IMPROVEMENTS IN CONSTRUCTING STEAM AND OTHER SHIPS, BOATS AND AERIAL MACHINES, so as to REDUCE THEIR RESISTANCE
Year: 1871

page_text: LETTERS PATENT to Richard Boyman Boyman, of Park Hill, Clapham
Park, Surrey, for the Invention of "IMPROVEMENTS IN CONSTRUCTING
STEAM AND OTHER SHIPS, BOATS AND AERIAL MACHINES, so as to REDUCE
THEIR RESISTANCE.”
Sealed the 29th September 1871, and dated the 10th April 1871.
PROVISIONAL SPECIFICATION left by the said Richard Boyman
Boyman at the Office of the Commissioners of Patents, with his
Petition, on the 10th April 1871.
I, RICHARD BOYMAN BOYMAN, of Park Hill, Clapham Park, Surrey,
3 do hereby declare the nature of the said Invention for "IMPROVEMENTS
IN CONSTRUCTING STEAM AND OTHER SHIPS, BOATS AND AERIAL MACHINES, SO AS
TO REDUCE THEIR RESISTANCE," to be as follows:-
The Invention consists in constructing steam and other ships, boats
and aerial machines according to the form of least resistance with
the greatest carrying or defensive power in a given length, discovered
by me.

page_text: In deject is to improve mayal architecture and to save part of He
first cost and weight of engines, boilers, and water, also to save con-
sumption of fuel and its weight. For besides saving in expense, much
less weight reduces immersion and resistance, and so saves more power
in overcoming such resistance..
.
The form of least resistance is a body which displaces the least
quantity of fluid with the greatest length of body and finest front and
end.
The fundamental principle of my Invention is that a body displaces
a certain weight of fluid in its whole length, and that the opposition of
the mass to continuous displacement and deflection makes the chief
resistance to the motion of the body.
Now the chief obstacle to the displacement of fluid is the midship
area, and this obstacle must necessarily be diminished in proportion to
the additional length of the ship, or the displacement could not be
kept the same. We take away then that part of the body which either
in breadth or depth, or both, costs most power to displace fluid, and
put such part where it will displace the same quantity of fluid, but
cost no power to do it except mere skin friction, for the additional
length simply follows in the wake of the body, whose resistance has
been already overcome by the bow. Hence the very part of the midship
area which it is necessary to take away and put into length to reduce
resistance may be made to reduce it still more by making the stern
finer and the bow much finer in order to displace the fluid far more
gradually than is now done. This may perhaps so reduce the resistance
as to make it inversely as the squares of the length of the body instead
of inversely as the length, as the law of least resistance is independent
of such increased length of bow.
There is, however, another resistance, that of the friction of the
immersed body against the fluid called "skin resistance," but I
have discovered that this is so small compared with the displacement
or primary resistance that the skin resistance may be practically
neglected.
It is not considered necessary to explain here the laws of physics,
mechanics, and philosophy, on which my discovery of the form of lcast
resistance is based, or to give the formulæ to embody its laws. I will
therefore describe my Invention for carrying my discovery into effect,
and for this purpose will take the ironclad "Northumberland" for illus-

page_text: tration; she is about 400 feet long, 59 feet broad, and has a mean
draught of 27 feet. By doubling her length and making her (2×400=)
800 feet long, with the same displacement her resistance would be
reduced one half. This would save about half of the first cost of engine
power and fuel and considerable weight, and by thus reducing immersion
and resistance would save more power and fuel. But to maintain the
same displacement with a length of 800 feet as with only 400 feet her
sides now above water must not be continued any longer. The additional
length of 400 feet must be merely covered over in a circular or angular
form, and be under water or nearly so.
Suppose it should be found that covering over such additional length
would add materially to the weight of the ship, and consequently to
her displacement, we must then cut down such part of the 400 feet
of her sides now out of water as would make up for the increased weight
of covering over the 400 feet of additional length required to be under
water. If then the deck and sides were reduced to only 200 feet in
length above water (800-200=) 600 feet of the whole length would
be under water or nearly so. It may not be necessary for war purposes
that turret or broadside ships should have a longer deck than 100 feet.
We should in such case first take from the sides and deck of the
300 feet cut down such weight as would be required to make up for
the increased weight of covering over the additional length of 400 feet
under water. All the weight that then remained would be added to
strengthen the turret and sides of the 100 feet exposed, in which case
(800-100 =) 700 feet would be under water. Such an ironclad would
be invulnerable compared with those of the present day, besides having
only half the resistance she has now: She would therefore be able to
keep the sea under coal twice as long as other ships, and having only
about half the draught would be able to go any where and do any thing
compared with the present ironclads.
The same principle applies to all ships of the present length, though
not so advantageously. For additional length with the same displace-
ment are the fundamental principles of my discovery and Invention.
Their practical advantages will be seen clearer by applying them to
the four following cases:—.
1. By doubling the length of a ship, and keeping the same displace-
ment, the capacity for the motive power and cargo would be about the
same with about half the resistance.

page_text: 2. By doubling the length and displacement with the same draught
the resistance would be about the same as before.. But then we get
about twice the capacity for the motive power and cargo which gives an
advantage equivalent to example 1.
3. By keeping the same length and draught the capacity and resistance 5
would be the same. But still the least resistance with advantage of
greatest defensive power would be obtained by constructing the ship
according to my Invention.
4. By keeping the same length and halving the draught we should
get about half the resistance but then only half the capacity.
]
Every example here given embodies my Invention of the ship of
least resistance with the greatest carrying or defensive power in a given
length even in examples 3 and 4, where the principle does not seem to
apply. For more than one half of the ship (covered in of course) will
in every case be under water or nearly so. Hence, such part will not ]
have to bear the weight of any sides. It can therefore be added to the
defence of the parts above water, so that even examples 3 and 4 will
combine the least resistance with the greatest carrying or defensive
power in a given length. As regards the examples applied to sailing
vessels where additional defence is not required. The weight taken :
from the sides of the part under water will be just so much gain added
to the speed or cargo. Or should such weight not be required to
strengthen an ironclad, the draught will be reduced and speed increased
in proportion.
It has been said that surface or skin resistance forms but a small part
of the resistance of bodies passing through a fluid instead of the skin
forming the whole resistance as is generally believed. This part of
my discovery enables me to increase the stability of vessels. This is
by fixing to each side of the ship balance boards projecting one to
twelve or more feet and extending the whole or part of the length of
the ship. These are to prevent rolling, and if somewhat curved top and
bottom they would hold the water better. They may also be made
hollow one or more feet deep for greater buoyancy, tapering at both
ends like huge cigars to reduce resistance, and these may form part of
the capacity of the vessel. They can, too, with the other parts of the
vessel under water be divided into water-tight compartments for safety.
Some of these anti-rolling projections may be made in different lengths,
hinged to the sides of the ship, and by means of rods and suitable

page_text: machinery in the ship may be drawn close to the sides and pushed and
kept down when required.
T
A further part of my Invention is that each side of the ship may be
made to project over the water several feet for berth accommodation or
other purposes. These projections may be supported by the water to
the extent of one or more feet deep and hollowed somewhat beneath
to hold the water better to prevent rolling. They will at the same
time form the freeboard, and protect the crew. Both ends must be
fined off as much as convenience will permit to prevent unnecessary
resistance.
It is doubtful if such very long ships as will best carry out my
discovery and Invention, and so save most engine power, fuel,, and
weight, could be propelled and turned conveniently with the present
screw, single or double. I combine therefore with such Invention my
former Invention of reaction propulsion described in my Specification
of 3rd March 1870, No. 623. And it may be found more convenient
in practice to make bow and stern of the same fineness so as never to
turn. Such ships too can be steered by my small hydro-propellers at
each end driven by locomotive high-pressure engines.
The form of least resistance is the form of least resistance for all
time. It can never therefore be superseded, and is applicable to every-
thing driven through a fluid--steam and sailing ships, yachts, life and
other boats, aerial machines and projectiles. It is well adapted for
steam life-boats propelled by one of my reaction propellers in the
middle and driven by high-pressure engines with a fire-engine or
similar boiler.
SPECIFICATION in pursuance of the conditions of the Letters Patent,
filed by the said Richard Boyman Boyman in the Great Seal Patent
Office on the 9th October 1871.
TO ALL TO WHOM THESE PRESENTS SHALL COME, I, RICHARD
BOYMAN BOYMAN, of Park Hill, Clapham Park, Surrey, send greeting.
WHEREAS Her most Excellent Majesty Queen Victoria, by Her
Letters Patent, bearing date the Tenth day of April, One thousand
eight hundred and seventy-one, in the thirty-fourth year of Her reign,
did, for Herself, Her heirs and successors, give and grant unto me

page_text: 1
the said Richard Boyman Boyman, Her especial licence that I, the
said Richard Boyman Boyman, my executors, administrators, and assigns,
or such others as I, the said Richard Boyman Boyman, my executors,
administrators, and assigns, should at any time agree with, and no
others, from time to time and at all times thereafter during the term
therein expressed, should and lawfully might make, use, exercise, and
vend, within the United Kingdom of Great Britain and Ireland, the
Channel Islands, and Isle of Man, an Invention for "IMPROVEMENTS IN
CONSTRUCTING STEAM AND OTHER SHIPS, BOATS AND AËRIAL MACHINES, SO AS
TO REDUCE THEIR RESISTANCE," upon the condition (amongst others) that I,
the said Richard Boyman Boyman, by an instrument in writing under
my hand and seal, should particularly describe and ascertain the nature
of the said Invention, and in what manner the same was to be per-
formed, and cause the same to be filed in the Great Seal Patent Office
within six calendar months next and immediately after the date of the
said Letters Patent.
NOW KNOW YE, that I, the said Richard Boyman Boyman, do
hereby declare the nature of the said Invention, and in what manner
the same is to be performed, to be particularly described and ascertained
in and by the following statement, that is to say:
-
1. My improvements in constructing steam ships and other bodies
passing through fluids so as to reduce their resistance depend on my
discovery in January last of the laws of fluid resistance which govern
the form of least resistance. These laws therefore govern the form of
my Invention, and are in opposition to those taught by the first scientific
authorities of the past and present. It is then manifest that a knowledge
of the laws on which my Invention is founded can alone enable me
particularly to describe and ascertain its nature, and in what manner
it is to be performed. I propose therefore to do here what it was not
considered necessary to do in my Provisional Specification, as there
`stated, namely, "to explain the laws of physics, mechanics, and philo-
sophy, on which my discovery of the form of least resistance is based,
and to give the formulæ which embody its laws."
2. This seems to be more required in a case where Newton, the
illustrious, the first geometer and mathematician of the world, directed
- his penetrating mind to the investigation of the form of least resistance
. and gave a formula for it. His form has been frequently tried and as
frequently abandoned with all its variations.. No one experimented with

