
shall see, that this latter part of the resistance mainly corresponds to the loss
of energy due to generation of waves in the boundary between salt and fresh
water. When calculated according to the formula (3) p. 43, the maximum velo-
city of the boundary-waves is, in the case eonsidered,7-3 cm. per second, which
velocity is indicated by a ? at the top of the figure. The "dead-water resistance"
is a maximum at about the same velocity (6 cm. per second), just as it
should be in accordance with the discussion in Chap. II, p. 47. It will be

1 Owing to the way in which the experiments were made, this value does not indicate
the greatest resistance at constant speed. The maximum resistance in this simplest
meaning is somewhat higher than the value 0'29 gr., indicated by the curve (4). See later.

62 EKMAN. ON DEAD-WATER. [norw. pol. exp.

shown later, that the agreement between theory and experiment is in this
respect, really, very good.

The laws of resistance will be more fully investigated, from a quantitative
point of view, in section F of this chapter.

The waves generated by the vessel.

The photographic illustrations will give a better idea of the waves in the
boundary, than any description will do; they must, however, be accompanied by
some critical remarks. The waves appeared quite distinctly even in the first
experiments on the small scale. Figs. 1 — 6, PI. XIV, show the aspect of these
waves as they were photographed from the side. — The salt-water, as well as
the boat, is seen quite black; the shallow fresh-water layer is brighter and al-
most exactly similar to the air, and between them the water-surface is seen
as a dark line; the boat is moving to the left. Figs. 2 and 3 are charac-
teristic of the shape of the waves when the boat is in "dead-water"; the salt-
water is then pressed down by the fresh-water in front of and under the stem
and is raised behind the stern — just as it should be according to the argu-
ments brought forward in Chapter II (p. 47). These disturbances of level give
rise to a train of waves following aft of the boat, which are even more di-
stinctly seen in the photographs taken from the large tank (Figs. 2 and 3,
PI. XV-XVII.).

All these photographs only show silhouettes of the waves, and conse-
quently cannot give a complete idea of their shape. To get a better re-
presentation of the waves, some photographs were taken obliquely from
below, in the way described above (p. 58). One of these (Fig. 1, PI. XIII)
is projected in a frame representing the glass tank; and Figs. 2 and 3,
PI. XIII, may be imagined projected in the same frame. By help of Fig. 10,
PI. I, which shows how the photographs were taken, these latter can then
be understood without any difficulty. The greatest part of the imaginary
glass tank is filled with clear salt-water, and above this latter is a shallow
layer of fresh-water (dark in the figure). The effects of the refraction of light
in the water are not taken into account, as this would not make the figure
clearer. As the light falls from behind, each wave-crest in the fresh-water
layer is illumined on top and behind, while its fore-side, as well as each
wave-hollow, is shaded. Bearing this in mind, the shape of the waves can

NO. 16.J QUALITATIVE RESULTS. 63

easily be imagined. Owing to the photographs being taken obliquely from
below — as also on account of the refraction in the water — their breadth
is seen 4*1 times reduced in proportion to their length. In order to see the
length and breadth of the waves in their true proportions, the figure should
consequently be seen sideways, so that its length becomes 4*1 times shorter;
this is attained, when the quadrangle below Fig. 1 looks like a square.
All details in the figure, except the waves, are, of course, then seen quite
erroneously.

The boat, a model of the Fram (scale 1 : 200) is, in the figures PI. XIII,
entirely hidden in the opaque fresh-water, and we only see the diverging train
of waves, the head of which indicates the position of the boat. The photograph
is reproduced on such a scale, that the boat's length in the figure, is 36 mm.,
or just the same as in the figures PI. XV— XVII. If this be noted, it can
be understood, on Fig. 3, PI. XIII, that the fresh-water is pressed down under
the bow of the vessel, there forming a little hollow in the salt water, whilst
at the stern the boundary is raised, so that the keel becomes visible in the
clear salt-water. The disturbances thus described, spread as diverging and
transverse waves very similar to the well-known wave-systems following a
steam-launch in smooth water (see for instance Fig. 3, PI. XII). The diverging
waves are very clearly seen in the figures, PI. XIII; the transverse waves, on
the other hand, do not appear very distinctly. This is evidently due to the
light having come from the side of the tank, so that the transverse waves
have no shadows. I have observed steam-launches from a hill athwart, and
their waves have then had a striking resemblance with those in the figures
on PI. XIII; unfortunately I have never had an opportunity of taking a pho-
tograph of such an instance. In Figs. 2 and 3, PI. XIII, the section of the
boundary becomes visible along the glass walls of the tank, as a sinuous
curve evidently indicating the transverse waves, as well as an oblique section
of the diverging waves (somewhat exaggerated through their reflection against
the walls). The velocity of the boat is smallest in Fig. 1 and greatest in Fig. 3.
The towing forces were in the three cases 0"25 gr., 0"50 gr., and 0-75 gr., re-
spectively; and the maximum resistance, calculated according to the rules given
below, should be 1 gr. One sees that the transverse waves increase very much
in length and height as the velocity of the boat is increased.

64 EKMAN. ON DEAD-WATER. [norw. pol. exp.

While the "relief-photographs" (PI. XIII) chiefly establish the diverging
waves, it might be supposed that the waves shown by the "silhouette-photo-
graphs" (PI. XIV — XVII) are only the transverse waves. Actually, however,
diverging waves would look like transverse waves on these photographs:
aft of the launch Fig. 4, PI. XII, for instance, three sharply marked diverg-
ing waves are seen, and it is obvious that if the launch be regarded right
from the side, they should look like the section of a train of transverse
waves. A similar illusion will in a still greater degree take place in the glass-
tank; for the diverging waves become reflected against the walls of the tank
and, in consequence, have their height there increased. Further it is a con-
sequence of the total reflection of light in the boundary between salt and
fresh water, that every place where the dark-coloured salt-water only licks
the wall of the tank, appears quite dark, because the light reaching the ca-
mera from these places must have passed merely through salt-water from one
side of the tank to the other (supposing that the boundary between salt
and fresh water is smooth, and feebly inclined). On the other hand, where
the salt-water is raised in the middle of the tank, it will not appear quite
dark, because the water is there stirred by the vessel so that the light might
pass through it under diffuse refraction. The silhouette photographs must
therefore chiefly show the wave-profile along the walls of the tank and con-
sequently give the appearance of transverse waves. On the other hand, the
transverse waves must have really been comparatively more developed in just
those cases in which "silhouette-photographs" were taken, than when the relief-
photographs were taken. For in the former cases either a smaller tank (Pl.XIV)
or a larger boat-model (PI. XV — XVII) was used than in the latter cases; the
tank was consequently relatively narrower, and it is known that the waves
become in that case more quickly transformed into transverse waves.

A photograph taken in June 1901 happened to show very clearly the true
shape of the waves which are shown by the silhouette-photographs. The
salt-water was rather strong (spec, gravity 1*16), but it was clear and not
coloured with Chinese ink. This photograph is reproduced in Fig. 1, PI. XII.
To make it more realistic, it is completed by a sketch of the upper part of
the Fram and her tackle. A relief-photograph of the small -FVam-model in
the small tank, is reproduced below (Fig. 2, PL XII), on such a scale that it
corresponds in all its details to Fig. 1. Figs. 1 and 2 examined together, give

NO. 16.] QUALITATIVE RESULTS. 65

a very clear idea of the shape of the waves. From the boat's stern a couple
of diverging, wing-shaped wave-hollows (elevations of the boundary) stretch out,
and where these waves strike the walls of the tank, the first stern-wave is
seen on the silhouette-photograph. After these waves, follows a couple of
diverging wave-crests (depressions of the boundary) which likewise strike the
wall. The waves following seem to approximate to the shape of transverse
waves. In Fig. 1, PI. XII, one may easily follow the profile of the waves
along the wall of the tank, and then recognize the shape of the silhouette
photographs (compare, for instance, Fig. 2, PI. XVI). In addition, the salt-water
in the middle of the channel is visible between the two first waves at the wall.

The most important point which the photographs described above clearly
show, is that the waves largely increase in height when the velocity of the
boat increased towards the critical velocity, but when this is passed, and
the boat is free from the dead-water, the waves disappear ; quite in ac-
cordance with the reasons given in Chap. II, and with the analogous pheno-
mena discovered by Scott Russell. The waves which are seen at a distance
aft of the boat, in the bottom figure on PI. XV— XVII, might possibly be
explained as a section of diverging waves, but probably they are simply waves
remaining from an earlier moment when the boat was still moving at below
the critical velocity.

Figs. 7 and 8, PI. XIV, illustrate the case in which the vessel moves
much faster than at the maximum wave- velocity ; in this case the difference
of specific gravity between the water-layers has no appreciable influence upon
the motion, which then takes place almost exactly as in homogenous water.
To show the motion of the water at different levels, these experiments were
made with three water-layers forming two boundaries 1 and 2 cm. below the
free surface; in the case of Fig. 7 as in the experiment, the middle water-layer
is black and- the others are clear, and vice versa in Fig. 8. The difference
of spec, gravity between each two of the water-layers is about 00005 only,
and the maximum wave-velocity is less than l-4 cm. per second. The velocity
of the boat-model, is about 5 cm. per second in Fig. 7 and about 7 cm. per
second in Fig. 8. (In the latter case spirals of black water were seen in the
middle layer, arising from vortices).

It was mentioned in Chap. II (p. 42) that in consequence of the wave-
motion in the boundary, there must arise very low waves in the surface of

66 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

the water — a slight depression just over each elevation in the boundary, and
vice versa. This was verified by a few experiments described above (p. 59).
Fig. 3, PI. IX, shows some of the wave-profiles in the water-surface, drawn
in these experiments. The numbers 1 — 9 to the left of the figure, denote 9
separate experiments. The horizontal line which is on a level with each of the
numbers, indicates the undisturbed water-surface in the corresponding experi-
ment; the boat-model is drawn black, on a scale of 1 : 20, in its due position
relative to this line. The disturbance of surface-level in the neighbourhood of
the boat is represented by the curved line: the vertical distances between it
and the line of undisturbed surface-level, are 25 times as great as the disturb-
ances of level observed in the experiments; the horizontal scale of the wave-
profile is the same as that of the boat itself, and the scale of heights is con-
sequently 500 times the scale of length.

A comparison of these profiles, with photographs of the boundary-waves
in similar cases, shows quite clearly the above mentioned connection between
the wave-motions in the surface and in the boundary. Compare, for instance,
the profile 6, PI. IX, and the photograph Fig. 2, PI. XVI -- both taken in
the case of a 5 cm. deep surface-layer, in which the boat moves at somewhat
below the critical velocity. Similarly, compare the profile 7, PL IX, and Fig. 4,
PL XVI (the water-layers the same as before, but the velocity of the boat
above the critical velocity). In both cases the shape of the surface is — when
leaving out of account the scale of heights — a reversed image of the shape
of the boundary. By calculation it can be shown that the ratio of the height
of the surface-disturbances to that of the boundary-waves, is of the same order
of magnitude as it should be according to the theoretical formula (1) p. 42. A
more rigorous testing of the agreement between theory and experiment in
this respect, is impossible, because the latter were not made with towing-forces
corresponding to oneanother.

The disturbance of the surface-level gives a very simple explanation of
the increase of resistance which is caused by the boundary-waves. Figs. 1
and 2, PL IX. are intended to illustrate this; they show the same surface-
disturbances as the profiles 6 and 7, Fig. 3, but on less exaggerated vertical
scale (50 times the horizontal scale). The boat is sketched in her true position
relative to the actual (disturbed) water-surface, and the illustrations then be-
come more realistic. In both cases illustrated, the towing force is 3 grammes,

NO. IB.] QUALITATIVE RESULTS. 67

but in Fig. 1 the boat is drawn by these 3 gr. at a velocity of 9-5 cm. per
second only, whereas in Fig. 2 the boat has from the beginning a higher
velocity, and is steadily towed at a speed of 27 cm. per second. At the lower
velocity the boat pushes a mass of water before her stem, and at the stern
she provokes a wave-hollow; her resistance is in consequence, in creased just
as if she constantly had to rise on an incline. She is then "in dead-
water". At the higher velocity, on the other hand, the boat moves on the
top of the low hillock of water, which she provokes, and she consequently
moves on a nearly horizontal surface. The analogy with the phenomena
in shallow canals, described by Scott Russell (see pp. 38 — 39) is apparent
(compare Figs. 1 and 2, PL IX, with Figs. 6 and 7, p. 39). But there is the
difference that the waves illustrated in PL IX are not free waves in the water-
surface, but an effect of the boundary-waves below, arising at a much slower
velocity than the wave-phenomena in shallow water illustrated on p. 39.

The energy which is represented by the disturbance of level, is, at the
lower velocity, constantly left behind as wave-motion; and the consequent loss
is refunded by the work done by the boat in pressing into the wall of water
before her. At the higher velocity, there is very little energy left behind, and
consequently very little work necessary for refunding the loss.

A disturbance of the water-surface similar to that in the case of "dead-
water", takes place also in homogenous water (see curves 1 and 2, Fig. 3,
PL IX), but at much higher velocities than in dead-water. It will be shown in
section F, that the pressure-resultant influencing the boat-model in consequence
of this disturbance of water-level, makes an important part of the resistance,
in homogenous water as well as in "dead-water". In the latter case by far the
largest part of this pressure-resultant is due to the boundary-waves.

The oscillations in the velocity of the boat; conclusions regarding
the wave-making resistance.

Before closing the description of the qualitative results, one very interest-
ing effect of the dead-water must be mentioned, although it probably does not
occur so markedly on the sea, as it did in the experimental tank. In spite
of the boat-model being drawn through the water by a constant weight, I
never succeeded in giving to it a steady speed, when a layer of fresh
water covered the salt water in the tank. It was on the contrary, quickly

68 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

accelerated up to a higher velocity than its mean velocity, it then slowed
down, took a new leap, and so on: in this way the velocity performed oscill-
ations, which where sometimes very considerable.

The diagrams PI. VII— VIII, showing the changes in the velocity with
the time, during some selected experiments, may illustrate this. The number
on the left of each diagram, refers to the number of the experiment, found in
the second column of the tables (in the next section of this chapter). The time
is reckoned horizontally from left to right, the distance between each two ad-
jacent vertical lines representing an interval of 1*09 seconds (in diagram No.
28S, it represents 0*436 seconds). The first part of the curve is left out on
every diagram, so that the epoch t — 0, at which the boat started, must be
imagined to be somewhere to the left of the figure. The velocity of the boat
is reckoned vertically, and the scale, in cm. per second is given to the left of
each figure: in all diagrams except No. 288. two intervals are equal to 1 cm.
per second. The velocity is, at equal intervals of time, marked by small circles,
and through them the curves are drawn.

The diagrams 18—47 refer to experiments in homogenous water. They
show a velocity, gradually increasing, if the initial velocity given to the boat
was too slow, or decreasing if it was too fast. Only in the experiments in
which no steering string was used (30—35, 41—47) did it sometimes happen,
that the velocity increased and again slackened, on account of the boat mak-
ing sheerings from its straight course.

When there was a layer of fresh-water on the top of the salt-water, the
motion of the boat took place quite differently. The changes of velocity in
such a case, are shown typically by the diagrams 77—83 (depth of the fresh-
water layer 5 cm.: spec, gravity of the salt-water 1*032). Experiment 77 was
made with a towing-force of 0'8 gr. (about one third of the maximum resi-
stance): in the course of about 40 seconds, the velocity goes through 3 com-
plete and quite distinct oscillations, but the amplitude of the variations is
not very great |0'4 cm. per second). The oscillations become more and
more marked, as the towing force is increased, and simultaneously, they take
a longer time. In experiment 80 (towing force 2"0 gr.) the velocity dropped
from a maximum of 9 cm. per second to a minimum of 5 cm. per second,
and one oscillation seems to have required about 25 seconds. When the towing-
force was 2-2 gr. (diagram 82), which was very near to the maximum resi-

NO. 15. | QUALITATIVE RESULTS. 69

stance, there was not time enough, while the boat was going the whole length
of the tank, for the velocity to perform a complete oscillation; after having
attained a maximum of 10 cm. per second, the velocity steadily slackened
and dropped down to 3 cm. per second. In experiment 83, the towing force
was only O'l gr. more, and the velocity increased at first in very nearly the
same manner as in the former case. But now the towing-force is sufficient
to overcome even the maximum resistance, which corresponds to the top-point
on the resistance-curve (4) in Fig. 8, PI. VI, and in the present case takes
place at a velocity of about 10'5 cm. per second; and the velocity, after having
passed this value, is more and more rapidly accelerated. This is easily seen
by the curve bending upwards when it has passed the horizontal line 105.

The changes or oscillations in velocity, were followed by peculiar changes
in the wave-motion, which clearly showed the cause of the former. When
the boat was unhooked and began to move, the boundary between the salt-
and the fresh-water was at first quite even. Gradually, quite small waves
arose, as in Fig. 1, PI. XIV, and the boat continued to be accelerated. After
a few seconds, the waves were greatly increased, the boat ceased to be ac-
celerated, and a "solitary wave"1 became visible under its stem (Fig. % PI. XIV).
If the towing-force was smaller than the maximum-resistance, the boat was
then rapidly retarded and the solitary wave, moving steadily at the highest
speed which the boat had, went on in advance. When it had reached a
position ahead of the boat (about as in Fig. 3, PI. XIV), the velocity of the
latter was nearly a minimum ; the solitary wave steadily distanced it, and the
waves abaft came nearer, broke and disappeared. Then, the boat took a new
leap, the waves began to increase, and the whole phenomenon was repeated.
If the towing-force was greater than the maximum-resistance, the boat
overtook the solitary wave, so that it gradually dropped astern from the po-
sition in Fig. 2, PI. XIV. to that in Fig. 4, PI. XIV. After that, the boat
had her velocity rapidly accelerated, and simultaneously the height of the soli-
tary wave under her keel, was more and more diminished (Figs. 4, 5, 6,
PI. XIV). She was then rid of the "dead-water".

A single permanent wave-crest moving along in the surface-layer (see Fig. 5, PL VI)
and quite similar to Scott Russell's solitary wave in shallow water, mentioned on
p. 39. Just as this latter, the solitary boundary-wave seems to move with about the
same velocity as long periodic waves.

70 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

The photographs PI. XIV, which were taken in the small tank, do not
represent very well, the waves behind the vessel, which are on the other hand,
better seen in PI. XV— XVII. Fig. 3, PI. XVI, shows the moment when the
waves begin to break; the velocity is just a minimum, and has dropped from
its maximum 9-4 cm. per second to 4-6 cm. per second (see diagram 81, PI. VII).
A few seconds after the photograph was taken, the boat had its speed acceler-
ated again ; and if the length of the tank had allowed it, the same phenomena
should have taken place once more.

The whole process took place in just the same way, whether the boat reached
down into the salt-water or not. Even if the fresh-water reached so much as
2 cm. below the keel of the boat-model, the oscillations in the velocity were
rather great (see diagrams 103—106, PL VIII). Figs. 1—3, PI. XVII, show
that the waves were, at the same time, very considerable. (The three last-
mentioned figures show the situation of the waves just after the velocity had
been a minimum: before the minimum was attained, the elevation of the
boundary, which is now seen under the keel of the boat, had a position more
astern).

If different velocity-diagrams be compared, it will be seen that the oscill-
ations take place more slowly, the smaller is the difference of spec, gravity
between the two water-layers. Compare, for instance, the diagrams 134 and 141
(difference of spec, gravity 0"01 and 0-02, respectively), 77 — 81 (difference of
spec, gravity 0-032), 148—150 (difference of spec, gravity 0-07), and 160—162
(difference of spec, gravity 0*16). Indeed, according to the rule, p. 52, the
period of the oscillations should alter inversely as the square root of the dif-
ference of spec, gravity, if, at the same time, the towing force were altered in
the same ratio as this latter. This rule is approximately verified by experi-
ments 141, 79, 149, and 161, in which the towing-forces stand to each other
approximately as the differences of spec, gravity.

The amplitude of the oscillations, relative to the mean velocity, seems
on the whole to be just as great when the difference of spec, gravity is 0"032,
as when it is 0'16 (see diagrams 77—81 and 160—162). This fact will be
made use of, later.

Some important conclusions regarding wave-making resistance may be
drawn from the above-described phenomena. They show that the corre-
sponding changes of the waves and the resistance, do not take place simid-

NO. 15.] QUALITATIVE RESULTS. 71

taneously with the changes of the vessel's velocity, but the waves and the
resistance increase gradually towards their final values, after the boat has
acquired a given speed; and this circumstance was evidently the reason of
the oscillations. It will be shown that the diverging waves are less apt to
cause velocity-oscillations, but the transverse waves more so especially if the
boat is moving at a speed near to the critical speed at which the resistance
is a maximum.

To make all this clear, first suppose that the boat at each moment creates all the
wave-energy which we find within the space moved through during that moment. The
wave-motion near the boat and the resistance to her, would then depend only on her
instantaneous velocity, so that, directly after the boat has her velocity increased, waves
of the height corresponding to the new velocity, are generated. In this case no oscillations
in the velocity would be possible; the boat would, on the contrary, be accelerated by a
force, equal to the difference between the towing-force and the resistance corresponding to
her actual velocity, and she would gradually attain the velocity commensurate with the
propelling force. She would never exceed this velocity, for as soon as it were attained,
the resistance would be exactly equal to the propelling force, and her velocity would, in
consequence, not be further accelerated.

Actually, the waves once created, propagate themselves to a certain extent in the
direction of the vessel's motion, and thus the wave-energy is partly supplied from behind,
the rest, only, being directly generated by the vessel. It is then clear that the waves will
be smaller at the beginning, when there are no waves behind them; and if the boat be
moved at a steady speed, some time must elapse, before the waves have obtained their
final height. For the same reason, if the boat has her speed incessantly accelerated, the
waves never reach the height corresponding to her instantanous velocity, but the changes
of wave-motion must always follow on the changes of the vessel's velocity. Similarly, when
the velocity is being retarded. With regard to the changes of the resistance, when the
boat begins to move at a steady speed, three cases are conceivable: either it depends only
on the speed of the vessel and not on the waves already created, or it is greater at the
beginning when the vessel must create waves in water, before motionless, or it is smallest
at the beginning and increases with the height of the waves. In either of the two first cases
there would be no velocity-oscillations: for as soon as the boat ceases to be accelerated,
the resistance then does not further increase, and therefore a higher speed than can be
constantly sustained, cannot be given by a constant force. It is therefore proved by the
velocity-oscillations, that the resistance increases with the height of the waves, when the
boat begins to move at a stationary speed, and that in consequence the changes of resi-
stance follow on tlie changes of the vessel's velocity.

The velocity-oscillations are now easy to understand. When the boat, initially at
rest, is set in motion by a constant force, the resistance does not balance the moving force
and stop the acceleration, before the boat has already a larger velocity than could be con-
tinually sustained by the moving force. The waves and resistance continually increase, and
the velocity begins to be retarded; the resistance increases until it has reached a value
corresponding to the actual velocity of the boat (but larger than the moving force). After
that, the velocity and the resistance both diminish. As the changes of the latter are con-
tinually behind hand, the resistance continues to be diminished even after it is equal to
the moving force, and the velocity has ceased to be retarded; the boat consequently be-
gins to be accelerated again. The velocity-oscillations are then a necessary consequence of
the law of wave-generation; only that they will be more or less stifled by viscosity. The
matter will really be somewhat more complicated, because the waves during the oscillations
alter their position relative to the vessel. When making the experiments, I had the im-

72 EKMAN. ON DEAD-WATER. [norw. pol. exp.

pression that this circumstance increased the velocity-oscillations, but a detailed discussion
seems to give a different result; in any case it has not altered the oscillations essentially.

By simple considerations, the conditions under which the velocity-oscillations will be
small or great may easily be found. For this purpose, we may regard a wave which
follows immediately after the vessel, as made up of two waves, one of them being the
wave which should at the actual moment be there only by the effect of the transmission
of waves from behind: the other wave is then the vessel's direct contribution to the
wave-motion. The sum of the heights of these two waves is equal to the height of
the actual wave. Let us now make the very reasonable assumption, that the wave-
height of the wave-contributions directly generated by the vessel, depends only on the
instantaneous velocity of the vessel (and on her shape, etc.) but not upon the waves al-
ready created. [This is true, as long as the motions are small, so as to be conformable to
linear differential equations. In general, the assumption may therefore be expected to be
approximately true]. The wave-making resistance depends only upon the contribution
which the boat must pay to the wave-energy, i. e., to the square of the wave-height. Now
suppose the vessel to move at a steady speed and the instantaneous height of the trans-
verse wave, nearest behind the stern of the vessel, to be li. After having been propagated
one wave's length, this wave will have a height = H \r , r being the ratio of transmis-
sion of wave-energy (see pp. 30 and 43) ' . During the same time, the boat has generated a
transverse wave of a certain height h, depending upon her instantaneous velocity v; and
as the waves have invariably the same position relative to the boat, the wave nearest be-
hind the stern will have a height equal to the sum of the above elementary waves, i. e.
h + H^r. The resistance due to transverse waves consequently varies as
(h + H \'r~y - {H ir~f = 2 Hh Vr + h\ . . . (a)

As h and r depend only on the vessel's velocity, the resistance then increases with
the actual wave-height H, when the boat is moving at a steady speed. When the mo-
tion has become stationary, the wave-height should also be invariable, and consequently
h + H V»" = H- If the value of h or of H, found from this equation, be put in the expres-
sion (a), the resistance will be as

H*(\ - r) (b)

or as

*»!±€ (0

1 -ir

Equation (6) shows that waves of a given height, cause less resistance, the greater be the
ratio of transmission of wave-energy; equation (c) shows that when the wave-generating
effect of the vessel is given, the wave-making resistance increases with the ratio of trans-
mission of wave-energy.

The effect of the diverging waves upon the resistance, is quite analogous. Their
velocity-component in the direction of the vessel is, however, only v sin2a, a being the
angle between the boat's keel-line and the crest-lines of the waves (see p. 37). That propor-
tion of the whole wave-energy moving along with the vessel, is in consequense, r sinV, and
this must be put instead of r, in the expressions (a), (6), and (c). The expression (a) then
shows, that the resistance due to diverging waves, increases in only a comparatively small
degree with the height of the actual waves, and more exclusively than the resistance due
to transverse waves, depends upon h, i. e. upon the velocity of the vessel. The diverging
waves therefore contribute less than the transverse waves, to the velocity-oscillations. The
transverse waves, again, will give rise to the greatest oscillations, in the case when r is
nearly 1, *'. e. when the boat is moving at nearly the critical velocity.

1 This and the following conclusions are, obviously, but approximate. For the laws of
propagation of simple harmonic waves, hold exactly true, only in the case of an end-
less series of waves, or, practically, for the middle waves of a large series.

NO. 16.] QUALITATIVE RESULTS. 73

The same result can be obtained in another way. If the boat, previously at rest, be
moved uniformly at a speed v, the transverse wave first produced will have the height h;
the next wave — that which is nearest to the vessel after she has proceeded 2 waves' length
— will have got a contribution It ]/r to its height from behind, and will therefore have a
total height h (l + VV). Similarly, the third wave will have a height

h (l + yj7) VF+ h = h (1 + Vr + tfr*),
and so on; and gradually, the height of the wave at the stern, approximates to its final value

n = o ' "

For diverging waves, it is only necessary to put r sin2« for r, just as above. The greater the

fraction r [or r sin2a), the more slowly does the series 2' V r" converge, that is: the more

slowly will the wave-motion and the resistance reach their final magnitudes. Again, the
more slowly the resistance reaches its final magnitude, the more will the changes of resi-
stance follow after the changes of velocity, and the greater will be the oscillations, in the
case of the boat being put in motion by a constant force.

This agrees well with the experimental result, that the velocity-oscillations, as well
as their time-periods, increased rapidly with the towing-force, i. e. with the velocity1. For
as the vessel's velocity was increased, the waves seemed to become to a greater and
greater extent transverse waves and comparatively less, diverging waves; and at the same
time the wave-length and consequently the quantity r, increased. In addition, the velocity-
oscillations were more stifled by friction the slower the velocity; for, as will be shown in
section F of this chapter, a relatively larger part of the resistance is due to friction, at
slower velocities, than is the case in the neighbourhood of the critical velocity.

The velocity-oscillations of the smaller Fraw-model in the large tank,
were somewhat smaller than those of the large model (see diagrams 284—287,
PL VIII). This partly depends upon the friction being in the former case
comparatively greater; but it also depends upon the different wave-motion.
For the smaller boat-model moved in a relatively wider channel than the large
model, and the waves created by it, were therefore to a greater extent diverg-
ing waves than in the case of the large model. The same will be the case
with vessels on the sea, as the water is there practically unlimited in hori-
zontal direction; and this possibly explains why the velocity-oscillations, although
very strong and evident in the experiments, are not observed by the sailors.

1 In contradiction to this result, the diagrams 147 and 156 show slower oscillations than
148 and 160 respectively. I believe, however, that the variations ol velocity in ex-
periments 147 and 156 depended on wave-motions which remained in the water from
the preceeding experiment and influenced the motion of the boat. I often required
much patience in waiting for the wave-motions in the boundary to subside, otherwise
they would disturb the motion. It has happened that by the effect of such residuary
waves the boat-model has got free from the dead-water, although, with the same moving
force it would have remained in dead-water if there had been no waves when it started.

10

74 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

The chief reason, for the latter fact, is, however, probably a much simpler
one. For as a rule, a sailing-vessel will be put in motion more gradually
than was the case with the boat-model in the experiments; and in the case
of a screw-steamer the propelling-force diminishes when the velocity is in-
creased, which circumstance prevents or reduces the velocity-oscillations.

To the above investigation, one more remark may be added, which will
be of use later. The wave-making resistance depends, from one point of
view, on the work spent by the vessel in generating waves; and in this way,
formula (a) p. 72 is deduced, giving the wave-making resistance in the case of
approximately stationary motion. On the other hand, the immediate cause
of the resistance, is the water-pressure which is exercised on the vessel by
the waves. The instantaneous resistance therefore depends only on the shape
of the waves and their position relative to the vessel — whether they are ge-
nerated by the vessel or not. [In this case we disregard the frictional resi-
stance as well as the resistance to the vessel's acceleration]. A vessel might
consequently experience resistance even when at rest, if she be only sur-
rounded by waves. In this case, however, the waves will not have any per-
manent effect upon the vessel, for by passing the vessel, they will consequti-
vely take every position relative to her, and their only effect upon the vessel
will therefore be an oscillatory motion, insensible if the waves are short com-
pared to the vessel and of small time period. The dependance of the resi-
stance upon the waves only, seems to be in contradiction to formula (a) p. 72,
as the latter also contains terms depending on the vessel's velocity. The
latter formula, however, is based upon the supposition that the vessel's velo-
city is uniform, and that the waves follow her at the same velocity. In this
case, the waves obviously take such a position relative to the vessel, that the
work done in overcoming the sternward water-pressure, is equal to the work
required for the generation of new waves.

The difficulties which the velocity-oscillations introduced into the determin-
ation of the connection between velocity and resistance, will be discussed ex-
plicitly in section D of this chapter. The most important one may, how-
ever, be shortly mentioned here. The maximum resistance in a given water-
layer, represented by the top-point of the resistance-curve, was determined
by a series of towing-experiments. A constant towing-force, each time greater
than in the preceding experiment, was applied to the boat-model, which was

N0- 1B-] QUALITATIVE RESULTS. 75

then unhooked and put in motion; the maximum resistance was supposed
to be equal to that towing-force which was just able to give to the boat
the high velocities at which it was not influenced by dead-water. One
would, however, obtain higher values of the maximum resistance, if the boat
were towed at different, steady speeds, and the corresponding resistance mea-
sured. Under the conditions of the experiments, the velocity of the boat-
model was rather quickly accelerated, by the constant towing-force, up to the
critical speed; and as the changes of resistance take place after the changes
of velocity, the resistance was not fully developed even when the boat was al-
ready brought beyond that range of velocities, at which it is influenced by
dead-water. It will be shown later, that the influence of this circumstance on
the determination of the maximum resistance, is rather significant.

The maximum resistance may, in consequence, be defined in two ways
— according to the results of experiments with constant towing-forces, or at
steady speeds. Reasons will be given in section D, for the choice actually
made.

Some other observations of various kinds, on the motion of the boat-
model and the water around it, will be mentioned as they arise in the dis-
cussion.

