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The fact (b), discussed and admitted
since 18j3 by the French Academy of
Science, makes Prof. Thurston's proposi-
tion (2) appear as a fallacy.

(3) In the case of ocean going vessels,^
friction rates with their weight and not
with their surface, it rates with the values
B and D, and is therefore no independ-
ent coefficient, no factor in the premises
at all.
and as an effect of weight it becomes
for smooth faces only an insignificant co-
efficient,* when compared with the sole
one by which indeed the resistance to
relative motion can be valuated. Beau^
foy found the cohesive action on wetted
smooth solid surfaces to act as an in-
crease of the effect of weight in relative
motion to amount to 0.32 kg. per square
meter.

Proceeding to Prof. Thurston's third
proposition, I find that he establishes
the hemisphere as a standard form for
comparing others therewith, or to serve
as the first form of B to be considered.
I beg leave to more closely accommodate
to mathematical precedent in selecting
the cube=l' as standard form for com*
parison, because our arithmetical and ster-
eometrical system admits of no other,
all values relating thereto and not to the
sphere. As first power for this cube I
then select the sole dimension for length
used, also by Prof. Thurston, assuming
that it be his intention, though not
stated, to exclusively speak of effective
length or of the length on the water-
line, for which length I have selected the
expression =d.

The form of vessel first referred to in

* How loDff time it takes for new results in solentiflo
research to reach even those most interested In these
results is well illustrated in th** mutter of friction.
The Annual of the Royal School of Naval Arch'teo-
ture and Marine Enelneerini; for 1879. in an article
'* Comparative Renttancet o( Ships, etc./' has the fol-
lowing^:

I The resistance opposing the motion of any vessel
I is of two kiDds-Ruiiace rriotion. Knd.XDhat ii commonly
catted direct head resistance. The same article si atfS as
experimental result; "the resistance from friction Is
less per foot of length for a long surface than lor a
short one." With all this the results of scientific re-
search on the subject made by the three French scien-
tists forty years earlier, were then unknown at the
Bnulish Royal Naval School, as they at present were
to Prof. Thurston.

Digitized by

188

VAN nostrand's engineering magazine.

proposition (3) can as to its volume then
be correctly expressed by :

I then may be permitted to generalize

the value - X^jSO as to render it applicable

to all cases and to all forms of vessels, or
to all values for B, and to do so by call-
ing this value the ratio of tJie volume of
the immersed part of vessel to the cube of
its length (=R.o.V.) Then I have a gen-
eral valuation for all vessels without ex-
ception in

B=(rxR.o.V.
Or, we may express this same value in a
more plastic manner and method by writ-
ing it as

'B-<Px{dxB.o,Y,)

This applied again to the hemisphere
[compare proposition (3)1 would read :

B=J*x — 2 — d.

When comparing the spherical form
with other forms d* constitutes the trans-
verse section and -^ — d, the length of

a body being in volume an equivalent

,,,,., 0.5236

of the hemisphere, or — = — represents

a coefficient to tlie section cP, the two
representing the value as " Transverse
average section '* of an equal volume of
uniform transverse section having d as
length.

Having thus prepared a basis f >r com-
parison of different forms for the same
volume, I may proceed to test proposi-
tions (3 and 4) on their merit. Proposi-
tion (3) speaks of the resistance to mo-
tion (=R), proposition (4) of the power
demanded to propel (=P). As the power
to propel required (=P) does not depend
on qualities of the vessel alone, but depends
also on the modus of applying such power
as against the resisting medium, and fur-
ther on the qualities and conditions of
the resisting medium, it is absolutely im-
possible to measure the value P by the
quahties of the vessel alone, as Prof.
Thurston attempts it in his fourth prop-
osition. But the resistance to motion
(— R) of vessels of all shapes, in all rela-
tive positions and at all velocities imag-
inable may be measured, rated and com-

pared by qualities exclusively of these
vessels themselves.

Therefore, when Prof. Thurston rates
the value P exclusively on qualities of
the vessel he commits an error. But if
we were to substitute the value for re-
sistance (R) for the value for " propelling
power required" P, even then would
proposition (4) not hold good, which, ex-
pressed in typical values, would read :

PorR=cr = MS.
Now MS, in the case referred to, is as

MS=|xi=0.3927

<r=2

and

As true it is, that 2 > 0.3927,

as true it is that the propelling power

canot be measured by tiie square of the

vessel's length, and also by the area of her

transverse major section.