page_text: it so much as Colonel Mark Beaufoy, as will be seen in his great
and laborious work, "Nautical and Hydraulic Experiments," preface
pp. XII-XVI-XVII-XXI. Mr. Scott Russell also tried Newton's
form of least resistance with steam vessels of 100 and. 212 feet long,
the unfavorable results of which the distinguished experimenter himself
explained at a Meeting of the Institution of Naval Architects, reported
in Engineering of the 29th of April 1870, extracts from which will be
found in my Specification of that year, No. 623, p. 37.
3. Moreover the learned Dr. Rankine is one of the most renowned
men of science of our time, Regius Professor of Civil Engineering and
Mechanics in the University of Glasgow, F.R.S.S. L. & E., and his work
on Ship Building, the Resistance of Vessels, and other cognate subjects
are the standards and guides of the schools. Now this high authority
teaches the reverse of my discovery, and his teaching is universally
followed. Unless then the philosophy, the physics, and mechanics of
my discovery be first established, the world will certainly not adopt an
Invention unless founded upon them, which in principal and form differs
so essentially from the formulæ of Newton and of Professor Rankine,, for
the resistance of ships, R=fv² S, also from the short ironclads recently
introduced into our navy, at a cost of many millions sterling, and eight
years of irrecoverable time.
4. It has been said in my Provisional Specification that the resistance
to bodies passing through fluids is composed of two things: (1) the
continuous displacement and deflection of the fluid mass; (2) the
friction of the immersed body against the fluid, called skin resistance.
It is also said in such Provisional Specification that I had discovered
that the skin resistance is so small compared with the displacement or
primary resistance that the skin resistance may be practically neglected.
It is this principle which is opposed to the doctrine of the Regius
Professor Rankine, as the mathematician will see in the Professor's
formula, R=fv S. For f is the co-efficient of friction of one square
foot of smooth surface. Beaufoy's experiments of 1798 make it 012 lbs.
at 1 knot an hour, "Nautical and Hydraulic Experiments," p. XCIV.;
v is knots per hour, and S is the immersed surface of the ship. Hence
Professor Rankine makes the frictional surface & the whole resistance,
leaving no resistance due to the weight of fluid resisting being displaced.
It is then necessary to show that this is a fundamental error in natural
philosophy, physics, and mechanics...

page_text: 5. By analogies and resemblances in nature between things apparently
different and by the unity of principle in diversity of action which con-
nects all her operations, my discoveries past and present have been made.
Nothing but implicit reliance upon these simple principles could have
enabled me to bear up and persevere in my labours against so much
positive assertion and contempt that my discoveries were delusions.
For it has been said among other things, that "I put myself in anta-
gonism to the first physical principle of all mechanical science." Still
harder things have been said, some of which are recorded in my
Specification of 1870, p. 18 to 21, as warnings to mathematicians who
are not philosophers, that they may study more the higher powers of
inductive philosophy and right reasoning, than the mere mechanism
of figures. By the same methods that have served me so well through
many years, analogy, resemblance, and unity of principle in diversity of
action, has my present discovery of the form of least resistance been
made. To these methods of discovery then must resort be had to explain
its principles.
'
It
6. A solid, whether at rest or in motion, resists change by reason of
its weight, and requires therefore an adequate force to produce change.
A fluid has weight, and is therefore governed by the same law.
must moreover be displaced before a body can pass through it. It follows
that its continuous resistance to being displaced must be the chief
resistance to bodies passing through fluids, and not the mere surface
friction, as maintained by the schools in the formula R=ƒv² S, given
in paragraph 4. Such then is the analogy and harmony between solids
and fluids. Both resist being moved out of their places.
7. Having then established the principle of displacement, as the chief a
resistance to bodies passing through fluids, we come to the form of
displacement. Here we must go again to the form of a solid. Scarcely
any amount of force would split oak, if a flat-headed divider were used
instead of a wedge. So again, four or five times the number of horses
would not perhaps draw a flat-headed plough through stiff clay land, a

page_text: A wedge-shaped plough is therefore used.
We must then split and
plough through a fluid with the same wedge formed bow, especially
as anything like the thump and shock of seas against a vessel would
retard her, and consume power. Hence in proportion to the length and
fineness of the bow; will it gradually and gently plough its way through
the fluid, simply turning it to the right and left, as a plough does the
furrows, at the least expenditure of power. Here again is harmony
between the form of displacing solids and fluids.
h =
22
v
2 g'
8. Suppose now the bow were cut off. The resistance to motion
would then be found by my dynamical formula R='6 had lbs. where
6 a is the maximum efficiency of plane and fluid impulse discovered
by me in 1842. I believe that the real practical efficiency of a plane
is only 5 a, but to be on the safe side it is here assumed that only 40
per cent. of the water escapes past the plane unutilized, instead of
.50 per cent. Now being the velocity of the vessel in feet
per second, and g the final velocity given to a falling body by the pull
of the earth at the end of the first second of the motion of the body.
This velocity is 32.2 feet, a is the area of the immersed midship section,
and d the density of one cubic foot of salt water=64-18 lbs. By this
|formula R= 6 had lbs. we might find the resistance of all vessels were
there no bow. Now we cannot change a law of nature merely by
putting on a piece of wood or iron, and calling it a bow. All we can
do is to reduce the resistance pursuant to a law of physics by the angle
of incidence of the bow, but to alter the principle of a law is beyond
our power.
9. There is further evidence that the resistance of fluids is, like the
earth to the plough, a dynamic and not frictional question. The furrow
made by the plough remains open, so that any length of body behind
would pass through without more expenditure of power to displace
the earth. Hence the power required depends on the midship area and
fineness of the wedge plough, not on the length behind it. It must
necessarily be the same with bodies passing through fluids, for a law of
dynamics cannot be changed merely by displacing a fluid instead of a
solid. When therefore the bow of a ship or aërial machine has once
opened a passage for the broadest part to pass through, the hull follows
without further resistance from the fluid which the hull displaces.
t
10. We thus establish two new and important principles for the

page_text: advancement of naval architecture, steam, and aërial navigation :—
(1), that the resistance to bodies passing through fluids is due to the
displacement of the weight of fluid, and in one foot lbs. only, as will be
seen by and by; (2), that the hull displacement, which is the chief
carrying capacity, causes no resistance. The formula of Professor
Rankine, given in paragraph 4, is the reverse, for it makes the resistance,
and consequently the expenditure of power, proportional to the whole
length of vessel, hull as well as bow. It is, moreover, fundamentally
wrong in a still more singular way; it makes no difference in resistance
whether the immersed midship area be only half what it was before.
For double the length of a vessel, and halve the draught, and the im-
mersed surface will remain the same, but the resistance will then bo
only half what it was before. Yet by his formula R = fv² S, the resist-
ance will remain the same, because the surface S remains the same.
Now a formula which is irrespective of the midship area immersed,
which makes the chief resistance, is necessarily wrong in principle,
besides being wrong in other respects.
11. The resistance of a weight is calculated in lbs., one foot lbs.
represented by R, and not in feet lbs. represented by Rv. But Professor
Rankine's symbol S includes the whole length of the vessel, and is
therefore a formula in feet lbs., another fundamental error in mechanics.
Now a vessel displaces a given weight of water win its whole length 7.
It follows that in one foot it will displace only
It is then manifest that wo being kept the same the longer the less d, 2
whence by simple logical deduction is evolved the form of least re-
sistance explained in my Provisional Specification. This is a body which
displaces the least fluid with the greatest length.
12. It does not suffice to displace the same weight of fluid by breadth
or depth, for that would increase the area of midship section, which
makes the chief resistance, so strangely omitted in Professor Rankine's
formulæ. It follows then, from the principle of least resistance here
enunciated, that the resistance to bodies passing through fluids is
inversely as their length, provided the displacement and bow and stern
be kept the same. By this simple process of reasoning was solved the 3
problem of ages, the form of least resistance, for all time. A fine bow

page_text: same; but such additional length and displacement increase the carrying
capacity without any additional engine power being required.
4. The midship area and form of bow have great influence on the
speed of the vessel, for the less the arca and the longer and finer the
bow the less the resistance, and consequently the greater the speed.
5. The resistance of vessels is proportional to the weight of water
displaced divided by its langth
It did occur to me that w should be only the weight of water
displaced by the bow and the length of the bow; but as there is greater 1
displacement at some parts of the vessel than at others we must take
the mean displacement through the whole length.
15. Omitting the co-efficient c, the displacement resistance in one
foot lbs. and the midship area resistance in one foot lbs. (were the bow
cut off) seem to me to have some necessary relation. If then the true 2
data of both be found, the displacement resistance R= 0155 lbs., and
the area resistance R= 6 had lbs. (both without the co-efficient c),
should, it is thought, agree sufficiently to show the truth of my present
discovery, that the chief resistance to bodies passing through fluids is
displacement in 1 foot lbs., and not surface resistance in feet Ibs., as 2
shown in the formula fo's. For it has been said, in paragraph 8,
that we could find the resistance of vessels by the midship area for-
mula if we but knew the value of the co-efficient c in such formula,
R=6chad lbs. Now h=1 and 2 g=644, and d=64-18. Therefore
the midship area formula becomes R = 6 ca v³ lbs. If then such 3
agreement be found between the two formulæ *0155 DD* and '6 av³, the
co-efficient c will be the same for both. Both would then be found
to agree, approximately, with my impulse formula of 1869 = for
paddle wheel and screw, R-3 VP lbs., and with my reaction formula,