C. NUMERICAL RESULTS.

The following tables form an extract from my experimental journal, which
contained accounts of 744 experiments in all. In this extract only such ex-
periments are included as are actually used in drawing the resistance-curves,
or as are in other respects, of interest. The experiments not recorded here,
were' either less instructive or were not satisfactorily performed, and were
therefore repeated.

The different columns give:

First and second columns, Date of the experiment and its number in
the table.

Third and fourth columns, The specific gravity S -—^ of the salt-
water (the bottom layer), and the depth in cm. of the fresh-water layer on top.

76 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

Fifth column, The additional "starting force" by which the constant
towing-force was augmented at the beginning of some experiments, in order
to give the vessel its constant velocity more quickly: it is half of the addi-
tional "starting weight" suspended.

Sixth column, The distance traversed by the boat-model before the addi-
tional starting-force was removed; it is twice the distance during which the
starting-weight was allowed to act.

Seventh column, The constant towing-force on the vessel in grammes.

Eighth column, The force which is necessary to give to the vessel its
actual acceleration at a given, definite instant. (For the calculation of this
force, see the next section of this chapter). In this column, a value is given
only in those cases in which the velocity gradually increases or decreases
towards its final value. When there were oscillations in the velocity, the
eighth column is blank.

Ninth and tenth columns, Corresponding values of resistance and velocity
under uniform motion. Ninth column gives the towing force diminished by
the quantity in the eighth column, i. e. the force necessary to draw the vessel
uniformly with its actual velocity; this latter is given in cm. per second, in
the tenth column. Both quantities then refer to a definite instant during the
experiment. "Maximum resistance" written in the eleventh column, denotes
that resistance and velocity are given for that moment, during the whole ex-
periment, at which the acceleration of the boat-model was smallest. In several
cases (when there were velocity-oscillations) the tenth column gives the mean
value, about which the velocity seems to have oscillated ; and the accelerations
are disregarded. In these cases, the eighth column is blank, and the ninth
column gives the same value as the seventh column. When the estimation of
the mean velocity in the tenth column is uncertain, the value is enclosed in
brackets. From some experiments it was quite impossible to determine a value
of velocity and corresponding resistance. Experiment No. 55 is such a case,
and here will be found in the tenth column. < 8'1 ; this indicates that the velo-
city increased up to 8*1 cm. per second and then slackened again.

In some cases, the diagrams representing the velocity of the boat-model
during the whole experiment, are inserted (in PI. VII— VIII). These experi-
ments are denoted in the tables, by an asterisk with the number in the second

NO. 15.]

NUMERICAL RESULTS.

77

column; and the corresponding velocity-diagram in PI. VII or VIII, is denoted
by the same number.

The photographs of some of the experiments, are reproduced (in PI. XII-
XVII). This is stated under "remarks" in the eleventh column of the tables.

Table I. Experiments in the small tank.

Model of the "Fram": Scale 1:200

B

-
01

Water-layers

Starting
force

O)

0)

Resistance

under uniform

motion

Date

0>

C
fc-

1

o «

bi>"3

u

£•"3

u

Oj &)

in

E

a

60

V

a
C

33

<£

to

_c
-£
o
H

c

t-i

"as
u

C

'55

<v

'o

JO

'a

>

Remarks

May 14

1

(no
salt

water)

23 cm.

05

5

o-i

001

0-09

7-5

i
Experiments 1 — 17, made

1900

2

0-5

7

o-i

o-oo

010

8-2

without steering-string.

3

0-5

15

0-2

0-02

0-18

12-4

4

0-5

20

0-2

o-oo

0-20

13-1

April 24

5

(no

5'0 cm.

!

02

o-oi

019

8-9

1900

6

salt

03

0-05

0-25

11-4

7

water)

0-4

006

034

13-7

April 24

8

(no

2"5 cm.

0-2

002

0-18

7-6

1900

9

salt

0-3

o-oo

030

10-2

10

water)

0-4

000

040

12-2

June 5

11

1-030

20 cm.

01

o-io

3-0

1900

12
13

14

0-15

0-2
0-25

015
020
025

3-7
4-1
4-9

15

0'5

1

03

002

0-28

7-3

Maximum resistance.

16

05

5

03

007

023

96

17

1-5

5

0-4

015

025

143

78

EKMAN. ON DEAD-WATER.

[norw. POL. EXP.

Table II. Experiments in the large tank.

Date

a

'u

p.

M

V
cm
O
U

O)

a

3

Water-layers

Starting
force

a

M

<s
'%

o

u
u

a

be

.5

u,

01

u
u

Resistance

under uniform

motion

Remarks

*.5

bo a

«5 *
v --

9,*a

U

o ri
-c &

Q *

grammes

CO

*>
u

"S

Resistance

'3

>

Boat model No.

1: the

"Fram", scale 1 :

100

Oct. 15

18*

(no

37 cm.

2-5

20

0-8

010 j 070

144

1900

19*

salt

2-5

30

10

013

0-87

16-5

20*

water)

2-5

40

15

007

1-43

21-0

21

2-5

60

2-0

016

1-84

23-8

Oct. 16

22

2-5

30

0-8

000

080

14-6

23

25

40

0-8

-005

0-85

153

Nov. 6

24*

2-5

12

025

000

025

7-4

25*

2-5

25

050

-0-03

053

11-5

26*

2-5

30

0'75

o-oo

0-75

145

27*

2-5

40

10

o-oo

1-00

156

28*

2-5

55

1-5

-003

1-53

20i

29*

25

67

20

000

2-00

235

Oct. 15

30*

2-5

20

0-8

011

069

143

No steering string used in

1900

31*

2-5

30

1-0

0-13

0-87

160

experiments 30 — 35.

32*

2-5

40

1-5

0-16

1-34

20-0

Oct. 16

33*

2-5

25

0-8

0-18

062

14-0

34*

2-5

35

0-8

005

075

155

Oct. 12

35*

0-8

Nov. 4

36*

1-024

0

2-5

6

015

000

0-15

55

The water was mixed with

1900

37*

25

3

01

o-oo

010

4-2

Chinese ink from pre-

38*

25

12

0-25

-0-03

0-28

7-4

vious experiments, and

39

2-5

25

0-5

000

0-50

11-5

its surface could not be

40

2-5

35

0-75

o-oo

0-75

14i

kept quite as clean as
usual.

41*

0-25

0-07

0-18

70

No steering string used in

42*

2-5

12

025

-0-02

0-27

7'2

experiments 41 — 47.

43*

2-5

25

0-5

-005

0-55

11-3

44*

2-5

6

0-4

009

031

8-3

45*

25

6

0'15

000

0-15

54

46*

2'5

3

01

-001

Oil

40

47*

2-5

3

01

001

009

4-0

NO. 16.

NUMERICAL RESULTS.

79

-|_»

C

o
B

Water-layers

Starting

0)

riesi.'
under

tance
jniform

Date

s
Q,

M
CD

o

h

CU

25

in

bo
c

0

SB
1

*a3

<

mo

;ion

Remarks

° £
be "a

a; ■*-»

Depth of
fresh water

CD

a
a

&

u

a
"S

u

CJ

c

CO
*CO
V

'3

"cd
>

Febr. 20

48

1030

1-0 cm.

0-15

015

3-2

1901

49
50
51

0-25

0-5

0-25

0-25
0-50
0-25

3-9

6-8
3-8

52

0-75

0-2

055

8

Maximum resistance.

-

-

0-3

0-45

11

(The registration of velo-

Oct. 24

53

1032

3-0 cm.

1-0

1 city failed. Phot. PI. XV,

1900

54*
55*
56*

1-2

1-6
2-0

1-2
1-6
2-0

5-8
< 81
<93

I Fig. L

Pliot. PI. XV, Fig. 2.
Phot. PI. XV, Fig. 3.
Phot. PI. XV, Fig. 4.

Oct. 25

57*

10

1-0

51

571

2-5

20

1-3

04

0-9

150

Dec. 1

58

1-030

30 cm.

0-15

015

2-9

Temp, of water 13° C.

1900

59

2-5

2

0-25

025

3-6

60

25

4

05

0-50

43

61*

10

1-0

(5-5)

62*

-o-i

50

1-0

1-0

56

63*

-025

50

10

1-0

(5-2)

64*

-03

50

1-4

1-4

(69)

65*

1-4

1-4

6-5

66

1-6

1-6

8-1

67*

1-7

0.1

1-6

10-5

Maximum resistance.

68*

2-5

15

1-5

00

1-5

106

69*

2-5

25

1-2

-005

1-25

10-0

70*

2-5

25

1-3

-0-05

1-35

11-3

71

2-5

40

15

0-2

1-3

161

Febr. 24

72

1030

4'0 cm.

15

1-5

65

1901

73

2-0

2-0

(7-5)

74

2-25

01

2-15

10-5

Maximum resistance.

75

215

01

205

11-0

Maximum resistance.

76

2-5

40

1-5

o-o

1-5

13-3

80

EKMAN. ON DEAD-WATER.

[NORW. POL. EXP.

a

Water-layers

Starting

U

u

Resistance

under uniform

a.

9

a

motion

Date

o

u
o
.a

s

C ci

isi a
6 *

CD ■*?

U

11

Q. en

CO
CD

I

e

CD
60

t/1

(-

J

c

CD

.8

be
B

"it

o
H

.9
"3

u
o

CD
CD

a

CO

'35
cw
PC

'o

>

Remarks

Oct. 23

77*

1032

50 cm.

08

0-8

5-8

Phot. PI. XVI, Fig. 1.

1900

78*
79*
80*
81*
82"

1-2
15
2-0
2-1

2-2

1-2
1-5

2-0
2-1

2-2

6-0
6-4
6-9
(6-9)
< 99

Phot. PI. XVI, Fig. 2.
Phot. PI. XVI, Fig. 3.

S3*

2-3

01

2-2

105

Maximum resistance.

84*

2-5

25

1-5

00

1-5

121

Phot. PI. XVI, Fig. 4.

Oct 24

85

2-5

30

13

0-2

1-1

140

(The same water used as on
{ Oct. 23.

Dec. 2

85i

1030

50 cm.

0-25

025

43

1900

[The water was standing

Dec. 3

86

87
88
89

015

0-25

0-5

0-7

0-15

025

05

0-7

2-4

3-9
4-9
55

I from Dec. 2.

(.Temp, of water 11'5° C.

90*

-o-i

75

0-9

0-9

55

91"

-0-2

75

1-2

12

6-2

92*

-0-2

75

1-5

1-5

(6-5)

93*

-04

75

1-5

15

6-6

94*

-0-4

75

2-0

2-0

(7-5)

June 14

95*

0-9

09

6-0

Fresh-water coloured with

1901

96

2-0

2-0

< 97

Chinese ink; salt-water
clear.

97

2-1

0-05

2-05

105

Maximum resistance.

Dec. 4

98

1-030

70 cm.

015

015

4-1

Temp, of fresh- water 10 ° C.

1900

99*
100*
101
102

0-25
0-5
0-75
1-0

0-25
0-50
075
10

50
66

7-2
76

Oct. 27

103*
104
105*
106*

0-8
1*0
1-2
1-5

0'8
1-0
1-2
1-5

7-0
73
7-7
8-0

Phot. PI. XVII, Fig. 1.

Phot. PI. XVII, Fig. 2.
Phot. PI. XVII, Fig. 3.

107

2-0

0-6

1-4

14-0

Maximum resistance.

NO. 15.]

NUMERICAL RESULTS.

81

c

a

a

Water-layers

Starting
force

Resistance
under uniform

Date

CD

X
o

1

0)

u

t-.

=2

to
H

o
H

a

.5

*-.

motion

Remarks

Spec. g. of
salt water

— en
Q 43

CO

B

a

u

03

(-

O)

a

0>

CD
O

B

CO
iSl

'en

CD

o
>

108

2-5

30

1-5

0-2

1-3

15

Phot. PI. XVII, Fig. 4.

109

2-5

30

1-25

00

1-25

14

110

2-5

50

1-0

00

10

15-5

Dec. 4

111

1-030

90 cm.

015

015

4-6

Temp, of fresh water 11 °C.

1900

112

0-25

0-25

61

113

2-5

12

0-5

0-50

7-3

114

2-5

5

075

0-75

7-9

115

1-0

10

8-5

116

11

11

S-8

117

1-2

1-2

90

118

1-5

02

1-3

12

Maximum resistance.

119

1-7

0-6

11

126

Maximum resistance.

Dec. 5

120

2-5

50

11

o-o

1-1

16-6

$The same water used as on
( Dec. 4.

Dec. 28

121

1-030

13-0 cm.

2-5

5

0-25

025

6-6

Temp, of fresh water9'5°C.

1900

122

2-5

8

0-5

050

9-0

123

2-5

15

0-75

0-75

9-7

124

1-0

1-0

< 117

125

2-5

15

1-25

015

1-1

14-0

Maximum resistance.

June 9

126

1-180

3'0 cm.

025

0-25

4-2

1901

127
128
129
130
131

05
30
4-5
5-9
8-0

0-5
30
4-5
59
80

53
10 6
11
13
<20

132

8-5

0-6

7-9

21

j Maximum resistance.

Dec. 7

133

1010

50 cm.

2-5

1

015

0-15

2-7

1900

134*

2-5

1

0-25

0-25

3-2

135

2-5

1

0-5

0-50

< 46

136

0-75

o-o

075

6-9

Maximum resistance.

137

25

20

0-4

o-o

0-4

9-2

Dec. 7

138

1-020

5'0 cm.

2-5

1

0-15

0-15

2-7

Temp, of fresh water 1 1 ° C.

1900

139
140

141*

2-5

1

0-25
0-75
1-0

0-25
0-75
1-0

3-7
5-0
5-5

11

EKMAN. ON DEAD-WATER.

[norw. POL. EXP.

*-*
c

0)

.1

Water-layers

Starting
force

i Resistance
under uniform

3

eg

motion

p.

<D

Date

K
9

C~.

o

<D
S

0 a>

1 —

Qi

S

S

"5

.a

(-r

=2

60
C

.s

U.

o

o

p

>>

-4-3

"3
o

Remarks

3
55

60

0)

o

"3
>

142

1-3

1-3

Still in dead-water.

143

1-4

02

1-2

94

Maximum resistance.

144

2-5

20

1-0

00

ro

110

145

2-5

30

0-82

00

0-82

11-5

June 12

146

1-070

5*0 cm.

05

05

61

1901

147*
148*
149*
150*

1-0
2-0
30
4-0

10
2-0
30
40

7-5

8-5

9-8

10-7

151

4-5

03

4-2

16

Maximum resistance.

152

4-5

30

35

01

34

18-2

153

4-5

50

30

0-2

2-8

21-5

June 10

154

1-160

50 cm.

025

025

4-0

1901

155

156*

157

158

159

160*

161*

0-5

0-75

10

20

30

50

70

0-50

0-75

1-0

20

30

50

7-0

6-5
7-8
9-0
115
120
13-6
147

162*

90

4

90

15-6

Phot. PI. XII, Fig. 1.

163

95

9-5

<22

164

100

0-7

93

25-4

Maximum resistance.

March 7

( Water-layers \

165

0-15

015

2-3

1901

166

) represented 1

0-25

0-25

3-6

167

j by diagr. 2, (
[ Fig. 2, PI. XI J

0-5

0-50

4-8

168

1-0

10

56

169

1-5

1-5

65

170

1-75

1-75

70

171

1-9

1-9

< 9-9

172

2-0

0-2

1-8

11-0

Maximum resistance.

173

2-5

35

1-25

00

1-25

12-4

174

25

35

1-4

0-3

1-1

160'

NO. 16.]

NUMERICAL RESULTS.

83

Date

—
•A

a

3

Water-layers

Starting
force

e*-t

O

fcf)

-

w

£

-<-»

—

7;

en

& en

60

a

>

o
H

=2

en

c

Resistance

under uniform

motion

Remarks

March 5
1901

175

176

177*

178*

179*

180

181

182

183

184

Water-layers

represented

by diagr. 1,

I Fig. 2, PI. XI

2'5
2-5
2'5
2-5

30
30
30
30

0-15

0-25

05

0-75

1-25

1-5

0'75

095

1-05

115

0-1

03

00

0-03

0-05

0'15
0-25
0-50
0-75
125
1-40
1-05
095
102
1-10

2-5

30

3-9

4-1

5-7

8-8

101

12-0

12-6

12-5

Temp, of fresh water 6° C.

Maximum resistance.

Boat-model No. 2: "Fram", Scale 1:100, trimmed.

Febr. 24

185

1-030

5"0 cm.

0-15

015

33

1901

186
187
188
189
190
191
192

0-25

0-5

0-75

1-0

1-25

15

2-0

025
050

0-75

1-0

1-25

1-5

2-0

3-9
4-9
56
6-2
6-6
6-8
6-9

193

2-15

02

1-95

106

194

2'5

30

1-5

05

1-0

16-8

Maximum resistance.

Boat-model No 3: Flat-bottomed.

Nov. 25

195

No

37 cm.

2-5

1

015

0-02

0-13

44

1900

196

salt

2-5

7

025

002

0-23

63

197

water

2-5

20

05

o-oo

0-50

96

198

2-5

35

0-75

-0-04

0-79

12-0

199

2-5

40

0-9

o-oo

090

134

200

2-5

60

1-5

o-oo

1-50

172

201

2-5

70

1-8

-0-14

1-94

18-8

202

2-5

75

2'1

-o-io

2-20

20-8

203

2-5

80

2-4

0-07

233

22-4

EKMAN. ON DEAD-WATER.

[norw. POL. EXP.

■4J

a

a

Water-layers

Starting
force

43
U

Resistance
under uniform

Date

a>

p.

a>

Cm

o

M

S>

a
si

o

60

c

o
H

bo
•S

u
to

%
o
o

<

motion

Remarks

O Q

. —

60 =3

o *

0) —

£1

: I

£>

a
e

a
us

W
Or
U

0)

a

o

c
3

Hi

'in

OS

>>
*3

>

Dec. 21

204

1-030

30 cm.

2-5

2

0-15

0-15

2-7

1900

205

2-5

2

0-25

0-25

3-4

206

2-5

1

0-5

0-50

4-4

207

10

1-0

5-4

208

1-25

1-25

< 7-2

209

1-5

1-5

< 8-2

210

1-7

1-7

< 8-7

211

1-8

1-8

< 9-3

212

1-9

1-9

< 9-8

213

2-0

o-i

1-9

106

Maximum resistance.

214

2-5

40

1-5

o-o

1-5

12-2

Dec. 21

215

1030

5'0 cm.

2-5

1

0-25

025

3-8

1900

216

2-5

1

05

0-50

4-8

217

2-5

1

0-75

0-75

5-5

218

1-0

10

5-6

219

1-5

1-5

6-5

220

2-0

2-0

7-5

221

2-5

2-5

6-3

222

2-75

0-25

2-5

11-0

Maximum resistance.

223

25

50

2-0

o-o

2-0

146

Dec. 28

224

1-030

9-0 cm.

2-5

1

0-25

0-25

51

1900

225

2-5

5

0-5

050

6-8

226

2-5

7

075

0-75

7-5

227

1-0

1-0

7-9

228

1-25

1-25

8-1

229

1-5

1-5

8-3

230

1-75

1-75

8-7

231

2-0

2-0

<ll-7

232

2-25

0-15

2-10

12-2

Maximum resistance.

233

2-5

35

1-6

o-o

1-6

13-4

Bo

at-model

No. 4

, Sharp-bottomed.

Dec. 17

234

(no

37 cm.

2-5

10

0-25

o-oo

0-25

6-7

1900

235

salt

2-5

15

0-5

006

0-44

9-4

236

water

2-5

20

0-5

o-oo

050

100

NO. 15.]

NUMERICAL RESULTS.

85

Date

^
S

--

a

3

Water-layers

60 S

a a

Starting
force

60

60

a

Resistance

under uniform

motion

CD

PS

Remarks

237

238

25

2-5

40
60

10
1-5

0-08
000

0-92
1-50

14-9

18-4

Dec. 20
1900

239
240
241
242
243
244
245
246

1-030

30 cm.

25
2-5
2-5

2'5

W

0-15

0-25

0-5

0-75

13

1-5

2-0

1-25

04

o-oo

0-15

0-25

0-50

0-75

1-3

1-5

1-6

1-25

31

4-1

4-9

5-4

73

< 9-9

110

12-6

[Maximum resistance.
[ (Time-pricks failed).

Dec. 21
1900

247
248
249
250
251
252
253
254
255

1-030

5'0 cm.

2-5
2-5
2-5

2-5

50

0-25

0'5

0-75

1-0

1-25

1-5

2-0

2-25

1-5

0-2

o-o

0-25
0'50
0-75
1-00
1-25
1-50
2'00
2-05
1-50

4-6

54

5-8

60

65

6-7

< 10-1

11-5

13-5

Maximum resistance.

Dec. 28
1900

256
257
258
259
260
261
262
263
264
265

1'030

9-0 cm

2-5
2-5
2-5

2-5

35

0-25

05

0-75

1-0

1-25

1-5

1-75

1-9

2-0

1-5

0-03

0'03
0-00

0-22
0-50
0-75
1-00
1-25
1-50
1-75
1-90
1-97
1-50

5-0

6-9

7-5

7-9

8'5

9-0

9-0

<ll-5

12-1

140

Maximum resistance.

Boat-model No. 5: Thin board.

Dec. 20

266

(no

37 cm.

015

045

6-2

1900

267

salt

2-5

5

0-25

0-25

8-8

268

water)

2-5

10

05

0-03

047

140

EKMAN. ON DEAD-WATER.

[nORW. POL. EXP.

Date

e

a

0>
D.

a>

0

a>

-a
S

3

Wate

r-layers

Starting
force

8

«
F-i

.2

60
C

o
H

Accelerating force

Resistance

under uniform

motion

Remarks

O a)
. —

bo si

(/J T.

Depth of
fresh water

CO

e
a

cS
u
60

t/3

O)

0

.0

"3

o

a

C3

to

"rfl

PS

*5
o
at

>

269

2-5

15

0-75

0-03

0-72

16-6

270

2-5

18

10

010

0-90

21-9

271

2-5

25

1-5

0-20

1-30

27-0

Dec. 21

272

1-030

2-0 cm.

0-15

015

3-8

1900

273

0-25

0-25

4-8

274

0-5

0-02

0-48

8-5

Maximum resistance.

Dec. 20

275

1-030

30 cm.

0-15

0-15

4-7

1900

276

0-25

0-25

5-8

277

0-5

003

0-47

8-5

Maximum resistance.

Boat-

model No

6: "

Fram"

Scale 1 : 200

Nov. 6

278

(no

37 cm.

2-5

4

0-15

0-005

0-145

11-7

No steering-string used in

1900

279

salt

2-5

8

0-25

0-005

0-245

16-2

the experiments 278-280 l.

280

water)

2-5

12

0-4

0-02

0-38

20-7

June 11

281

1-136

2-5 cm.

0-25

0-25

8-0

Phot. PI. XIII, Fig. 1.

1901

282
283

0-5
0-75

0-50
0-75

9-4

Phot. PI. XIII, Fig. 2.
fPhot. PI. XIII, Fig. 3 (Re-
\ gistr. of velocity failed).

June 9

284'

1-180

2'5 cm.

0-25

0-25

8-6

No steering-string used in

1901

285*
286*
287*

0-75

10

1-25

0-75
100
1-25

11-4

12-2

(13-8)

the experiments 284-291.
Time-record unsuccessful.

288*

1-5

015

1-35

18

Maximum resistance.

-

-

0-5

1-0

25

June 9

289*

1-180

3-0 cm.

0-25

0-25

9-2

1901

290*
291*

0-5
10

0-5
1-0

110
133

1 This was originally not recorded in the journal; the results however show that the
steering-string cannot have been used.

NO. 15.] EXPERIMENTAL ERRORS AND CORRECTIONS. 87

D. EXPERIMENTAL ERRORS AND CORRECTIONS.

On account of the small scale on which the experiments had to be carried
out, even a small error in the determination of resistance might be of im-
portance in applying the results to the case of full-sized ships. Most of these
errors have, however, practically the same value (at a given velocity of the
boat) independently of whether the boat moves with a small resistance in
homogenous water, or with a great resistance in "dead-water". They have
consequently no essential influence upon the determination of the "dead-water
resistance" (see p. 61); and this is the part of the resistance which is of the
greatest interest to us. An approximate determination of the resistance in
homogenous water is sufficient for our purpose.

With regard to the measurements in homogenous water, as well as in fresh layers
above salt water, the following points may be noticed.

1) The measured resistances are somewhat too high, owing to the friction against the
steering string (p. 59). To approximately determine it, some experiments in homogenous
water, were made without, as well as with, steering string (see experiments 18—47, p. 78).
The friction, found from these experiments, is represented graphically by the faint curve
in Fig. 1, PI. X. As it was difficult to make the boat go straight, without using the
steering string, the determination of the friction is only approximate. It was eventually
found most convenient not to make any correction for it, and the values of resistance given
in the tables and on the diagrams, therefore include friction. Exception must be made in the
case of most experiments with the small .Fram-models, in which the steering string was
not used. When steering string was not used, it is always mentioned in the tables.

2) Tlie friction in the wheels of the towing-apparatus, was as already mentioned, al-
lowed for when adjusting the towing-weights. This friction varying from 16 mgr. in the
case of the smallest towing-forces, to 82 mgr. with a towing force of 10 gr , was by
control-determinations found to be practically the same at the end of the experiments in
June 1901 as in November 1900. It is consequently without influence upon the measurements.

3) The loss of towing-force owing to the small ^inclination of the towing-string from
the horizontal line, was, when calculated, found to be quite insignificant.

4) The dust which was constantly settling on the surface, was a source of resistance.
It gathered up ahead of the boat and] formed a rigid disc, which was pushed before
just like an ice-floe would be. The resistance which it caused, seemed to be independent
of the velocity of the boat, but it increased with the quantity of dust on the surface. The
"dust-floe" grew larger and thicker, as the boat moved from one end of the tank to the
other; and the resistance increased correspondingly. If there was very much dust, it would
even stop the boat in spite of a towing force of half a gramme or more. To get rid of this
error, which was noticed in the very first experiments, the dust was skimmed off in the
manner described on p. 57. This operation ] was made generally twice a day, sometimes
more often; and in this way, the errors due to dust, were kept within 2 or 3 cgr., in
any measurement of resistance inserted in the tables. In most cases, it has probably not
been more than a centigramme.

5) If the surface be even very little contaminated, so that its surface-tension be reduced,
it will cause an increased resistance, as was mentioned on p. 53. In the eddying wake

88 EKMAN. ON DEAD-WATER. [norw. poL. exp.

aft of the boat, the surface-film might have a tendency to be ruptured, and the surface-
tension takes its maximum value or in any case becomes increased1, whereas no such effect
takes place ahead of the boat. Not much attention was paid to this circumstance, before
the completion of the experiments, and it would in any case have been difficult to avoid
the error caused by it.

The greatest possible variation of the surface-tension being from 0'0755 to 0"0407 or
00348 gr. per cm.1, and the .FVawi-model being 11 cm. broad, the resistance caused by
surface-tension could theoretically amount to 0034-8 X H = 038 gr. The surface-
tension has not, however, its minimum value in its equilibrium state (see F. Nansen 1. c.
pp. 38 and 43) but takes a mean value. In our case, it might rather have been nearer to the
maximum value, because the surface was repeatedly cleaned by expansion. The effect of
the blotting paper in reducing the surface-tension (F. Nansen 1. c. p. 63 seq.) cannot have
been very considerable, because the area of it in contact with the cleaned surface was al-
most nil. Further, as the breadth of the boat-model decreases very evenly towards its
stern, the maximum surface-tension could hardly act in any case upon more than a small
part of the whole breadth of the boat. For these reasons it is probable that the resistance
due to the surface-tension effects, has not been more than 01 gr. for the highest velocities,
and much smaller for the smaller velocities at which "dead-water" occured. In a few cases,
exactly similar experiments were made before and immediately after the surface was cleaned;
the results agreed with the above supposition, that the surface-tension effects was of very
little importance. They might possibly have been somewhat greater in the case of dead-
water than in homogenous water, because in the former case the motion of the water aft
of the boat, is more turbulent.

6) Owing to the boat moving in a rather narrow channel, the frictional resistance
and the pressure-resultant caused by it, may have been too high, for the same reason given at
the top of p. 47. The experiments made, do not allow the value of this error being de-
termined with any certainty; this would require a greater accuracy in the determination of
the resistance especially in the case of the small boat-model, than was actually obtained.
A comparison between the curves (1) in Figs. 8 and 9, PI. VI, shows however, that the
resistance to the small .Fram-model was practically the same in the small and in the
large tank. (The model used in the former case, had a rougher surface than that used
in the latter case, see p. 59). This error cannot therefore have been very great, and has
probably been quite inappreciable; its influence on the determination of the "dead-water
resistance" has certainly been of no importance whatever.

On the other hand, the narrowness of the tank may have influenced the dead-water
resistance, by altering the wave-motion. This circumstance will be examined below in
section F of this chapter.

7) When the boat had not time to acquire a steady speed, the towing force must be
diminished by the force accelerating her, in order to give the resistance to uniform motion
(see columns 7, 8, 9, of the tables). This correction which in the case of the actual mea-
surements, was always comparatively small, is equal to the product of the boat's acceler-
ation and her inertia. The inertia which comes into account is, however, somewhat more
than the mass of the boat itself; for the surrounding water must be accelerated as well as
the boat. It was therefore determined experimentally in the following way. In experiments
46_47 the towing force was O'l gr., and the velocity 4 cm. per second. According to
the diagrams on PI. VII, the acceleration was practically nil, and O'l gr. is consequently
the resistance at 4 cm. per second. In experiment 35 the towing force was 0'8 gr.; and
the diagram on PI. VII shows that the velocity increased from 2'5 to 5"5, that is by 3 cm.
per second, in 4 intervals of time. The mean velocity during the interval being 4 cm.
per second, the resistance to uniform motion was as before, O'l gr.; and the accelerating

1 Compare the treatise "On hydrometers and the surface-tension of liquids", by Fridtjof
Nansen. No. 10 of this report, p. 21.

2 L. c. p. 27. Lord Rayi.eigh, Phil. Mag., 5 Ser., v. XXX, p. 386.

NO. 15.] EXPERIMENTAL ERRORS AND CORRECTIONS. 89

force was consequently 0'8— 01 = 0'7 gr. As each interval of time is T09 seconds, the

acceleration was 3 / 4"36 = 0688 cm./sec. 2 = 0-00070 g. The virtual inertia of the boat is

consequently 0-7/00007 = 1000 gr„ which is 125 per cent of the boat's own weight.

Several such estimations gave between 110 and 130 per cent. I have used the mean, and

assumed the virtual inertia of each boat-model to be 120 per cent of its own weight.1

In the case of the large .PVa)»-inodel (weight 800 gr.) an acceleration of 1 cm./sec.

1*20X800
in one interval of time then corresponds to a force = . „,.;;„,,■ = 0'90 gr. In this wav,

P09X981

the values in the 8th column of the tables, are calculated. From the corrected resistances
given in the 9th column, the resistance-curves in the case of homogeneous water (Figs. 1—3,
PI. X), are calculated according to the formula

resistance = C, + C2 [velocity]2;
the constant term being necessary owing to the friction against the steering string. This
formula is in good agreement with all measurements at velocities below 15 cm. per second.
For higher velocities the differences between calculated and observed resistance, are greater
(up to 0'2 gr.), but this is of less importance because the range of velocities at which
dead-water resistance was measured, lies below 15 cm. per second. The curves for the small
JVam-models (Figs. 8 and 9, PI. VI) are not calculated, but are drawn evenly through
the separate points determined experimentally.

When the boat was moving in dead-water, its velocity periodically in-
creased and diminished (see pp. 67 seq.). In this case the only possible
way of applying the results, was to take the mean about which the velocity
seemed to oscillate, and assume the resistance at this velocity to be equal to
the towing force. These mean velocities are given in the 10th column of the
tables, and are represented on the diagrams PL VII — VIII, by a short hori-
zontal line on the left hand side of each diagram (see for instance diagrams
77 — 81, PL VII). When the towing-force was not near the maximum resi-
stance, the velocity-oscillations were quite regular, and the mean velocity could
then be determined very accurately. When, however, the towing-force was a
little below the maximum resistance only an uncertain determination, or no
determination at all, could be made of the velocity (see for instance, diagrams
81 and 82, PL VII. The upper left hand corner of the resistance-curves, could
therefore be drawn only approximately. See further the explanation of the
tables, p. 76.