Knowing already either one or the
other of Mr. Thurston's propositions (4)
to be false, it may further be shown,
that both are fallacies, even when reduc-
ing the value P to the value R as exclus-
ively rational in the premises,
^d it may also be proven that
R=<rxR.aV.
be correct for all cases of motion of im-
mersed or submerged solids relative to
fluids (water, air), and for bodies (ves-
sels) of all forms and under all variations
of relative position of the given form to
the direction of motion, as long as it be
properly understood :

(a) That d is in all cases the length
(axis) in the direction of relative
motion.
{b) That such part of the fluid as re-
mains comparatively stationary
with the solid as a consequence
of the form of the solid and of
the cohesion proper of the fluid,
must be considered in all dynam-
ical relations as a supplementary
volume to that of the solid.
To express the proposition
R=^xR.o.V.
in words, the reading would be as fol-
lows:

*' The resistance offered by an immersed
(or submerged) solid (vessel) to relative
motion as against the liquid (or fluid)
(immersing or submerging) varies for all
forms and relative positions as the trans-
verse average section^ or as the section
of an ideal solid, to which the length of

Digitized by

THE LIMIT OF SPEED IN OCEAN TBAVEL.

189

the given solid in the direction of rela-
tive motion is the length (=6?), the ideal
solid having a uniform transverse section,
and the volume of both being equal."

" And such resistance is neither repre-
sented by the transverse major section
nor by the square of the solid's construc-
tive length."

I may then be permitted to render
proof for such thesis.

As I undertake to overthrow tradi-
tional and so far uncontradicted prop-
ositions in dynamics, there is a resulting
class of proof for what new thesis I pro-
pose. I therefore may be pardoned for
the use of such elementary method.

Only by returning to the very simplest
of given conditions is it possible to over-
throw errors, set up by time and tradi-
tion as invulnerable dicta, having assumed
almost the general acknowledgment as if
they were axioms.

I propose to make use of a burette
having a transverse section and bottom
=1*, and to fill it with water of a density
=1 to an elevation of 10-0.6236. And
I propose to use a solid sphere with a
diameter =1 and a consequent volume

=rx 5 =0.5236.

D

and also of a density =1.

Carefully avoiding all effect of ffil, as
foreign to the problem underhand, which
concerns only the measurement of dis-
placed volumes, I immerse the described
sphere in the described column of water.
From the conditions, as stated, it will
then be found to have resulted, that the
buoyancy of the sphere is attained at the
point of its total immersion. But its
total immersion will occur at a point
0.5236 higher than the elevation at which
the column of water stood previous to
the immersion. And the elevation of the
total column of water and sphere therein
submersed will be

=10-0.6236 + 0.6236=10.

And the upper l*of the column will then
consist of 1* X 0.5236 solid -f l*x 0.4764
liquid.

It is on the basis of the conditions as
thus given that I shall consider the fur-
ther effect of relative motion of solid and
hquid.

Be it assumed that the solid sphere after

being fully immersed shall descend in
this column of a uniform transverse sec-
tion = 1", and of an elevation =10 for a
distance=], equal to its own diameter
(in this case=c/, or as the length in the
direction of motion). While at the start
of this later motion and under an assumed
elevation of 10, the upper 1' consisted of
rxO.5236 solid -K 04764 liquid, and the
2d 1' thus consisted exclusively of liquid
in volume as 1', subsequent to the fall
for a distance =1, the upper or 1st 1*
will consist of all liquid, an addition
thereto having been made for -h 0.5236 of
liquid, which same portion has been
raised from the 2d 1' to the Isl 1'. Ex-
pressed in words this fact would be

'^By a fall in submersion for the 4is-
tance of its own length measured in the
direction of motion, a solid raises a vol-
ume of the liquid equal to its own vol-
ume for the distance of its own length
measured in the direction of fall."

Would I use in place of the burette a
horizontal trough measuring l*xlO, and
filled with water in volume equal to
(I'X 10)— 0.6236, and immerse therein
the sphere of a diameter =1, thus filling
the trough, and if then I would move
the sphere horizontally the effect would
then be a horizontal displacement of the
same character and value in place of a
vertical displacement in the previous
case.