page_text: R=2 Va (V-v) lbs. for bydro-propulsion, provided the normal re-
sistance is not increased by a foul bottom, or by the vessel driving
a wave before her, or any extraneous cause; for then the impulse
formula would give a higher result.
-3 VP
16. My formulæ for impulse and reaction just given are alone reliable.
Hence those in paragraph 14 are of no practical value, because the
many things that affect the general resistance, bow, stern, midship area,
displacement, and length, vary so much that we cannot find the value
of the co-efficient c without experiments with every vessel.. The formulæ
in paragraph 14 are merely given to show, in symbols, the true principles
of my discovery of the resistance of bodies passing through fluids. To
find what such resistance is of vessels of every form, size, and speed
we must resort to the dynamics of unchanging forms in motion, and
find their modulas of efficiency, and from that the resistance. It is
manifest that this can neither be more nor less than the moving
power that overcomes it; also that this power, like that of all other
bodies in motion, must be governed by fixed and unchanging laws.
The formulæ embodying these laws have been given in the last part
of paragraph 15. But the problem of the resistance of bodies passing
through fluids being displacement and frictional can only be solved by
the laws of dynamics and of friction. The dynamical part of the question
has been already disposed of.
17. The great authority for this being the chief resistance of bodies
passing through fluids is the learned Dr. Rankine, whose formula for
it has been given in paragraph 4, R=fv³ S feet lbs. There is no abler
man of science in his line, more tolerant, more conscientious, more merit-
giving, more courteous. Hence his standing is so high, and his reputa-
tion so great, even European, that it is necessary to destroy his formula,
or it will destroy me; that is, it will destroy the thought, the labours,
and the expenditure of 29 years at intervals, as well as six Patents
(including the present) obtained since April 1866. For all are worthless
if his formulæ fv² S feet lbs. and R = P lbs. are true; because these
and those professors who adopt them are in opposition to me. Thus
have they deterred every one applied to from joining me in introducing

page_text: my past discoveries, so great is the authority of the Regius Professor
and the schools. Since then no one in the world but myself can show
the fundamental errors of these two formulæ, and death may prevent
my doing so elsewhere, the right of doing so here is claimed for the
improvement. of naval architecture and steam navigation, the intro-
duction of aerial navigation, and the just protection of the labours
and expenditure of 29 years of mid life, the best part of the life of
man.
18. The formula for the resistance of ships R = ƒ v² S feet lbs. was
first brought to my notice by the distinguished Professor in his paper
of the 13th of August 1866 in my possession. It was to disprove my
discovery in April of that year, that the law of plane and fluid impulse
of equal area (which had been discovered by me in 1842) applied to the
paddle wheel and screw, as well as to the undershot water wheel, and
thereby entailed the same loss to begin with, namely, 40 or 50 per cent.,
called by me the loss of primary velocity. Now the resistance of vessels
cannot be more than the power that overcomes it. Consequently this
law of plane and fluid impulse of equal area made the resistance of
vessels only one half of what Professors Rankine, Main, and others
made it, by their formula for equable motion R=P, as will be shewn
by and by.
19. Remarkable indeed is the evidence adduced by the learned Pro-
fessor and of the most positive kind, in support of his formula R=ƒ v² S
feet lbs., so fundamentally wrong, as shewn in paragraphs 10 and 11.
Besides an unvarying formula for every varying forms (bow, midship
area, stern, and displacement) is a contradiction. Now there is no
science known to man where so small an alteration in form makes so
great a difference in results as fluid and solid action, as is known to my
cost. Yet the Regius Professor says in his paper of the 13th August
1866, "It is well established by direct experiment (and not merely by a
* inference from indicated diagrams) that the resistances of similar
shaped vessels of different sizes, driven at speeds not exceeding a
" certain limit depending on the length of the vessel, vary nearly in
proportion to the immersed surface of the vessel, and to the square
" of the speed, so that the useful work in a given time varies nearly as
"the immersed surface, and as the cube of the speed."
66
.et
20. Again at p. 24 of the same paper the Professor says, "It was

page_text: ==
" established by the experiments of Beaufoy that the frictional re-
"sistance of water to a surface gliding through it edgewise is expressed
nearly by R fo³ S. This agrees almost exactly with the first term
" of Weisbach's formula for the friction of water in pipes. This formula
"is fully confirmed by experiments on long narrow finely shaped
"vessels, for example, by the experiments of Morin on the towing of
"swift canal boats.-Notions Fondamentales de Mécanique, page 380,"
and at p. 26 it is observed "the expression fo³ S unquestionably gives a
"lower limit, below which the resistance cannot possibly be." Yet,
"unquestionably" are all these experiments wrong, or the learned
Professor has drawn wrong conclusions from them.
•3 V P (*3 x 85-87 x 40616
28.696
ข
=
21. For by his formula R=fv³ S feet lbs., the Professor himself
makes the resistance of the "Victoria and Albert" at 17 knots as high
as (*012 × 172 × 12000 =) 41616 lbs., though it is by my formula of
1869 R =
-) 15231 lbs. only, above which such
resistance "cannot possibly be." Here then is the large difference of
(4161615231 =) 25385 lbs., and it is true although my formula was
not discovered by experiment but simply by pure mathematical analysis
of the laws of impulse; still it will last in opposition to the experiments
of Beaufoy, Morin, Weisbach, and the formulæ and authority of the
Regius Professor, and the first engineers of our time.
68
22. For in a paper read on the 27th November 1862, which the
Professor was good enough to send me in support of his paper of
the 13th August 1866, he says, The law which experiment has shown
" to be at least approximately true is, that the resistance of vessels
" varies as the surface of contact, and as the square of the velocity of
66
66
gliding (R=fv³ S), and its results have been found to agree very
closely with those of experiment, and have also been used since 1858
"by Mr. James R. Napier (the eminent ship builder and engineer of
Glasgow), and the author, with complete success in practice, to
" calculate before hand the engine power required to propel vessels
" at given speeds." Nothing, apparently, can be more conclusive
against my present discovery, that the chief resistance to vessels is
the displacement of the fluid in one foot lbs., shewn in paragraphs 6
and 11, and not "surface of contact" in feet lbs.; but the errors of such
experiments were in some measure pointed out in my Specification of
1870, No. 623, p. 13, paragraph 18, and p. 14.

page_text: .
66
"
23. In a subsequent paper of the 16th of August 1866, it is observed,
by the same eminent authority, that "the calculations of the lower
"limit of resistance are not based on any supposition, but on direct
experiments on the force required to make certain surfaces glide
" through the water." Moreover in a paper of the 21st September
1866, the Professor affirms (in opposition to my contention) that there
is a material difference between the action of a fluid on a plane, and
the action of a plane on a fluid. "When a jet," he observes, "strikes
a plane mechanical power has been expended to produce the jet, and
"if any part of the jet escapes deflection by the plane, the power which
" has been expended to produce the motion of that part of the jet
" is lost.
But when a plane strikes water that is at rest, the case is
"different in this respect; the particles of water which wholly escape
being acted on by the plane have no power expended on them, and
" those which are partially (or in other words imperfectly) acted on by
"the plane have proportionally less power expended upon them than
" those which are fully acted upon, so that the loss of power is by no
means so large a fraction of the total power expended as the escape
" of water is of the total water acted on."
"
66
24. How strange all this will seem by and by. The plane must set in
motion and displace a mass of water of the same area as the plane or it
could not pass through. All the slippery and mobile fluid passed over
by an uninclosed plane is not, because it cannot be, driven all astern, as
if it were iron. Or there would be no difference (1) between a fluid and
solid, (2) between the action of an enclosed plane in hydraulic machines
and an uninclosed plane like the paddle wheel and screw. Now it is
clear that the only reason for the complexity and cost of enclosing
pumps and having valves, and the conscquent loss of power, is simply to
prevent the still greater loss of the water escaping, called leakage. It
follows, that as all the water cannot be driven before an uninclosed
plane as it is by an enclosed one, the water that does escape must be so
much loss of power, for all motion lost is power lost. This was shown
to be 50 or 40 per cent. by my experiments in 1842 with a fluid against
a plane of the same area. Therefore, by induction, there must necessarily
be the same loss when the same plane moves against the same fluid.
25. All the experiments therefore with towing boats and otherwise
relied on by the Regius Professor must be some of those false facts

page_text: which have misled mankind in astronomy and other branches of science
from the earliest time to our own. Newton himself was misled for
many weary years by one of these false facts, an erroneous measure-
ment of the earth's radius. And this was universally received as true
by the men of science of his day, even as the Professor's experiments, or
erroneous deductions from them, are received by scientific men of our
own. When Picard's geodesic measurement led to the true radius of
the earth, Newton found that it confirmed his theoretical discovery
of the laws of universal gravitation. So when proper experiments come
to be made on the resistance of vessels, or proper deductions are drawn
from those already made, if correctly made, they too will be found
in conformity with my own theoretical discovery enunciated in this
Specification.
26. The erroneous experiments referred to, or erroneous deductions
from them, are however further supported by the following reasoning
in the Professor's paper of the 21st September 1866:-"It must be
admitted that the actual performances both of the paddle wheel and of
the screw, if judged by the aid of formulæ deduced from direct experi-
ments on the frictional resistance of water and the towing of boats,
appear better as regards economy of power than our previous knowledge
of the mutual actions of fluids and planes would have led us to
anticipate. It seems to me that there is reason to believe that undis-
turbed water when first laid hold of by a paddle or screw blade or an
oar presents a greater resistance than water whose particles have
previously been set in motion!" On the contrary all reason, as it seems
to me, is against it.
27. For it would seem by this that the Regius Professor denies one of
the fundamental principals of physics, the reciprocal action of fluids and
solids, which makes the resistance of a vessel in motion the same as
when at rest in a stream of the same velocity. In the nature of things
there can be no difference. There is only one law of dynamics for every
body in motion, whether wood, iron, water, steam, or air, and this is
embodied in the formula established by me and given in my Specification
of May 1866, No. 1497, p. 20 to 24. The working force of motion is for
a body moving against one at rest hw= 2 lbs. Whatever then be
the value of the weight w, the force or resistance is proportional both to
the formula and the power, if fully imparted. Hence, whether the par-
บริ
B