To avoid the inconvient velocity-oscillations, I attempted to start the boat
with a smaller force and then, when it had reached its greatest velocity, to
increase the towing-force approximately so as to keep this velocity uniform.

1 This is the same ratio which is given by Fronde for full-sized ships. See p. 489 in
White 1. c. p. 33, where this quantity — 120 per cent of a ship's weight — is called
her "virtual weight".

12

90 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

The necessary arrangements were made very simply, and worked satisfactorily ;
nevertheless, the method was not successful. The oscillations were somewhat
diminished, but they were on the other hand less regular than before, and
the estimation of the mean velocity was therefore more difficult and less
reliable (see diagrams 62—64 and 90—94, PI. VII-VIII). This method
was therefore soon given up and a constant towing-force used during the
whole experiment. Only when the towing-force was very small, was a
small extra starting-force used.

Special attention was paid to the determination of the maximum resi-
stance. As was pointed out on p. 75, this may be defined in two different
ways: either as the greatest resistance which the boat would experience at
any steady speed (below the maximum wave-velocity) ; or as the greatest
constant towing-force not able to bring the boat beyond that velocity, when
starting from rest. Theoretically, the former definition would offer the greatest
interest; but it would be very difficult to measure this maximum resistance.
A towing apparatus arranged for different uniform velocities and combined
with a sensitive dynamometer, would be required for that purpose; and further
a much longer tank, than that I had, would be a necessity, because the resi-
stance in the neighbourhood of the maximum, increases very slowly up to its
final value (see p. 73). The maximum resistance defined in the latter way,
is comparatively easy to measure; and it is also of more practical interest
than the former. The maximum resistance according to the former definition,
is equal to the propelling force which a vessel must have, so as to be never
troubled by dead-water; according to the latter definition, on the other hand,
it gives the propelling force which a vessel must have to get rid of the
dead-water (by simply stopping for a while and then making head-way again),
if she be accidentally caught by it. In either case, the maximum resistance
is physically a just as strictly defined quantity, and the rules in Chap. II, E,
are obviously applicable to it. For all these reasons, I have desisted from
determining the maximum resistance at steady speed and have kept to the
latter of the above mentioned definitions.

The maximum resistance was therefore determined by towing the boat
repeatedly with gradually increased towing-forces. Take as an example the
experiments 77—84 (spec. gr. of salt-water 1'032; depth of fresh-water 5 cm.).
With a towing force of 2'2 gr. (exp. 82) the boat was held in dead-water.

no. 15.] EXPERIMENTAL ERRORS AND CORRECTIONS. 91

since the velocity increased to a maximum and then diminished again. With
a towing force of 2'3 gr. (exp. 83), the velocity is accelerated more and more
slowly up to 10-5 cm. per second, and then the acceleration begins to in-
crease; which shows that the resistance was greatest at a speed of 105 cm.
per second and diminished again with further increasing velocity. The boat had
consequently got rid of the dead-water, and it is concluded that the maximum-
resistance is between 2-2 and 2-3 gr. For a more exact approximation, the
acceleration of the boat was taken into account in the following way. In
experiment 83 the velocity increased, when the acceleration was a minimum,
with about 0-12 cm. /second per time-interval, which corresponds to an acce-
lerating force of 01 gr. The greatest resistance during the whole of this
experiment was consequently 2'3 — 01 = 2*2 gr. But it should obviously have
grown larger if the towing force had had any value between 2-2 and 2-3 gr. ;
and it should have attained its greatest possible value, if the minimum acce-
leration had been nil, i. e. if the towing-force had been equal to the "maximum-
resistance". The "maximum-resistance" is therefore assumed to be the mean of
the towing-force (2S gr.), and the greatest resistance during the experiment
(2.2 gr.), in this case 2.25 gr. This method, of approximation, has been
used in drawing all the resistance-curves ; and it seems to be confirmed when
applied to experiments with towing-forces exceeding the maximum-resistance
by different quantities.

If, at the beginning of an experiment, there were even slight waves in
the boundary, they might have disturbed the results by increasing or decreas-
ing the resistance at the critical moment (compare foot-note, p. 73). Although
it was necessary to wait rather a long time in between two experiments, for
the wave-motion to subside, it is possible that small errors in the determi-
nation of the maximum resistance are introduced on this account.

From experiment 82 we may on taking into account the retardation of
the boat, conclude, that the difference between the maximum resistance at steady
speed and the maximum resistance according to our definition, may be rather
considerable. When the velocity had dropped to 5 or 6 cm. /second, it
was retarded by 075 cm. /second in one time-interval, which indicates an excess
of resistance above the towing-force, of 075 X 0-90 = 0-67 gr. (see p. 89); the
resistance was consequently 2-2 + 0"67 = 2-87 gr. By subtracting the resist-
ance in homogeneous water (0-15 gr. at 5'5 cm. /second, see Fig. 1, PL X) we

92 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

get a dead-water resistance of 2*72 gr. ; while experiment 83 gave a maximum
resistance of 2-25 gr. at 10'6 cm./second and a dead-water resistance of
2-25 — 043 = 1*82 gr. only. It is not probable that the maximum dead-water
resistance at steady speed should be smaller than the greatest dead-water
resistance in an experiment such as 82; and it might consequently be expected
to be 50 per cent greater than the maximum dead-water resistance according
to our definition, or even more. In open water, where the waves spread more,
to the sides, the difference may however, be smaller (compare p. 73).

The above-mentioned attempts to give to the boat a more uniform motion
(pp. 89 — 90), were then, for one more reason unsuitable. For if the towing
force be increased gradually during the course of the experiment, the maxi-
mum resistance obtained, will have another, not definable, value between the
maximum resistances according to the two before mentioned definitions.

To determine a few points on the resistance-curve between the maximum-
resistance and minimum-resistance points a starting force greater than the
maximum resistance was used, and an attempt made to remove it when the
resistance was diminishing and just equal to the constant towing force (see for
example experiment 84). If the velocity was retarded, or continued to be
accelerated after the starting weight was lifted off, a corresponding correction
was applied to the resistance. It is apparent that these measurements could
not be but rough approximations, for the motion will be influenced by the
waves just before generated at a lower speed. They establish however, the
continuity of the resistance-curve and give an idea of its shape. Wilh regard
to the part of the resistance-curve beyond the minimum-resistance point, the
measurements are still more unreliable. I have for this part of the curve
supposed that the resistance is very nearly the same as in homogeneous water.

At the time of the experiments, I did not pay much attention to the
temperature of the water; and in the following applications I have for the

sake of simplity assumed the specific gravity S tfs of the fresh-water to be 1.

As the temperature in most cases, was below 15°, the differences of specific
gravity between fresh-water and salt-water, were as a rule, somewhat smaller
than here given, sometimes by more than 0-0005.

NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 93

E. EXPLANATION OF THE VARIOUS EFFECTS OF THE DEAD-WATER

PHENOMENON.

All the accounts of dead-water, received, agree that the phenomenon is
necessarily connected with the existence of a more or less fresh water-layer
on the top of the heavier sea-water. It is proved by theoretical and experi-
mental investigation above, that a vessel moving in such a place, creates waves
in the boundary between the two water-layers, and that on this account, very
marked effects on the speed of the vessel will occur; and it will be shown
below, that from the existence of such waves all essential effects and pecu-
liarities of the dead-water phenomenon can be very simply explained. In the
next section of this chapter it will, in addition, be shown that the resistance
and speed-reduction due to the wave-generation, is of just the proper order
of magnitude to explain the effects of the dead-water; so that the correctness
of the explanation may be regarded as completely substantiated.

If the surface-layer be running as a current on the top of the heavier
water below with a velocity of its own, this circumstance will be a contri-
butary cause to the loss of steering-power, which may however, often be
entirely due to the boundary-waves mentioned above, and quite independent
of such a surface-current.

Several very different theories — more or less impossible or insufficient — have been
put forward with the view of explaining dead-water; and it would be to no purpose to
criticise them all. One of them may however be mentioned, as it has recently been pu-
blished in a well-known journal (Annalen der Hydrographie und Maritimen Meteorologie,
1904, Heft. I; "Totwasser", von Kapt. H. Meyer). Kapt. Meyer mentions several cases
of dead-water which, as they refer to places from whence I had before only very scanty
information, are of great interest here, and I shall therefore permit myself to make
an abstract of them in a supplement at the end of this treatise. Finally, Kapt. Meyer
presents a detailed explanation of the phenomenon in its various aspects. He explains not
only the loss of steering but also the speed-reduction, as due to currents of different direc-
tion or velocity: since a ship is resisted by a very great force when moving in an athwart
direction, and moves easily, only in the direction of her keel-line, he concludes that she
must on the whole be difficult to move, if she stick in two currents of different directions
so that motion athwart through at least one of the water-layers, cannot be avoided. "Wenn
man bedenkt, dass ein schwimmendes Schiff vermoge seiner Bauart nur in seiner Kiel- oder
Liingsrichtung mit verhaltnismassig geringer Kraft durch das Wasser bewegt werden oder
solches durchschneiden kann, dagegen in seiner Dwars- oder Querrichtung nur mit grosser
Kraft in minimale Bewegung zu bringen ist, so wird es begreiflich, wie schwer es halten
muss, ein Schiff vorwarts zu bewegen, das in zwei wagerecht getrennte Wasserschichten
taucht, sofern beide nicht die gleiche Richtungsbewegung haben, es mithin keine derselben
in seiner Lfingsrichtung durchschneiden kann."

94 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

This conclusion would be correct if the resistance against a vessel were directed along
the same line as her velocity relative to the water. But just because the water offers a
greater resistance to the athwart motion than to the headway motion of the vessel, the
resistance will have a more athwart direction, if the vessel be moving obliquely through
the water; that component of the resistance which acts in the direction of the keel-line,
and opposes the vessel's head-way motion, will obviously be independent (or nearly inde-
pendent) of her athwart-motion or of a current impelling the vessel sideways. If Kapt.
Meyer's deduction were correct, it would also appear, that a sailing-vessel should be unable
to make head-way in a strong side-wind because the water makes a great resistance against
her leeway-drift. Likewise, the "otter-board" used for keeping a fishing-line with hooks
strained sideways from a moving boat, would not be able, in spite of the strain in the line,
to run up almost in a line with the vessel, as it actually does.

One more mistake in the same paper, may be pointed out, although it is not of the
same definite importance in estimating the value of the explanation given. Kapt. Meyer
distinguishes distinctly between two cases; viz. when the two water-layers move with dif-
ferent velocities but in the same direction, and when they move in different directions.
In the former case a vessel should not be essentially influenced by the currents when
moving in their common direction of velocity, but in the latter case the vessel must always
be impelled from the side, by one of the currents at least, in whatever direction she might
move. The latter is, however, not true, since there is always one direction in which both
currents have the same velocity component; and if heading perpendicularly to this direction,
the vessel will apparently be carried sideways with a velocity equal to that velocity-com-
ponent, and will cut the water at all levels in the direction of her keel-line. That a vessel
is able to cut both currents in the direction of her keel-line, is also clear, for the simple
reason that the case considered may be reduced to the case of a current moving on the
top of still water, by simply superposing on the whole system a velocity equal and opposite
to the velocity of the under-current.

The loss of speed; the sudden appearance ami disappearance of the
dead-water ; its apparent capriciousness.

The generation of boundary-waves and the consequent loss of speed proved
by the experiments, has been repeatedly pointed out above, and it is therefore
not necessary to further enter into this subject very closely. It is common
knowledge that a vessel when moving, under ordinary circumstances at a good
speed, creates appreciable waves in the surface, which contribute to the re-
sistance; and when she attains a certain higher speed depending on her di-
mensions, these waves and the resistance caused by them, increase so forcibly
as to practically restrict the vessel's speed to within this limit. In shallow
water there will be a corresponding limit, which as shown by Scott Russell
(see pp. 38 seq.), is comparatively low, and is determined by the depth of the
water. If the vessel's velocity is raised above this limit (which is the maxi-
mum wave-velocity) the waves practically disappear and the resistance corres-
pondingly diminishes. The case of dead-water is quite analogous. But the
boundary-waves causing it, arise at a much slower velocity than do the

NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 95

surface- waves, and also disappear at a much slower velocity than these latter;
and this is the reason why the velocity is so considerably reduced by the
dead-water, whenever it is upon the whole, influenced by it.

The physical reason why the waves in the boundary are created, and
the way in which they are able to exert resistance upon the vessel, have
been explained above, from different points of view (see particularly pp. 66 — 67).
Here it may be sufficient to keep to the two facts that the vessel generates
waves in the boundary, and that they (owing to the energy required for
their maintenance) cause resistance. As far as other details are concerned,
the explanation may be based upon the resistance-curves and other experi-
mental results.

As was mentioned on pp. 60 — 61, curve (4) in Fig. 8, PL VI, shows that
the change of the boat's velocity from below to above the maximum wave-
velocity (and vice versa) must always take place suddenly. And as the ne-
cessary condition for the generation of large boundary-waves, and ipse facto
for all the effects of the dead-water, is, that the vessel move at below the
maximum wave-velocity, the same resistance-curve involves the explanation of
the fact that the dead-water always appears and disappears suddenly. This
matter may hre more explicitly slated; and for that purpose it is convenient
to alter the units of velocity and resistance in Fig. 8, PI. VI, to refer to a case
more similar to that of full-sized ships. If we e. g., imagine the velocities
to be given in decimetres per second and the resistances in tons, instead of
in cm. per second and grammes respectively, it follows from Froude's rule
(pp. 51 and 53) that the curves in Fig. 8, PI. VI, refer to a vessel of one
hundred times the size of the model used in the experiments, i. e. a vessel of
the same shape as the "Fram" but of half her size. The depths of the
water-layers must at the same time be imagined to be as many metres as
they were centimetres in the actual experiments.

Suppose, for example, this vessel to sail — in open sea-water of ample
depth — before a fair breeze giving her a speed of 14 dm. per second (2"8
knots). According to curve (1), the propelling force should then be 0-24 ton.
Now suppose that the vessel reaches a place where the sea-water (of spec,
gravity P03) is covered with a 2 m. thick, layer of fresh-water. Curve (4)
referring to this case, shows that the speed of the vessel will be hardly appre-

96 EKMAN. ON DEAD-WATER. [norw. pol. exp.

ciably altered (from 14 to 13.8 dm. per second)1, and the change of water has
no effect on the vessel. If now the wind gradually slackens, the velocity of
the vessel diminishes slightly more than it would have done under ordinary
circumstances (because the vessel must to a greater and greater extent generate
diverging boundary-waves), and is 12 dm. per second, when the propelling
force has fallen to 021 ton. But if the wind slacken a very little more,
the velocity of the vessel drops right down to 4 3 dm. per second (0.86 knot);
the reason is that with decreasing velocity the resistance due to boundary-
waves begins to increase more than the frictional resistance decreases, and
particularly, when it has fallen below 7'3 dm. per second, large transverse
boundary-waves are created and contribute towards the resistance — the vessel
has taken dead-water. If the wind now recovers its initial strength, the
only effect is that the vessel has her velocity increased a little (to 4'7 dm.
per second), but she still lies in dead-water, and consumes her energy of
propulsion upon large boundary-waves. Only if the wind freshens still
more, so that the propelling force gets the better of the maximum resistance
0'29 ton, is her velocity at once increased from 6 to 15'6 dm. per second
(full 3 knots); and the large boundary-waves simultaneously disappear —
the vessel has got free from the dead-water.

A vessel may evidently get into dead-water or get rid of it, even if the
wind is not altering. The vessel may for instance move in a brackish surface-
layer on the top of salt water, at a speed at which she is still insensible to
dead-water. If the vessel enters a more and more fresh, surface-layer, or if
the thickness of the latter alters suitably, its effect upon the resistance is in-
creased (as will be shown in the next section of this chapter), and particularly,
the maximum resistance represented by the top point of the resistance-curve
and the minimum resistance at a somewhat higher velocity, are increased.
When the minimum resistance (which in the above example was 0"21 ton) is
large enough to get the better of the force of propulsion, the velocity is at

For the sake of simplicity, it is supposed for the present, that the curves in Fig. 8,
PI. VI, are exactly correct, although their determination (as well as the applicability
of Froude's rule) was to a great extent only approximate. Especially is it assumed,
that the resistance is always the same at the same velocity, although it actually de-
pends also on the manner in which the vessel is set in motion (see p. 75). The
errors which these suppositions involve, are of no importance, as far as our present
qualitative discussion is concerned.

NO. 15.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 97

once retarded, and the vessel is caught by dead-water. Independently of whether
it is the water-layers or the propelling-force which is changed, it will have
no peculiar effect on the speed of the vessel, until the propelling-force is
equal to the minimum or the maximum resistance; but then the vessel with
a sudden change of velocity, falls into dead-water or gets rid of it, as the
case may be. This obviously explains the fact lhat as a rule, only sailing
vessels and towed ships are liable to dead-water; the propelling force of a
steamer being in most cases sufficient to get over the maximum resistance.
It also explains the experience of sailors, that they (at a given place and at
a given season etc.) are safe from dead-water when going at above a certain
speed; because the vessel's speed is a measure of her force of propulsion.

Keeping to our first example (Fig. 8, PL VI, curve 4), suppose the vessel
to move — under sail or steam -- at a speed of 14 dm. per second. If the
vessel- accidentally — for example by currents or dining a manoeuvre — has
her speed reduced to somewhat less than 9 dm. per second, oidy for a few
moments, the resistance becomes increased, the velocity is further decreased
to 4'6 dm. per second, and the vessel is then in dead-water. This explains
why vessels, according to the experience of several sailors, are most liable to
dead-water when making turns in their course or as a consequence of bad
steering. It also explains the capriciousness with which the dead-water some-
times seems to occur. Indeed, it is often a matter of mere chance whether
waves, manoeuvres, changes in the wind, etc., conspire together unfavourably
or favourably — in other words so as to bring a vessel into dead-water or
out of it. Currents in the surface-layer depending on boundary-waves1 may
especially be one of the causes affecting the speed (see foot-note, p. 73).
One vessel may therefore fall into dead-water, while another quite similar, or
a worse vessel, goes past her a short distance away without experiencing any
trouble at all.

The appearance of the sea-surface.
The various descriptions in chapter I, of the appearance of the sea-surface,
do not agree with oneanother, in all their details. A close agreement was

These may have been created by other vessels in dead-water, or by various other
causes, as for example by the motion of one water-layer above another just as a wind
affects the water-surface, or by accidental or periodic motions at sea reaching the mouth
of a fjord covered with a layer of light surface-water.

13

98 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

indeed hardly to be expected, and all the more, because the observations were
made casually, and, in most cases, without any intention of afterwards giving an
accurate description of them. Nevertheless, as far as their main features are con-
cerned, they may all be explained from the boundary-waves which have been
studied above, theoretically and experimentally. Wind, currents, and other
circumstances vary in many ways, and may, as will be explained below, also
account for variations in the appearance of the phenomenon.

Dr. Nansen observed, when he was steering in dead-water off Taimur,
very low waves following on the sea-surface, to the sides of the vessel and
in her wake (see Fig. 1, PI. IV). These waves are evidently the low surface-
waves, (see pp. 42 and 65 — 66), which are a secondary effect of the waves in
the boundary between salt and fresh water. Their crest-lines should then follow
the lines of the boundary-waves ; and indeed, it is not difficult to recognize the
shape of these on the sketch, Fig. 1, PI. IV. (See further below). The height
of the waves is also not in contradiction to this explanation. The photo-
graphs, Figs. 2 — 3, PI. XV and XVI — illustrating cases, which must have
been similar to that off Taimur — show boundary-waves of 2 or 3 millimetres'
height; or if allowance be made for the exaggeration of the wave-height on
account of the oblique reflection of the waves against the walls of the tank,
1*5 or 2 mm. at least. As the vessel on these photographs, is on the scale
1 : 1 000, it is very probable, that the Fram may have been followed by
boundary -waves of 1*5 or 2 metres' height from hollow to crest. The difference
of specific gravity between the two water-layers was supposed to have been
about 002, and the height of the surface-waves would then, according to for-
mula (2) p. 42, be nearly 0'02 of the boundary-waves, that is 3 or 4 cm. I
have observed that waves of such heights and of 10 metres' length or even
more, may be perceived without any difficulty, in smooth water.

It is not very extraordinary, that the above mentioned long and low waves
have not been observed on any other occasion. Indeed, they will probably
escape one's attention it the sea is even moderately rippled by the wind ; and
in a very slight wind, the dead-water waves created will, as far as sailing-
vessels are concerned, be too low for them to be observed in the water-surface.

Several narrators have seen two or more stripes on the sea-surface,
stretching obliquely abaft of the vessel or across her wake. They are de-
scribed in different ways — as streaks of hopping wavelets (accounts Nos. 3

NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 99

and 5) or as "rips" or paths in the water, resembling the boundary lines between
currents of different velocities or directions. To explain these observations, it
is sufficient to remember that the boundary-waves already mentioned, essen-
tially consist in veritable currents, running alternately here in the one and
there in the other direction in the shallow surface-layer. Along the slopes of
the waves, there will consequently be boundary-lines, where the currents en-
counter and part from each other: at the former places the wavelets in the
surface become short and steep (hopping); on the other hand, wherever the
surface-currents issue in opposite directions, the surface, owing to the rising
water, is smooth and unrippled or else has a whirling appearance.

According to this explanation, the shape of the stripes should be the
same as that of the crest-lines of the boundary-waves. To judge from the
experiments, the boundary-waves are very high only in the case when the
vessel generating them, has a speed somewhat below their maximum velocity
(2/3 of it, or more); and in this case their crest-lines are more extended to the
sides [as e. g. in Fig. 4, PI. V, see p. 48], than are ordinary ship-waves. It
might therefore be expected that the shape of the dead-water stripes should,
whenever they have been very noticeable, have been something like this figure.
For reasons which have been already mentioned, it cannot however be expected
that the descriptions of the dead-water stripes should completely agree with one
another, or that they should be in all their details reliable. If we therefore
make allowance for some discrepancies, we recognize on the whole, a remark-
able similarity between the sketches of the stripes (PL IV), and of the lines
in Fig. 4, PI. V. This is particularly true in the case of Figs. 1 and 6,
PI. IV and even of Fig. 5, PI. IV; the stripes in Fig. 8, PI. IV apparently
follow the transverse waves, while in Figs. 9—15, PI. IV they seem to in-
dicate a couple of diverging waves1.

It seems remarkable that in some cases the transverse waves (stripes)
are seen, and in other cases the diverging one's. The reason probably is
that the propelling force of the vessel — and consequently her velocity — has
been comparatively greater in the former cases than in the latter. It is proved
by the experiments, as well as by calculations of which a summary will be

1 It may be added that most of the narrators had no information on the explanation
here given; and in the case of all the sketches and descriptions it is impossible, that
they could have been influenced by a knowledge of this explanation.

100 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

given in an appendix below, that the transverse waves, very small at lower
velocities, increase forcibly by accumulation, when the vessel's velocity ap-
proaches the maximum wave-velocity. The reason of this is that much the
greater part of their energy is then transmitted with the same speed as the
waves and the vessel herself. The diverging waves will not be exaggerated
to a similar degree, at velocities approaching the above-mentioned critical
velocity, because even at this velocity, a fraction only of their energy, is
transmitted in the direction of the vessel's motion (see p. 37). The transverse
stripes, generated by the transverse waves, may therefore at these compara-
tively high velocities be more distinctly seen than the diverging stripes. At
lower velocities the diverging waves are more comparable in height with the
transverse waves, and it is obvious that in this case particularly the headmost
couple of diverging stripes should appear more distinctly than the other stripes;
because the water inside it. is owing to the boundary-waves, a mass of
oscillating currents which prevent the wind-ripples forming, and the headmost
stripes form the boundary between this unrippled, whirling area, and the area
outside it, which is rippled by the breeze (compare the description in the last
paragraph but one, on p. 20, as well as Fig. 1, PI. V). Quite in accordance
with this explanation, is the observation of Mr. Eriksen (Account No. 8)
that a couple of diverging stripes are seen when the wind is very slight,
but transverse stripes when the wind freshens a little. Some details in account
No. 7 (at the bottom of p. 16) probably point to the same facts as these ob-
servations of Mr. Eriksen.

That the dead-water stripes really indicate waves in the boundary be-
tween salt-water and the lighter surface-water, is directly proved by an obser-
vation of Mr. G. A. Larsen (p. 14): when a vessel in dead-water has passed a
moored vessel, the latter is pushed backwards and forwards, as she is reached by
the stripes, one after the other. This shows that the water is really oscillating,
and the wave-length would, in consequence of statements given on p. 14, be
equal to twice1 the distance between two stripes. It cannot be a case of
ordinary surface-waves, because with this wave-length, they would have an

1 If the wave-length were equal to twice the distance between two stripes, it might be
expected that each second stripe would have a different appearance to the others.
Mr. Larsen says nothing about this, and 1 am not able to decide in what respect the
description might possibly be incorrect, or its explanation incomplete. It is not
improbable that the apparent disagreement depends on the phenomenon being different

NO. is.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 1M

incomparably greater velocity than a vessel in dead-water; and the only possible
explanation is therefore, that the oscillations depend upon boundary-waves.

There is another observation (see account No. 8), which is in remarkable
accordance with the above explanation of the dead-water stripes: they draw
nearer to the vessel or farther off, according as her speed is slowered or in-
creased. The reason is that the wave-length must be increased at the same
moment as the vessel's speed (compare pp. 35—36), i. e. the distances from
the vessel to the wave-crests, grow longer. It is further mentioned, that the
stripes remain on the water, when the vessel has got rid of the dead-water
and is sailing from them; it is obvious that it should be so, if the stripes
depend upon waves which continue to move at their own velocity even after
the force generating them has ceased to operate.

Several observations, although described in different ways, obviously refer
to the above mentioned dead-water stripes. For example: "a system of sharply
defined, but small waves generated on each side of the vessel" (account No. 5;
Fig. 11 PI. IV); "a number of small whirl-pools (eddies) are seen in the
boundary between the 'ice-floe' and the water outside it" (account No. 7);
"the ship was followed by two sharply defined wakes, the one slightly curved
to the port side and the other more strongly bent to starboard" (account
No. 13). Perhaps the following descriptions also indicate dead-water stripes:
"A line of distinction can often be observed between the dead-water round
the ship and the 'living water' outside" (account No. 9); "the water round the
ship was somewhat stripey" (account No. 11); "it was as if a floating spar
were lying fair across the vessel's stem" (account No. 37); "I saw a long
stripe stretching from the bow far over the water on each side, dividing the
water into two parts etc." (account No. 38). In the last-mentioned case it is
said that the vessel (30 m. long) required 5 or 6 minutes to pass by the stripe,
which would hardly be possible if the stripe had been fixed in space; on
the other hand it might have been a couple of dead-water stripes which
gradually dropped astern, when the vessel got rid of the dead-water.

It often happens that the dead-water stripes are asymmetrically
arranged or that one stripe only, is seen to the one or to the other side

under different circumstances, such as different depth of the surface-layer, and so on.
It would however, lead far beyond reasonable limits, if I were to try to thoroughly
clear up this and several similar details.

102 EKMAN. ON DEAD- WATER. [norw. POL. EXP.

of the vessel (see Figs. 12, 14, 9, 13, PI. IV). Such irregularities are, however,
very easily explained, and the explanation is, in most cases, already given
in the accounts. The stripe to the windward side, might possibly be invisible
owing to the effect of rather strong wind-ripples (compare account No. 8),
although under different circumstances, if for instance the boundary-waves
are larger, the ripples may only have the effect of making the stripes more
apparent owing to the contrast between the smooth area inside the stripe and
the ripples outside it. If the vessel is sailing in a shallow fresh-water surface-
current and reaches right down into the still salt-water below, the surface-water
will run past the vessel with a certain velocity. (That such shallow surface-
currents exist in the Kattegat, was directly proved in the case reported by Count
Hamilton, account No. 14). The motion of the stripes (boundary-waves) relative
to the vessel, is then a resultant of their own velocity through the surface-water,
and the velocity of the latter past the vessel; and in consequence, the stripes
will be bent in the direction of the surface-current. This was apparently the
case in the accident described by Mr. Sidner (account No. 13). It might
perhaps be questioned whether this accident was not an effect of the surface-
current only, but the two stripes ("wakes") issuing from the stern, and
indicating the diverging waves, are so characteristic of dead-water that there
is really little doubt about it. Neither should the current alone have had the
effect of retarding the speed of the vessel. When there is a surface-layer of
lighter water on the top of the heavier sea-water, the former is evidently very
often acted upon by other forces than the latter; it will in consequence run
as a distinct surface-current on the top of the sea-water, and it must there-
fore be expected that the dead-water phenomenon will often be modified by
surface-currents. When a vessel is sailing with the wind from the side, her
leeway-drift might sometimes have a similar effect, so as to give to the stripes
a direction more to windward (compare account No. 6 and Fig. 12 PI. IV).

The motion of the water around the vessel.

It is commonly observed that the water surrounding the stern of a vessel
in dead-water seems to follow the vessel; and this is apparently confirmed
by the fact, that if a small boat is in tow astern, it is sucked up to the
vessel and cannot be kept clear. These observations may, however, be ex-
plained as merely an effect of the above-mentioned boundary-waves; and the

no. 16.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 103

belief that the vessel drags along a bulk of surface-water, is certainly an
easily explained illusion.

As the boundary-waves follow the vessel, their wave-crests and wave-
hollows remain in an invariable position relative to the vessel. If the wave-
motion gives to the water at a particular spot a velocity with the vessel, it
would appear as though a bulk of water were being dragged along with her,
although it is really always a new mass of water which follows the vessel
for a short distance. It is exactly analogous to the case of a boat sailing
before the wind with just the same speed as a breaking wave at her side.
In the case of dead-water, on the other hand, the illusion will be more
complete, because the vessel moves at a slow velocity, and the waves causing
the motion of the water, are themselves not visible.

It only remains to be seen in what direction the surface-water around
the vessel will be moved, as a result of the wave-motion. From the photo-
graphs PI. XV — XVII there appears to be a wave-hollow (elevation of the
boundary) right around the stern, and if this were the case, the surface-water
itself, would have a sternward motion. The photographs Figs. 2 and 3 PI. XIII
— and still better, Fig. 2 PI. XII — however, show that there is really a wave-
crest immediately around the stern, but not very far to the sides of it. The
surface-ivater nearest to the stern would consequently move in the same
direction as the vessel. Its velocity would not, according to the theory of
the boundary-waves, be so great as the velocity of the waves themselves
i. e. of the vessel (see p. 45); but it will be increased by the suction of the
vessel's stern, and the water might therefore follow the vessel. The situation
of the boundary-waves relative to the vessel, also agrees very well with the
statement (p. 13) that the water is pushed before her stem and is running
astern along her sides, at an increased speed. The fact that the wash of a
tug does not encounter the bow of a towed vessel, but is pushed aside (p. 14),
is obviously a consequence of the forward motion of the water before the bow.

A few simple experiments were made in verification of the above conclu-
sions as to the motion around the stern. A small davit was fitted in such
a way to the stern of the boat (the large .Fram-model ; scale 1 : 100) that it
could be fixed in different positions. A small wooden bar was suspended
from the davit like a pendulum, and reached into the water; its inclination
then showed the velocity of the water relative to the vessel. In homogeneous

104 EKMAN. ON DEAD-WATER. [norw. pol.EXP.

water, the pendulum was always inclined aftwards, even when hanging as
near to the vessel as possible, and this shows that the water had a stern-
ward velocity or else had a forward motion slower than that of the vessel.
When the salt-water was covered with a layer of fresh-water and the boat
was moving in dead-water, the pendulum if suspended some distance out
from the vessel, was inclined aftwards; but if it hung just astern (within
2 or 3 cm. aft of the boat and within about 1 cm. of her median plane), the
pendulum was drawn in towards the boat, and was only occasionally repelled.
Observation of small particles of dust on the surface, gave the same result.
On both sides of the vessel the particles were carried aft past the vessel, but
immediately astern they followed her. A grain of dust was once noticed
which was carried aft past the vessel, and, when about 5 or 6 cm. astern,
was sucked in again towards, and continued to follow the vessel. The
phenomenon seemed to be analogous to that of the wake following just
astern of a vessel even under ordinary circumstances; but in the case of
dead-water this forward-moving wake is much more developed.