And then the result may be expressed
by:

^'The motion of a solid in immersion for
once its own length, measured in the di-
rection of relative motion displaces a
volume of the liquid being equal to the
solid's own volume."

For want of space I must desist from
further demonstration of the absolute
and general correctness of this proposi-
tion, but must leave it to critical readers
to ascertain the fact for themselves. The
proposition is true for all dynamical re-
lations as between solids immersed and
immersing fluid.

I shall draw attention only to one use-
ful conclusion to be drawn from this
proposition amongst many it will permit,
one relating immediately to the subject
under hand. And the conclusion thus
drawn represents a definite answer in it-
self to one of the questions, according to

Digitized by

190

VAN NOSTRAND'S ENGINEERING MAGAZINE.

An ocean steamer measuring on the

800
water line a length =800 feet

3.28

=243.9 meters weighing and displacing
in initial immersion 38,000 tons, or per

meter of immersed length ' =155.8

ions, does move from its front to its keel
per meter of travel 155.8 tons of water.

If such steamer shall travel 2,000 meters,
with a speed of about a nautical mile in
■every three minutes, or twenty miles an
hour, then its pumping capacity should be
2000
=-^X 158.8 tons = 103.866f tons or

cubic meters of water per minute, when
no power is wasted in creating waves.
And the horizontal column of water
having the length of travel to be moved
lor the distance of the immersed length
of the ship will have a uniform trsuos-
verse section =155.8 square meters.

The raising of this quantity of water
for 1 foot in one minute would demand
6.295 theoretical horse-power. If the
Bssumption of Prof. Thurston be correct,
that such a ship would require for the
production of approximating such speed
35,000 horse-power, then the horizontal
removal from front to stem for a dis-
tance of 800* must be equivalent to the

.... . 35,000 . _ ^ ....
raismg thereof ^ =5.56 feet high,

which it need not be under proper meth-
od for removal on the proper line of mo-
tion.

Having thus demonstrated the labor
perf ormable by each steamer under given
conditions, I may proceed to answer the
question of shape in as definite a man-
ner.

In my elementary experiment I have
demonstrated with a shape of volume
having, as ships have a non- uniform
transverse section, or with a transverse

major section of =j.

But a cylinder of equal length =c?=l
having a uniform transverse section AS=

^, being in this as in all cases by

D

volume=(f X R.O. V. as AS=cP X R.O. V. =

1* X 1 ^ possesses an equal volume with the

sphere considered, d being =1 for both.

But AS : MS=2 : 3.

If these two different forms for the
same volume are treated as I have treated
the sphere all the effects of motion and
displacement obtainable and perceptible
from the remaining result are identical.
The transverse average section is in com-
mon to both, the major section being only
a quality for one, which has in no wise in-
fluenced the remaining result of displace-
ment. And with the remaining observ-
able result of effective displacement
alone I am dealing at present

What is called head resistance is in-
deed no more than the increase of vol-
ume of moving solid by shape causing
part of the medium to also move with
and as if a supplementary part of the
solid volume, and may be treated as a
special matter, when first the influence of
volume be properly understood, and of
shape in general for equal volumes. The
effect being the same the resistance such
as dassified must be the same, and thus
not the transverse major but average
section is conditional to the measure-
ment of resistance, and such resistance
is in consequence properly expressed by

R=crxR.o.V.

The effect of the indicated motion of the
sphere is undeniably uniform, and not in-
termitt ent for all motion at uniform veloc-
ity. The displacement for the length of
motion =v is in consequence the same as
such by a body of equal length =1 hav-
ing a imiform transverse section. And
this uniform transverse section is in all
possible cases-=d*xR.o.V.

Thus the permanent, lasting constant
effect of relative motion of submerged
solid and submerging liquid is properly
expressed as R=^xR.o.V.

The next step to be taken in my ele-
mentary demonstration will be to con-
sider the effects of motion and displace-
ment by equal volumes with different
axes in the direction of motion. I there-
fore make also use of a parallelopiped

B=rxf=rxfi=o.5236.

b o

And I propose to consider the motion in
submersion of this parallelopiped once in

the direction of its axis (2* = ^, and an-

o

other time in the direction of its axis

«?**=1. When moving on its short axis

Digitized by

THK LIMIT OF SPEED IPf OCEAN TRAVEL.