page_text: ticles of water of the weight w have been previously set in motion and
impinge against a plane a, or the same plane impinge against the same
particles of the weight w, the force of motion and resistance must
necessarily be the same. There is no law to make any difference, and
without law we should never stir a step in science, nor without it believe
any thing that comes from erring man.. There is nothing to my mind
more worthless than experiments without law; they are the least intel-
lectual, and therefore the least to be depended on, the lowest grade of
science, unworthy of a philosopher, for he seeks law in all things, and
without it asserts nothing with any certainty, knowing that he is but as
a man groping in the dark.
28. The distinguished Professor honored me with a long corre-
spondence on this interesting question in 1866, which the illustrious
Newton himself did not disdain. It is a great subject, for it will be seen
by and by that the future progress of naval architecture, the saving
many millions of tons of coals and money in steam navigation, and the
introduction of aerial navigation, all depend (1) on refuting the doctrine
of the learned Doctor and the schools, that surface constitutes the chicf
resistance of bodies passing through fluids, and (2) on establishing my
present discovery, that it is the continuous displacement and deflection
of the fluid in one foot lbs.
29. Nevertheless his formulæ, experiments, and the authority of the
schools were in 1866, and have since been, discarded for a still greater:
the analogies, harmonies, and simplicity of the laws of God, called the
laws of nature. For it was manifest to me that He would never make
two distinct sets of laws for such a petty thing as "plane and fluid
impulse; one to entail a loss of 40 or 50 per cent. when a fluid moves
against a plane of the same area, as discovered by me in 1842, and
another set of laws to entail no loss at all when the same plane moves
against the same fluid! Where is the philosopher who will believe it;
believe what is so opposed to common sense and our knowledge of the
simplicity and unity of the laws of the universe? No reliance then can
be placed on any authority which would establish what is so repugnant
to the wisdom of philosophy, which discards the complex for the simple,
and rests not till she find it. It is wiser and safer then in science, as in
all things, to discard the experiments of erring man than to believe in
the contradictions of the All wise. Any such inconsistency as two

page_text: opposite and contradictory laws for the same thing is not even con-
ceivable by the philosophic mind. We may then be sure that the
experiments referred to are either wrong or that wrong deductions have
been drawn from them.
30. The erroneous formula of Professor Rankine R=fv³ S feet lbs.
seem to have had material influence in giving us short ironclads, the
worst type of vessel yet introduced into the navy, because opposed to the
two essential requisites of steam ships, great capacity for fuel and small
horse power for continuance. In a paper "On the Form and Dimensions
of Ironclads," read before the Royal Society, and reported in Engineer-
ing, 30th of October 1868, its distinguished author, Mr. E. J. Reed, C.B.,
late Chief Constructor of the Navy for eight years, observes, "Let us
assume in this case that Professor Rankine's rule for the calculation of
" horse power and speed holds, viz., that the indicated horse power
"equals the augmented surface multiplied by the cube of the speed and
"divided by a certain co-efficient of propulsion, where the augmented
" surface is the immersed surface multiplied by a co-efficient of augmen-
tation, which is equal to 1+4 (sine of greatest obliquity of water
line) 2+ the 4th power of the same sine. The co-efficient of pro-
pulsion for a clean iron ship of good form is 20000."
$6
66
=
"
31. After elaborate calculations given in his paper the late Chief
Constructor observes:-"It is easy to see how the difference between the
"horse powers of the two curve of = sines' ships arise. The immersed
" surface of the longer vessel exceeds that of the shorter by 14669
square feet. At the speed of 14 knots the frictional resistance per
square foot of surface = 1.96 lbs., and consequently the excess of this
" resistance upon the larger ship is 14669 × 1.96 = 28310 lbs. This
" resistance has to be overcome through a distance of 14 knots per hour,
" and taking the effective work of one indicated horse power to be equal
" to 200 knot lb. per hour (which is the quantity used by Professor
"Rankine in his calculation) we obtain,
“Indicated horse power expended in overcoming the excess of

page_text: sr
" which corresponds very nearly to the difference between the engine
power of the two ships. As the immersed midship sections differ so
"little in the two cases, the difference of horse power due to this source
"would obviously be very slight."
32. Such then is the most advanced science of the most advanced
men of science of our time connected with steam navigation and naval
construction, which it seems necessary to put on record to show the
novelty of my discovery and Invention founded upon it, for their
doctrine gives us short ships as the most economical, whilst mine gives
long. If then theirs were the true laws of fluid resistance steam
navigation and naval architecture could not advance much, if at all,
beyond the present short ironclads, whilst acrial navigation would be
impracticable, because aerial machines are required of a thousand feet
long or more. If then resistance increased with the surface of length
the weight of engines, boilers, water, and fuel to overcome it would
exceed the power of buoyancy to float them. Happily for man the
Creator has made no such law, and therefore the navigation of the skies
is certain.
"
66
· 33. No doctrine, however, seems more firmly established than that of
Professor Rankine, as will be further seen in an extract from Engineering |
of the 7th September 1866, containing an investigation of resistance
by Professor S. Houghton. It is there observed that "the Professor
"in calculating the amount of resistance follows the principles laid
"down by Professor Rankine in his "Treatise on Shipbuilding.' The
"whole difficulty of the calculation," Professor Houghton observes,
" turns upon the calculation of the augmented surface, which is effected
by Professor Rankine on the assumption (conformable to repeated
experiments) that the augmented surface and its resistance are the
same as that of a trodioidal ribbon, whose length is equal to that of
"the boat on the plane of floatation, whose breadth is the mean a
" immersed girth of the boat, and whose co-efficient of augmented
"surface is 1+4 sine a+sine a; where a is the angle of greatest
obliquity to the horizon formed by a tangent to the trochord." Here
again it is taken for granted that the surface resistance is not merely
the true principle, opposed to my discovery that it is displacement) but
that such surface resistance is "conformable to repeated experiments,"
which is assuredly contrary to the fact; for no experiments can alter the
"
"

page_text: laws of plane and fluid impulse and establish any such inconsistent laws
as touched on in paragraph 29. Such however are the errors and
teachings of the schools.
34. Another of their fundamental errors must here be pointed out,
because were it true all the thought and labour and expenditure since
my first discovery of plane and fluid impulse in 1842, and my six
Patents since 1866 would be worthless. Such error is, that the resistance
of the vessel R is equal to the pressure on the paddle wheel or screw P
called "the equation for equable motion R=P.” The authorities for
this formula are, "Tredgold on the Steam Engine," and Professor Wool-
house the editor, Appendix, p. 59; "The Marine Steam Engine, designed
chiefly for the use of Naval Officers and Engineers," by Professor Main,
of the Royal Naval College, Portsmouth, who was the senior wrangler
of his year; edition of 1849, p. 272, and 4th edition of 1860, p. 319;
"The Steam Engine and other Prime Movers," by Professor Rankines.
1859, p. 550; report by the same author, dated the 13th of August 1866,
in my possession; and "On the Theoretical Limit of the Efficiency of
Propellers," by the same author, in "The Engineer of January 11th,
1867, p. 25. By these distinguished authorities the resistance of bodies
passing through fluids is made about three-fifths more than the true
resistance, pursuant to the laws of impulse discovered by me in 1842
and 1866, and embodied in my formulæ of 1869.
35. All discoveries lead to something beyond their immediate object.
We cannot then say to what the present one may lead when it is shown
30 that the resistance to bodies moving in fluids is only about two-fifths
of what it is made by the first men of science of our time. The following.
table will establish this fact:-

page_text: 36. Founded as this table is on the laws of impulse nothing can
refute it but proof of the two opposite and contradictory laws to govern
the same things (plane and fluid impulse and the reciprocal action of
solid and fluids) referred to in paragraphs 27 and 29. When a fluid
impinges on a stationary plane of the same area the loss of power is only
40 or 50 per cent. to begin with; but when the plane is set in motion
there is a further loss due to the different relative velocities in columns
14 and 15. This was called by me the residuary phenomenon of the
primary velocity loss, until I discovered in 1869 the laws of impulse
which accounted for it, as shown in the table in columns 13 and 17,
which vary with the relative velocities and v, in columns 14 and 15.
Such table then records, for all time, the difference between true
inductive science based on the realities of nature, which never yet misled
man, and never will, and the empirical science of the schools based
cither on erroneous experiments or on wrong deductions from true ones.
The laws of impulse govern the action of the paddle and wheel and
and thereby entail such losses of primary velocity or pressure to
begin with. But not knowing this law, Professors Woolhouse, Mornay,
Labrousse, Barlow, Rankine, Main, all Europe and America in short,
have assumed that the whole pressure P is utilized in overcoming the
resistance of the vessel R. So on mere assumption have they main-
tained to this day their "equation of equable motion R=P," as shewn
in paragraph 34. In this way they make the resistance of bodies through
fluids about three-fifths more than it is as shewn in the table.
screw,
37. The data there given have been obtained with the greatest care.
Some are taken from the papers of Professor Rankine of 1866 in my
possession, some from the Engineer recording the experiments of the
Nautilus and Volunteer of the 13th April 1866, and some from
the Admiralty returns of the 7th of June last, liberally furnished at
my request. The data of the Banshee were kindly sent me by her
distinguished builder, Mr. Oliver Lang, in his letter from Chatham
Yard, of the 24th September 1849, since which time this beautiful and
economical vessel has been my guide in all my calculations and
comparisons with my own Inventions. For her great speed of 18.5
miles an hour with only 1566 indicated power was a marvel 22 years
ago. Professor Rankine makes her immersed surface 5200 square feet,
but the 3540 sent me by her builder soon after she was built is no