According to the above described experiments, the statements that the
water appears to be dragged with the vessel, may be supposed to be quite
correct; but the area within which the water really follows the vessel, is
probably not very wide. If the vessel has a stern broad and bluff, so as to
produce a heavy wake, we may expect this area to be comparatively wider
than in the case of the .Fram-model, with which the experiments were made.
In every case it might, according to the experiments, be sufficiently wide, for
a small boat towed astern, to be drawn up.

Those cases in which it is said that the vessel was partly or completely
surrounded by a wide expanse of water dragged along with her, I am inclined
to explain as due to an illusion. The accident described by Mr. Kroepelien
(p. 20; Fig. 1 PI. V) exemplifies this very well. Behind the two "rips"
stretching from the bows, the water is smooth and unrippled ; which is easily
explained by the dead-water waves steadily bringing up new quantities of
water to the surface. On looking at this large, smooth area steadily following
the vessel, and at the agitated boundary-lines between it and the water outside,
one might well believe that the whole bulk of water was moving through
the sea with the vessel. Such a mistake is so much the easier to make,
since the speed of the vesse through water, is very small; further, because

NO. 15.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 105

the water around the vessel's stern actually follows her, and because the
water in front of the "bulk" — just behind the two rips, which evidently
indicate wave-crests — has actually a forward-motion against the sea-water
outside, and thereby causes a roar. When it is said that the bulk of water,
which follows the vessel, comes nearer to or draws farther off from the vessel,
according as the wind slackens or increases, the real cause of this observa-
tion is obviously to be found in the corresponding changes of position of the
dead-water stripes.

When treating of the motion of the water behind the vessel, the oscillatory
movements observed by Mr. Larsen (see p. 14) should also be taken into account.
As has already been mentioned on p. 100, they are, however, a so obvious
consequence of the "dead-water waves", that no further explanation of them
is needed. Mr. Larsen's statement, that the moving effects of the dead-water
waves upon another vessel at her moorings, are greatest in the case of a ship
being towed down the river, can also be explained. The moving effect will
as a rule be greatest at the wave-crests, where the fresh-water is thickest,
because at the wave-hollows, a vessel of not too small a draught dips into
the salt-water below, which has a motion against that of the fresh-water and
consequently diminishes its effect. And the velocity of the fresh-water in a
wave-crest will be increased if the waves are travelling down river, and
vice versa if they are travelling up river.

The loss of steering.

The very common fact, that a vessel, when in dead-water, loses her
steering-power, finds its simple explanation in the above described motion of
the water around the stern. The fresh-water just around the rudder, moves
forward with the same velocity as the vessel, or even faster; the salt-water
just below, has perhaps a sternward velocity, but since the thickness of the
fresh-water is increased just around the rudder (i. e. it is a wave-crest there),
only a comparatively small part of the rudder is in the salt-water. A large
part of the rudder is consequently working in forward-moving water,
and that thoroughly explains why the power of the helm is lost, or at any
rate largely reduced.

The degree and the manner, in which the steering is affected in dead-
water, vary infinitely ; it is hardly necessary, and it would indeed require too

11

106 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

much space, to try to explain the particular effect upon the steering, in each
separate case reported. On the other hand it appears worth while to try to
show how the dead-water might affect the steering in the different ways
related in the accounts received, and consequently to show that these are not
in disagreement with the explanation of the phenomenon here given.

Screw-steamers do not lose their steering at all, because the screw throws
a jet of water astern, against which the rudder is able to work.

The steering of sailing-vessels may be affected in different degrees; in
some cases the vessel becomes quite unmanageable (see accounts Nos. 5, 6,
7, 8, 10), in others she can still be manoeuvred, but only with difficulty
(accounts Nos. 8, 9, 12, 38), again she may even have her steering-power
uneffected, while her speed is almost lost (account No. 11). These differences may
for instance, be explained as due to different thicknesses of the surface-layer; the
thinner the forward-moving surface-layer, the larger will be that part of the
rudder which reaches into the salt-water, and has its power unaffected. The
shape of the stern will very likely be of importance too, since the forward-
motion of the water will be a minimum if the lines of the stern are sharp
and fine. Finally, the dead-water may have a very marked effect upon the
steering, whenever the wind or current tends to turn the vessel round from
her course with great force; while it may be of no influence, if the vessel
be set to have no inclination to turn from her course into one or the other
direction. In this respect the difference of draught fore and aft, may often
be of great importance, as was pointed out by Mr. Colin Archer (p. 15).

Dead-water often causes a vessel to turn in one particular direction,
as for instance, when she runs up into the wind and lies with her sails shivering.
This is obviously only a consequence of the powerlessness of the helm; for
a vessel is usually, owing to the arrangement of her sails, liable to run up
into the wind, and she will succeed in doing so, when the power of the helm
from any cause becomes reduced.

In other cases a surface-current may cause similar effects, especially if
at the same time the steering-power is reduced by dead-water. If the fresh-
water is running on the top of the sea-water, as a surface-current somewhat
shallower than the draught of the vessel, this will be carried away in the
direction of the current, and the sea-water below, having another velocity,
will take hold of her keel. It might then take better hold of one end of the

NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 107

vessel than of the other — especially if she lies deeper aft than fore — and
would consequently endeavour to turn her in a particular direction. The ship
obviously ought to turn her stem in the direction of the surface-current, just
as Mr. Eriksen mentions (p. 18). In this way it is also possible to explain,
why a vessel in a particular case, could be manoeuvred as long as her course
was within the angle between two particular directions, while it was impossible
to bring her into a course beyond this angle (accounts Nos. 13 and 14); if
the surface-current, under-current, and wind combined, try to keep the vessel
in a certain direction of equilibrium, the power of the helm might be sufficient
to turn her only to within a certain angle to each side of this direction of
equilibrium.

If the surface-current is strong enough, it may, of course, have a similar
effect upon the steering, even if the power of the helm be not reduced by
dead-water. When the steering is influenced, although the ship keeps
her ordinary speed — as Mr. Eriksen mentions (p. 18) is sometimes the case
in the Kattegat — the cause is certainly a surface-current and not dead-
water. It might therefore be possible, that the accident in account No. 14,
depended on a surface-current only — especially as no effect upon the vessel,
except on the steering, is mentioned. The only circumstance, in this case,
which is very characteristic for dead-water and which makes it probable that
this has been the cause of the phenomenon, is that the steering was lost
suddenly when the sail-area was diminished, and was not regained when
the sails were set again.

The sudden effect produced by the stopping of the engine,

It was noticed that the Fram, when in dead-water, stopped dead
when the engine was stopped — in one or two or even in only half a
ship's-length (see pp. 10, 11, 12), and she even seemed to be sucked back
again. Mr. G. A. Larsen has noticed the same thing when towing lighters
at the mouths of the Glommen River. According to him, the lighter stops
short, and then moves alternately backwards and forwards several times as
the "dead-water stripes" pass by, when the engine of the tug is stopped
(see p. 14).

Although the explanation of these phenomena is, in reality, very simple,
I nevertheless made a few experiments in verification. The larger of the

108 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

two .Fram-models, was dragged through the tank by means of a constant
towing weight. When it had gone half the length of the tank or more, I
simply took the towing-string with my fingers, and held it steadily slack.
The results of these experiments were, on the whole, in accordance with the
above mentioned observations; in homogeneous water the boat stopped
gradually, moving some boat-lengths, after the towing-string had been slack-
ened, while in "dead-water" it moved only a few centimetres. In the latter
case the motion was furthermore not constantly the same; sometimes the
boat stopped short, sometimes it lost its speed more gradually, and then
began to sway several times, first forwards and then backwards, as the
waves passed it; sometimes the motion was modified in other ways.

The explanation of the phenomenon is quite simple with the help of a
concrete case. Imagine the Fram moving, first under ordinary circumstances
and in another case in dead-water. As will be mentioned in the next section
of this chapter, the propelling force of her engine is about 1000 kgr. (or more
correctly 1000 g kgr. X cnl- X second ~2, g being the acceleration due to
gravity); this is therefore, in both cases, the resistance experienced by the
vessel when moving at full pressure. Her inertia is about 1000000 kgr.,
when the influence of the surrounding mass of water is taken into account
(see the next section of this chapter). When the engine is stopped, the
resistance is the only force influencing the vessel; she will therefore have a
retardation of 1000 gl 1000000= 1 cm. X second ~2. I. e.\ in each second,
her velocity will be diminished by 1 cm. / second. Under ordinary circum-
stances (in homogeneous water) the Fram had a speed of at least 4 knots,
or 200 cm. / second. If her resistance were invariably 1 000 kgr., this speed
would then be completely lost in 200 seconds, and the space covered by the
vessel in this time would be 20000 cm. or 200 m. The resistance in reality
decreases very nearly as the square of the velocity; and supposing this law
to be exact, it would be found that 200 seconds after the engine had stopped,
the vessel would still have half her original velocity and would have in the
meantime moved 277 m. In dead-water, her speed was about l-2 knots, or
only 60 cm. / second. The retarding force is, however, the same as in the
former case; the ship would therefore lose her speed in 60 seconds, and in
this time she would have moved only 1800 cm. or half a ship's-length. It
must be remarked, that in this case, in opposition to the former case, the

NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 109

resistance does not decrease correspondingly with the velocity of the vessel
since it is chiefly due to wave-making and only to a very small extent to
friction. The wave-making resistance depends on the size of the boun-
dary-waves and their position relative to the vessel (see p. 74); and as the
vessel stops very quickly, the boundary-waves, owing to their great length
and slow speed, do not alter their position relative to the vessel, very
much during this time: The resistance might consequently, in a particular
case, persist even after the velocity is completely lost, and this explains the
observation made on the Fram, that the ship was sucked back again.
This result, namely that the Fram when in dead-water, should lose her speed
after going a distance of about 18 m., agrees remarkably well with the
observations at Taimur and at Bergen.

If the vessel moves in dead-water in a narrow channel, she will, as shown
by the experiments, be followed by a long train of transverse boundary-waves.
When she has stopped, she will be overtaken by these waves and will swing
to and fro under their action, just as was observed by Mr. G. A. Larsen.
It is here of interest to notice, that Mr. Larsen's experience is derived princip-
ally from working on rivers, where the conditions are more favourable for
the formation of transverse waves. In open water, the transverse waves, by
spreading to the sides, diminish more rapidly in size at a distance from the
vessel; and this is probably the reason why similar swingings were not
observed in the case of the Fram.

The varying ways in which the boat moved in the different experiments,
obviously depend upon the velocity-oscillations, described on pp. 67 seq. The
velocity of the boat and the height and the position of the waves relative to
the vessel, continually change from one instance to another. As the experi-
ments were not all made in exactly the same way, the values of these
quantities — and consequently of the resistance — at the instant at which
the towing force was annulled, may therefore have been different in different
cases. It is obvious that this accounts for the differences mentioned. I have
given reasons for supposing that the velocity-oscillations are on the open
sea, always very small; the effect of the dead-water on a vessel, when
her engine, is stopped, should therefore be less variable than in the
experiments.

110 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

According to Mr. G. A. Larsen, the dead-water stripes may, in particular
cases, repeatedly disappear and recur again. This may possibly depend on
velocity-oscillations, and as a matter of fact, Mr. Larsen derives his experi-
ence chiefly from towing on a river, where owing to the narrowness of the
waterway, these oscillations would be greater than on the open sea.

How to get free of the dead-water.

The principal hindrance caused by the dead-water is, as far as steamers
and towed ships are concerned, the loss of speed; while in the case of sailing
vessels, the loss of steering is a still greater trouble.

To get a steamer or a towed ship free from dead-water, the point to
aim at then, is to regain her speed. Practical experience seems to have
discovered just the best possible means of accomplishing this (see the bottom
of p. 7), although they have not all been so successfully explained. The
simplest way, which also has the advantage that it is practicable for steamers
as well as for towed vessels, is just to stop for a while and then after the
boundary-waves have disappeared, to suddenly go full speed ahead again.
It is shown (pp. 75 and 91 — 92) that a considerably smaller force may be
sufficient to get a vessel free from dead-water when she is starting from rest,
than when she is moving at a gradually increasing speed; and there is there-
fore a good chance of succeeding in this way. If necessary, the manoeuvre
may be repeated, at suitably chosen intervals. It is said that vessels
towed in dead-water have sometimes got free after having run aground
(p. 13). Very possibly the simple stopping is the explanation of this, with
perhaps the addition of the fact that the steam was at top pressure when
the vessel at length got off. But the desired result might have had another
important origin, which will be mentioned below.

Several means tried with the object of getting free from the dead-water
seem calculated to mix the fresh surface-layer with the salt water below.
Tug-masters for example sometimes take their tug to and fro along the sides
of the towed ship and then make full speed again; or they will shorten the
tow-rope so that the screw can stir up the water around the vessel in tow.
It will however be shown in the next section of this chapter, that the reduction
of the dead-water resistance caused by a moderate mixing of the water-layers,
is very small; and to sufficiently affect the water layers in this matter of mixing,

NO. IB.] EXPLANATION OF THE DEAD-WATER PHENOMENON. Ill

must certainly be a long and difficult work. I am therefore inclined to explain the
effect of these methods as very largely to be ascribed simply to the fact that
the tug stopped for a while, when making the manoeuvre. The mixing may
in addition have been of some little use, and an even greater effect in reducing
the resistance might be ascribed to interference between the systems of waves
created by the tug and by the vessel towed, when the tow-rope is shortened.
The effect of any of the expedients given in the list on p. 7 in reducing the
resistance may certainly he regarded as nil, as far as the effectiveness depends
on the mixing of the water-layers.

It is said that a vessel sometimes gets loose from dead-water when passed
by a steamer (see accounts Nos. 8 and 13). So far as I can see, the only
possible explanation of this fact, is that the steamer has produced boundary-
waves which, on reaching the vessel, have diminished her resistance at a
favourable moment. It is however difficult to understand why a vessel not
in dead-water, should generate considerable boundary-waves; and altogether
these facts must be accounted among those not thoroughly explained, unless
we suppose they depended merely upon chance of some kind, or else that
the maximum resistance was very little more than the vessel's propelling force,
so that an exceedingly small start was sufficient to quite free her from the
dead-water.

There is another very interesting method of getting rid of the dead-water,
which may often be very useful, and which is also confirmed by experience
(see Kapt. Meyer's account from the Congo, in the supplement). It is this:
simply go as near as possible to the shore, where the vessel has only
very little water under her keel. If the fresh-water layer is nearly as deep
as the vessel, or deeper, the salt-water layer will then have a very small
thickness, (or none); according to equation (3) p. 43 the maximum wave-
velocity will then in any case be very small, and the vessel will in consequence
easily get rid of the dead-water and may steer from the shore again, if there
is no risk of falling into it once more. Even if the fresh-water layer is only
about half as deep as the vessel, the resistance will be reduced in the same
way ; partly owing to the diminished maximum wave-velocity, and partly because
the vessel's body when reaching from the surface above to the bottom
below, will give to the water particles a nearly horizontal motion and

112 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

so will not disturb the boundary1. It is clear that a vessel getting free
from dead-water after having run aground (see p. 13) might owe a good deal
to the simple fact that she was there in very shallow water.

It is obviously more difficult for a sailing vessel to get rid of the dead-
water. To stop and then to set all sail again suddenly, will hardly be possible
especially as the steering-power is lost. But by diminishing the effect of
the wind upon the sails to a minimum and then after a while increasing
it again as quickly as possible, it might nevertheless often be possible to get
free. If the wind-direction, the possibility of manoeuvring, and other circum-
stances allow, it would certainly be advantageous to steer inshore into as
shallow water as possible (see above).

There may be cases in which neither of these methods proves success-
ful or is available, and in which the vessel cannot be freed from dead-water.
It will in this case be a great advantage to be able to manoeuvre the
vessel, even if her speed be reduced. If there are no strong currents in the
water, this would as a rule be possible simply by using a rudder so situated
that the water surrounding it has a sternward motion or at least, does not
move with the vessel. It is shown, that aft of the stern, to the side of the
vesseVs midline, the water is running sternwards at a considerable rate ; and
the chances therefore appear very favourable that with an auxiliary
rudder or simply with an oar, in this region, the vessel can be steered
even in dead-water.

The occurrence of dead-water.

It follows from the experiments and their discussion in the next section
of this chapter, that the resistance due to the generation of boundary-waves,
may be considerable if the difference of specific gravity between the surface-
water and the sea-water below, be not too small, and if the former have a
thickness comparable to the draught of the vessel (between half and twice
as great, say). It is not essential that the transition from salt to fresh water

1 This is obvious, because the motion will then be symmetrical with regard to the
boundary; at any rate if the vessel has sides vertical from the water-line right to the
bottom. It would have been very interesting to have an experimental confirmation of
these points, but I did not think of this method of getting rid of the dead-water,
before the experiments were finished.

No. 16.1 EXPLANATION OF THE DEAD-WATER PHENOMENON. 113

should be very sharp, nor is the vessel's shape of any material importance.
It would therefore be expected, that dead-water occurs at about all places
where a considerable quantity of fresh-water Hows out over the sea.

The answers obtained in reply to an appeal published in foreign
newspapers (see p. 8) do not seem to agree with this conclusion. On the
contrary, it seems to follow from the replies that dead-water is very little
known except in Scandinavia ; and only in Norway is it of common occurrence.
Only a few cases of dead-water in other parts of the world e. g. in the
Mediterranean, the Congo River (see the Supplement), and off the Fraser
and Orinocco Rivers — have come to my notice. In addition, dead-water is, by
Norwegian seamen, said to occur on the Gulf of Mexico and off the St.
Lawrence and the great rivers of South America; and on the French rivers
Loire and Garonne, phenomena are known which possibly are due to
dead-water1. (See further Chapter I.)

To completely clear up this apparent contradiction, I neither have a sufficiently
complete and reliable knowledge of the actual distribution of the phenomenon,
nor am I well enough acquainted with the hydrographic conditions of the
coasts, and especially of the river-mouths, in different parts of the world. I
will therefore, only try to show here, how the above mentioned facts may
probably be explained.

There are three circumstances which must be considered, namely : the
conditions of formation of the water-layers, the kind of vessels navigating the
place concerned, and the seamen's attention to the phenomenon.

The formation of considerable fresh-water layers by rain-fall, may be
regarded as exceptional, and the melting of ice does not come into account
in this connection, outside the polar regions; the occurrence of dead-water,
must consequently be as a rule, restricted to places where rivers fall into the

It may be pointed out that in the case of Accounts No. 32 and 39—42, it cannot be
decided whether dead-water has been the cause of the accident, or not. They have
been inserted each on its own merits, because no other accounts from the particular
neighbourhoods concerned, were available. It is hardly necessary to point out that
the fact mentioned in No. 45 p. 32, might for instance just as well have been caused
by sludgy ice or some other circumstance resisting the vessels, as by reason of a
case of dead-water. On the other hand, it seems very likely that the cases under No. 43
and Account Nr. 44 refer to cases of dead-water — in the last two of these cases the
vessel had lost her headway almost entirely, and alter a while (when after having
stopped rowing, they began again?) she regained her speed.

15

114 EKMAN. ON DEAD-WATER, [norw. POL. EXP.

sea. According to Penck 1 estuaries are essentially of three kinds, which
he calls bar estuaries ("Barrenmiindungen") funnel estuaries ("Mi'indungs-
trichter"), and deltas. The funnel estuaries are formed hy strong tidal currents
which wash away the ground as far up the river as they reach. The
quantities of sea-water flowing up and down, at flood and ebb, in these
estuaries, are many times greater than the river-water carried by the river
itself. In very large and full rivers, the river-current is not stopped by the
rising tide, and the flood-current runs in as an under-current; if the river carries
less water, the direction of the current in the estuary, is determined by the
tide. In either case, the river-water and sea-water mix and give brackish
water in the estuary (Penck p. 501). Such places are obviously not favour-
able for the formation of dead-water. The tides have not had the same
erosive effect upon the two other kinds of river-mouths, which are instead
formed by the erosive or sedimentary effects of the river-water itself. The
channel must consequently be entirely filled up by the river-water; and the
particles carried with it, either settle down directly on the bottom or are
carried in again from the sea by an under-current of salt-water, to form a bar
which silts up the mouth. The river consequently falls directly into deep water.
If the mouth is on a straight coast or at a cape, there may often be no
conditions favourable for the formation of dead-water, for in such a case the
river-water may be either carried off by currents, or the water-layers may be
mixed as an effect of ocean waves. Only when the river falls into a deeper
estuary or cove, will its water have an opportunity of spreading out over the
sea as a distinct layer of gradually decreasing depth ; and at such a place
dead-water is most likely to occur. [This is the case for example with
Congo River and Outa River.] Even in such places, however, little or no
dead-water will be felt, if they are navigated chiefly by steamers, or by
vessels of a draught much greater or much smaller than the depth of the
surface layer.

In conclusion there are several circumstances necessary, to make the
conditions for dead-water really good ; and at a large number of river-mouths
these conditions are obviously not fulfilled.

1 Dr. Albrecht Penck. Morphologie der Ei-doberflilche. Stuttgart 1894. Zweiter Teil.
P. 497 seq.

NO. 15.] EXPLANATION OF THE DEAD-WATER PHENOMENON. 115

The long and deep Norwegian fjords with no strong tidal currents,
obviously offer excellent opportunities for the river-water to spread without
mixing as a layer of gradually diminishing thickness, on the top of the salt-
water. Furthermore, they are to a large extent navigated by sailing-vessels
(and some of them by towed lighters), which as already mentioned, are
particularly susceptible to the influence of dead-water. Norwegian seamen
therefore become well acquainted with the phenomenon and easily recognize
it when meeting it in foreign seas, as well as on their own waterways. On
the other hand, a man who meets it once or twice and has not heard of it
before, will not be likely immediately to think that he has to do with a quite
new and obscure phenomenon; but he will if possible, put it down to the
effect of simple and easily explainable causes, such as e. g. currents, whirlpools,
muddy water etc. This is so much the more plausible because in many
cases, someone or other of these cases has actually contributed its share to
the dead-water effect.

It is therefore probable from the seamen's accounts and the experimental
investigation conjointly, that dead-water occurs strongly and particularly often
in the Kattegat, the Norwegian fjords and in the arctic regions, as well as at
some river-mouths in different parts of the world, and that under favourable
circumstances it may occur everywhere where fresh-water flows out over the
sea. On looking through the collection of accounts of dead-water beyond
Scandinavia (in Chap. 1 and in the Supplement), it seems highly improbable
that they should supply a complete and correct representation of the geogra-
phical distribution of the phenomenon; on the contrary, the places mentioned
in this collection more probably represent just the few cases which have
by chance come under notice. It is to be expected that when the pheno-
menon has been more generally noticed, we shall soon get a fuller knowledge
of its occurrence in different parts of the world.

F. EMPIRICAL LAWS OF RESISTANCE IN DEAD-WATER.

Influence of the difference of spec, gravity between the water-layers;
the different causes of resistance.

Fig. 1 PI. XI shows different curves of resistance for the larger Fram-
model (1 : 100). The lowest curve refers to homogeneous water. The other

116 EKMAN. ON DEAD-WATER. [norw. pol. exp.

full-drawn curves apply to the case of a fresh-water layer af 5 cm. depth;
the specific gravity of the salt-water below, in each case (l'OlO — 1-160), is
given over each curve. The velocities of the boat-model, are plotted horizontally
in cm. per second, and the resistance to the boat, vertically in grammes. The
vertical distance between the lowest curve and one of the others, gives, for
the different velocities, the "dead-water resistance" in the case concerned.

As might be expected, the effect of the fresh-water layer is, upon
the whole greater, the greater the specific gravity of the salt-water below.
The exact relationship is very simple. In Chap. II (p. 52) it was shown
theoretically that if the difference of specific gravity between the upper
and the lower water-layer be increased y times, the wave-making re-
sistance against a vessel in dead-water, mill increase in the same ratio,
if at the same time her velocity be ]ly times increased. It was also shown
that the same rule holds approximately true for the frictional resistance. It
will be shown below, that the "dead-water resistance" depends chiefly on
wave-making, and only to a smaller extent on friction ; and the above rule
should therefore hold very nearly true for the entire dead-water resistance.
The experiments are in complete agreement with this rule; as is best seen
if it be applied to different series of experiments in reducing them all to the
case of a difference of spec, gravity equal to 0"030, say. For instance, the
series of experiments Nos. 133—137, 138-145, 85V2— 97, 77—85, 146—153,
154—164 (see the tables pp. 80 — 82), were all made in a 5 cm. deep fresh-
water layer, but the spec, gravity of the salt-water below was l'OlO, 1"020,
1-030, 1-032, 1-070, 1160 respectively. If then, in the 1st series the veloci-
ties be multiplied by V>3 and the corresponding dead-water resistances by 3,
in the 2nrl series, by V.3/2 and 3/2 respectively, in the 4th series by V3/3'2
and 3/3-2, and so on, and if resistance curves be drawn for each series of
reduced values, it will be found that they all coincide very nearly with
oneanotber, and the divergences themselves are chiefly of an experimental
character and not systematic. The maximum resistance does not differ in
any of the reduced curves by more than 0-2 gr., from that found by direct
experiments with salt-water of specific gravity T030. The agreement is just
as good when the series 58—71 and 126 — 132 are compared (fresh-water layer
3 cm.: spec, gravity of the salt-water 1-030 and 1180). Considering that the
specific gravity in these experiments, varied by as much as from 101 to l'16and

NO. 16.] EMPIRICAL LAWS OF RESISTANCE. 1 1 7

from 103 to 1'18, it is clear that for variations actually occurring on the sea,
the rule will hold almost exactly.

The curves in Fig. 1 PI. XI, show the remarkable fact, that within a
certain range of velocities, the resistance may be increased by diminishing
the difference of spec gravity between the two water-layers, and vice versa.
For instance, at a velocity of 7 cm. per second, a difference of spec. g. of
O030 gives a resistance of 1*8 gr., and a difference of spec. g. of 0160, 0'6
gr. only. The reason is evidently that in the latter case, the difference of
spec. g. was too great for the vessel to give rise to any appreciable waves
at that velocity; indeed in this case it was not possible from the side of the
tank, to detect the least disturbance in the boundary1, while at the same
velocity, and with a difference of spec. g. of 0"032, the waves were very
considerable (see PI. XVI Figs. 2 and 3)2. If the bottom-layer were mercury
instead of salt-water, the boat would generate practically no waves within
the range of velocities used in the experiments, and would move with just the
same resistance as if the boundary were replaced by a rigid bottom (the depth
of the surface-layer being more than the vessel's draught). When the spec,
g. of the salt-water is sufficiently increased, the resistance at a given velocity
will diminish towards this limit. The resistance-curve in 5 cm. of homogeneous
water should consequently be something like the dotted curve in Fig. 1 PI. XI
— or perhaps it should approximate somewhat more nearly, to the curve for
salt-water P160 — *. e. the resistance should be somewhat more than twice
the resistance in deep homogeneous water.

In conclusion, the resistance in "dead-water" may be subdivided in
various ways. The difference between the resistance in "dead-water" and in
homogeneous deep water, is the above mentioned "dead-water resistance".

1 In experiment 155, only very slight diverging waves could be seen through the clear
fresh-water from above. In experiment 157 they were very beautiful, and very low
transverse waves could also be detected although with difficulty. Only when the
velocity was at least 12 cm. per second (experiment 159), were the waves large enough
to be seen from the side of the tank.

2 The wave-making resistance might of course, increase, with the difference of spec,
gravity although the wave-height decreases; because the wave-energy is proportional
to the difference of spec gravity. The latter circumstance is however, insufficient to
balance the effect of the largely decreased wave-height. It follows from the rule p.
52 that the wave-making resistance (or the dead-water resistance) will increase with
decreasing difference of spec, gravity, if it increases according to some higher power
than the square, of the velocity; the curves in Fig. 1 PI. XI, show an actual increase
even equal to the sixth power of the velocity.

118 EKMAN. ON DEAD-WATER. [NORW. POL. EXP.

It is due to the wave-making as well as to the effect of shallowness. The
latter part of the resistance depends on the water's diminished passage past
the vessel; it is at the lowest velocities, approximately represented by the
vertical distance between the dotted curve and the lower continuous curve, in
Fig. 1 PI. XI. At higher velocities, it is smaller than this, and at velocities
greater than the maximum wave-velocity, it practically disappears altogether.
That it does so is obvious, because the entire dead-water resistance vanishes;
the physical reasons for it are indicated in Chap. II, p. 47. The resistance
represented by the dotted curve, may be called "shallow homogeneous-water
resistance". At below the critical velocity the resistance may be divided into
two parts, of which the one is approximately equal to the "shallow homoge-
neous-water resistance", and the other is the "wave-making resistance" due
to boundary-waves. According to the arguments brought forward in Chap.
II (p. 47), the resistance in homogeneous deep water, as well as the resistance
due to shallowness, depends partly on friction and partly on pressure, while
the wave-making resistance depends essentially only on the latter.

The relationship between the different curves in Fig. 1, PL XI, shows
clearly and conclusively that the greatest part of the dead-water resistance,
is due to wave-making. From the measurements of surface-disturbance (see
p. 66 and the diagrams PI. IX) we are able to approximately calculate the
pressure at different points. The pressure-resultants against the boat-model,
calculated in this way are in complete agreement with the above estimation
of the different parts of the resistance and their causes; and although this
calculation cannot be more than a first approximation, it may therefore be of
interest to cite it here.

The table on the next page contains the chief results of the measurements of surface-
disturbance. The experiments were made with the larger from-model. The numbers in
the 1st column, refer to the corresponding numbers of the diagrams in Fig. 3 PI. IX. The
2nd— 6th columns have the same signification as the 3rd— 7th columns in the tables p. 77.
The 7th column gives the final velocity, or if there were velocity-oscillations, the mean towards
which it approximated. The 8th column gives the greatest difference of level of the water-
surface, measured on the original drawings, which are copied in PI. IX.

If the waves were moving freely, solely on account of gravity and the inertia of the
water, it should be possible to calculate the ratio between the wave-heights at the surface
and in the boundary, according to equation (1) p. 42; in this case the moving forces are
concentrated in the neighbourhood of the salt-water fresh-water boundary. Actually how-
ever, the waves nearest to the vessel, are forced ; and the moving forces are to a certain
extent distributed over the vessel's surface, i. e. in the middle of the surface-layer. In
this case it is obvious that the corresponding equation for long waves (2, p. 42) gives a
better approximation ; the 9th column gives the greatest difference of level in the boundary,

NO. 15.]

EMPIRICAL LAWS OF RESISTANCE.

119

calculated in this way. Considering that the surface-disturbances must be measured some-
where in between the walls of the tank and the course of the vessel, these values agree
as well as could be expected, with the wave-heights shown by the photographs PI. XV—
XVI.

Starting

tn

Difference of

Pressure

09

"3 §

u 'C

| 1

a m

3 Oi

Water-layers

force

B
B

C

bo
t-<

iS

60

o
H

O

V

tn

a

_>;

o
>

* 1
•s .s

3

« a)

a, 2

<U 3

O .2

>

* a

b a

a 3

-a .a

3 ^

-a «
o _S
"£ "a
M °
3
X

surface-level

resultant

"a
w

° 5

U
0>

tn

.s

en

° "3

■£ &
"a.

O

05
0)

a
a

S

1*

60

W

u

<v

a

"S

0)

u

stem

to

stern

(b-i-b-4)

10 cm.

from
stem

to 10 cm.
from
stern

(h2-h3)

>
u

0)

to

Xk

o

73

"a
o

"3
o

1

_

37 cm.

2-5

40

10

17-0

0-15

0-15

o-ii

0-45

2

»

2-5

90

2-5

27-0

0-40

0-4

025

11

3

1-070

5'0 cm.

10

7-3

0-32

4-9

0-2

o-i

0-5

0-63

4

11

«

1-5

8-2

0-52

80

05

0-25

1-25

1-17

5

«

ii

2-0

8-6

0-77

11-8

0-65

0-3

1-6

1-64

6'

«

n

30

95

1-2 (?)

18(?)

0-9 (?)

0-45 (?)

2-25

2-56

72

»

n

4-5

70

3-0

27

0-49

7-5

(about nul)

8

1-030

30 cm.