191

=fr = -a total volume=D(*) is displaced

within a moving distance =V(*)=^ =<r.

When moving on its long axis fl?"=l,

a total volume D(")=r^ is displaced only
o

within a moving distance V(")=l, but in

Tt

moving only a distance V*=x the result-
ing displacement D'*' from motion on^^the
axis d=\ would only be

"6 ^6 ""6^'

and therefore

By

D^D-=R«:R«"=?:|,=1:^
R=d«xR.aV.

we have R*=^X-i=l,

and R»'=rx|^=|

and B': B-=l : %

o

or at the precise inverse rate of their sub-
merged length measured in the direction
of motion.

The result of this experiment, the full
And further testing of which must also be
left to critical readers, then would be ap-
plicable on ships and ocean travel in the
following form :

^^ The resistance to two ships in motion
both having the same amount of volume
submerged, but being of different length,
rates for one and the other at the in-
verse ratio of their (submerged) length
measured in the direction of their mo-
tion, the shorter one, with same volume
finding the greater resistance (under
equal velocity), and a resistance increased
at the the same rate as its (submerged)
length in the direction of motion is short-
er than that of the vessel of same sub-
merged volume with which it is com-
pared."

As early as November, 1881, I di-
rected attention by publication to the
fact, that a correct rating for resistance
of ships for insurance purposes, for speed
measurement, and for nautical construc-
tion may be obtained from this formula,
<Comp. F. & M. Rd., Nov., '81.)

If in the light of these results we sub-
ject Mr. Thurston's proposition (3) to a
critical test, we may establish the rela-
tive resistance (=R<«>) of a hemisphere
to motion by R=(/'xR.o.V. as R(«)=r

y - — jr, as often as the diameter 1 is in
6x2'

the direction of motion. A cylinder of a

transverse section=:r^=0.2618 with a

length d=l would produce the absolute-
ly identical effect in displacement with
equal velocity.

Which, then, is the elongated form
" tohich gives the minimum head resist-
ance,^' referred to by Mr. Thurston as
nonplus vXtrOy as between which and
the hemisphere the practicable achieve-
ment must remain intermediate?

The displacement theory can give an-
swer also to this query.

By building a vessel of the same

submerged volume R=^ u^ ^^ shape

of two half cones of an elevation =1 with
bases joined, the result will be a length
(;=2and

by volume=2"xR.o.V.=:7^,

12'

and by

and

R.aV.=

n

8X12'

R=2*x

Tt

Tt

8X12"'24'

Or, again, by doubling the length for the
same volume the resistance is reduced
to one half.

Therefore, there is good reason for
lengthening the axis in the direction of
motion, and good reason for facing mo-
tion with a sharp angle in order not to
increase the moving volume, because real
head resistance is the cause of moving a
part of the liquid, as if it were a part of
the solid.

It is sufficient to know that the essen-
tial conditions by which the resistance of
a vessel to motion must be rated is its
submerged volume as a consequence of
its weight, and that the main quality les-
sening resistance thereof is the distribu-
tion of such given volume and weight
over as great a length and as small a
transverse average section as possible.

Proceeding then from the valuation of
resistance (=R) to valuating propelling

Digitized by

192

VAN NOSTRAND'S ENGINEERING MAGAZINE.

power required (=P), it follows from
the facts, as shown, oamel j, that resistance
does not rate as cT the square of length,
and does not rate as MS, the transverse
major section, that neither P the pro-
pellmg power can thus rate.

The propelling question, or the ques-
tion of overcoming such resistance to
motion, demands

(a) The production of the highest me-
chanical power by the least weight
of machinery and coal.
{b) The application of such power in
the most effective method against
the medium offering both the re-
sistance to motion and to the
propelling power applied.
All endeavors of late years have ex-
clusively been in the direction of the
point a. Since the substitution of the
screw for the paddle-wheel no progress
has been made in the direction of the
point b, but as the world is ready for one
step more, it will inevitably be made, and
I would be much pleased if nautical con-
structors would deign to take the hint
and try the pump once more, but this
time taking the water from the ship's
front and ejecting it stem ward in a
straight line in absolute conformity with
the intended motion, taking the precau-
tion to take up the water in a narrow
vertical line at the head, and to eject
stem ward on as broad a face as practicable
BO as to lessen the resistance in the direc-
tion of motion, and to increase it where it

is contributive to motion. In the method
of jet propeller, hitherto exclusively
tried, the inlets and outlets were in abso-
lute conflict with the teachings of my
new displacement theory.