page_text: note :-
, doubt correct. This is confirmed by the fact that she displaces only
580 tons, whilst the Vixen displaces 1237 tons. Now the Engineer of
the 2nd November 1866 contains a mathematical analysis by the editor
of the resistance of the Waterwitch, to which there is the following
"If the augmented surface of the Waterwitch be taken at !
7000 square feet, her resistance at 8.9 knots by Rankine's rule is 5545
lbs., very nearly agreeing with the above." Since then the displace-
ment of her competitor, the Vixen, was twice that of the Banshee,
the immersed surface of the Vixen must be about double, and this
would make that of the Banshee =3500 square feet, which is 1
within 40 square feet of the 3540 given by her builder in 1849. This
extract again shows the prevalence of the erroneous doctrine of surface
friction being the chief resistance to bodies passing through fluids.
7000
2
38. The extract from the Engineer just given is important. For at
that time, 1866, were being tried against each other the Nautilus 1
hydraulic, and the Volunteer paddle wheel, competitive vessels; also
the Waterwitch hydraulic, and Vixen and Viper twin screws, com-
petitive vessels. The last three were built by Mr. E. J. Reed fairly to
test the comparative merits of the two different systems of propulsion.
These trials attracted great attention in England, France, and the 2
United States, and were investigated by many mathematicians far
greater than myself; among the most renowned by Professor Rankine,
the Rev. J. A. L. Airey, of Merchant Taylors' School, and Mr. R. D.
Napier, of Birkenhead, one of the most thoughtful and original men of
science and mathematicians of the day. Independently of one another 2
they all made the resistance of the Nautilus and Waterwitch even less
than that of the Volunteer, Vixen, and Viper was made by my impulse
formula of 1869 R- lbs. Now this was not in existence in 1866
when these admirable mathematicians found the resistance of the vessels
referred to, neither has so low a resistance as theirs been questioned,
nor any material difference in the indicated power, speed, size, line,
and draught of the different competitive vessels. Hence the resistance
of the Nautilus is that of the Volunteer, and that of the Waterwitch of
the Vixen and Viper,
'
3 VP
v

page_text: Vixen in column 12 of the table, and the effective pressure in column 8.
It can never then be refuted that the difference between the two is
the loss of engine power shown in column 13. Now no one but myself
discovered this loss or accounted for it by induction from my discovery
in 1842, merely because their minds had, not been prepared by the same
studies to understand and seize the opportunity presented by the experi-
ments of the vessel referred to in 1866. My discovery in 1842 was, as
observed before, that when a fluid impinged against a plane of the
same area there was a loss of 40 or 50 per cent. of the power to begin
with, in consequence of the fluid escaping past the plane unutilized.
The paddle wheel and screw are planes of the same area as the water
they impinge against. Therefore they too must lose the same amount
of power, because they are not confined to prevent the water escaping
as in pumps and all other hydraulic machines.
40. The laws of physics which regulate the amount of loss according
to the relative velocities of paddle wheel or screw V, and vessel v, are
called impulse. These laws are embodied in my formulæ of 1869, given
in my Specification of 1870, pp. 26, 27, and no other law in the
universe will account for such variable losses at all relative velocities,
as those shown in the table, columns 17 and 18. Neither will any other
law or any other formula make the resistance of the Volunteer and
Vixen so close to that of their competitors the Nautilus and Water-
witch, found by Professor Rankine and others by a different method in
1866, as stated in paragraph 38.
41. It has been said, and the fact is, that the opposition of the school to
my inductive discovery of 1866, and the two formulæ R=P lbs. and fø³ S
feet lbs., have prevented its introduction. Now as my labours have been
for 29 years at intervals, it seems due to science and myself to refute
such formulæ here, even more fully than in paragraphs 27 and 29. It
is better to make a full end of them once and for ever, that they may do
no more mischief. It will then be seen by the table, that in three out
of the four examples there is so great a discrepancy as more than
50 per cent. between the two formulæ of Professor Rankine in columns
8 and 9. One therefore must be wrong, yet both he maintains are true.
The positiveness with which his formula R=fo³ S feet lbs. is upheld
has been shown in paragraphs 19, 20, and 22. And in his paper of the

page_text: 7th September 1866, the Professor says, at folio 5 and 16, "The equation
of equable motion is R=P, R being the resistance of the vessel, and P
the propelling force. And Rs (s being the slip -) is the only
possible loss of work connected with the longitudinal motion of the
water." Thus is my inductive discovery in April 1866 of the additional
longitudinal loss of 40 or 50 per cent. to begin with, called by mo
the loss of primary velocity, pronounced to be "impossible." And
this by one of the first scientific authorities of the age who has given
his special attention to the subject. This then is another of those true
"impossibilities" which fill the history of science, and make it so
interesting from the days of the persecuted Columbus and Galileo to
our own. Does the same penalty attach to all discoveries and through
all time?
2
42. It would be idle to refute the fallacies which have been advanced
to account for the great difference between the Professor's two formula
R=P lbs., and fo² S feet lbs., shown in the table, columns 8 and 9.
Because true science listens to no excuses, no makes-up, no throwing
up waves here and none there, no uncertainties. It is all yea, yea, or
nay, nay, with her, absolute certainty or rejection. Hence nothing can
be urged to account for such difference, but what must necessarily be
fatal to the formula which gives it. For a formula is the highest reach
of mathematics, because the most concise and useful embodiment of a
law of God, which is exact, universal, and reliable. If then a formula
be none of these, it does not embody such law, and is therefore lawless
and worthless in the greatest degree.
43. Ii will be seen in the table that the resistance of the "Victoria and
Albert," found by the Professor's formula fo² S feet lbs. so nearly agrees
with his other formula R=P lbs. only, that we may consider them
identical. For a slightly less co-efficient than 012 would make them
both equal. But this unfortunate coincidence is only further evidence
that both formulæ are without law. For were R=P the paddle wheel
and screw would be perfect machines, inasmuch as the whole pressure P
would be utilized in overcoming the resistance R. This however is
contrary to philosophy. For man being imperfect himself cannot make
a perfect machine. Therefore R cannot be equal to P. Moreover it is
contrary to one of the fundamental principles of mechanics, which is,
that the whole pressure cannot be imparted to the working elements of

page_text: a machine. There is always a loss somewhere. Therefore again R
cannot be equal to P.
44. The more we investigate a true law of the Great Law Maker, the
more we find it in harmony with all His other laws. Whilst the more
we look into a false law the more we find it out of gear and unworkable
with His other laws. So it is with the Professor's formulæ. The same
bodies brought together under the same circumstances must ever produce
the same effects. Now the paddle wheels of the Banshee and Victoria
and Albert are both feathering and therefore identical in principle.
They are too applied to first-class vessels whose economy of power has
never been surpassed at the same speed to my knowledge. The table
shows in columns 14 and 15, that their relative velocities are within a
decimal or two the same. Therefore by virtue of those adamantine laws
which the Creator has ordained to govern all things, fixed and unchange-
able, their modulas of efficiency must necessarily be the same.
The
Professor's formula ought then to make them so, and mine does.
.
45. But the table shows that the resistance of the Banshee is, (by the
Professor's formula R=ƒ v³ S)=11148 lbs. at a speed of 27-13 feet a
second =v. Hence Rv=U=the useful effect.
indicated efficiency is, by my formula IE=
.18190
Consequently the
1819 x 11148 x 27.18
1566
=
35-7 per cent. Now the indicated efficiency of the Victoria and Albert
1819 x 41616 x 28.696
2980
is from the same table, IE=
=72.9 per cent. Now the
same causes must always produce the same effects. Hence so great a
difference in effect as (72.9-35.7=) 37.2 per cent. from the same causes
(the mutual action of the same bodies on the same principles) is alone
sufficient to destroy the validity of the Professor's formula ƒ v³ S feet lbs.
even had this not been done in paragraphs 24, 27, and 29. My own
formula in columns 17 and 18 gives the same efficiency for both vessels
because their relative velocities are the same, but different efficiencies
for all the rest because their relative velocities differ.
46. It has now been shown that analysis of the above formula con-
firms what was said of it, that it is fundamentally wrong in two things:
(1), that it allows no power for displacing and deflecting the water;
(2), that it is a formula in feet lbs., instead of in one foot lbs., in which
alone all resistances are calculated. Take, for instance, the Hercules,
she displaces 8677 tons in her length of 325 feet, consequently 39935 =
8677

page_text: 26-7 tons in one foot. Were this weight of water flowing through a
pipe, whether by the work of gravity in a natural stream, or by artificial
power, two powers would be required; (1), the far greater power to
overcome the resistance of the weight of water to motion; (2), power
to overcome the friction of the pipe. Here again we see that analogy,
harmony, and unity of principle in diversity of action which runs
through all nature, "and makes the whole world kin," and which have
more or less led me to my discoveries. For the true resistance of solids
moving in fluids as discovered by me is the same as that of fluids
moving against solids or in pipes, because the same two powers are
required. Reverse the motion as we may, the solid ship against the
fluid, or the fluid against the solid ship at moorings, still we cannot
reverse the law. The same power for the same weight and velocity of
water will be required in both cases and must necessarily produce the same
results. For this is not merely pursuant to common sense, but to one of 1
the fundamental laws of physics, the mutual action of fluids and solids.
The philosophic mind accustomed to apply the same processes of thought
to all matters, cannot even conceive anything different. For such mind
being in harmony with the universe cannot conceive'what is not.
47. There is no harmony in Professor Rankine's formula with the flow 2
of water in pipes, or with anything in nature. For it omits altogether
the far greater power required to set a given weight of water in motion,
and deals only with its friction, which in one foot lbs. is insignificant.
Therefore to bring this up to something like the pressure P the whole
frictional length of the vessel is included in the formula R=fv³ S feet 2
lbs., instead of being lbs. through one foot, which is the true
frictional resistance. For to meet with a frictional resistance of 325 feet,
the Hercules must be propelled 325 feet. On the same principle, in
order to displace 8677 tons of water she must be propelled 325 feet
through it. To do either in advancing only one foot, which is the 3
standard of resistance, cannot be. It follows that a formula so wrong
in two fundamental principles, mere friction and feet lbs., cannot be in
harmony with the other two formulæ of Professor Rankine, given in the
table in paragraph 35, columns 8 and 9. Forf v³ Sv in columns 9 and 15,
equivalent to R v should agree with Pv in columns 8 and 15, and both 3
with the efficiency in column 16. But they all differ. and are all wrong.