10

5-2

0-60

21

0-4

0-17

0-75

0-81

9

n

n

1-5

7-6

094

32

06

03

1-2

1-12

The pressure-resultant against the boat-model, is calculated for its middle-body and for
its ends, separately. The calculation is made in the following way; the first line in the
table on the next page, gives the area of the midship-section of the boat model (below the
water-line), as well as those parts of it which lie above and below a level 3 cm. below
the water-surface, and the two lines following, give the means for the corresponding areas
at equal distances from the stem and the stern. From these areas, mean cross-sections
are calculated for the middle-body reckoned to 10 cm. from the ends, and for the rest of
the boat. The former numbers (A) and the latter (B), as well as the differences (A— B),
are given in the same table.

If the water-pressure in one horizontal plane, be pt at the stem, p2 10 cm. aft of
the stem, p, 10 cm. before the stern, and p4 at the stern, then the sternward pressure-
resultant R will be given approximately by

R = B (p, - p5 + p3 - Pi) + A (p2 - p3)
= B (p, - p4) + (A - B) (p2 - Pa). W

The values ofpt.po, p3, p4, have to be calculated from the surface-disturbances. As
was pointed out above, the moving forces are not concentrated only in the salt-water fresh-
water boundary, but are also distributed in the middle of the surface-layer; and the
formulae for the case of "long waves" (5 and 6, p. 44) therefore give better approximations

1 The disturbance of surface-level was greater than could be measured with the level-
gauge. The dotted part of diagram 6, is therefore hypothetical.

2 The diagram could not, in this experiment, be traced accurately enough, to permit of
a calculation of the pressure-resultant.

120

EKMAN. ON DEAD-WATER.

[NORW. POL. EXP.

than the exact formulae for free waves. As far as the pressure in the salt-water is
concerned, only a rough approximation is necessary, because the corresponding terms in
the expression for the resistance, become very small. Equation (5) p. 44 is used, as
well for homogeneous water as for a surface-layer. In all the formulae, g (the accelera-
tion due to gravity) may be thrown out, if gramme be used in its frequent sense of force.

Areas

of cross-sections

0-3 cm.

3—5 cm.

entire

below

below

surface

surface

36 cm.2

28 cm.2

8 cm.2

Mean of sections 10 cm. from stems

32 —

26 —

6 -

« j) n ** » >' »

17 —

15 —

2 -

Mean section of middle-body (A)

34 —

27 -

7 —

„ „ ,, the ends (B)

16 —

14 -

2 —

(A-B)

18 -

13 -

5 —

1) Homogeneous mater.

The values of B and (A - B) in (a) are to be taken from the first column in the
table above. If hl( ho, h3, h4, are the heights of the surface-level (in millimetres) at the
sections to which p,, p,, p3, p4 refer, (h2-h3)/10 and (hl-h1)/10 may be substituted
for (p2-p3) and (pi-p4). and (a) becomes

R = 1-6 (h, - h4) 4- 1-8 (h„ - h3) grammes (b).

2) Fresh-water layer 5 cm. deep.

The boat moves entirely in the fresh water. We have just as in the former case,
R = l-C(h1-h1) + l-S(h2-h3) (e).

3) Fresh-water layer 3 cm. deep.

The pressure of the fresh-water and of the salt-water, must be calculated separately,
according to formulae (5) and (6) p. 44. As the wave-length I is about 90 cm., Zml/l
may be put equal to 02. The values of B and (A - B) in the 2nd and 3rd columns of
the table above, are to be used. We then obtain

R = (1-4 -0-2X0-2) (11,-114) + (1-3- 0-2X0-5) (h2-ha)
= 1-36 (h , - hj + 1-2 (h, - h„) grammes (d).

The differences of level (h, - hj and (h2 - h3) are found in the 10th and 11th columns
of the table p. 119; the pressure resultant calculated according to one of the formulae (b),
(c), or (d), is given in the 12lh column.

The acceleration of the boat-model in the two first experiments, was inappreciable,
and the entire resistance was consequently equal to the towing-force. The numbers in
the 6th and 12th columns of the table p. 119, then show, that in homogeneous water,
about 45 per cent of the resistance was due to pressure, and only the other 55 per
cent to friction. Indeed a certain pressure is necessary to overcome the friction against
the water moving past the vessel astern; another part of the pressure-resultant is iden-
tical with the eddy-making resistance.

It is therefore assumed that even in dead-water 45 per cent of the resistance not due
to wave-making, depends on the pressure alone and that the rest is due to frictional
resistance. The pressure resultant would then be equal to the wave-making resistance plus

no. 15.] EMPIRICAL LAWS OF RESISTANCE. 121

45 per cent of the rest, or approximately, to the whole resistance less 55 per cent of the
shallow homogeneous-water resistance. The whole resistance may be assumed equal to the
towing force found in the 6th column of the table p. 119. The "shallow homogeneous-water
resistance" is, in experiments 3—6, easily found by means of the velocity given in the
table, and the dotted curve in Fig. 1 PI. XI. For experiments 8 and 9 it may be found
in the same way, if a curve corresponding to the dotted curve Fig. 1 PI. XI be drawn by
using the experiment 126—132. In that way, the pressure-resultants found in the 13th
column of the table p. 119 were calculated. They agree, as well as could be expected, with
the values in the 12th column, found from the observations of surface-disturbances. (It
may be pointed out here, that if in [he calculation of the former values the entire
resistance be not assumed equal to the towing force but be determined according to the
resistance-curves in Fig. 1 PI. XI and Fig. 1 PI. X, from the velocity, the agreement with
the values in the 12th column will be found almost exact). In this agreement we have a
sort of control upon the correctness of the explanation of the dead-water resistance.

The influence of the depth of the fresh-water layer.

Owing to the simple connection between the difference of spec, gravity
of the water-layers and the dead-water resistance, it was not necessary in
what follows to vary the specific gravity of the salt-water. This was therefore
the same in most of the experiments, namely l-030.

Fig. 1 PI. X shows the resistance-curves for the larger -FVaw-model in a
fresh-water layer of 1, 3, 5, 7, 9, and 13 centimetres' depth, as well as in
homogeneous water. The velocities are plotted horizontally in cm./second,
and the resistances vertically in grammes. The influence of the fresh-water layer
upon the resistance, decreases, as might a priori be expected, when its depth
becomes either very small or very great. It is (at most velocities) greatest,
when the fresh-water is 4 or 5 cm. deep ' , i. e. about the same as the draught
of the boat; a smaller as well as a deeper fresh-water layer causes a smaller
resistance. It is easy to find a plausible explanation of this latter fact. On
the one hand, the wave-making power of the boat, is smaller, the farther the
latter is from the boundary where the waves are generated, and on the other
hand, its wave-making power will be diminished, if it reaches into the salt-
water, since that part which is below the boundary and that above it, coun-
teract oneanother. Furthermore, if the depth of the surface-layer is small, it
will put a limit to the height of the waves which can be generated, and con-
sequently to the wave-making resistance.

To keep the figure clear, the curve for fresh-water 40 cm., is omitted. It may easily
be drawn from the numbers in the table (p. 79). The maximum resistance is found
to be 2'2 grammes.

16

122 EKMAN. ON DEAD-WATER. [norw. pol. exp.

It is often believed that the great resistance to a vessel in dead-water,
is felt only when the vessel reaches into the salt-water. This opinion, which is
not in accordance with the explanation of the phenomenon as an effect of
wave-generation, is not confirmed by the experiments. On the contrary, they
show that when the depth of the surface-layer is even twice as great as the
draught of the vessel, its effect upon the resistance is still very considerable,
the resistance being at certain velocities, four times as great as in homoge-
neous water, and the maximum resistance being only about 40 per cent smaller
than when the depth of the surface-layer is the same as the vessel's draught.
In the latter case its effect upon the resistance has its greatest value, as has
already been mentioned. On the other hand, the curves show, that when a
vessel pulled by a given force, is in dead-water, her velocity is, as a rule,
slowed down more, the thinner be the fresh-water layer.

It would be useless to try to express the above mentioned experimental
results as a mathematical formula, it is better to use them, as they are given
in the diagrams.

The resistance-curves in Fig. 1 PI. X clearly show their connection with
the maximum velocity of the boundary-waves. The latter quantity is represented
at the top of the figure, by a small circle containing a number indicating the
depth of the fresh-water layer in centimetres, and by a small pointer below in-
dicating the maximum wave-velocity. For instance, it is 5"35 cm./second in
the case of a 1 cm. fresh-water layer, 9'00 cm./second in the case of a 3 cm.
layer, and so on1. The velocity at which the dead-water resistance is a
maximum, cannot of course, be determined very accurately, although the
resistance-curves are drawn from the experiments as exactly as possible. Ac-
cording to the resistance curves, it is in most cases somewhat smaller than
the maximum wave-velocity; the ratio increases with decreasing depth of the
surface-layer, being 0-7 or 0"75 if this is 9 or 13 cm., 0*9 if it is 3 cm., and
even above unity if it is only 1 cm. When the depth of the surface-layer

1 The numbers are calculated according te equation (3) p. 43, and the finite depth of
the salt-water, is consequently taken into account. If the latter had been very deep,
the maximum wave-velocities would have been somewhat greater. The difference
would have been only 1 per cent for a 1 cm. surface-layer, but 7 per cent for a 5
cm. surface-layer and 20 per cent for a 13 cm. surface-layer. The relationship given
in Fig. 1 PI. X, between the resistance and the depth of the surface-layer, may there
fore be regarded as chiefly qualitative, as far as the greatest depths are concerned.

NO. 15.1 EMPIRICAL LAWS OF RESISTANCE. 123

was small, the boat however, generated a so called solitary wave, which on
account of its considerable height, may have had higher velocity than the cri-
tical velocity (3) p. 43. The velocity of solitary waves in shallow water is
given by the same formula as that of long waves of small amplitude, if the depth
of the water be only reckoned to the top of the wave (see foot note 1, p. 40).
Rough experiments indicated, as might be a priori, expected, that solitary
boundary-waves follow the same law. ff the maximum wave-velocity be cal-
culated in this way by measuring the depth of the surface-layer at the crest
of the solitary wave, it will be found that the velocity corresponding to the
maximum dead-water resistance, has a nearly constant ratio to it (about 0"73).
That this ratio remains unchanged when the difference of spec, gravity
between the water layers is varied, is a consequence of the rule on p. 52
and equation (3) p. 43, combined.

The influence of the sharpness of the boundary.

The actual conditions are in reality not so simple as they were arranged
in the experiments; the transition from heavy salt-water into light fresh-water
is in general not quite sharp, but is extended over a considerable region in
which the salinity decreases upwards. Experiments 165 — 184 pp. 82—83,
are intended to show the influence of this circumstance; and the results are
represented in Fig. 2 PI. XI.

The vertical distribution of spec, gravity in these experiments, is repre-
sented by accessory, step-shaped diagrams in the same figure. In Case (2),
for instance, the spec, gravity is 1*000 down to 4 cm. below the surface, 1*010
from 4 to 5 cm., l-020 from 5 to 6 cm., and 1*030 at 6 cm. below the sur-
face and down to the bottom. In both cases the water-layers may be ima-
gined as formed by the partial mixing of an originally fresh, water layer and
a bottom-water of spec, gravity 1*030. These imaginary, sharply defined
water-layers are represented on the diagrams by dotted curves (the spaces
between the dots are unfortunately too small, so that they look almost like
full-drawn curves). In Case (1) the mixing is very thorough, in Case (2) it is
less complete; in both cases, the mixing proceeded during the experiments,
so that the broken lines on the diagrams, passed into smooth curves. The
water-layers seemed on the whole to be more apt to mix in these experi-

124 EKMAN. ON DEAD-WATER. [norw. pol. exp.

merits than in the case of two sharply separated layers, apparently hecause
of the small difference of spec, gravity between each two adjacent water-layers.

The resistance in the "mixed" water-layers is represented by the heavy
curves 1 and 2. For the sake of comparison, faint curves representing the
resistance in the corresponding unmixed water-layers (fresh-water layers,
3 and 5 cm. deep respectively; saltwater of specific gravity 1"030) are also
given. The velocities seem to be upon the whole, a little more reduced in the
case of the mixed water-layers than in the case of the corresponding pure
fresh-water layer; and the reason is obvious, because in the former case a
smaller velocity is sufficient to disturb the equilibrium of the water-layers,
and consequently to cause wave-motion. But this difference is of no prac-
tical importance. On the other hand, the maximum resistance is some-
what reduced by the mixing. The reduction is however, not very conside-
rable; the maximum dead-water resistance being only diminished by 11 per
cent — and the entire maximum resistance by 14 per cent — in Case (1),
in which the mixing extended uniformly right up to the surface.

The fact that in the sea, the lighter surface-layer is in general not sharply
defined from the bottom-water, will therefore not invalidate the applicability
of the experimental results. In any case it will be possible to make a sui-
table correction by help of the curves Fig. 2 PI. XI. Fresh-water layers as
sharply defined from the salt-water below, as in diagram (2) — or even
sharper — are not unrare near the coasts.

Application of the experimental results to the case of full-sized ships.

Froude's rule (p. 51) was proved to hold exactly for wave-making resi-
stance in frictionless water, and reasons were given (p. 53) that it should
hold approximately for the frictional resistance. It may therefore be expec-
ted to hold very nearly true for the entire dead-water resistance, since the
greatest part of this is caused by wave-making. In other words: if the
dimensions of the vessel, the depth of the water-layers, and other linear
dimensions are increased in the proportion I, and if the vessel's velocity
is increased in the proportion ^X, the dead-water resistance will increase
as P.

For a rough verification of this rule, we may compare two series of
experiments, one with the small Fraw-model, and one with the large one

NO. 15.J

EMPIRICAL LAWS OF RESISTANCE.

125

(experiments 11 — 17 and 72 — 76). The small model was drawn in the small
tank, and the large one in the large tank, in fresh-water layers of 2 and
4 cm. depth respectively. The dimensions of the boat-models are then in the
same ratio as the depths of the surface-layers; but the width of the tank
was, by comparison, a little greater in the latter case. The spec, gravity of
the salt-water was in both cases, P030. The results of the experiments with
the small model are represented graphically by Curve (4) in Fig. 8 PI.
VI. From the results of the experiments with the large model we shall by
Froude's rule calculate the resistance against the small model and after-
wards compare with the directly observed values. The calculation is inserted
here as an example.

Experiment 72 shows a resistance to the large model, of 1*5 gr., at a
velocity of 6'5 cm./second. These figures are found in the first and second
columns in the table below (first line).

The Fram, scale 1 : 100

Spec. g. of salt w. 1'030; surface-layer 4 crn.

(observed values)

The Fram, scale, 1 : 200

Spec. g. of salt w. 1'030; surface-layer 2 cm.

(calculated values)

Total
resistance

Velocity

Dead-water
resistance

Dead-water
resistance

Velocity

Total
resistance

1-5

2-0
2-15
2-05
1-5

6-5

7-5

10-5

110

133

1-32
1-76
1-72
1-58
0.83

0165

0-220
0-215
0-198
0-104

4-6
53

7-4
7-8
94

0-20
0-26
0-29
0-28
0-22

The resistance in homogeneous water at the same velocity, is according
to Fig. 1 PI. X, 0-18 gr.; the difference 15— 0-18 = P32 is the dead-water

resistance and is given in the third column.

Now

HP = 0165;

6j5

V2

= 4-6.

The dead-water resistance experienced by the small model at a velo-
city of 4-6 cm./second, should then according to Froude's rule, be 0165 gr.
These figures are given in the 4th and 5th columns. According to Curve (1)
in Fig. 8 PI. VI the resistance in homogeneous water, at the last-mentioned
velocity, is 0-032 gr. This added to 0-165 gives the total resistance against
the small model, and the rounded result 0-20 gr., is found in the 6th column.
The other figures in the table are calculated in the same way.

126 EKMAN. ON DEAD-WATER. [norw. pol. exp.

The values of velocity and resistance calculated in this way, are repre-
sented in Fig. 8 PI. VI by the faint curve (5). The curves (4) and (5) should
consequently coincide if the measurements, and the method of comparison
were exact. The agreement may be regarded as very good, and as far as
the maximum resistance is concerned, the difference lies within the limits of
experimental errors. The difference between the two curves at velocities
below the critical one, will be explained below, as due to the different width
of channel. The application of the experimental results to the case of
vessels on a different scale, may consequently be made according to the
scheme used in the Table p. 125.

The agreement between Curves (4) and (5) in the case of the maximum-resistance,
does not exclude the possibility of appreciable errors, if the measurements be applied to
the case of full-sized ships. For the larger .Fram-model must have its dimensions 6"6 times
doubled in order to attain the size of the Fram herself (the power 6-6 of 2, is 100). Sup-
posing that the agreement between Curves (4) and (5) for the maximum dead-water resi-
stance, is trustworthy to within 5 per cent of the measured quantity, the experimental
result when applied to the case of the Fram herself, might then include an error of as
much as 38 per cent (the power 66 of 1*05 being 1'38). In any case the above comparison,
proves that Froude's rule gives results which are of the right order of magnitude; and
there is apparently no reason for supposing that it should not be practically exact.

We may conclude also from experiments with salt-water of different spec, gravities,
that the friction had not so much influence in the experiments as to destroy their appli-
cability on a larger scale. For by using the artifice on p. 52 it follows from Equations (b)
and (c) p. 50, that the influence of the friction upon the motion, will be diminished just
as much when increasing the linear dimensions in the ratio r, as when increasing the
difference of spec, gravity 4q in the ratio r3. As the agreement between experiments
with differences of spec, gravity = 0-01, 0-02, 0 03, 0'07, and 016, is very good (see p. 116),
we may therefore expect the same agreement between for example, experiments on the
scales 1 : 100 and 1 : 50 with a difference of sp. gravity 0'02; and when the scale is further
increased, the agreement is likely to be so much the more certain. The same conclusion
could be drawn from the fact that the amplitude of the velocity-oscillations, was just as
great when the difference of spec, gravity was small, as when it was great; because the
velocity oscillations are more stifled by friction, the smaller the difference of spec, gravity.

One more circumstance must be examined before applying the results of
the experiments. They were performed in a rather narrow channel, while
in cases actually interesting us, the vessel is moving on a more or less
open and extensive water-surface. The effect of this circumstance, upon the
frictional resistance and upon the sternward-pressure caused by it, has been
mentioned in section D of this chapter; and it was then pointed out that in
any case it would not appreciably influence the "dead-water resistance". On
the other hand, the wave-making resistance might be influenced, the waves
being to a greater extent transverse waves, when the vessel is moving in
a narrow channel.

NO. 15.]

EMPIRICAL LAWS OF RESISTANCE.

127

To get an idea of the degree to which the experimental results must be
corrected on account of the narrowness of the channel, we may compare two
series of experiments made in the large tank, one series with the small
Fram-model and one with the large model. The former series (experiments
284 — 288) was made in a 2-5 cm. thick fresh-water layer on the top of salt-
water of sp. gravity 1480, and the results are represented by Curve (2) ("wide
channel") in Fig. 9 PI. VI; Curve (1) in the same figure, gives the resistance
in homogeneous water according to experiments 278 — 280. The second series
(experiments 154 — 164) was made in a 5 cm. thick fresh-water layer on the
top of salt-water of specific gravity 1*160. We can in the way indicated
on p. 116, construct from the resistances in this case, the resistance-curve for
the case of salt-water of specific gravity 1480. And further, we may from this
curve according to the scheme on p. 125 construct the resistance-curve for the
case when all linear dimensions are diminished in the proportion 1 to Va. For
this purpose, the dead-water resistances are multiplied first by 18/16 and
then by (V2)3, that is by 9/64; and the velocities are multiplied by l/l8/16
and by l/j/2, i. e. by 3/4. The calculation is given in the table below,
just as in the table on p. 125.

The Fram, scale 1 : 100

Spec. g. of salt-water 1*16;

fresh-water layer 5'0 cm.

Breadth of the channel 40 cm.

(Observed values)

The Fram, scale 1 : 200

Spec. g. of salt-water 1'18;

fresh-water layer 2'5 cm.

Breadth of the channel 20 cm.

(Calculated values)

Total
resistance

Velocity

Dead-water
resistance

Dead-water
resistance

Velocity

Total
resistance

0-25

0-50

075

10

2-0

30

5-0

7-0

9-0

9-5

93

40

6-5

7-8

9-0

11-5

12-0

136

14-7

15-6

<22

25-4

0-15
031
0-50
0'68
1-49
2-45
4-30
619
8-10
7-75
6-98

0'02
0-04
007

o-io

0-21
0-34
061
0-87
1-14
109
0-98

30

49

5-9

6-7

8-6

90

10-2

110

11-7

<16-5

19-0

004
008
0-12
0-17
0-30
0-44
0-73
1-00
1-28
1-35
1-31

The values in the last column are obtained by adding to the numbers in
the 4th column the resistances in homogeneous water, found from Curve 1

128 EKMAN. ON DEAD-WATER. [norw. pol. exp.

in Fig. 9 PL VI. By means of these values and the corresponding velo-
cities in the 5th column, Curve (3) in the same figure, is constructed. This
curve then, represents the same case as Curve (2), only with the difference,
that in the latter case, the boat is moving in a 40 cm. wide channel,
while the former case refers to a 20 cm. wide channel. [The numbers in
the 6th column should really be calculated by adding to the numbers in the
4th column the resistances in homogeneous water in a 20 cm. wide channel.
But as our object is to compare the dead-water resistances, it was more
suitable to reckon them from a common curve, e. g. from Curve (1). In any
case the difference is very small.]

A comparison between the two curves seems to prove that the narrow-
ness of the channel has no remarkable influence on the maximum resistance
as it has been defined on p. 90. The velocities corresponding to given resi-
stances are, however, somewhat smaller in the narrow channel than in the
wide one1. As shown by Fig. 1 PI. I, the large tank is rather spacious for
the small boat-model; and the photographs on PI. XIII seem to show that
the waves have spread just as in open water. It is therefore probable that
the resistance in open water would follow a curve, much nearer to Curve (2)
than the latter is to Curve (3). As the influence of the narrowness of the
channel is then, not very great and, especially as it does not effect the
maximum resistance appreciably, it is not necessary to make any allowance
for it in applying the results.

Unfortunately, hardly sufficient experiments were made with the small
boat-model in the large tank, to answer the above questions so completely
and positively as had been desirable. At the time, it was not noticed that
these particular experiments would be of such especial interest, and it was
afterwards too late to have them repeated.

The influence of the shape of the boat-model.

According to some of the narrators in Chapter I, vessels of different
shapes should be to different extents, liable to dead-water. Their statements

1 It seems therefore probable that the difference between the resistance-curves (4) and (5)
in Fig. 3 PI. VI (see p. 126) depends on the different width of the channels. For, as
shown by Fig. 1 PI. I, the small tank is narrower compared with the small Frani-
model, than is the large tank compared with the large Fram -model.

NO. 15.]

EMPIRICAL LAWS OF RESISTANCE.

129

in this respect are, however, not very reliable and definite, and a few experi-
ments were therefore made to determine with certainty whether vessels of
different shapes are influenced in markedly different degrees. The boat-
models used in these experiments, had about the same size as the larger
Fram-mode\ ; their length at the water-line was the same, namely 36 or
36'5 cm. Other principal dimensions etc. are given in the table below.

Boat-models.

Number
of the
model

Description

Weight

in
grammes

Wetted

Surface

cm.2

Draught

"Drag"

or

Trim

For

Aft

Middle

1
2
3
4
5

(The Fram). Round-bottomed

The same, trimmed

Flat-bottomed model

Sharp-bottomed model ....
Thin rectangular board . . .

800
800
1050
926
230

450
450
527
574
565

42

3-2
4-4
7-0
0-5

4-7
5-7
4-4
7-0
0-5

44
44
44

7-0
05

05

25

0

0

0

Model 1 was the before mentioned model of the Fram; its lines are
given in Fig. 8 PL I, and its athwart-section in Fig. 1 PI. X. Model 2 is
the same as No. 1, only that the loading weight was moved from midships
to the stern so as to make the trim greater. Models 3 and 4 have diffe-
rent midship-sections, as may be seen in PI. X. In other respects, the
models 1, 3, and 4, are made as nearly as possible similar to one another,
so far as is consistent with the different midship-sections; Model 3 had a
stem somewhat more bluff below the water-line, than had the others.
Model 5 was only a (bin rectangular board, 36 cm. long and 14-7 cm. wide
and dipping 4 or 5 mm. into the water; at its ends it was thinned out to
nothing1.

Experiments with Model 2 were made only in a surface-layer of 5 cm.
thickness (Experiments 185 — 194 p. 83). If the resistance-curve is drawn ac-
cording to the results obtained, it will be found almost identical with the
corresponding curve for Model 1. The resistance in homogeneous water, may
be assumed to be nearly the same for both models. As the trim of Model

1 It should have been mentioned on p. 59, that all boat-models except the one used in
the small tank, were made at " Liljeholmen s boat-building yard".

17

130

EKMAN. ON DEAD-WATER.

[norw. POL. EXP.

2 is very considerable, it may therefore be concluded that the trim of a
vessel has practically no influence on the dead-water resistance. In what
follows, only the mean draught is therefore taken into account.

The experiments with Models 3 and 4 were to show the influence of the
athwart-section of the vessel. They represent two extreme types of vessels
which are both used, and which may be characterized by a nearly rectan-
gular section (flat-bottomed vessels) and a nearly triangular section (sharp-
bottomed vessels). Between these extremes is Model 1 with a round (circular
or elliptical) athwart-section. The resistance-curves PI. X seem to show that
there is a marked difference of resistance to the 3 models. I shall here only
compare the maximum dead-water resistance, which is of special interest to
us; the corresponding velocities of the different boat-models are practically
equal to one another. The following table gives the maximum dead-water
resistance to each model, in water-layers of different thickness; the spec, gra-
vity of the salt-water being in all cases 1"030.

Depth of
fresh-water

Maximum dead-water resistance

Model 1

Model 3

Model 4

1 em.

0-30 gr.

3 -

1-35 -

1-53 gr.

1-37 gr.

4 -

1-84 -

5 -

1-75 -

2'15 -

1-70 -

7 -

1-30 -

9 —

1-00 -

1-56 -

1-42 -

13

0-60 -

As, however, the models 1, 3, and 4, have not the same weight and
draught, it is not possible by directly comparing these numbers to find the
influence of the different athwart-sections; it is necessary for that purpose to
reduce them to refer to vessels of the same weight and the same mean draught,
but with different cross-sections. To directly apply the results to the case of
full-sized ships, I have chosen the weight 800 tons (800000 kgr.) and 44 m.,
which is the mean draught of the Fram at that displacement. First imagine
all linear dimensions (particularly the depth of the surface- layer and the di-
mensions of the boat-model) increased in the same ratio, so that its draught

NO. 15.]

EMPIRICAL LAWS OF RESISTANCE.

131

becomes 4-4 m. According to Froude's rule the maximum dead-water resi-
stance will then increase in the same ratio as the vessel's displacement. If
further, by a moderate alteration of its breadth, or its breadth and length,
the displacement be made equal to 800 tons, we may assume that the dead-
water resistance will continually alter, approximately as the vessel's displace-
ment, as long as its shape or "type", its draught and speed, and the water-
layers are unaltered. The whole reduction is, in consequence, made by increas-
ing the maximum dead-water resistance in the same ratio as the weight of
the boat, and the depth of the fresh-water layer in the same ratio as its mean
draught. The table below gives the numbers of the preceding table, reduced
in this way.

Depth of

fresh-water

(spec, gravity

of salt-water

1-030)

Maximum dead-water resistance of vessels
of 800 tons weight and 4'4 m. mean draught

Type 1
Round-bottomed

Type 3
Flat-bottomed

Type 4
Sharp-bottomed

1 m.

0-30 tons

1-9 -

1-18 tons

3 —

1-35 -

1*16 tons

315 —

1-47 —

4 —

1-84 —

5 —

1-75 -

1-63 —

5-7 —

1-23 -

7 —

1-30

9 —

100 -

1-19 -

13 —

060 -

The results contained in this table, are represented by the heavy curves
(1), (3) and (4) in Fig. 3 PI. XI, which give the maximum dead-water resi-
stance i as functions of the depth of the fresh-water layer. The faint curve (2)
shows approximately the velocity at which, according to the experiments, the
dead-water resistance would be a maximum (when the total depth of the water
is 37 m.); the velocities are plotted vertically in m. per second and the depths
of the fresh-water layer horizontally, on the same scale as in the case of the
other curves. [If the depth of the salt-water were infinite, and if the waves
created were very low, Curve (2) should theoretically have been a parabola].

1 In the figure stands "wave-resistance", which is not quite correct.

132 EKMAN. ON DEAD-WATER. [noRW. pot. exp.

The curves (1), (3) and (4) show that there is a marked, although not
very essential difference in the dead-water resistance, between vessels of such
different types. The sharp-bottomed boat (with triangular cross-section) ex-
periences comparatively greater resistance than the round-bottomed one, if the
surface-layer be thin, and smaller resistance if the surface-layer be thick.
In the case of the flat-bottomed boat (with rectangular cross-section), it is
vice versa. The reason is apparent: if the vessel reaches below the fresh-
water layer, that part of its body which moves in salt-water does not con-
tribute to the wave-making and to the dead-water resistance, but would rather
have the contrary effect. Other circumstances being equal, that vessel which
has comparatively the greatest part of its body in the fresh-water layer, will
therefore experience the greatest resistance. On the other hand, as long as
the vessel moves entirely in the fresh-water layer, it will generate more waves,
and consequently experience more resistance, the nearer its whole body is to
the fresh-water salt-water boundary where the waves are generated.

The influence of the ratio between length, breadth and draught of the
vessel, was not examined, as it seemed likely that it would have brought the
investigation beyond reasonable limits. This omission is however of no im-
portance, as long as the dimensions of the vessel considered, are in approx-
imately the same ratio as in one of the models 1 — 4.

The above results do not confirm the experience of seamen that a sharp-
built fast-sailing vessel should be worse in dead-water than one of bluff
design (Accounts Nos. 3, 7, and 9, Chap. I). But as a matter of fact, the
contrary is stated in Account No. 8. The more general experience may perhaps
be explained simply by the circumstance that the finely constructed vessel had
a relatively smaller propelling force compared to its displacement.

The force necessary to free a vessel from dead-water under given
circumstances, may, according to the theory given above, be approximately
calculated as follows.

1) In accordance with the particular shape of the midship-section of the
vessel, select one of the resistance-curves (1), (3), (4) Fig. 3 PI. XI, or if neces-
sary, draw a new curve by interpolation.

2) If the mean draught of the vessel is 4*4 m., the depth of the fresh
(or brackish) surface-layer may be sought out along the horizontal axis in
Fig. 3 PI. XI. If her mean draught is D metres, the depth of the surface-

NO. 16.] EMPIRICAL LAWS OF RESISTANCE. 133

layer is first to be divided by D and multiplied by 4-4. The corresponding
velocity given by curve (2), and the resistance given by the selected resistance-
curve, are noted.

3) The last-mentioned quantity is the maximum dead-water resistance,
if the vessel has a weight of 800 tons, and if the difference of spec, gravity
between the surface-layer and the sea-water below, is 0"030. If these quan-
tities are w tons and d respectively, the resistance given by the selected
curve must be multiplied by w/800 and by d/003, i. e. by wd/24.

4) In the case of a gradual transition from fresh surface-water into salt
sea-water, the diagrams in Fig. 2 PI. XI give an indication of the extent to
which the resistance found in (3), must be diminished on account of this
circumstance.

5) Multiply the velocity found in (2), by iDjVi and by Vd/0'03; the
result is approximately the velocity corresponding to the above (1 — 4) calcu-
lated maximum dead-water resistance. Add to the latter the resistance to
the vessel in homogeneous water at this velocity; the sum then gives approxi-
mately the maximum resistance in the given water-layers. If the propelling
force of the vessel is greater, she will not under ordinary circumstances fall
into dead-water; and if she accidentally does so, she will be able to get free
again by stopping completely for a while, and by then going full speed ahead
again. If once in dead-water, and if this manoeuvre be not carried out, the
vessel might, however (as was mentioned on p. 110) be kept in the (lead-
water in spite of a considerably greater propelling force.

Application of the experimental results to the case of the "Fram"

at Taimur.

The only case of dead-water from which we have definite and reliable
statements about the water-layers as well as of the vessel's speed and force
of propulsion, is that which happened to the Fram west off Taimur (see
Chap. I pp. 9 — 11). It is therefore of interest to see whether the experimental
results are in accordance with these statements or not.