" 'llie ship of the next century " need
not be, as Prof. Thurston forestalls it,
a naval Babylonian tower, but it will be
one of rational dimensions, being in har-
mony with such dimensions as the human
race can properly master and control ; but ,
"M« ship of the next century^^ will first
apply its motive power in a more rational
method than the jwopeller screw repre-
sents. The crank-shaft will be done
away with. The water, to be moved from
head to stem in order to produce relative
motion, will be conducted not on a cir-
cuit around the good ship's body, but
right through it lengthwise in a straight
line, and the water rejected at the stem
will steer the vessel. And the propelling
power will be applied to the screw at
its circumference, in place of its center
if a screw be used at all. And in conse-
quence the weight of machinery for ex-
ercising the same propelling power will
be materially less. And the resistance
of the water at the stem being increased,
and the resistance at the head being les-
sened, the same amount of power will
produce greater speed. Thus, not a
"Leviathan" representing increased di-
mensions, but an *• Investigator '* repre-
senting the progress of human thought^
will be " the ship of the next century."

THERMO-ELECTRICITY.

From "The Bleotrician.**

Although many combinations of con-
ductors producing a greater or less E.M.F.
under the influence of heat have already
been described, the search for bodies
which possess this property has acquired
a fi^reat interest on account of their pos-
sible application to thermo-electric gen-
erators. M. G. Chaperon has, according
to the Hevt^ Ltdustrielle, methodically
studied from this point of view a certain
number of chemical compounds, chiefly
chosen amongst those which can be easily
reproduced in their active state. The
method employed in this research is
characterised by being applicable to frag-

ments of any form whatever, and, if need
be, of very small dimensions. It consists
in applying two points of one of these
fragments to two metallic walls, which
conduct heat well, whose temperatures
are evaluated as closely as possibly, and
which serve as electrodes to show and
measure the E.M.F. of the couple thus
formed. One of these walls is that of a
thin silver tube traversed by a current of
water at the temperature of the surround-
ing air, and forming part of a pair of
pincers with which the body under con-
sideration is held. By means of these
pincers a second point of the body is ap-

Digitized by

STRENGTH OF OBLIQUE ARCHES.

193

plied against a hot wall, that of an iron
crucible full of fusible alloy, and into
which a thermometer is plunged. Con-
tact ought to be insured by a constant
pressure. The procedure is then to
measure during slow variations of tem-
perature a series of values of the dif-
ference of potential of the two plates.
The iron crucible is united to the elec-
trical measuring apparatus by a silver
wire sufficiently long for its extremity to
remain cold. The E.M.F. measured is
then, in virtue of the law of successive
contacts, that of the couple formed by
the body which is under investigation
and silver. For certain compounds cap-
able of attacking iron a thin leaf of silver
is also interposed at their point of con-
tact with the crucible. For more elevated
temperatures another arrangement has
also been employed, in which the hot
contact is taken at a point of a silvered
copper bar heated at one extremity. The
temperature is evaluated at another point
of the same section of this bar with a
second body already studied, and which
thus serves as thermometer. In the
various couples thus formed the contacts
of active substances with the electrodes
ought to take place by small surfaces,
Vhich are as distant from one another as
possible, in order that the temperatures
of these contacts may be as nearly as
possible those of the electrodes, which

alone can be estimated. One thus obtains
with substances in general bad conduc-
tors elements of an enormous resistance ;
therefore the rapid measurement of the
E.M.F.'s is only rendered practically
possible by the use of Lippmann's elec-
trometer. Besides, this onij serves to
show the equilibrium of the force meas-
ured with that given by a potentiometer
with wire of a reduced form giving ycVr*'^
of a volt. It is possible with this conjoint
apparatus to obtain sufficiently easily
curves representing the law of variation
of the E.M.F.*s as functions of the fall of
temperature. M Q. Chaperon then
quotes some examples of measures thus
made on substances little studied and
enumerated below. Positive bodies:
iodide of silver, phosphide of zinc, sul-
phide of tin, crystallised galena, oxide of
copper in a very thin plate, arsenide of
zinc. Negative bodies ; sulphide of silver

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