page_text: THE IMPORTANCE OF A TRUE MEASURE OF THE RESISTANCE OF BODIES
PASSING THROUGH FLUIDS, FOR THE IMPROVEMENT OF NAVAL
ARCHITECTURE, and IntroduCTION OF AERIAL NAVIGATION.
.
48. No discord can be found in any of the laws of the Creator, and as
my formula of 1869 embody these laws no discord can be found in them,
th
PE=U+L=V*— Va=P (**) feet lbs.
.6 V
48 V .1819
2
E=and IE=+==1" U per cent.
49. The symbols mean as follows:-P is the effective pressure on the
paddle board or screw after deducting from the indicated power I the
friction of the engines f, here taken at 20 per cent.; V is the mean
velocity of the propeller in feet per second, is the velocity of vessel,
also in feet per second; a is the dynamic area of paddle wheel or screw;
R is the resistance overcome; U is the useful effect or power utilized
per second; L is the whole loss of the principle of impulse, 1st, of the
primary velocity 7, discovered by me in 1842 and 1866 (that which is
denied by Professor Rankine and the schools), and 2nd, ↳ the loss of
residuary velocity, improperly called slip; PE is the power effective
expended on the propeller after deducting engine friction; E is the
theoretical modulas of efficiency of the paddle wheel or screw depending
on the relative velocities of propeller V and vessel v; and IE is the
indicated efficiency per cent. assuming 20 per cent. to be the friction of

page_text: propulsion will be seen in my
50.
FORMULE FOR REACTION PROPULSION.
R=P=2 Va (V-v) lbs.
R
a= v(v) square feet.
U-2 Va (V-v) v=Rv feet lbs.
L=(V−v)³Va=R (7) feet lbs.
PE=U+L=V'— Va=R (+) feet lbs.
v
1819 U
E=2 And IE=1200=1819
•
The last two formulæ give the efficiency per cent. on the indicated 1
power, taking the losses of my system at 25 per cent. of the effective
power PE, and the engine and shaft friction at 20 per cent. on the
whole. E is the theoretical efficiency due to the principle of
reaction which distinguishes it from the much less theoretical efficiency
of impulse E-7 in paragraph 35, column 17, and paragraph 48. But
2 v
V
+0
2 v
no such efficiency in reaction as + can be reached in practice because
of my losses, taken at 25 per cent., and 20 per cent. on the whole for
engine friction.
1
51. But by comparing the two formulæ for impulse and reaction the
mathematician will see the great saving of the principle of reaction 2
propulsion. For here there is no loss of primary velocity to begin with.
Therefore R-P pure and simple. These formulæ are taken from my
Specification of 1870, pp. 27, 30, because it has been shown how unre-
liable are the old standards of the schools for the resistance of bodies
passing through fluids R=P lbs., and R=f v³ S feet lbs. We may also 2
be sure that plane and fluid impulse which begins with a loss of 40
or 50 per cent. of engine power (from so much of the propelling water
escaping past the floats unutilized) can never reach so high an efficiency
as that given in the formula of Professor Rankine in the table
22+
??
paragraph 35, column 16. There are then no other formulæ than mine for å
finding such resistance and efficiency when propelled by paddle wheel
and screw. Nor can there ever be any other for such machines, because
two different laws of nature do not govern and control the same thing.

page_text: Consequently the great difference between the two laws of impulse and
reaction, shown in my formulæ in paragraphs 48 and 50, can alone
determine the saving by reaction, which is my principle of propulsion.
2 PE
52. In my said Specification of 1870, page 30, line 23, the formulæ
for reaction are thus put,―
· R=P=V'—v²+(V−v)³ a=2 Va (V−-7)=1100 (x-1)= and the
last formula but one is again given for R in reaction, in page 42, line 18.
This may mislead without explanation. The value of the friction (ƒ)
in this formula for reaction 1100 I-S has been omitted in such Speci-
V+0
1100 (I-f
V+D
fication in explaining the symbols there. Forf here includes the friction
and losses of my reaction propellers as well as engine friction; whereas
fin the same formula for impulse, R=
lbs., includes only the
engine and shaft friction. Now as the friction and losses of my system
of propulsion may vary, it will be better to find the resistance of vessels
propelled by reaction by the unvarying and certain formula in para-
graph 50, R=2 Va (V-v), and not by 1100 (1-1), or by PE, which are
correct for paddle wheel and screw because they include only the engine
and shaft friction.
V+v
53. The following also requires explanation. The formulæ for reaction
at page 30 of such Specification of 1870 and in paragraph 50 of this,
are also applicable in principle to aerial machines propelled by reaction.
But the density of a cubic foot of air is only about 07850 lbs., instead
64-18
-07859
of 64 18 lbs.== =816-64 times less. Consequently the resistance
of differently formed aerial machines at all speeds will be found approxi-
2 Va (V-v)
mately by the formula R='
816-64
lbs., when propelled by reaction.
54. Prior to the above formulæ for measuring the resistance of
bodies of all forms and sizes and all velocities, mechanically propelled
through air or water, all was lawless and uncertain, as shown by the
empirical formulæ of the schools. All is now governed by fixed and
unerring laws, and therefore brought within the dominion of the exact
sciences. The importance of this for the improvement of naval archi-
tecture will be best seen by one or two examples. The Blanche and
Danäe were built as much alike as the engineer and constructor could
make them. But on trial under similar circumstances one was found.

page_text: much faster than the other; which it was cannot just now be re-
membered. Another instance is given in the Times of the 23rd
September 1870, where it is said that "the Vanguard appeared by the
result of the official trials to be much faster than the other three ships
of her class, namely, the Audacious, Invincible, and Iron Duke,
although of the same build, tonnage, and horse power." Now the em-
pirical formulæ of the schools would fail to detect the different resist-
ances of these vessels, just as they have of the Volunteer and other
vessels in the table in paragraph 35, columns 8 and 9. Mine, however,
for impulse in paragraph 48, would find the true resistance of the
Blanche and Danae, Vanguard, and others, and so teach the naval
architect the best type of vessel to follow.
55. It is sometimes necessary to pull down before we can build up,
and this is the case in all new discoveries. For they are the detection
and refutation of the prevailing errors of mankind, which from the
earliest times have stopped all progress in science and civilization until
they are detected. Now the true formulæ of the schools for the resist-
ance of bodies passing through fluids are the great prevailing errors
in science of our day, and have apparently led to the expenditure of
some millions of money on the worst type of ship introduced into the
British Navy, called "short ironclads," as shown in paragraphs 30.and
31. So far then as regards the past and present. It is now proper to
show how the same formulæ would stop all progress for the future in.
naval architecture, steam and aerial navigation, were such formulæ
founded on the laws of fluid resistance.
56. The table in paragraph 35, columns 8 to 13, shows what wrong
results this formula R=f v³ S gives in the descending scale, that is,
when the immersed surface in column 6 is not sufficient to make the re-
sistance equal to P, in the other empirical formula R=P in column 8.
We have now to show how fatal to improvement such formula, if true,
would be in the ascending scale, and so make its refutation still more
complete. Or it may perpetuate short ironclads, or some other false
system of naval architecture, in the greatest maritime nation that the
world has seen.
57. The ascending scale is this. If we double the length of the
Victoria and Albert, but keep her draught the same, her immersed
surface will be twice what it is shewn to be in the table in paragraph 35,

page_text: column 6. Consequently, by the formula of the Regius Professor, her
resistance (in column 9) would then be doubled, and be
R=012×41616=83232 lbs.
But by my discoveries in propulsion in 1842-1866 and 1869, and my
present one, that the resistance of vessels does not depend upon surface
friction, the resistance cannot be more than
R=3 VP
"
3 x 35.87 x 40616
28.696
=15231 lbs.
Now the difference of (83232-15231=) 68001 lbs. shows how great
would be the difference in the cost and weight of engines, boilers,
water, and fuel required to overcome a resistance of 83232 lbs., instead
of only 15231 lbs. If, moreover, the resistance increased with surface,
according to the prevailing doctrine, aerial navigation would be im-
practicable, because, as said before, the extensive surface required to
float such a weight of engines, water, and fuel to overcome such huge
resistance could never be economically obtained.
*012 x 17 x 2 x 12000
600
58. Now the real surface resistance of the Victoria and Albert, if
600 feet long, could be only r=-
=138.7 lbs., instead.
of 83232 lbs. by the Professor's formula. For it has been said that the
resistance of bodies passing through fluids, air or water, is made up of
two distinct things, governed by distinct laws, (1) displacement; (2)
friction. Now both are in one foot lbs., not feet lbs., as given by the
formula fo³ S. If then d= the displacement resistance, and ƒ that of
friction, the total resistance will be R=d+flbs.
59. There is no higher or more honorable and respected authority than
that of Professor Rankine, except the laws of nature, which are the laws
of God. How sincerely convinced the Professor is that his formula "is
well established by direct experiments and not merely by inference from
indicated diagrams" has been shewn in paragraphs 19, 20, and 22: But
experiments based on nothing must come to nothing; and experiments
which cannot be referred to any law are lawless, and therefore worthless;
for without law nothing has permanence. Thus all formulæ based only
on the experiments of fallible man are of the meanest and lowest class,
therefore the least reliable. For again and again in my own experience
the experiments of one man, and of distinction too, have been con-
tradicted by those of another of equal distinction. The experiments, for
instance, in paddle wheel and screw propulsion are all worthless, because
they have led to three false formulæ R=(V-v)², R=P lbs., and