TJie force of propulsion of the ship, may be roughly calculated from
the indicated H. P. of her engine. From the "Alters mekaniske Verksted",
where the ship was built, I was informed that the engine with a speed of
6 knots (3*1 m. per second) developed 210 I. H. P. Of this work only a part

134

EKMAN. ON DEAD-WATER.

[nORW. POL. EXP.

is available for propelling the ship, the ratio between the useful work of the
propeller and the indicated work of the engine being generally called the
"propulsive coefficient". For a single-screw ship with thick wood stern- and
rudder-posts, the propulsive coefficient is estimated at about 40 per cent1.
The useful work should then be 84 H. P. = 6 300 kgr. m. per second, when
the ship had a speed of 3'1 m. per second; which gives a force of propulsion
= 6300/3'l = 2 032 kilogrammes. This value however, when compared
with the results of Froude's famous and excellent towing-experiments with
H. M. S. Greyhound2, seems rather too high. The dimensions of the Grey-
hound compared with those of the Fram are:

Greyhound

Fram

Ratio

Extreme breadth . . .
Wetted surface ....

48-8 m.
10-1 m.

4-2 m.
1180 ra.8

700 m.9

36-25 ra.

110 m.
4'5 m.
800 m.3
450 m.2

1-35
0-92
0-93
1-48
1-55

The resistance of the Greyhound, when towed at a rate of 6 knots, was
1'4 english tons or l-42 meter-tons. Supposing that the resistances of the two
ships are to each other as the areas of their wetted surfaces, the resistance
of the Fram at the same speed should be 0'92 ton, only. This supposition
is certainly approximately true; for at such slow speeds, by far the greatest
part of the resistance is due to friction against the ship's hull (see White's
"manual"). It is true that the Fram was proportionately shorter than the
Greyhound, and as Froude has proved, this circumstance slightly increases the
frictional resistance per unit of wetted area. But on the other hand, the dimen-
sions of the boats, and their displacements, show that the Greyhound cannot
have had such fine lines as the Fram. Finally, the Fram's resistance i. e.
her force of propulsion at the speed considered, has probably not been more
than 1 ton at most. This corresponds to a propulsive coefficient of 20 per
cent, which is not improbable, as the Fram's screw was made extraordinarily
thick to stand the shocks of the ice, and its effect was hindered by very

1 See White, 1. c. p. 33, p. 543.

2 White, 1. c, p. 475-476.

NO. 15.] EMPIRICAL LAWS OF RESISTANCE. 135

big stern-posts. The screw is able to develop a somewhat greater force,
when the vessel has her speed diminished by a hindrance, but I cannot from
the information which I have been able to get, say to what extent.

The next question concerns the depth and spec, gravity of the water-
layers. Exact measurements of the water-layers were not made. But it is
recorded that the water at the surface was almost fresh, whereas through
the bottom-cock of the engine-room perfectly salt water was obtained. The
specific gravity of the surface-water was measured. Its greatest values while
the Fram was in dead-water on Aug. 29th was nearly 1-008, and it was 1-005
on the two other days1. To judge from the measurements on other occasions,
the water at 5—10 metres' depth has probably had a specific gravity of 1-023
or l-024. The difference of spec, gravity between the surface-layer and the
sea-water below should then have been as much as 0-016 during the whole
time on Aug. 29th, and 0019 on the other days. Prof. Nansen suggests
that the water-layers might have been analogous to those measured on July
11th 1894 (I. c. pp. 249—250), and that the light surface-layer might have had
a thickness of about 25 m. The densities in situ were according to the
measurements taken on the day: at 0"05 m. 1*001, at 0*12 m. 1*001, at 1 m.
1*001, at 2 m. 1*002, at 3 m. 1-023, at 5 m. 1024, and at 10 m. 1-024.
These measurements made in an analogous case, prove that the boundary
between the two water-layers might well have been rather sharp.

There was only one direct observation on the thickness of the surface-
layer: the salt-water was on a level with the bottom-cock. This was 3*5 m.
below the constructed water-line, and as the ship lay at the time perhaps
half a metre deeper, it would seem that the fresher surface-layer in any case
cannot have been more than 4 m. thick. It must however be remembered
that the water was taken through the bottom-cock, while the ship was in
motion, and consequently there were waves in the boundary between the
salt and fresh water. The bottom-cock is situated 5 or 6 m. from the stern;
and the photographs on PI. XVI— XVII show that the salt-water owing to
wave-motion may have been there raised probably one metre or more above
its mean level. The surface-layer might consequently have been as much
as 5 m. thick or even a little more.

1 See Fridtjof Nansen, On the Oceanography of the Nortli Polar Rasin (Vol. Ill of these
reports) pp. 158—159.

136 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

To calculate the greatest resistance by which the Fram could have been
held fast in the dead-water, let us assume first, that the fresh surface-layer
was 2'5 m. thick. The Fram's draught at that time, was 5 m. or more, say
5-1 or 5'2 m. aft. Her mean draught was then probably 4"9 m. According to
the rules given on pp. 132 — 133, we have therefore in Fig. 3 PI. XI to take
2-5 i— = 2'25 on the horizontal scale. The corresponding resistance given
by curve (1), is 0"87 ton, and curve (2) gives a velocity of 0-8 m. per second.
The difference of specific gravity between the water-layers is assumed to be
0016. The displacement of the Fram with 4-9 m. mean draught is about
950 tons. The maximum dead-water resistance would consequently be

n o7 w 950 X 0-016 „.,, .

0 87 X Or = 0 55 ton,

and the corresponding velocity

0-8 l/— — = 0'6 m- Per second
r 30 4-4 r

or 1"2 knots. As the Fram's speed, when not in dead-water, was at that
time 4"5 knots with the full force of the propeller (1 ton), the resistance at
1*2 knots in homogeneous water may have been (l,2/4-5)2 = 007 ton. The
whole resistance should then be 0-55 + 0'07 = 0'62 ton only, and the ship
would consequently not be held in dead-water.

As mentioned above, the depth of the surface-layer might, however, have
been as much as 5 m. or even a little more. Suppose it was 4 "5 in.; which

would give nearly the greatest possible resistance. In Fig. 3, PL XI, we

4-4
then have to take 4*5 j^ = 4-04, on the horizontal scale; the corresponding

resistance given by curve (1), is P85 ton, and the velocity given by curve (2),
is 0'85 m. per second. Multiplying by the same factors as above, we obtain
a maximum dead-water resistance of 1*17 ton at a velocity of 1*3 knots.
The resistance in homogeneous water is at that speed 0'08 ton, and the
whole maximum resistance would consequently be about 125 ton, which is
more than sufficient to hold the Fram in dead-water. It may be remem-
bered, that this resistance 1'25 ton, denotes the propelling force necessary to
free the vessel from the dead-water, if the engine be stopped and after a
while given full speed again; while a still greater force would be necessary,
if this manoeuvre be not carried out.

NO. 15.] EMPIRICAL LAWS OF RESISTANCE. 137

While in dead-water on Aug. 30th and Sept. 2nd— 3rd, it is possible that
the difference of spec, gravity between the water-layers never fell below 0-019,

19

and the maximum-resistance might then have been as much as^ X 1'25 = 15

ton. On Aug. 29th and 30th, the boiler required cleaning, and consequently
the force of propulsion was somewhat reduced. These circumstances might
perhaps be counter-balanced by the fact that the force of the propeller is
greater at the low speeds considered, than at full speed; although I am not
able to say how much influence the speed may have had on the force of
propulsion.

The velocity, at which the resistance was a maximum, should according
to the above calculation have been 1*2 or 1*3 knots, and this should conse-
quently be an upper limit for the actual velocity. This calculation is based
upon experiments in the comparatively narrow tank, while in open water the
velocities become somewhat greater (see Fig. 9, PI. VI). It is, however,
highly improbable, that the vessel had the velocity corresponding to the maxi-
mum resistance, because then she might at a favourable moment have got
rid of the dead-water. From a comparison of Curves 2 and 3 in Fig. 9
PI. VI, it follows, that the Fram's speed when in dead-water, was very
probably between 1'2 and 1'5 knots; which agrees remarkably well with
the speeds alleged by Prof. Nansen.

The above calculations prove that under suppositions consistent with
the actual measurements of the water-layers, the observed effects of dead-
water may be explained from the experimental results, even as far as abso-
lute quantities are concerned. But they also show another point of interest.
The excess of the maximum-resistance above the force of propulsion, is
rather moderate, even assuming the former to have been the greatest possible
allowed by the observations made at the time; probably this excess has been
very small. When the Fram was steadily struggling and steaming ahead,
the power of the dead-water may have grown considerable; but it is very
possible that if she had stopped and after a while, had suddenly made full
speed, she would after a few such spurts, have succeeded in getting entirely
free (see p. 110). The Fram had a triple-engine, which could be shifted into

compound; and then for a short time, it was possible with great waste of

18

138 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

steam, to raise her speed by two or three knots. By wasting steam in this
way for only a few minutes, the Fram would almost certainly have got
rid of the dead-water; and this accomplished, the engine might then have
been shifted into triple again. In this way she would with considerable
saving of coal have reached her harbour in a small fraction of Hie time
which actually was spent.

no. 15.] APPENDIX. 139

APPENDIX.

NOTE ON THE MATHEMATICAL TREATMENT OF THE WAVES AND THE

WAVE-MAKING RESISTANCE.

Keeping to suitably simplified cases, it is possible to calculate mathe-
matically the wave-making resistance at different velocities, in shallow water
as well as in "dead-water". The results of these calculations as far as worked
out, agree remarkably well with the experimental measurements; which is not
always the case with exact solutions of hydrodynamical problems. Such
agreement seems indeed to be rather usual in the case of wave- and other oscil-
latory motions, presumably because these motions are stable. Below, some
of the results will be given and compared with the experimental results, but
the method of calculation will be only indicated; a fuller account of the me-
thod and its application to some other problems, will be given on a subse-
quent occasion.

In No. Ill of a series of papers: "On stationary waves in flowing water"1,
Lord Kelvin has solved a problem which in a way represents the case of a
vessel moving in a shallow and narrow channel. The channel is supposed
to be of rectangular section, and the vessel is replaced by a small ridge on
the bottom, right across the channel. The ridge is supposed to be very low,
and with smooth and even slopes.

(Sir William Thomson) Phil. Mag. Ser. 5 Vol. 22-23 (1886-87). No. Ill is found in
Vol. 22 p. 517. A few errors which influence, although not essentially, the results of
this paper, may perhaps be noted. The factor 2 on the right hand side of (26) p. 523,
should be omitted, and the two last members in (30) p. 524, as well as the right hand
side of (31), (34), and (40), should in consequence be doubled. In (47) and (48) p. 528,
the denominators 1 +■ Djb should be replaced by 1 — Djb.

140 EKMAN. ON DEAD-WATER. [norw. pol. EXP.

Under these circumstances, and if Kelvin's notation be slightly altered,
the height h of the water-surface above its mean level, is expressed by the
integral

cos(ga)

i. A

<p(o)

da , (1)

where

—a A n —a

e -\- e 1 e — c

and where

A = the cross-section of the ridge producing the waves,
D = the depth of the channel;

x = the horizontal distance from the ridge to the point in the water-
surface under consideration, counted positively in the direction
opposite to the motion of the ridge relative to the water; and
s = the ratio between the velocity of the ridge through the water
(or of the water relative to the immovable ridge) and the maxi-
mum velocity V</D of waves in the channel.

1
To calculate the integral (1), Lord Kelvin breaks up the function -r-r

into partial fractions which put its singularities in evidence, and h is then
obtained as a series of exponential functions. When s >• 1 all the sin-
gularities are imaginary values of a, and in this case the expression of
the level-disturbance (1) is infinitesimal at some distance from the ridge, and
represents a constant quantity of energy. There is then no wave-making

resistance. When s< 1, —t-x is infinite for one positive value of a, and to

cp(a)

this value corresponds a term in (1) representing a series of harmonic waves,
and which may be calculated by help of an indeterminate definite integral
evaluated by Cauchy, namely

cos px ,
q* — x*

= + g- sin pq for p > 0

n (3)

= — g- sin pq for p < 0

When the sole object is to determine the resistance, the calculation may
be made much simpler, since we can leave out of account any term in the
expression for h of the form

NO. IB.] APPENDIX. 141

00

ip(a) cos (yjff) da ,

in which ip(a) is a uniform analytic function of a, regular for all values of
a ^> 0, and when

ip'(a) | da

I

is finite ; | xp' (a) | being the modulus or "absoluter Betrag" of xp' (a). By
partial integration it is easily seen that such a term decreases infinitely with
increasing x, and that it in consequence represents a local disturbance in the
neighbourhood of the ridge, which causes no resistance.

The right hand member of (2) is a holomorphic function for all finite
values of a; it has no zero for positive values of a if s > 1, and when s< 1
a simple zero for one positive value ax , only. It is then easily seen that in

the former case — 7-r satisfies the above conditions for ip(a) , so that (1) gives
q>(a)

no wave-making resistance. When s <C 1 we may write (1) in the form

2«r, cos (j^o)

A_

TtD

(ffa — ff,V(ff,) ^-D

./

ifj (a) cos f j. a J da (4)

1 2gt

W-pM (ff2_ffi2)9,>l).

where <p' (a) is the first derivative of f(a).

The function tf> {a) obviously satisfies the above conditions for the second
integral in (4) to make no contribution to the resistance, and this integral is
therefore left out. As a result of (3), the first integral in (4) gives

h = -W(a7)sin{5'Ji) for-'->°

fo = + ^W) Si" (Iffl) for*<°-

When an endless series of waves which annul the waves for x < 0
are superposed, so that there are no waves ahead of the ridge, those behind
the ridge become doubled, and we obtain for x positive,

D<p' (fft

•ZA. . ( X\

^) sin p D)

142 EKMAN. ON DEAD-WATER. [norw. pol. exp.

From this expression, which is identical with the final result in Lord
Kelvin's paper, the wave-making resistance R is easily found in the way indi-
cated on p. 37. The wave-energy per unit area of the water-surface is

q being the density of the water and H the amplitude of the waves. The
wave-making resistance is

R = B(i — r)E,

where B is the breadth of the ridge, i. e. of the channel, and r is the ratio
of transmission of wave-energy (see p. 36), found by means of a well-known
formula of Lord Rayleigh (see for instance Lamb, Hydrodynamics art. 221).
From this, it follows

1 4gi

R

_ , 2(7. —la.

gqBA2 e '— e ^

D2

/>.

!-)V

2 / \ ' (7 2S2 ff,2S

The broken curve in Fig. 2 PI. VI represents the resistance calculated in
this way, as a function of s, that is of v/v,„. The unit of resistance is chosen
arbitrarily. It is seen that the resistance is inappreciable as long as v is less
than \vm; it increases with v and is a maximum when v = vm, at higher
velocities it is, as before mentioned, nul.

In a similar way the waves and the resistance in the case of dead-water,
may be calculated. The boat may be imagined to be replaced by a small
ridge stretching in the upper surface, right across the channel and moving
along with a velocity v. The disturbances of the salt-water fresh-water boun-
dary (reckoned downwards from its equilibrium level) are then given by
the same formula (1), where however the function f (a) is somewhat different.
If the two water-layers are equally deep, y is found to be given by (2) as
before, s being the ratio of the velocity of the ridge to the maximum velocity
of the boundary-waves (3, p. 43) K If the salt-water is by comparison infi-

The fact that the laws are the same in homogeneous shallow water and in the bound-
ary between two different water-layers of equal depths, gives an interesting and con-
venient method of studying wave-motion on a small scale, since the boundary-waves
can be made to move at a conveniently slow speed and — even when of small
dimensions - without the disturbing effect of capillarity.

no. IB.] APPENDIX. 143

nitely deep (and if the difference of density Jq be regarded as infinitesimal)
<p is, with the same notation as before,

a a - o

9>(*) = e-^2— 2— • (6)

The function cp is a holomorphic function for all finite values of a, with

no zero for positive values of a if s > 1 and with only one simple zero

a = ffj if s < 1. Just as in the case of the former problem we then obtain

no waves if s > 1 ; and

2.4 . ( x\
h = — -^ — -, — j sin ff, „ for positive values of x,
Dcp (ffj \ D)

if 8< 1, and if there is supposed to be no wave-motion ahead of the ridge.

The resistance R is then calculated in exactly the same way as before,

and

e — S2

This quantity is represented by the broken curve in Fig. 3 PI. VI in the
same way as (5) was represented in Fig. 2 PI. VI. In the present case it will
be seen that the resistance is a maximum at below the maximum wave-
velocity (for v/Vm = 0-77 about). When the vessel's velocity is further
increased to vm, the resistance decreases to nul.

In Figs. 2 and 3, PI. VI the theoretical curves are drawn for comparison
alongside experimental ones, the latter representing as nearly as possible the
resistance due to wave-making. As the waves are assumed in the theoretical
calculations, to be created by a ridge stretching across the channel, while
a boat-model was used in the experiments, there can be no question of com-
paring the absolute value of the resistance according to experiments as well
as calculation. The scale of resistance is therefore simply chosen so that
the highest points of the experimental and of the theoretical curves shall be
at the same level. The scale of velocities is the same for both curves.

The heavy full-drawn curve in Fig. 2 PI. VI represents the wave-making
resistance in a shallow canal, according to Scott Russell. For this purpose
the resistance given by Curve E in Fig. 4 p. 38 is diminished by a quantity in-
creasing as the square of the velocity, and which is at velocities above 8 miles an
hour, approximately equal to the total resistance given by E; the rest is assumed
to be the wave-making resistance and is represented as above mentioned, in

144 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

Fig. 2 PI. VI. The maximum wave-velocity v»> is, according to the data in
Scott Russell's paper, assumed to have been 8 miles an hour. The faint
curve in the same figure represents on the same scale the quantity subtracted.

The two full-drawn curves in Fig. 3 PL VI represent the dead-water
resistance according to Fig. 1 PI. X — the heavy curve in the case of a
5 cm. fresh-water layer, and the faint curve in the case of a 9 cm. surface-
layer. Strictly speaking, the wave-making resistance and not the dead-water
resistance, should be compared with the calculated wave-making resistance.
The difference between these two quantities could, however, be determined
only for very small velocities and not for velocities at which the wave-motion
is considerable. In any case, the difference is not very great.

It is obvious that the agreement between the calculated and the experi-
mental resistance-curves could not be complete: because in the experiments
the boat also created diverging waves, which persisted and caused resi-
stance, even at velocities higher than the maximum wave-velocity; and part
of the dead-water resistance was also due to friction. Finally, owing to the
oscillations in the velocity, (see pp. 67 seq.) the resistance measured, was not
the resistance at steady speed. The agreement between the experimental and
theoretical curves in Figs. 2 and 3 PI. VI may under these circumstances be
regarded as surprisingly good. The peculiar shapes of the theoretical resistance-
curves in homogeneous shallow water and in "dead-water" are, indeed, easily
recognized on the experimental curves, without any explanation. It is worthy
of special notice that the ratio between the velocity at which the dead-water
resistance was a maximum, and the maximum wave-velocity, should according
to theory be about 077 while the experiments gave practically the same value
namely 073 (see p. 123).

The case in which the vessel moves in open water instead of in a narrow
channel has also been investigated in the same way and the waves affecting the
resistance evaluated in finite functions. In this calculation the vessel has been
replaced by a small reversed cupola put in the water-surface ; the wave-height
was found to decrease inversely as the square root of the distance from the
vessel. As the numerical calculations particularly of the diverging waves, have
at present not been completely worked out, I must here confine myself, to
one point of interest concerning the transverse boundary-waves. An approxi-
mate calculation of the resistance due to these latter was made, and the result-

N0- 150 APPENDIX. 145

ing resistance-curve was found to be very similar to the broken curve in Fig.
3, PI. VI, except that the resistance is a maximum at a slightly higher velo-
city than in that case. This result agrees well, as far as the transverse waves
are concerned, with the experimental results. Even the absolute height of the
transverse waves indicated by the photographs on PI. XVI, seem to agree in
order of magnitude, with theory.

19

146 EKMAN. ON DEAD-WATER. [norw. pol. exp.

SUPPLEMENT.

Kapt. H. Meyer mentions in "Annalen der Hydrographie und Maritimen
Meteorologie", Heft I, 1904, a case, of which the chief points are briefly cited
below.

"In August 1874, in a fresh sea-breeze, we entered the Congo River with a brig draw-
ing 3'8 m., speed about 5 knots. At the mouth, in the neighbourhood of Shark Point,
there was a distinctly seen "rip" forming the boundary between the sea-water and the
river-water; after having passed this rip, the ship suddenly ceased to answer her helm
and after oscillating for a time, about her course, laid herself right across the current.
Manoeuvres with the sails were of no avail, although the wind was fresh. The river-water
flowed past the vessel as if she were grounded. Gradually she drifted right across to the
shore on the north side of the river and here we anchored. The ship then laid herself
along the current; a double wake was observed, the two directions of which formed an
angle of about two points. We endeavoured once more to sail with the fresh and favour-
able wind, but the ship neither made head-way nor answered her helm, and we therefore
anchored again.

"The next day the current seemed to be somewhat weaker, the other circumstances
the same as before. Again we tried to sail with the sea-breeze but with the same result
as before; finally we were obliged to lie to.

"On the third day, a dutch pilot, who was acquinted with local conditions, helped
us to reach Banana with the sea-breeze. He let the ship drift so near in shore that she
must according to our opinion have had very little water under her. The current was there
considerably weaker; we steered along the shore always in about the same depth of water,
and continually with the usual double wake aft. At first, she did not answer her helm,
but gradually she recovered her steering-power and finally steered quite well.

"A barque which lay in Banana when we came there, had a like experience.

"A month after, we left Banana and the ship again lost her steering in the neigh-
bourhood of Shark Point; just as before, we drifted over to the other shore and were
obliged to anchor. After having again tried without success to sail away from the coast
with the sea-breeze, we tried at night with the land-breeze, and then succeeded."

The double wake mentioned by Kapt. Meyer, seems to prove that dead-
water has been, in any case a contributive cause of the accident. Kapt.
Meyer cites some other accounts of vessels which have lost their steering
on the mouth of the Congo under similar conditions; although the double
wake is not mentioned in any of them. One of these cases, when a vessel

N0- 15-1 ACCOUNTS OF DEAD-WATER. 147

in spite of a speed of 4 knots, did not answer her helm, proves that the
surface- and under-currents alone, may sometimes be sufficient to deprive a
vessel of her steering-power.

Kapt. J. Fruchtenicht of the ship "Wilhelm" mentions in a report in
"Ann. d. Hydr. etc.", 1881, p. 28, the following case:

"The water from the Fraser River sometimes spreads over the Georgia Strait and
gives rise to so called dead-water. On June 20th 1880, the ship (draught 7 m.) was towed
by a steamer and at this place she was held fast in spite of the full power of the tug.
The depth was according to a sounding taken, more than 100 m. After an hour an attempt
was made to set more sail and to fall faither from the wind, and we then gradually got
up speed again. No different currents could be observed."

Mr. Hahn, Navigation Instructor in Leer, mentions in the same journal (Heft IV, 1901)
that dead-water is often met with on the Murmatl coast where it is believed to depend
on under-currents; and in Baffins-Bay, in the neighbourhood of Labrador.

148 EKMAN. ON DEAD-WATER. [nobw. pol. EXP

EXPLANATION OF THE PLATES.

PI. I. The apparatus (see pp. 54 seq.).

Fig. 1. Cross-section of the large tank. The water-level and the cross-
sections of larger and the smaller Frown-models are indicated.
The dotted lines denote the cross-section of the small tank.
The large tank seen from the side, Scale 1 : 20.
Shows the way in which the glass panes are fitted in the tank.
The towing apparatus.
Apparatus for registering velocity.
Arrangement for producing suitable water-layers.
Arrangement for cleaning the water-surface.
The lines of the large Fram-model.

The arrangement for observing the waves from the side. When tak-
ing photographs (Fig. 1, PL XII, and PI. XIV— XVII) the oil-lamp
I was replaced by a flash-lamp.

Fig. 10. The arrangement for taking the "relief-photographs" (Fig. 2, PI. XII,
and Figs. 1—3, PI. XIII).

PI. II.

Map of Scandinavia, illustrating the occurrence of dead-water according
to seamen's accounts (p. 8).

PI. III.

Maps illustrating certain accounts in Chap. I.

Fig.

2.

Fig.

3.

Fig.

4.

Fig.

5.

Fig.

6.

Fig.

7.

Fig.

8.

Fig.

9.

NO. 15.] EXPLANATION OF THE PLATES. 149

PI. IV and Fig. 1 PI. V.
Sketches illustrating the appearance of the dead-water.

Fig. 1. Sketch by Prof. Nansen, showing the crest-lines of the waves which
followed the Front in dead-water (p. 11).

Figs. 2—5. Sketches by Mr. Aanonsen (p. 19).

Figs. 6-7. Sketches by Mr. G. A. Larsen (p. 13).

Figs. 8— 9. Sketches by Mr. Eriksen (p. 17). (The three "rips" aft of the vessel
in Fig. 8, must obviously be imagined to stretch in the water-
surface perpendicularly to the vessel's wake, although they are
drawn vertical, in the plane of the paper).

Fig. 10. Sketch by Kommandorkaptein Kroepelien (p. 20).

Fig. 11. Sketch by Mr. Colin Archer (p. 15).

Fig. 12. Sketch by Admiral Sparre (p. 16).

Fig. 13. Sketch by Kaptein Scott-Hansen (p. 11).

Fig. 14. Sketch made by the author, according to statements from Kom-
mendorkapten Sidner, and revised by the latter (p. 22).

Fig. 15. Sketch by Lieutenant Wallander (p. 23).

Fig. 1, PI. V. Sketch by Kommandorkaptein Kroepelien, illustrating the same
case of dead-water as Fig. 10, PI. IV (p. 20).

PI. V, Figs. 2—5.

Curves showing the shape of the crest-lines of dead-water waves according
to calculation (p. 48). (The depth of the salt-water is in the calculation, as-
sumed to be infinite compared to that of the fresh-water layer).

PL VI.

Fig. 1. (See pp. 43-44).

Figs. 2— 3. Comparison between theory and experiment (pp. 143 144).

Fig. 4. Graphic representation of boundary- waves ; the waves in the upper

surface exaggerated (pp. 42—44).
Fig. 5. A solitary boundary-wave (p. 69).
Figs. 6-7. (To p. 46).

150 EKMAN. ON DEAD-WATER. [norw. POL. EXP.

Fig. 8. Experimental resistance-curves with the small Fram-model (pp.

60-61).
Fig. 9. (To p. 127).

PI. VII- VIII.

Curves representing the variation of velocity (plotted vertically in cm./sec.)
with time (plotted horizontally), in some selected experiments (see pp. 67 seq.).

A short horizontal line at the left of a diagram represents the mean velo-
city as given in the tables. A short vertical line across the curve (in diagrams
54, 77, 80, 81, 84, 103, 105, 106) indicates the moment when one of the pho-
tographs in PI. XV — XVII, was taken.

PL IX.

Figs. 1 — 2. Show the different shapes of the water-surface around a vessel ;
Fig. 1: at a low velocity, in dead-water; Fig. 2: at a higher velo-
city, without dead-water. The disturbance of the water-level ex-
aggerated. (Pp. 66—67).

Fig. 3. Curves showing the disturbances of water-level, highly exaggerated
(pp. 66 and 118 seq.).

PI. X.

Fig. 1. Curves of resistance experienced by the larger Fram-model (1 : 100)
at different velocities and in fresh-water layers of different depths
on the top of salt water. The small circles at the top, indicate the
theoretical maximum-velocity of waves in the respective water-layers.
(Pp. 121 seq.).

Figs. 2 — 3. Similar curves for different boat-models (pp. 128 seq.).

PI. XI.

Fig. 1. Resistance-curves showing the influence of the difference of spec,
gravity between the water-layers (pp. 115 seq.).

Fig. 2. Resistance-curves in the case of several superposed strata of dif-
ferent densities (pp. 123—124).

NO. 15.] EXPLANATION OF THE PLATES. 151

Fig. 3. Curves for calculating the maximum dead-water resistance experi-
enced by vessels of different shapes and in different kinds of water-
layers (pp. 131—133).

PL XII.

Fig. 1. Photograph from the side, of the larger Fram-model in dead-water;

Experiment 162, p. 82. The photograph is completed by a sketch

of the upper part of the Fram and her tackle. (Pp. 64—65).
Fig. 2. "Relief-photograph" (taken as indicated by Fig. 10, PI. I) of the

waves in a case analogous to Fig. 1, and intended to make the

latter clearer (pp. 64—65).
Figs. 3 — 4, Photographs illustrating the train of waves following a vessel under

ordinary circumstances.

PI. XIII.

Photographs of dead-water waves taken obliquely from below (pp. 62—63).
Fig. 1. Experiment 281, p. 86.
Fig. 2. Experiment 282.
Fig. 3. Experiment 283.

PI. XIV.

Photographs from the side, of the small Fram-mode\ in the small tank
(pp. 62, and 69).

Figs. 1—6: in a 15 cm. thick (clear) fresh-water layer on the top of (black) salt-
water of spec, gravity P020 and P028 respectively; towing forces
01-0-3 gr.

Figs. 7 — 8: in three water-layers, black and clear allernately, with very small
differences of spec, gravity (p. 65).

PI. XV.

Photographs from the side, of the larger Fram-model in a 3 cm. thick
fresh-water layer; Experiments 53 — 56, p. 79. Salt-water black; fresh-water

152 EKMAN. ON DEAD-WATER. [norw. pol. exp. no. «].

lighter. The hoat dragged hy a force, in each case greater than in the pre-
ceeding. In Fig. 4 very little is wanting to free it from the dead-water.
(Pp. 62 seq.).

PI. XVI.

Photographs from the side, of the larger _FVa?»-model in a 5 cm. thick
fresh-water layer; Experiments 77, 80, 81, 84, p. 80. Salt-water black; fresh-
water lighter. (Pp. 62 seq.).

Figs. 1 — 3: in dead-water, with a towing-force, increased in successive ex-
periments.
Fig. 4: at a high speed, without dead-water.

PI. XVII.

Photographs from the side, of the larger .Fram-model in a 7 cm. thick
fresh-water layer; Experiments 103, 105, 106, 108, pp. 80 — 81. Salt-water
black; fresh-water lighter. (Pp. 62 seq.).

Figs. 1 — 3: in dead-water.

Fig. 4: at a high speed, without dead-water.

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Pl. XIV

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Fig. 2.

Fig. 3.

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The Norwegian Polar Expedition 1893—96. No. 15.

Pl. XV.

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Pl. XV If.

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XVI.

PROTOZOA ON THE ICE-FLOES OF THE
NORTH POLAR SEA

BY

FRIDTJOF NANSEN.

(WITH 8 PLATES.)

D,

INTRODUCTORY REMARKS.

"uring my first visit to the East Greenland Sea in 1882, I noticed
that in the summer, when the surface of the ice-floes was much melted, it
got a very dirty and often brownish colour1. This was especially noticeable
on thick and very old ice-floes — what 1 call the real polar ice — which evi-
dently came drifting southward along the East Greenland Coast from very
high latitudes, probably after having crossed the then unknown sea near the
North Pole. 1 supposed that this dirty brownish colour was chiefly due to
dust from the atmosphere brought down on the ice by falling snow. To some
smaller extent 1 thought it might also be due to impurities or organisms in the
sea-water which had been frozen into the ice, and which were now aggregated
by the gradual melting of Ihe ice at the surface. During this voyage I also
noticed another feature, viz. that the thinner and comparatively new ice, one
or two feet thick was frequently coloured reddish brown on the under side'2.
By examination under the microscope on May 9, 1882, I found that the co-
lour was due to a layer of algae, chiefly diatoms3, adhering to the under-
side of the ice, f had, however, no opportunity, nor the knowledge then suffi-
cient to pay more attention to these highly interesting features.

1 See "Naturen", vol. XI, Bergen 1887, p. 214.

! This ice with a red underside was called "seal-ice" by the sealers, because they said
that the seal preferred to lie on floes of that kind. This might not be improbable; for
where there are so many diatoms in the water, there are probably also many Cru-
stacea, which form the food of the seal {Phoca groenlandica).

3 According to the drawings I then made, the diatoms seem to have been Coscinodiscus,
Fragilaria, Navicula directa, and others.

1

FRIDTJOF NANSEN. [norw. pol. exp.