page_text: f v³ S feet lbs. Yet these experiments are vouched for by the first
scientific authorities, as shown in my Specification of 1870, page 16,
paragraph 20, the errors of which were detected by my formulæ of 1857,
the produce of pure thought.
.
60. So too have been detected the experiments relied on by Professor
Rankine. These, moreover, are contradicted by the experiments of the
first experimental philosopher on the resistance of vessels that ever lived,
Colonel Mark Beaufoy. His munificent and patriotic son, my former
neighbour, gave me his great work, "Nautical and Hydraulic Experi-
ments," printed at his own private press, bought for the purpose in 1833
and 34. Their labours may be called gigantic without exaggeration,
for the first volume contains 688 pages of large quarto full of experi-
ments, and the Editor says, at page XXXII., that "the united experi-
ments made by the English and Swedish philosophers have not cost so
little as 50,000%. sterling." Yet the truth of science compels me to put
on record for its advancement that these and all the labours and cost of
the past and present have not the value of my simple impulse formula
R=
lbs., the result of abstract thought, by induction from an
abstract experiment with a jet of steam in 1842.
• 3 VP
ย
61. The wrong done to science by relying on experiments without law
will be seen by the following experiments of Beaufoy, which contradict
those relied on by Professor Rankine, and clearly disprove his formula.
R=fo S, that the chief resistance of vessels is frictional.
So re-
markable did they seem to Beaufoy that he thus directs particular
attention to them at page XXIV. of the preface of his work before :
referred to:-"Among the conclusions suggested by the tables one of
the most curious is, that the increasing the length of a solid of almost
any form by the addition of a cylinder in the middle exceedingly
diminishes the resistance with which it moves provided the weight in
water continue to be the same, a fact, I apprehend, that cannot be
explained."
$
62. Here is a true fact, because pursuant to a true law of nature
ḍiscovered by me, a fact put on record three quarters of a century ago.
For my present discovery is in harmony with such experiments, namely,
that the resistance of bodies passing through fluids is not frictional but
displacement in one foot lbs., therefore inversely as the length of the
body provided the displacement be the same. For this is Beaufoy's
condition, provided the weight in water continue to be the same,"
"

page_text: displacement being the equivalent of the weight of the body which
causes it. If, then, we double the length of the Victoria and Albert
and keep her displacement or weight in water the same, her resistance
will be (by Beaufoy's experiments and my law) only half what it was
3. before. But by the Professor's principle of surface forming the chief
resistance R=fos S feet lbs. her resistance would still continue the
same, because her immersed surface would be the same.
• 63. We have now shown by another example what was shown by my
paddle wheel formulæ in 1857, and in my Specification of 1870, page 16,
paragraph 20, how misleading and opposed to true mental science are
formulæ based on experiments without law; for here in the ascending
scale, paragraph 57, in the descending scale in the Table, in paragraph 35,
columns 8 and 11, and in the medium scale, in paragraphs 61 and 62, the
Professor's formula R=fv S feet lbs. is wrong in all.
64.. This fact is further confirmed by another briefly referred to before.
The chief resistance to bodies passing through fluids depends on the area
of midship section opposed to the fluid. We cannot then lengthen a
body and keep the displacement the same without reducing the draught
and midship area in proportion, and consequently reducing the re-
sistance, as stated in my Provisional Specification. Now this result
is pursuant to my law that the resistance is inversely as the length
provided the displacement be the same. And this, as before observed,
is confirmed by the experiments of the first man of his class in 1798,
himself ignorant of this law that made them what they were, and not
otherwise. It follows that a formula is necessarily wrong which, like
that of the Professor's fv³ S feet lbs. makes resistance of fluids inde-
pendent of that which causes the chief resistance, namely, the area of
midship section opposed to the fluid. Consequently all the experiments
referred to by Professor Rankine in paragraphs 19, 20, and 22 were
either wrongly made, or have led to wrong deductions, shown by the
experiments of Beaufoy in paragraphs 61 and 62.
•
65. Here then is another pleasant verification of my invariable
principle of scientific investigation, referred to in my Specification of
1870, p. 24, where it is observed, in reference to my discoveries in
propulsion, "Certainly the experience of the Regius Professor, Mr.
Napier, to whom he refers for confirmation, and the great engineering
firm, is very great, the last relying on "the results of very careful
experiments which have in actual experience. turned out true." No,

page_text: with all deference, they have not. I there observed, "All they say can
only be met by a far diviner and higher power, the unerring logic of
sound induction. Practice may err, true theory never. I never trust
therefore to mere experiments unless verified by the laws which
govern and control them, for facts must be in harmony with laws.
Tell me the laws, and I will believe your experiments; if you cannot
I reject them. None of these eminent men could give me the laws
of physics which made their experiments what they said they were.
Therefore I rejected them, as lawless and worthless." Had I not done
so always, long before that Specification, then, and now, I should have
wasted much of my time and substance on worthless schemes, and have
been deterred altogether from continuing those inquiries which led to
my past and present discoveries.
66. And for the honor and glory of inductive science it may be
permitted me to record here, for the encouragement of others ridiculed
and opposed by the schools, that nothing has served me but pure
inductive theory in the case of the paddle wheel and screw, and
dynamical analogy in the case of the existence of bodies, to oppose to
the great authorities and experiments brought against me. For there
are no such experimenters in fluid resistance as Beaufoy, of England,
Morin, of France, and Weisbach, of Germany. Moreover these are
supported by the European authority of the Regius Professor of the
University of Glasgow, and Mr. James R. Napier, in paragraph 22; by
the late Chief Constructor of the Navy, Mr. E. J. Reed, C.B., in
paragraphs 30 and 31; by the scientific journal "Engineering," in para-
graph 30; the Reverend Professor Haughton, in paragraph 33; by the
"Engineer," another scientific journal, in paragraph 37; and lastly by
the oldest of all, the Mechanics' Magazine of the 20th September 1860,
page 191, from which the following is an extract:-"The Resistance
of Ships." "The following is a summary of a paper read before the
Mechanical Section (of the British Association for the Advancement of
Science) on an investigation of the resistance of ships, by Professor
Rankine. The principal conclusions arrived at are; That friction con-
stitutes the most important part, if not the whole, of the resistance to
the motion of ships that are well formed for speed; that its amount can
be deduced with great precision from the form of the ship, by proper
mathematical processes; that the engine power required to overcome it
varies nearly as the cube of the speed, and as a quantity, called the

page_text: The PerpetuATION OF SCIENTIFIC ERRORS; THE HARMONY OF LAWS
OF NATURE, AND THEIR CONFIRMATION OF ONE ANOTHER.
I.
67. It is far harder to unlearn than to learn, to unteach than to
teach, as will be seen by the following extract from my paper to the
Admiralty in 1867 :-" We may confidently rely on a theory logically
deduced from a fundamental law of physics. Having therefore discovered
in 1842 the great superiority of reaction, the frictional formula which
contradicted it, f V2 S, could only be empirical, not founded on a law of
nature. Still the law which governed the frictional resistance of vessels
cluded discovery until last month, when, having occasion to refer to
Beaufoy's work, 'Nautical and Hydraulic Experiments,' my perseverance
―for I claim nothing more—was rewarded by reading the following ro-
markable experiment in the Preface, p. XXIV.:-'Among the conclusions
suggested by the tables, one of the most curious is,' that the increasing
the length of a solid, of almost any form, by the addition of a cylinder
in the middle, exceedingly diminishes the resistance with which it
moves, provided the weight in water continue to be the same. A fact,
I apprehend, that cannot be easily explained.' No, I could not
explain it then; the day of interpretation had not come.
$
$
But the law
was at once revealed to me. For, by induction, the resistance of
vessels is not directly as the immersed surface, embodied in the
formula R=f VS, but inversely as the length of surface, in certain
proportions. I found too that this singular law does not depend, as
Beaufoy says it does, on the weight of the body in water continuing
the same, provided the greater weight proceed from the greater
length." This was written four years ago nearly, and the last two
lines, "I found too, &c., have just come before me for the first time
since. But there is no time now to consider this part of the question, in
the new light of displacement, and not friction. But it seems to me
that if the draught be kept the same, the weight, and consequently
displacement, may be increased by length indefinitely, without either
increasing or decreasing the resistance.
}

page_text: 68. Believing in the erroneous teaching of the schools, when such
paper of 1867 was written, it was desirable to account for the anomaly
of frictional resistance decreasing with length, and thus wrongly was
it accounted for in such paper. "We see in this law of decreasing
resistance another departure, for some wise purpose, from the ordinary
laws of nature, like freezing water and latent heat. For it is plain that
as we increase the surface moving in a fluid we must increase friction,
resistance, and retardation. And we do. This fact is found in water
flowing through pipes, the knowledge of which forms one of the funda-
mental principles of my system of hydro-propulsion. But in vessels
passing through water increased resistance due to increased surface is,
and is not. For by increasing the surface in length, in certain pro-
portions, some strange law comes into operation, and not merely
neutralizes the ordinary law of friction and resistance, due to such
increased surface and to the square of its velocity, but actually makes
the resistance of the whole mass less than it was before, 'exceedingly
diminishes the resistance with which it moves.' This is the mystery.
What that law is, and in what proportion it operates, I know not. All
I know is that I have discovered, whilst writing this paper, the existence
of some law which makes the resistance of vessels less than that due to
the surface of contact, in opposition to what is enunciated in every
work on ship building, followed by every naval architect, scientific
mathematician, and engineer, and embodied in the formula of Professor
Rankine Rƒ V*S.”
69. The false. principle of the formula fo³ S was not then seen, that it
included the friction of the whole length of the vessel in passing over
only one foot, and was therefore a formula in feet lbs., instead of 10 lbs.
Now it has been asserted that if many men's minds are engaged on the
same thing, they will all make the same discovery sooner or later, and
therefore no one should have the benefit of priority. This assumption is
contradicted by the history of discovery and Invention from the earliest
times; by the philosophy of the human mind, which is in harmony with
divers objects, and not in the same degree with only one; and by the
wisdom and beneficence of the Deity, from whom cometh down every
good and perfect gift; who so wisely never gives precisely the same
powers to every one, for the same object, but something different to each,
for the common benefit of all. This truth is confirmed by so many
different minds seeking the laws of the resistance of bodies moving in