In 1888, I again saw the North polar ice in the Denmark Strait, on my
way to the crossing of Greenland. I then used the opportunity of collecting
a few samples of the mud on the ice-floes. One sample was taken from a
thick layer of mud which had evidently somewhere come from the neigh-
bourhood of land, whilst another smaller sample was collected from a greater
area of the ordinary ice-surface, which had the common dirty appearance.
The ice-floes from which the samples were taken were very old and thick; they
had evidently drifted in the sea for several years, and had probably crossed
the North Polar Basin. These samples were afterwards examined and described
by Dr. A. E. Tornebohm and Professor P. T. Cleve1.

Dr. A. E. Tornebohm found the samples to be largely composed of mi-
neral grains of different kinds. But the mineral grains in the smaller sample,
collected from the greater area of the dirty ice-surface, were extremely small
and difficult to determine. In this sample a great many diatoms also occur-
red, which were examined by Professor Cleve who found 16 species and va-
rieties, which were all of them identical with species of diatoms collected by
Kjellman, during the Vega Expedition (in 1879), on an ice-floe near Cape
Wankarema on the north-east coast of Siberia, near Bering Straits. These
diatoms had been described by Cleve in 1883, and twelve of the sixteen spe-
cies, found in my samples from the Denmark Strait, were hitherto only known
from the ice-floe near Cape Wankarema. This seemed to indicate that the
ice I had seen in the Denmark Strait, had actually come from the Siberian
side of the North Polare Basin; as I had already assumed for other reasons.
But how the diatoms had come on to the surface of the ice, or where they
had originally lived neither Cleve nor I could tell2.

During the Expedition with the Fram, I had my attention directed towards
all kinds of dust on the ice-floes. In the summer of 1894 the snow and ice
on the surface of the floe-ice was melted by the sun, and ponds of fresh
water were formed on the floes round the Fram. This began in the first part
of June. On June 11th, 1894, I noted in my diary (hat the ice was rapidly

1 H. Mohn and F. Nansen, Wissenschaftliche Ergebnissc von Dr. F. Nansens Durch-
querung von Grflnland 1888. Petermann's Mitteilungen, Erganzungsheft No. 105,
1892, pp. 104-108.

5 Professor H. H. Gban, has given a full account of what has been written about diatoms
from the polar ice, in vol. IV, No. 11, pp. 5 et seq., of this Report. Most of the papers
there cited by him were, however, published after our departure in 1893.

NO. 16.] PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA.

melting on the surface, and many great and small fresh-waterponds had been
formed on the floes, so much so that it was not even agreeable to walk about
without water-tight shoes. We were then in about 81° 39' N. Lat. and
122° 9' E. Long.

fn July I observed that numerous small brownish specks or, as it were,
small accumulations of sediment were beginning to form on the ice-bottom of
most fresh-water-ponds, especially on the thick floes which had been formed
before the previous winter. Similar brownish spots were also formed on the
socalled "ice-foot" in the channels along the margin of the floes1. By exa-
ming these brownish accumulations, from the bottom of the ponds and from
the "ice-foot", under the microscope, I found in the midle of July, to my aston-

Fig. A. Diagram illustrative of the melting of the ice. a, Pond of fresh water on the ice-
floe. .6, Layer of fresh melting-water, resting on sea-water (S). c, Ice-foot, d. Lumps of
algae floating near boundary between fresh-water and sea-water, e, Small accumulations of
algae t on ice-foot, f, Small accumulation of algae in the pond on the ice.

ishment that they were composed of algae, chiefly diatoms, living and mul-
tiplying in this water on the ice; to some smaller extent they were also com-
posed of a little mineral dust and of dead fragments of diatoms, Chcetoceras,
Coscinodiscus etc., which had evidently been frozen into the ice on its
formation; and their shell-fragments had now when the surface layers of the
ice ; melted, been set free again and gathered on the bottom of the ponds
and on the ice-foot. But among the living diatoms I also observed a good
many moving organisms of various kinds. The biggest and most conspicuous

1 By the melting of the snow and of the upper layers of the floe-ice a good deal of
nearly fresh water (with a salinity of 1 or 2 per mille) is formed during the warmest
summer months, June, July and the beginning of August. This water either accumu-
lates in hollows in the floes to form ponds (Fig. A, a), or runs off into the channels
and cracks between the flows where it forms a layer (Fig. A, b), 1 or 2 metres thick
(see Memoir No. 9, vol. Ill pp. 305-309) of nearly fresh water resting on the cold sea-
water (Fig. A, S). This surface layer of water becomes comparatively warm and has
therefore a corrosive>ffect upon the edges of the floes by melting away the ice near
the water level, whilst the lower part of the ice situated in the very cold sea-water
is not affected, and it consequently projects, often several feet (see Fig. A, c), and is
called the ice-foot.

FRIDTJOF NANSEN. [norw. pol. exp.

were Infusoria, but numerous smaller organisms of great mobility belonging
to the Flagellata or similar groups, were also observed and studied. In nearlv
all samples of these brownish accumulations I also very frequently observed
a comparatively big bassilum, of a simple rodlike appearance, rapidly oscilla-
ting, and often forming long chains.

The brown spots on the bottom of the ponds (Fig. A, f) and on the ice-foot
(Fig. A, e) grew gradually larger from day to day; but owing to their dark
brownish colour they absorbed more heat from the sun than the surrounding

white ice, and then the ice under them was more
rapidly melted away, and they sank deeper and
deeper into the ice, and formed small cylindrical
holes (Fig. B) often several inches deep and perhaps

an inch or more in diameter, with very sharp
Fig. B. Diagram illustrative

of the accumulation of algae and square edges. The bottom of these vertical

in holes on the bottom of , , in -. fii 1 -.i i • 1

, ., . T holes, was gradually quite tilled with a brownish

ponds on the ice. a, Ice. ° J »

b, Fresh-water. c, Holes. mass of diatoms, which could easily be sucked up

with a glass tube.

In the channels between the ice-floes, especially in the narrow ones,
where there was very little movement in the water, both Dr. Blessing and
myself observed in July, 1894, numerous small globular lumps, generally of
a reddish colour, or sometimes with a more bleaked whitish colour. These
floating lumps grew rapidly larger from day to day; they began as small,
hardly visible specks, but eventually attained considerable size, one or two
inches in diameter, or even much more.

In my diary for July 18th, 1894, I find the following remarks about these
lumps floating in the channels between the floes: First I mention mucous
greenish brown masses composed solely of a brown alga, Melosira1, which
occurred often in great abundance at a certain depth (of about 1 metre or
more) "almost in every small channel, especially the more enclosed ones, and
one could see, that on the sides of the ice-floes, at a certain depth, a greenish
brown layer spread over the surface of the ice, and far down into the water.
It looked as if it was the same alga which here grew on the ice". I then

1 In 1882 I found quantities of this alga in the stomach of a bear, who seems to eat
them as vegetable food.

NO. 16.] PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA.

state that "in the water a great deal of smaller mucous lumps were also
floating; they were partly white partly yellowish red, and I collected many
of them. Under the microscope they appeared to be composed of accumula-
tions of diatoms and a great many round red cells (see PI. VIII, Figs. 7 & 8)
filled with round refractive red globules". This large, globular alga (PI. VIII,
Fig. 7 & 8) gave the lumps their reddish colour, where, however, this alga
had died and become colourless, the lumps got a white appearance externally.
"These lumps of diatoms and alga? were all of them floating at a certain
depth, about 1 metre l under the water-surface, where in some small channels
they might occur in great quantity. At the same depth the above mentioned
greenish brown alga (Melosira) was also chiefly distributed, whilst parts of it
rose to the surface. These parts were often greenish brown as usual, but also
often whitish and were evidently dead. It is clear that the lumps of diatoms
as well as the Melosira keep themselves floating just at the depth where the
upper layer of fresh-water (melting-water from the ice) rests on the under-
lying salt sea- water. The water on the surface was perfectly fresh2 (i. e. it
could be used as drinking water) and the lumps of diatoms sank in it, whilst
they floated when they came lower down". (Fig. A, d).

These floating lumps composed of diatoms and the unknown red glo-
bular alga (PI. VIII, Figs. 7 & 8) were very fragile and fell to pieces as soon
as they were touched. They therefore had to be collected with great care.
In these lumps I also found numerous Infusoria, and other small protozoa
moving about between the diatoms; they were very similar to those found
in the accumulations of diatoms in the ponds on the ice-floes.

The diatoms found in these free-floating lumps, as well as on the "ice-
foot" and in the ponds on the ice have been described by Professor H. H. Gran
in a special memoir (No. 11, in vol. IV of this Report).

I studied on the spot, as well as I could, the Infusoria and other Protozoa
found along with these diatoms, and at the same time I made numerous
drawings of them, some of which have been reproduced on Pis. I— VIII.

Not being conversant with the subject and having no literature of the
kind at hand, I could not determine the species, but could only make

1 Somewhat later in the season, the thickness of the layer approached 2 metres, at least

in some channels.
1 It contained between 1 and 2 per mille salt.

8 FRIDTJOF NANSEN. [norw. pol. exp.

drawings and notes of what I saw; I hoped however that I should later get
an opportunity of studying them more closely. My time was taken up in
many ways, so that I could not give much time to them then, and before
the middle of August, 1894, the ponds and channels between the floes were
covered all over with ice, and 1 finally got no further opportunity of studying
them at all, as I left the Fram on a sledge journey before the next summer.

Since my return from the expedition I have been occupied with other
investigations, and have not been able to give any time to the matter.

Miss Kristine Bonnevie has, however, done me the great favour of
looking through my drawings and notes and of selecting those figures which
may be of most interest. They are here reproduced on Pis. 1 — VIII. I owe
her much gratitude for her very valuable assistance. We both agree, that
the material at hand is hardly sufficient for the determination of the species
even in the hands of an expert on the subject.

As it appeared possible, however, that my observations, imperfect though
they are, might be of some interest to future students of this matter, I pub-
lish them in the form they were brought home. They may at least serve to
draw the attention of future travellers to this interesting life on the drifting
ice-floes of the North Polar Sea.

It might seem puzzling, how these organisms have got into the ice in
the first place. The probability is that they, or rather germs of them, have
been frozen into the ice when it was formed at the surface of the sea. When
the ice again melted the germs developed in the ponds on the ice in the same
way as the diatoms, and were also carried by the melting water into the
channels between the floes.

It seems probable therefore that these infusoria were of marine origin
like most diatoms found in the same ponds. The water of these ponds con-
tained, however, only between 1 and 2 %o salt.

It seems hardly probable that the infusoria could have been carried by
the wind through the air. Some of them were found on comparatively white
and clean floes, which had been formed during the previous autumn and winter,
far from any sea-shore or open water.

N0- 16-1 PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA.

LACRYMARIA, sp.
PI. I, Figs. 1—14; PI. II, Figs. 5-7.

This infusorium occurred very commonly both in the free-floating lumps
of algae, in the channels between the ice-floes, and in the accumulations of
diatoms in the ponds on the ice. The individuals were as a rule transparent
and colourless, but in some ponds on the ice I also found numerous animals
of exactly the same external appearance and shape, but which were dark-
green, or almost black. The normal, transparent form will first be described.
When it moved actively about, as was generally the case, it had a more
or less elongated form (PL I, Figs. 1, 2, 14). The body was very mobile and
could be stretched out and become rather slender (Figs. 2 and 14) or it could
be shortened and become thicker (Figs. 1 and 3, Fig. 1 is the same indivi-
dual as Fig. 2) or it could even be contracted into a spheroidal, motionless
globe (Fig. 10). When the body was stretched out, it could bend in a worm-
like manner (Fig. 2) and then it could rapidly wind its way between the dia-
toms, or could swim freely through the water while its body generally ro-
tated slowly round its longitudinal axis. The length of the body of well
developed individuals might, under these conditions, be 0-10 mm. (Fig. 1) or
more.

At the anterior end there was a proboscis-like protuberance, which during
activity could be pushed out and bent vigorously to the sides whilst, in a
more quiescent state when the animal was contracted into a spheroidal form,
the proboscis was partly retracted. This proboscis was provided with numerous
long cilia, which were in perpetual active motion. Whether these long cilia
were actually fixed to the proboscis, or merely situated at its base, surrounding
it, was not ascertained. The surface of the body was provided with some-
what shorter not very dense cilia. They were somewhat more numerous at
the posterior end.

In most individuals furrows could be seen, winding in left banded spirals
along the outside of the body (Figs. 3—7, 13—14).

As far as I could make out, the spirally wound ribs thus produced, were
seven in number (at least on the anterior part) and ended in seven (?) lobes
round the proboscis (see Fig. 5, where four of these lobes are seen). These
ribs could sometimes also be seen on the posterior end (Fig. 3).

10 FRIDTJOF NANSEN. [norw. pol. EXP.

On several occasions I believed I was able to make out that the eilia
on the surface of the body, were situated along the spirally wound furrows.

Some individuals did not, however, show any indications of these spi-
rally wound furrows. This was, for instance, the case with the one, illu-
strated in Figs. 1 and 2. This specimen was on the whole very big and well
fed, "and it is possible that the furrows may have apparently disappeared,
owing to the abundance of food which had dilated the outer membrane. I
consider this explanation more feasible than that this was another species.
It behaved othervise in every respect, like the other specimens.

The nucleus of the animal was situated in its central region, and was,
as seen in individuals killed with osmic acid, sometimes oblong (Figs. 6 — 8),
and sometimes extended into four branches (Figs. 4—5).

A vacuole was very frequently seen in the posterior region (Figs. 4, 5,
14). It was sometimes divided into three smaller vacuoles (Fig. 10).

The cell-contents were as a rule, at least in the outer layer, filled with
numerous globules (see Figs. 1 and 2), which were probably drops of oily
substance (nourishment) dispersed in the protoplasm. These globules were
more sharply defined by the effect of a very thin solution of osmic acid
(Fig. 9). After the specimens, having been stained, had been transferred to
Canada Balsam the globules had entirely disappeared ; they (Figs. 4—6) had
probably been dissolved. The oily globules were in the transparent speci-
mens colourless, or they might have a slightly greenish tinge.

In the interior of specimens transferred to Canada Balsam, refractive
grains were often seen (Figs. 4 and 5). They were evidently mineral grains
or debris of diatom-shells, which had been taken in with the food. In Fig. 4 a
good many such grains are seen accumulated in the vacuole near the pos-
terior end. In Fig. 5 similar grains outside the individual are also seen
adhering to the cilia round the proboscis.

When the animals were killed with osmic acid or chromo-aceto-osmic
acid, they sometimes retained more or less of their elongated shape (Figs.
4—7). But sometimes they contracted into a more or less spheroidal form
like Figs. 8 and 9, and the spirally wound furrows then often disappeared.
Fig. 9 was an individual which while alive, had the same appearance and
was in the same preparation as Fig. 3.

NO. 16. PROTOZOA ON THE ICEFLOES OF THE NORTH POLAR SEA. 11

The dark specimens. I mentioned above that among the diatoms in
some ponds on the ice, I sometimes found numerous individuals actively
moving about; they had externally exactly the same shape and appearance
as the above transparent forms, and behaved in the same manner, but they
had a dark green, or almost black colour (see PI. II, Fig. 5). I do not think
that this was a different species, but rather believe that the dark colour might
be due to the food which the animals had eaten; and the stain might pro-
bably be contained in the oily globules. For the colour was evidently due
to dark grains or globules dispersed in the otherwise colourless protoplasm
(see PL II, Fig. 5). Unfortunately I did not get an opportunity of examining
whether these dark grains or globules were dissolved by transferring the spe-
cimens to Canada Balsam1.

When individuals of this infusorium, either of the transparent form (Figs.
1 and 3) or of the dark form just mentioned, were followed under the micro-
scope for some hours, they were generally seen at last to contract into sphe-
roidal almost motionless globes shown in PL I, Figs. 10—12, and PL II,
Figs. 5—7. Figs. 10 (PL I) represents a colourless individual which was fol-
lowed from the very beginning, when it had the normal shape, like Figs. 5
and 3, and moved actively about, until it had contracted as represented, and
remained nearly motionless. The proboscis was now much reduced, and
merely formed a short protuberance. In the posterior region three vacuoles
were seen. (The figure is drawn with comparatively small magnification.)

On July 28, 1894, I followed the formation of the quiescent globular
form of several dark individuals. The process was quite the same as observed
on transparent, and colourless individuals. I have given the following descrip-
tion of it in my note-book:

1 In my note-book, July 2i, 1894, I find the following remarks aboufthese dark speci-
mens: "Individuals of exactly the same shape, appearance, and size as Figs. 6 & 7,
but perfectly dark or almost black, are seen in great number in the samples of dia-
toms from this ice -floe. Whilst the transparent form, Fig, 7, is, as a rule, colourless,
some individuals from this floe were greenish brown, I presume owing to chlorophyll
obtained from digested algae. I also presume that the dark colour mentioned above,
may be due to particles of food. The dark stain seemed to Joccur in the form of
lumps or globules, situated very near each other but still with transparent intervals
between them (cf. PI. II, Figs. 5 and 6). On one of these dark specimens I saw a dark
sausage-shaped body being pushed out of the posterior pointed end, the animal was
then in rapid motion. This dark body adhered for some time to what I consider to
be the anal opening, but soon dropped away. The oral opening I have not been able
to ascertain".

12 FRIDTJOF NANSEN. [norw. pol. exp.

"In the beginning of the observation the animal had the same regular
shape as the ordinary transparent and colourless form (PI. I, Figs. 3, 4 and 5).
The animal now began to swim about rapidly backwards in the open spaces
of water, continually rotating round its longitudinal axis the same direction
as the spiral-windings which are left-handed. The proboscis was stretched
far out, being dragged after, apparently in an inert state. Neither in this
nor in a later individual did I see the proboscis move while in this state.
The body was now gradually shortened and finally assumed a perfectly glo-
bular shape as in Fig. 6, a. Whilst this happened the proboscis disappeared
to same extent, and only a short protuberance (Fig. 6, a) remained. It seemed
to me as if the rest of it might have been dropped, but it may probably
have been contracted into the body. In certain positions of the animal, e. g.
in a lateral aspect when the proboscis and anal region were seen simul-
taneously, it looked as if the cilia were situated several together at certain
intervals (PI. II, Fig. 6, o). This was very often the case only on one side
of the animal (see Fig. 7, c, under side). I sometimes was able to count 9
such small tassels of cilia on one side between the anterior and posterior end.
In other positions of the animal, when it was seen more from one of the
ends, and had a perfectly round appearance (PI. II, Fig. 7, a) the cilia were
more uniformly distributed along the whole circumference of the body. I got
the impression that the cilia were chiefly situated along the furrows of the
spiral windings, e. g. in PI. II. Fig. 7, e there seemed even to be indications
of such small depression, in which the cilia were situated, along the under
margin of the animal. In the oral and anal region the cilia were more
densely distributed, and were also longer, especially in the oral region.

"After a while the globe, (PI. II, Fig. 6, a) burst, and parts of the con-
tents were spread outside the membrane (Fig. 6, b). There were a great
number of rapidly oscillating, dark green grains, of exactly the same colour
as the cell contents. They seemed to be the cause of the dark colour of the
animal. By means of their oscillating movement these grains swam far away
in all directions1. After about half an hour they became mostly quiet, until
finally the whole mass seemed perfectly dead. The observation was made in
a drop of water, hanging under a cover-glass, in a microscope aquarium. The

This oscillatory motion may probably liave been due simply to the surface tension.

NO. 16.] PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA. 13

bursting of the cell could not therefore be due to pressure of the cover-glass,
as I had thought possible on other previous occasions. Neither was dessica-
tion the cause, for as far as I could see there was plenty of water in the
drop. But something may probably have been wrong with the water, because
another infusorium that lived in the same drop, also seemed to die after a
while."

"PI. If, Figs. 7, a, b, c, and d, are drawings of another individual of the
same kind, which I observed under the microscope for 12 hours, on July 28,
1894. Fig. 7, a was drawn at noon, and the last drawing, Fig. 7, d, was
made at midnight on the same day. The animal was living all the time,
and the cilia were in rapid motion, especially during the first six hours. The
long cilia round the proboscis were especially active, and were bent far towards
all sides. After 9 hours (Fig. 7, c), the cilia were still in constant motion in
the anal region, but perfectly quiet in the anterior portion of the animal. The
proboscis had now almost entirely disappeared, only a small protuberance
being left. After 11 hours no cilia moved. The form of the animal was
during the first six hours almost perfectly globular, even in a lateral aspect
(see Fig. 7, 6). It became then more oblong, like a short egg (Fig. 7, c), thus
it remained for four hours (Fig. 7, d); but then (after eleven hours) it again
became perfectly globular.

"In the anal region at the posterior end, a colourless, limpid space often
occurs (Figs. 7, b, c, d); which is sometimes larger sometimes smaller, but
always with the same locality in the anal region, where the latter is slightly
pointed. Small dark grains frequently occur inside this clear space, and are
seen to move. They sometimes pass from the dark cell-contents into the
limpid space approaching the cell-membrane. A little later the limpid space
is suddently and entirely closed by the dark mass; which after a while begins
to withdraw slowly from the membrane, to give room for the limpid space
again. While this is going on the cilia outside are in active motion1.

1 On one such occasion I saw a spore-like body come out from these moving cilia, and
it appeared to have come through the anal opening, but might nevertheless have come
from the surrounding water. It had an oblong form, narrow in the middle like an
hourglass or the figure eight ; of yellowish colour, it was extremely small, and hardly
visible with the magnification used (Zeiss CC and 5). It had a rapid oscillating motion;
it moved about for a while, and then became quiet. Several similar corpuscles were
seen in the neighbourhood. Half an hour later a perfectly similar corpuscle came out
from the cilia.

14 FR1DTJ0F NANSEN. [noew. pol. EXP.

This colourless space is evidently a vacuole. At the posterior, slightly pointed
extremity of the body, I believe I have seen a small opening in the mem-
brane of the animal; but I have never with certainty seen anything being
pushed out through it".

"The contents of the cell have the same dark green granular appearance
in all these dark individuals. Near the margins single grains can be distin-
guished, of the same size and appearance as the oscillating grains seen in
Fig. 6, 6".

"Here and there small colourless vesicles occur, which might be vacuoles
if it had not been for their small size — they are not much greater than the
dark grains or globules — nor have I seen any contractile movement in them,
although they seem to change slowly".

PL 2, Fig. 5 represents a similar spheroidal, motionless form of dark in-
dividual seen on another occasion (July 24, 1894). But here the cilia were
apparently longer and more numerous than in most other individuals observed,
and no indication of the spirally-wound furrows was to be seen.

PL I, Figs. 13 and 14 probably represents another but nearly allied spe-
cies of this same genus of Infusorium. It was observed on August 2nd, 1894,
amongst diatoms from a pond in a floe. In its mobile state (Fig. 14) it was
conspicuously more extended and slender than the above described form.
"I followed it for a long time, and there was a striking difference between
the elegant worm-like movements with which it moved through the narrow
passages between the alga?, and those of the thicker form above, in both
dark and transparent modifications. It was never seen to contract to a shape
approaching that of the latter, and the body seemed to be also more "mus-
cular", as the spirally wound furrows became more conspicuous on contraction
(Fig. 13).

After a while, it contracted into the motionless stage; but this did not
occur in the same manner as often observed (see description above); it took
place more gradually and quietly: It did not run about in long circuits back-
wards through the water; the "muscles" were more and more energetically con-
tracted, the spirally-wound ribs became more prominent and protruded (Fig. 13).
They are possibly somewhat more numerous than in the above form. As in
the latter there is a vacuole near the posterior end, and this is conspicuously
visible both in the mobile and in the quiescent slate. In its quiescent state

NO. 16.] PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA. 15

it is not as globular as is the above form, and further the spiral-windings
are very prominent".

To this description from my note-book I may add that it may be pos-
sible that this was simply an individual of the same species as above, only
less filled with foot.

In the reproduction of Fig. 13 there are a few mistakes. On my ori-
ginal drawing there were many cilia pointing backwards in the anal region,
which have been forgotten here. The cilia on both sides of the body are
in my original orawing situated in the spiral furrows, and not on top of
the ribs.

Both figures (13 and 14) are drawn without the aid of camera lucida,
and with' comparatively small magnification.

CHILODON(?) sp.

PI. II, Figs. 1-4; PI. Ill, Figs. 1-7, 9, 14.

This form seemed allied both to Orthodon and Chilodon. It was not,
as far as I could see, uniformly covered with cilia, but had its cilia arran-
ged in a double series round along the length of the amind (PI. Ill, Fig. 5).
This infusorium was very common in the accumulations of algae in the ponds
of fresh-water on the ice-floes where it moved rapidly about. As it occurred
sometimes in ponds on comparatively clean and white ice-floes, it seems pro-
bable that the animal did not originate from anywhere near the land, for
such ice-floes had been formed on the sea, during the previous autumn and
winter, far from the coasts.

For a description of this infusorium the reader is referred to Pis. II and
III and the Explanations of these Plates.

It is perhaps doubtful whether several species were observed. PI. II,
Fig. 4 was much larger than the species reproduced in PI. II, Figs. 1—3 and
PI. Ill, Figs. 1 — 7, and possibly belonged to a different species. The usual
length of the individuals was about 0*05 mm. or a little more, whilst PI. II,
Fig. 4 was 0-099 mm. long.

PI. Ill, Figs. 9 and 14, were somewhat smaller than the above individuals,
they were about 0'043 mm. long but possibly belonged to the same species
or a similar species.

16 FRIDTJOF NANSEN. [norw. pol. exp.

PI. IV, Fig. 6 probably also represents a species allied to the above in-
fusoria (PI. II, Figs. 1 — 4). It was taken from free-floating lumps of algae,
in a channel between the floes, and was of about the same large size as
PI. II, Fig. 4 which it resembled much. Its length was 04088 mm.

PI. Ill, Figs 10 — 13 and 15—16 represent small animals which were often
seen in preparations from accumulations of algae in the ponds. They pos-
sibly belong to similar species as the above infusoria. For description see
Explanation ot the Plate.

STYLONYCHIA(?) sp.

PI. IV, Figs. 1-5.

This infusorium was often seen moving rapidly about both in the accu-
mulations of algae from the ponds on the ice, and in the yellowish red lumps
or communities of algae floating at a certain depth (about one or two metres)
in the channels between the floes. For description see Explanation of the
Plate.

The species seems to be at least nearly allied to the genus Stylonychia
but it does not perfectly agree with the descriptions of the latter.

ORGANISM REPRESENTED PIS. V AND VI.

While I was examing the big organism represented in PI. VIII, Figs.
1 — 3, a small organism came slowly "padling" into the microscopic field. It
was oblong and, with the small magnification I then had, seemed to resemble
exactly, the individual reproduced in PI. V, Fig. 7, A. I changed objectives
to look at it under higher magnification (Zeiss F, oc. 4) but it was imposible to
find it. Instead, I found on the same spot the organism reproduced PI. V,
Fig. 1. At first this individual did not move; but gradually the protoplasmic
part, b, began to contract (Figs. 2 & 3), and then to separate from the more
refractive part, a (see Fig. 4). It soon separated entirely and moved away
from a (Fig. 5). Then a cilium also suddenly became visible, which had not
been seen previously. At the same time b got a more regular oval form
(Figs. 5, 6), and a longitudinal line was seen along the the middle, dividing
the contents into two parts with a round corpuscle or vacuole in each (Fig. 6, b).

NO. 16.] PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA. 17

By means of the cilium, b now took a small circuit, all the while in rapid
motion, while the movements had previously been slow and more amoeba-
like. It returned, however, to a and vibrated round it, as though linked to
the spot. After having observed this stage for some time, I was interrupted
by other observations (see below).

When I returned I found the organism Fig. 8, whilst a had apparently
disappeared, it had probably again been enclosed by b. A stalk was also
visible by which the organism was affixed to the glass slide. Whether this
stalk had existed before under a (in Figs. 1 — 6) without being seen, it is
difficult to say, but it is hardly probable. The individual was vibrating
rapidly on its stalk by means of the cilium p.

I had not observed it for very long before it began to divide (Fig. 9),
b being, as it were, skinned off from a by reversing. The a in this figure
had a striking resemblance to a in Figs. 1 — 6, it had the samme clear, refrac-
tive and sharply defined contents, in which three small globules or grains
were visible. After a while b had entirely separated from a except only for
a slender thread (Fig. 10). At the same time another immobile thread or
tail (h) was seen adhering to b besides the cilium.

The thread fixing b to a was stretched and lengthened (Fig. II)1, 6 mov-
ing rapidly towards different sides; but then the thread was again shortened,
and b enclosed a (Fig. 12), as it were, for a last intimate embrace, before
finally parting, a was now entirely enclosed in b (Figs. 13 — 16; Fig. 15
drawn from above, and the stalk (s) not visible) and at last it could not be
distinguished any more; apparently it dissolved in the protoplasm of b. In
certain attitudes two threads (Figs. 16 and 17, h and h') could now be seen
attached to it; one of which may later have again disappeared. A longish
body now became visible in the interior of the cell (Figs. 17 — 20, k). This
body became more distinct and gradually changed somewhat in shape (PI. V,
Figs. 17 — 20, k, PI. VI, Fig. 1, k) at the same time as the organism changed
its outer form. Suddenly a reappeared inside the cell, and 6 again began
to separate from it (PI. VI, Fig. 2); soon after to leave it finally (Fig. 3). At
the same time a drop-like protuberance was formed on the side of a (Fig. 2 d).
I believed at first that it was simply a viscous drop, as a similar globule was

1 The figures PL V, Fig. 11— PL VI, Fig. 10 are drawn with smaller magnification
(Zeiss obj. F, oc. 2) than PL V, Figs. 1-10 and PL VI, Figs. 11-19 (Zeiss obj F, oc. 4).

3

18 FRIDTJOF NANSEN. NORw. POL. EXP.

seen close by (Fig. 2, x), but I now rather think that it was the first begin-
ning of the bud-like formation which was further developed later (Figs. 13 — 19).
I followed b (Fig. 4) on its wanderings for some time. It moved for-
wards by means of the cilium (p) and dragged the tail (h) after itself, exactly
in the same way as the organisms in PL V, Fig. 7. It gradually changed
its shape (Figs. 4—9). The longish body or nucleus inside, which was at
first situated athwart it (Figs. 4 — 6) in the posterior end, gradually took a more
longitudinal position (Figs. 7 — 6) and the organism itself became more oblong.
At the same time the "nucleus" began to narrow in the middle (Figs. 6 — 7)
just as though a division were being prepared, but it came to nothing during
the time of observation. At last it became fixed to the glass slide by the
tail or stalk (h). The motion which had hitherto been rather rapidly vibrating,
now became quieter, and at the same time, the exterior shape of the body be-
came more spheroidal (Fig. 10). I observed this stage for a long time, but
no changes were seen. At last I had to break off for dinner. When I came
back dew had formed on the cover-glass, and when this had been removed
I sought in vain for the organism Fig. 10. I then returned to a in Fig. 3,
which had remained almost unaltered all the time (Fig. II)1. The two cor-
puscles or grains in Fig. 3, a had now united into one (Figs. 11, k), and this
globule which I called "nucleus", moved slowly towards the end where the
stalk adhered (Fig. 12). The bud-like protuberance (d) remained in position
but gradually increased in size (Fig. 12). Near the "nucleus" (k) one or
sometimes two grains were seen. In the evening (Fig. 13) a drop was being
secreted from the cell. The protuberance, d, now gradually increased in size
very slowly (Figs. 13 — 19. In fig. 15, the body is turned over so that d is
seen on the under side, whilst in Fig. 12, it was on the upper side). In the
meantime the "nucleus" underwent several changes. In Fig. 16 it had ejected
a grain (x) which moved towards the protuberance, but again returned to
the "nucleus" (Fig. 17). In Fig. 17 the "nucleus" was lengthened and con-
stricted, and a grain or "nucleolus" was thus given off (Fig. 18, /?. The grain
/? is somewhat too small in this figure). After this, two grains were always

Thie and the following figure (Figs. 11 — 12) are drawn under much greater magnifica-
tion (about 1800 diameters, Zeiss F, 4. and long tube) than Figs. 1-10 (Zeiss F, 2;
magnified 760 diameters) Fig. 11 was drawn with the aid of the camera lucida. Figs.
13—19 were drawn somewhat smaller magnification (Zeiss F, 4, and medium long
tube, about 1500 or 1600 diameters), Figs. 13 and 14 with the aid of the camera lucida.

NO. 16.] PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA. 19

seen, one on each side of the "nucleus" (Figs. 18—19), /? being the larger.
Other small dark grains (Fig. 18, a) were seen moving slowly round in the
cell, and keeping near to the membrane.

The observation was now interrupted by an accident.

While I was studying the above organism, the organism PI. V, Fig. 7, A
came into the microscopic field. Thinking it was the same kind of organism in
an earlier stage I followed it for some time. It moved forwards by means of
the cilium p, and dragged a long thread or tail (h) after it, which was per-
haps destined to become a stalk. For some time no apparent changes took
place. The anterior part, somewhat resembling Fig. 1, a, was very mobile
towards both sides (see Fig. 1,B). I saw also another individual of the
same kind, but in this case the anterior part was still more loosely connected
with the posterior part; and it was still more mobile. At last this organism
disappeared entirely from sight between some diatoms. While hunting for it
I also came across another similar individual which was, however, less elon-
gated (Fig. 7, C), and with no indication of anterior or posterior parts. In
the interior two corpuscles or possibly nuclei (?) were, however, visible.

SUCTORIA gen.? sp.
PI. VIII, Figs. 1-3.

When this organism was first seen under the microscope, in the morning of
July 30, 1894, it was spheroidal tentacles like PI. VIII, Fig. 2 and with radi-
ating filiform tentacles. A nucleus (?) in the centre and a great vacuole («,) on
one side were visible. While I was observing it, it ejected at its left hand side
a part of its grained cellular contents (see Fig. 1). As, however, the water
began to diminish under the cover-glass, a fresh drop was added ; at the same
instant the individual contracted energically and got the appearance of Fig. 1 .
I could not decide whether this contraction was due to the new water, or to
ejection of the cellular contents. After a while it again assumed its regular
spheroidal form (Fig. 2). During the contraction of the animal the great va-
cuole, v1, was partly divided into three vacuoles; a similar division some-
times happened, when the vacuole contracted while the body had the regular
form. After some hours another vacuole (v*) also appeared on the other
side of the nucleus. It may possibly have been there before, as it was

20 FRIDTJOF NANSEN. [norw. pol. exp.

on the under side of the body; but I had not seen it. At the same
time the first vacuole (situated on the upper side of the body, nearest the
eye) was considerably reduced. The contractions of the vacuoles occurred
curred at long intervals. The tentacula were slender, straight, apparently
rigid, and ending in a slight knob. I did not sec them move, but there was
occasionally a slight vibration in them.

The interior of the body was filled with big refractive globules (Fig. 3, b)
which may be reserve nourishment. They do not approach close to the sur-
face. In the outer layer a great mumber of small grains occur (Fig. 3, a)
which have a rapid, half oscillating movement, while swimming about. What
I assumed to be the nucleus, was situated near the upper side of the body,
and there were i Fig. 2 no refractive globules but only small oscillating grains
between it and the outer membrane or surface. It appeared as an oblong
granular mass. The granular appearance might have been due to threads.

The colour of the organism was slightly yellowish green, which seemed
to be due to the refractive globules (Fig. 3, b).

Length of individual about 0095 mm.

I kept this organism under observation during the whole day (July 30)
till interrupted by a bear in the evening.

When I came back after a few hours, the water had been much reduced
by evaporation, and the organism had become much contracted on the one
side. When fresh water was added it again expanded, and then I left it for
the night.

The next morning, July 31, 1894, it had about the same appearance, but
was slightly contracted, and somewhat reduced in size. Later on in the day,
while I was following the developement of the organism illustrated on Pis. V — VI
which was in the same preparation, the cover-glass was several times touched
by the microscope, and great masses of the cell contents were twice squeezed
out. The first time the organism was much contracted and of irregular shape
(like Fig. 1) but after a while it returned to its regular, spheroidal form. After
the second time I could observe no motion in the organism. The big glo-
bules (Fig. 3, b) which had been spueezed out into the surrounding water ap-
peared at first to have a nearly homogeneous structure, but the contents
of rome began in the evening to be differentiated into one or two "nuclei"
and a granular mass (PI. VI. Fig. 20, c). Some of them also began to

NO. 16.] PROTOZOA ON THE ICE-FLOES OF THE NORTH POLAR SEA. 21

show a slightly vibrating movement, see PI. VI, Fig. 20, 6 and c. Whether
a (Fig. 20) had also originated from the above organism, I could not say for
cerlain; it was lying between some of these globules and had the same ap-
pearance, but gradually began to move away by means of its cilium.

The small grains (Fig. 3, a) which had been squeezed out with the cell
contents, appeared to have grown in size during the afternoon, and were
darker than the bigger globules. I did not directly see, that any of them
began to move, but they had a striking resemblance to many small dark glo-
bules which were seen vibrating between the greater globules.

PI. VI, Figs. 20, d, was a body which was in rapid vibration near some
of these globules.

GLOBULAR ALGA.

PI. VIII, Figs. 7-8.

I have mentioned above (p. 7) that, in July and first days of August,
1894, numerous globular lumps of algae were floating in the channels between
the ice-floes, at a depth of about 1 metre; somewhat deeper in August, per-
haps nearly 2 metres. These lumps were composed of diatoms, and to a large
extent, also of a yellowish-red globular alga, of considerable size. This alga,
when alive, gave the floating lumps a reddish colour, and the colour was
the deeper the more numerous were the algae.

The diameter of this alga (PI. VIII, Fig. 7) was generally between 010
and 0'16 mm.

Its cell contents were surrounded by a layer of yellowish red refractive
globules (see Fid. 7), situated near the membrane. These globules varied
somewhat in size. They gave the alga its reddish colour, and were formed
by an oily substance, which was blackened by osmic acid. While Fig. 7
was being drawn, and when the alga probably began to die, the oily glo-
bules united and became continually larger until they fused into one mass
which left the cell as big reddish drops; the cell-contents then became en-
tirely colourless. These globules, were as already mentioned, dispersed
in the outer layer of the cell-contents, while its interior was transparent and
colourless. The red globules were, however, as a rule lying so close
together, that it was impossible to see through them into the interior of

FRIDTJOF NANSEN. [norw. pol. exp.

the cell. Only at one place on the upper side of the cell, near x in Fig. 7,
was there an opening not covered by the globules where it was possible to
see into the interior. Here a small oblong body (as) was seen. When the
under side of the cell came into focus the red globules were again seen, as
indicated by the grey dots in the figure. Whether the open space (at as) was
a vacuole, could not be decided, as no movement was observed in it.

The cell was surrounded by a membrane.

No nucleus could be seen in the living specimens, as the oily globules
covered the interior from sight. It seems hardly probably that the open
space at as, could indicate the situation of the nucleus, as it was not defined
by any membrane.

In a specimen killed with chromo-aceto-osmic acid, and stained with para-
carmine an oblong nucleus, about 0037 mm. long, 'was seen near the outer
membrane, on one side side of the cell.

Forms of this alga like Fig. 8 (PI. VIII), with a furrow on one side,
were often seen. The structure was the same as in Fig. 7, but the oily glo-
bules were more closely situated, and made the cell still less transparent.
The globules near the furrow were colourless in this specimen. The diameter
of the cell was Oil mm. It is possible that this form with the furrow has
been produced as the result of violence from outside.

I got no time for studying the life of this alga, and can therefore say
nothing about its development, or process of multiplication.

PL. I.

Fig. 1. Lacrymaria sp. Living individual, from a lump of alga? floating in a channel
between the ice-floes. July 20, 1894. Transparent and colourless. Magnified about
760 diameters (Zeiss obj. F, oc. 2; cam. luc).

— 2. Lacrymaria sp. Same individual as Fig. 1; while moving. Less magnified (Zeiss

obj. F, oc. 2; freehand sketch).

— 3. Lacrymaria sp. Rough sketch of moving individual; from same place as above.

July 20, 1894. The globules of the cell-contents are in the figure only indicated
in the anterior part (Zeiss obj. F, oc. 2; freehand).

— 4 and 5. Lacrymaria sp. An individual of the same species as Fig. 3, and pro-

bably also, as Fig. 1, but with the spiral-furrows very distinct. Killed with Osmic
Acid, stained with Borax-Carmine, and transferred to Canada Balsam. From a pond
on the ice. July 24, 1894. In Fig. 4 the specimen is seen somewhat obliquely;
the anterior end being lifted slightly upwards. Fig. 5 represents the same speci-
men turned over on one side and at full length. Magnified about 1150 diameters
(Zeiss Horn. Im. '/i8> oc- 2; cam. luc).

— 6 and 7. Lacrymaria sp. An individual killed with Osmic Acid (Fig. 7) and after-

wards stained with Borax-Carmine (Fig. 6). From a pond on the ice. July 24,
1894. Magnified 760 diameters (Zeiss obj. F, oc. 2; cam. luc).

— 8. Lacrymaria sp. From the same sample as the previous individual. Killed with

Chromo-Aceto-Osmic Acid.

— 9. Lacrymaria sp. From the same samples as Figs. 1 and 3. July 20, 1894. Killed

with Osmic Acid. Magnified about 760 diameters (Zeiss obj. F, oc. 2; cam. luc).

— 10. Lacrymaria sp. Living specimen, in contracted, motionless state. From a pond

on the ice. July 28, 1894. (Zeiss obj. F, oc. 2; freehand sketch).

— 11 and 12. Lacrymaria sp. Living specimen, of the same species as above, in con-

tracted motionless state. From a pond on the ice. July 28, 1894. Fig. 12 was
drawn 6 hours later than Fig. 11; the individual was then possibly dead; there
was no movement of the cilia, and a great many of them had disappeared. Mag-
nified 460 diameters (Zeiss obj. CC, oc. 5; cam. luc).

— 13 and 14. Lacrymaria sp. Living individual, from a pond on the ice. Aug. 2, 1894.

Magnified about 500 diameters. Length of animal in Fig. 13 0'044 mm. Freehand
sketches; Fig. 13 drawn after Fig. 14.

The Norwegian N- Polar Expedition1893- 96 N?I6

Pl.l

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F. Mansen ad nat del

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PL.

Fig. 1. Chilodon (?) sp. Living, from a pond on the ice. August 1, 1894. It was just
brought under the microscope, but remained motionless, and there was no motion
of the cilia. The small corpuseles, a, in the protoplasm (ectoplasm) were in rapid
oscillation. The animal showed no change of form or structure as long as it
remained under observation. Magnilied about 1600 diameters (Zeiss obj. F, oc. 4,
with lengthened tube, cam. luc ).

— 2. Chilodon sp. Living but motionless, from a pond on the ice. August 1, 1894.

Probably same species as above; seen from the side. The small grains in the proto-
plasm were in rapid oscillation, m, Mouth, a, Anal opening. A vacuole is seen
in the posterior end on the dorsal side. The animal was much contracted and
probably died while being drawn. The great accumulation of food (?) on the
anterior dorsal side was sharply defined as if by an apparent membrane. This
accumulation, was externally surrounded by a layer of refractive globules. Ap-
parently dark spots, looking like grains or even like a reticulum (see Fig. 2),
were formed by refraction between the globules. These globules formed only
a layer in the exterior part of the formation, for when the microscope was
focussed on its central part a more homogeneous mass was seen, filling the interior,
whilst only a layer of globules was seen along the margin under the apparent
"membrane" (see Fig, dorsal side). This accumulation of globules changed after a
while. The stripes passing along the animal are possibly contractile fibres. They
also seemed to pass towards the place in the posterior end, which is presumably
the anal opening. A distinctly defined, tract or belt passed towards this place,
and looked as if it might be a canal. Magnified about 1600 diameters (Zeiss obj. F,
oc. 4, with lengthened tube, cam. Inc.). Length of animal was 0049 mm.

— 3. Chilodon sp. Living but motionless, from a pond on the ice. Aug. 1, 1894. Seen

from the right-hand side. The animal was possibly dying, as the body seemed
more contracted and rounder than was generally the case. In this individual there
were six greater and smaller accumulations of globules of the same kind as the
one in the previous figure. (I have also seen similar accumulations in other indi-
viduals in the same sample). Even here the layer of refractive globules sur-
rounded a more homogeneous mass. Some similar globules were seen dispersed
in the protoplasm of the animal as in Fig. 1, either single or united, some few
together. After a time some of the great accumulations of globules began to dis-
solve and the globules were dispersed singly in the protoplasm, in the same way
as usual (Fig. 1). Both in this and the previous specimen only a few oscillating
small grains were seen, but the refractive globules were in slow motion. In the
anterior end of the animal several longer cilia were seen situated near the margin
and on the ventral side. The right margin of the animal is seen as a dark streak
or belt along the figure, in Oral opening.

Magnified about 1600 diameters (Zeiss F, 4, with lengthened tube, cam. luc).
Length of animal 0'054 mm.

— 4. Chilodon sp. Living, from a pond on the ice, Aug. 1, 1894. Probably a species

different from the above. This specimen was somewhat more oblong before it was
sketched. Its exterior form was much like the above, only that it had a more
pointed posterior end, and the oral opening was perhaps somewhat differently
situated, being directed more towards the anterior end (?).

This individual is evidently somewhat contracted, perhaps in the act of forming
a cyst, as after a while some colourless mucuous substance was secreted from the
left side (on the right hand side of the drawing). At this period the cilia seemed
to have nearly disappeared. The refractive globules were in active oscillation.
Magnified about 760 diameters (Zeiss obj. F, oc. 2, cam. luc). Length of animal
0099 mm.

— 5. Lacrymaria sp. Living but contracted and motionless. From a pond on the ice,

July 24, 1894. Magnified about 760 diameters (Zeiss obj. F, oc 2, cam. luc).

— 6, a & b. Lacrymaria sp. Living, but contracted and motionless, only cilia moving

in Fig. 6, a. From a pond on the ice. July 28, 1891. 6, some time after a with
membrane burst, and oscillating grains spread towards all sides. Magnified 460
diameters (Zeiss obj. CC, oc. 5; cam. luc).

— 7, a—d. Lacrymaria sp. Living, from a pond on the ice. July 28, 1894. The

individual was observed during twelve hours from noon (Fig. 7 a) till near mid-
night (Fig. 7 d). The cilia were seen moving the whole time, but ceased to move
near midnight. Magnified 400 diameters (Zeiss obj. CC, oc. o; cam. luc).

TheNorwegian N- Polar Expedition1893- 96 N?I6.

Pin

F. Nansen ad.nat. del.

Trykt i den private Opmaaling. Chra.

PL. III.

Fig. 1. Chilodon (?) sp. Fresh state, probably dead. From a pond on a comparatively
clean ice-floe. July 24, 1894. Magnified about 760 diameters (Zeiss obj. F, oc. 2,
cam. luc).

— 2. Chilodon sp. Fresh stale, probably dead. From another pond on the same

ice-floe as above. July 24, 1894. Magnified about 760 diameters. (Zeiss obj. F,
oc. 2; cam. Inc.).

— 3. Chilodon sp. Living. Conjugation of two individuals probably of the same species

as above. From the same place as above. July 24, 1894. They were observed
in this situation, unaltered for a long while. The vacuoles were the whole time
pulsating. They were moving rapidly, being dragged along by the one individual.
At last they died (Zeiss F, 2, freehand).

— 4. Chilodon sp. Killed with Chromo-Aceto-Osmic-Acid. From same place as above.

July 24, 1894. v Vacuoles. Magnified 700 diameters. (Zeiss obj. F, oc. 2; cam.
luc).

— 5. Chilodon sp. Fresh state, probably dead. From the same ice-floe as above.

July 24, 1894. Individual of the same species as above seen from the end. The
pointed (anterior) end is near the margin at a. and would have become visible,
outside the margin, by a slight turn of the animal. The double series of cilia
wind round the body and meet at its end, at c. Magnified about 760 diameters.
(Zeiss F, 2; cam. Inc.).

— 6. Chilodon sp. Fresh state, just dead. From the same sample as Fig. 3. Magni-

fied about 760 diameters. (Zeiss obj. F, oc. 2; cam. luc).

— 7. Chilodon sp. Killed with Chromo-Aceto-Osmic-Acid, stained with Borax-Carmine.

From pond on the ice. July 27, 1894. Same species as Figs. 1—6, the specimen
is seen from the anterior pointed end which is at a. v Vacuoles, a third vacuole
is seen on the other side. The oral opening was very distinct. Magnified 1000
diameters. (Zeiss F, 3; cam. luc).

— 8. Stylonychia, (?) sp. This is probably a cyst of the same form as PI. IV, Fig. 1.

It was quite motionless. Thick stiff hairs at both ends.
Magnified 460 diameters (Zeiss obj. CC, oc. 5; cam. luc).

— 9. Chilodon (?) sp Living, in active motion. From a pond on the ice, seen with

specimens of the dark and the transparent forms of Lacrymaria. July 28, 1894.
Magnified about 460 diameters (Zeiss obj. CC, oc. 5, freehand sketch).

— 10. Living, in active motion. From a pond on the ice. July 28, 1894. Small animals

of this kind were often seen amongst the algse from the ponds on the ice. It is
possibly the same species as Fig. 12; but as far as could be seen the cilia were
chiefly situated on the one side only. They had a twitching and one-sided motion.
Half an hour later all movement had ceased, and two colourless water-clear refrac-
tive drops were secreted from each side (Fig. 11). During this process the animal
was reduced to a small globule (Fig. 11); its protoplasm became less transparent
and the grains closer together.

Magnified perhaps about 460 diameters (Zeiss obj. CC, oc. 5; freehand sketch).

— 11. Same individual as Fig. 10. (Zeiss CC, 5; freehand sketch).

— 12. Living, in active motion. From a pond on the ice together with specimens of

Chilodon. July 28, 1894. Animals of this small kind were often observed. They
v'were always as small as this individual. They seemed to be round in transverse
section and covered with cilia all over. Magnified about 460 diameters. (Zeiss
obj. CC, oc. 5; freehand sketch.

Fig. 13. a — c. Living. From a pond on the ice. July 29, 1894. Conjugation (?) of small
oscillating infusoria, of a similar appearance as Figs. 15, but they were smaller
so that no cilia could be distinguished. They united during rapid oscillating
movements, the one athwart the other, with the flat ventral (?) sides against each
other. Thus united they walzed rapidly around for a while; then the movements
ceased, and the one assumed a rounder shape in longitudinal aspect (see Fig.
13 c, the upper individual), a and c are seen from the side, 6 from above (Zeiss
obj. CC, oc. 5; freehand sketches).

— 14. Chilodon (?) sp. Living, but motionless. From a pond on the ice. July 28, 1894.

Perhaps the same or nearly allied species as Figs. 1—6 (?).
Magnified 460 diameters. (Zeiss obj. CC, oc. 5; cam. luc).

— 15, a — c, and 16. Living. From a pond on the ice. July 29, 1894. An individual

seen in different positions: a obliquely from behind, b from the side, and c from
above. This figure should be more regularly oval than it is here reproduced. The
animal had apparently a flat ventral side, and a vaulted dorsal side. Ventral side
densely covered with long cilia; on the dorsal side shorter cilia were also visible.
One apparent vacuale was visible. At first the animal was in active motion,
affixed, as it seemed, by some mucuous threads or cilia to the silica spicule of a
diatom, and it could therefore advance only slowly. After some time the move-
ment ceased gradually, and its shape become more rounded (Fig. 16). Several
refractive drops were then secreted (Fig. 16, d), and its size was reduced. After
a while the motion became again more rapid, and during its rotalions it was now
seen that the flatness on the ventral side had nearly disappeared and it had got
a more oval or nearly globular shape.

Magnified 460 diameters (Zeiss obj. CC, oc. 5; cam. luc).

The Norwegian N.-PolarExpedition1893-96 N?I6

pi. in

13.

c.

F- Nansen ad natdel

Trykt i den private Opmaaling, Chra.

PL. IV.

Fig. 1. Stylonychia (?) sp. Living, but motionless. From a lump of algae floating in a
channel between the floes about 2 metres deep. August 4, 1894. The small cor-
puscles inside the animal oscillated rapidly. During the drawing of it the animal
contracted, and the notch at the anterior end (left hand side of the drawing), dis-
appeared almost entirely. Then it again expanded and got the same appearance
as before, only the caudal bristle, pointing straight backwards in Fig. 1, had
now got a spiral winding as in Fig. 1, A. This twisting may possibly be clue to
the drop of Osmic Acid which was added to the preparation a couple of hours
before.

Magnified 1280 diameters (Zeiss obj. F, 4; cam. luc).

— 2. Stylonychia (?) sp. Killed with Osmic Acid. From the same place as above.

August 4, 1894. The same species as above seen from the side.
(Zeiss obj. F, oc. 4; cam. luc).

— 3. Stylonychia (?) sp. Living. From a pond on the ice. Taken July 28, 1894, and

kept alive in a bottle till August 6, 1894 when it was sketched. Same species as
above, a seems to be small accumulations of food (small alga?), b is a small
vacuole just under the outer membrane; the small refractive grains were in a
strikingly rapid motion inside this vacuole. No longitudinal furrows could be
seen on this side of the body. Vi and v2 big, clear vacuoles, but no pulsation
could be observed. A third vacuole could also be seen inside Vg, when the animal
moved, but it was not visible in this position; it seemed to be situated more on
the other side of the body. It was of about the same size as v2- While the
animal was being drawn, the thick bristles at c dissolved, as far as could be seen
into numerous slender threads or hairs. The two thick bristles at d, which at
first were undivided and pointed, now dissolved near the end into several threads
as is seen in the figure, and was finally transformed into a bundle of threads or
hairs. The thick bristles near a and Uj gradually disappeared, and this was also
the case with the hairs or cilia near the margin between e and y3. At e and on
the right hand side of t)3 some dilapidated remains of hairs remained. While this
was going on the animal contracted somewhat in length, and assumed a rounder
shape; simultaneously two colourless water-clear drops were secreted, one in the
posterior end at V\ and one opposite u2, on the right hand side of the drawing.
The vacuole v3 had in the mean time disappeared, and so had the small vacuole b,
or it had been much widened, for many of the small refractive grains were seen
oscillating and dispersed over a wider area.

The animal is transparent and colourless with refractive, greenish globules dis-
persed chiefly in the exoplasm as usual.

(Zeiss obj. F, oc. 4; cam. luc).
4. Stylonychia (?) sp. Same species as above, and from same place as Fig. 1
Aug. 4, 1894. Killed with Osmic Acid.

Magnified about 1280 diameters (Zeiss obj. F, oc. 2; lengthened tube; cam. luc.

Length of specimen 0040 mm.

— 5. Stylonychia (?) sp. Same species as above, and from same place. Aug. 4, 1894.

Killed with Osmic Acid.

Length of specimen 0'038 mm. (Zeiss obj. F, oc. 1. cam. luc).
— 6. Chilodon (?) sp. Probably a species similar to PI. II, Fig. 4. From a lump of
algae floating nearly 2 metres deep in a channel between the ice-floes. Killed with
Osmic Acid. Length of specimen 0-1088 mm. (Zeiss obj. CC, oc. 5; lengthened
tube; cam. luc).

TheNorwegian N.-PolarExpedition1893-96 N?I6.

PL IV

F. Nansen ad. nat del.

Trykt i den private Opmaaling, Chr

\

PL. V.

All figures with exception of Fig. 7 represent the same individual in different stages.
From a pond on the ice, taken July 30, 1894.

For description of figures see pp. 16—19.
Figs. 1—6. Living. Freehand sketches drawn with Zeiss obj. F, oc 4, on July 31, 1984
morning.

Fig. 7, A — C. Living. Two similar organisms (A and B is the same individual). Freehand
sketches, Zeiss obj. CC, oc. 5. July 31, 1894, morning.

Fgs. 11— 20. Living. Zeiss obj. F, oc. 2; freehand sketches. July 31, before and afternoon.

TheNorwegian N- Polar Expedition.1893- 96 N?16

PI. V

F. Nansen ad nat. del.

Trykt i den private Opm aa ling. Chra.

PL. VI.

All figures, with exception of Fig. 20, represent the same individual as PL V.

For description of figures see pp. 16 — 19.
Figs. 1 — 10. Living. Zeiss obj. F, oc. 2, freehand sketches. July 31, 1894, before dinner.
Fig. 11. Living. Magnified about 1800 diameters. Zeiss obj. F, oc. 4, long tube, cam.
luc. July 31, 1894, 6 p. m.

— 12. Living. Same magnification as Fig. 11, freehand sketch.

— 13. Living. Magnified about 1500 or 1000 diameters. Zeiss obj. F, oc. 4, cam. luc.

but tube somewhat shorter than in Fig. 11. July 31, 1894, 9 p. m.

— 14. Same magnification as Fig. 13, and cam. luc. at 915 p. m.

— 15. Freehand sketch. Same magnification. The organism is so turned that d has

come on the under side of the body, and is seen through it. 9'30 p. m.
Figs. 16 — 19. Freehand sketches. Same magnification. (Zeiss obj. F, oc. 4). July 31,

1894, night.
Fig. 20, a — d. Formations seen while studying the organism PL VIII, Figs. 1—3, amongst

its cell contents, squeezed out. (Zeiss obj. F, oc. 4; freehand sketch).

The Norwegian N.- PolarExpedition1893-96 N?16.

PI. VI

.5.

13.

F. Nansen ad nat. del.

Trykt i den private Opmaaling, Chra.

PL. VII.

Fig. 1 a— c. Small flagellatum-like organisms (or germs?) of this kind were very common
jn most preparations taken from the accumulations of alga? in the ponds on the
ice. The three figures represent the same individual in different positions, c is
less magnified (760 diameters) than a and 6 (12S0 diameters). It is from water
taken on July 28, 1894, and kept for six days in a bottle in the laboratory. The
refractive small globules in the interior, were generally situated near the one end,
but in other, and greater individuals, they seemed to be more uniformly dispersed.
Most of the globules were yellow, whilst some were reddish brown (see the
greater, darker grain in Fig. 1, a). X is a protuberance on the side of the body.
In another individual a similar protuberance was situated in the opposite end of
the cilium.

The individual here represented was at first more elongated and oval, but when
the movement began to cease it became more spheroidal as in the figures. The
length of the specimen without the cilium was 0'0139 mm.

Fig. 1 a and b, Zeiss obj. F, oc. 4; cam. luc. Fig. 1, c, Zeiss obj. F, oc. 2 >
cam. luc.

- 2. Similar organism from a half percent solution of Sodium Chloride made by Dr.

Blessing with water from a pond on the ice. and kept in his cabine for several
days. Killed with Osmic Acid. Aug. 3, 189*. Length of body was 00087 mm.
(Zeiss F, 4, medium long tube, cam. luc). Other individuals were round, but had
the same appearance and similar yellow or brownish globules inside.

- 3. Fresh state. Aug. 2. 1894. Bodies similar to this, of the same size and appea-

rance, often observed in preparations of algas from the pond on the ice. They
were sometimes hexagonal like this, and sometimes approached the pentagon.
They had a yellowish colour. While being drawn, it changed in shape to some
extent, the hexagon became less regular, the two sides were curved inwards, and
more corners were formed (a). Magnified 1280 diameters. (Zeiss obj. F, oc. 4,
cam. luc).

- 4, a—c. Living. Aug. 2, 1894. A great number of organisms of this kind were seen

m all preparations taken from the same bottle as Fig 1, (taken July 28, 1894)
They are possibly individuals of the same kind as those illustrated Pis. V and
VI. The appearance was much the same, they were perfectly colourless, and
there was no distinct structure in the interior. ' The tail or stalk on all of them
was, however, fixed to the side of the body (Fig. 4, a and c) and not to the end,
opposite the cillium. Some had a more elongated body like PI. VI, Fig. 7. only
the anterior end, at the cilium, being more pointed (Fig. 4, a). Fig. 4, b is the
same individual as a, drawn a little later; it was not possible to decide whether
X had been developed as a protuberance or bud from the body, or had been
fixed to it from outside; it was suddenly seen at the side of the organism.
At the same time the vibrating movement ceased. It is not known whether
the cilium then disappeared, but it could not be seen any more. At this moment
the individual was unfortunately carried away by currents in the water, and the
observation terminated.

Fig. 4, a and b magnified about 1200 diameters (Zeiss F, 4, freehand sketch)
and c 760 diameters (Zeiss obj. F, oc. 2. freehand sketch).

The following organisms (Figs. 5—12) were all of them seen alive in prepa-
rations from the same water as Fig. 2, (a half percent solution of Sodium Chloride
made by Dr. Blessing). The figures are rough freehand sketches made with the
same magnifications (about 1400 diameters, Zeiss obj. F, oc. 2, long tube).
Fig. 5, a, b. A very refractive, almost structureless body, with no movement, a repre-
sents a later stage than b. The bud-like protuberance on the side was formed
during the observation.

— 6, a, b. Very small bluish organism, fixed to the glass at the end opposite the

cilium. b was later than a.

— 7. Very small organism fixed to the glass in the pointed end (/).

— 8. Came swimming, and fixed to the glass at /. This individual was much smaller

than the following.

Figs. 9—11, and 13. Represent the same individual, but the order is wrong. Fig. 13 a — c
was first drawn, and shows the individual as seen from different sides. The
other sketches of this individual was drawn in the following order: Fig. 11, d,
C, b, a, Fig. 10 and Fig. 9. The individual was the whole time fixed to the glass
at the pointed end (/).

Length of body without cilium, 0007 mm.

Fig. 12, a — c An individual which was at first fixed (Fig. 12 c and 6); but then loosened
itself and swam away (Fig. 12, a).

The Norwegian N-PolarExpedition1893-9S NS16.

PI.VH

c.

OL^

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11.

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■7

F. Nansen ad.nat. del.

Trykt i den private Opmaaling, Chra

PL. VIII.

Figs. 1—2. Suctoria gen. sp. Alive. For description see pp. 19—21. From a pond on
the ice, July 30, 1894. Magnified about 760 diameters (Zeiss obj. F, oc. 2; cam.
luc).

Fig. 3. Margin of the same individual. Magnified 1280 diameters (Zeiss obj. F, oc. 4;
cam. luc).

— 4. From a pond on the ice, July 24, 1894. Killed with Osmic Acid, stained with

Borax Carmine. Organisms of this kind were often seen in different preparations
of algee from the pond on the ice. They were never seen moving. The whole
surface of the organisms was densely covered with sand-grains, some of which
were long and very refractive, looked like silica spicules of diatoms. In this
figure only those grains are drawn which were visible in one microspic field,
simultaneously with the nucleus. The cell did not appear to have any outer mem-
brane. Magnified 1150 diameters (Zeiss Horn. Im. ' / 1 s» oc. 2; cam. luc).

— 5. Probably a larger individual of the same species as Fig. 4. From a pond on the

ice, July 27, 1894. Killed with Chromo-Aceto-Osmic Acid, stained with Borax-
Carmine. Drawn in the same way as Fig. 4, so that only those sand-grains situ-
ated on the same level as the nucleus are visible. Magnified about 1000 diameters
(Zeiss obj. F, oc. 3; cam luc).

— 6. Several individuals of this kind, were seen in a preparation from a lump of alga?

floating in a channel between the floes, nearly 2 metres deep. They had a rapid
vibrating, flagellata-like movement, but were fixed, as it seemed, to diatoms. The
grains inside them were refractive with a greenish blue colour. There was appa-
rently a spiral-winding in the body, which became visible by the effect of the
Osmic Acid (see Fig. 6). The cilia were as far as could be seen in ciliatory
motion, but it was probably the tail which produced the vibrating flagellata-like
movement of the body. The length of the tail could not be decided. A vacuole
was very distinctly visible in the posterior end, but was never seen contracting.
Where the body was fixed, could not be seen, but to judge from the mouvements
it was on the under central part.

Aug. 3, 1894. Magnified about 1000 diameters (Zeiss obj. CC, oc. 5, long tube ;
cam. luc). Length of body without tail 0027 mm. Killed with Osmic Acid.

— 7. Globular Alga. Living. From channel between the ice-floes, Aug 3, 1894 Mag-

nified about 460 diameters (Zeiss obj. CC, oc. 5; cam. luc). Diameter of cell
0'15 mm.

— 8. Globular Alga. From same place as Fig. 7, Aug. 3, 1894. (Zeiss obj. CC, oc. 5;

cam. luc). Diameter of cell O'll mm.

The Norwegian N- Polar Expedition1893- 96 Nfl6.

PI. Vffl

F. Nansen ad nat del.

Trykt i den private Opmaaling, Chra.

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