page_text: fluids, and the form of least resistance, and not finding them, from the
days of Newton to our own.
70. But there is perhaps no more remarkable confirmation of such
truth than in the extracts in paragraph 67 from my paper to the Admiralty
in 1867. For there the plainest clue to my present discovery is given,
since it is said, that "the resistance of vessels is inversely as their
length." This is the first part of the law of such discovery.
And only
three lines above those words, in paragraph 67, the principle itself is given
in the words of Beaufoy, "provided the weight in water continue to be
the same," which is the equivalent of my expression, displacement. Some
one then had only to put these two things together in their proper order
and write "the resistance of bodies passing through fluids is inversely
as their length, provided the displacement be the same." How near
Beaufoy was to the discovery in 1798, and I in 1867, will be seen by the
above extracts. The eye saw, but the mind did not understand. The
day of revelation had not then come.
71. Thus it was perhaps that such discovery was not made by Beaufoy
in 1798, by mo in 1867, Professor Rankine, Mr. E. J. Reed, the scientific
adviser of the Admiralty, nor one of the eminent mathematicians and
engineers to whom the paper of 1867 was sent. It would seem then
that discovery is the natural mental growth of individual minds especially
prepared and nurtured by long habits of observation and reflection in
some particular pursuit. Another instance of this law is seen in my
first discovery in 1842, of the remarkable difference between the two
principles of impulse and reaction, explained in my Specification of May
1866 and 1870. The experiments of 1842 conveyed nothing to the
minds of the late Mr. Brunel, the present Mr. James Pillron, or myself
at the time, nor were they even understood by me until (1866-1842=)
24 years afterwards, nor was it until (1869-1842 =) 27 years after,
see the experiments that the laws which governed the principles of
impulse were discovered and embodied in the formulæ given in para-
graph 48. Thus not only do those not make any given discovery whom
it is asserted would have made it, but they are the very persons who
most strenously deny and oppose it when it is made, even when
established by irrefutable proofs, as my discovery of the loss of primary
velocity of the paddle wheel and screw has been from 1866. to. this day,
to my grievous loss.

page_text: 72. So far as my researches have gone Beaufoy seems to have been
the first to enunciate the erroneous doctrine of friction being the chief
resistance to bodies passing through fluids. For in recording his curious
experiments given in paragraph 67, he observes, "it is a fact I apprehend
that cannot be easily explained." Why he could not himself explain
it was because he adopted the erroneous doctrine of surface friction.
This will be seen in the following extract, p. XXIV. of his work,
"Hydraulic and Nautical Experiments":"The common opinion, that
the greatest breadth of a ship should be given to the middle, in pre-
ference to any other part nearer the bow, seems to have arisen from
a desire of diminishing the angle of incidence. But though the
advantage of that dimunition is undoubtedly great, yet it is more
than balanced by the disadvantage of the increase in the surface."
73. This would be so were the resistance in feet lbs., as given in
Professor Rankine's formula fo³ S; but as all resistance is calculated
in one foot lbs., or simply lbs., no increase in length of surface can
increase the resistance, as Beaufoy says it does. On the contrary, his
own experiments, given in paragraphs 61 & 67, contradict him. For he
found that "increasing the length of a solid exceedingly diminishes
the resistance, provided the weight in water (my displacement) con-
tinue to be the same." Necessarily so, because the area of midship
section immersed, which is the chief resistance, is reduced in the same
proportion as the length is increased, as before explained. But Beaufoy
believing that surface friction was the chief resistance and knowing
that such surface remained the same when lengthened, and yet that
"the resistance was exceedingly diminished," observed, naturally enough
from his erroneous point of view, "a fact I apprehend that cannot be
easily explained."
.
74. Nor could it ever be explained were surface friction the chief
resistance to vessels. How it was tried to be explained by me before
the mind could emancipate itself from the false teaching of the schools
that surface friction caused the chief resistance has been shown in para-
graph 68. It seemed to be a departure from the known laws of nature,
but change the venue, as the lawyers say, from friction in feet lbs. to
displacement in one foot lbs., and to the consequent reduction of the
chief resistance (the area of the midship section as the length increases
with the same displacement) and "the curious"" phenomenon observed
by Beaufoy is seen at once to be the necessary result of a fixed law of

page_text: physics, namely, that resistance is decreased by the midship area (or
draught) is decreased, though the immersed surface remain the same.
And so the problem, which seemed insoluble to him in 1798, and to
others since, is at last solved, simply by looking at it in a different
point of view to that of any one else. And that is how all discoveries
have been, and will be made.
75. Yet no single department of human knowledge known to imc
has engaged more the attention of so many eminent men. Herschel
refers to the motion of fluids in his Natural Philosophy, p. 180. And
the following are some of those who have for more than a century,
endeavoured to discover the form of least resistance, and the laws by
which the resistance of different forms might be ascertained, for the
improvement of naval architecture and steam navigation-Newton,
Euter, D'Alembert, Bossut, Chapman, Reach, Beaufoy, Rankine, Scott
Russell, E. J. Reed, C.B., M. Dupuy-de-Lôme, late Chief Constructor of
the French Navy.
76. The British Association for the Advancement of Science has
within the last six years appointed two committees of some of its
most distinguished members, and therefore of Professor Rankine, to
make experiments on the resistance of vessels, and to report; but their
labours have come to nothing, as shewn in my Specification of 1870,
page 34, paragraph 64; page 35, paragraph 66; and page 37. Moreover
Mr. Froude, one of the ablost men of our time on these matters, is now
engaged in making experiments on the resistance of vessels at different
speeds on behalf of our own government, and with the same certainty
of failing as his predecessors. Because even as man cannot find out
God, so the inferior cannot find out the superior. Experiments, the
lowest grade of science, have never discovered the highest reaches of
science, and never will. Pure science can only be discovered by
pure thought, shown by all the greatest discoveries of mankind, from
Columbus and Copernicus to Newton and Watt.
77. The problem of resistance has been like a weight upon my mind
since Professor Rankine in 1866 first asserted his formulæ R=P, and R=
fo³ S, in refutation of my discovery of the loss of primary velocity in the
paddle wheel and screw. Now experiments depend upon the individual,
continually going wrong; laws upon God who never does. The four
formule of the schools P=(V-v)³, P=R, R=ƒv² S, and are all
0+

page_text: asserted to be "established by actual experiments, and have in practice
turned out true." Yet are they all wrong, for there are no such laws
of force and motion in existence applied to paddle wheel or screw
vessels; but how the formula R= ƒ³ S worried me until its error in
principle was detected in January last will be seen, though only to a
small extent, in my previous Specifications. In that of May 1866, at
p. 32, line 24, and p. 25, line 31%; in that of 1867, p. 8, line 13 to
page 41, line 5. Also in my last Specification of 1870, p. 11, line 15
to p. 18; also at page 24, line 17 to 37, and page 47, line 4 to page 48,
line 10. All these show my conviction at the time that the formula
ƒ v³ S was wrong in fact, because in opposition to the law of plane
and fluid impulse discovered in 1866 by induction from my discovery
in 1842. It was opposed there to varied but harmonious completeness
and perfection of the universe, and to the unity of principle in diversity
of action by which all things work harmoniously together for good
without interfering with or contradicting one another.
78. It took me, however, five years at intervals to discover where the
formula was wrong in principle, as well as in fact. The resistance of
bodies passing through fluids was looked at in every light that a vivid
imagination could suggest. This was to account for "the curious ex-
periment" which so puzzled Beaufoy, in paragraph 61, that "increasing
the length of a body, and preserving the same frictional surface and dis-
placement, exceedingly diminished the resistance." The reason given
in my paper of 1867 in paragraph 68 never satisfied me. At length it
happily occurred to me in January last to consider the ship dynamically
and not frictionally, as a body displacing the same weight of water as
itself in its whole length, and consequently so much weight of water.
per foot according to the length of the vessel. Therefore when in
motion it must do so too, and continuously displace and deflect a weight
of water equal to one foot of immersion all round at the velocity v.
But with a co-efficient to reduce the resistance to displacement
depending on the fineness bow and other things. The true principle
of resistance being thus discovered led by necessary steps to the form
of least resistance, explained in my Provisional Specification, and in
paragraphs 11 and 12 of this. Then came the analogy between the a
ploughing through the water and through the earth, and so my ideas
gradually took the form given in my Provisional Specification and here.
79. Now as no law of the Creator interferes with any other, but does

page_text: in many cases support some other law, it is proper to show that such
is the case here, for the speedier advancement of science by the intro,
duction of my discoveries. For the present discovery confirms the one
of 1866, of the loss of primary velocity in the paddle wheel and screw
equal to 40 or 50 per cent. of the power imparted to them, and which
consequently makes the resistance so much less than is taught by the
school.
80. For example, the formula for equable motion of Rankine, Main,
and others has been given in paragraph 34; it is R=P. The value
of P for the Banshee is 22569 lbs., shown in the Table, paragraph 35,
column 8. But by my discovery of 1842 and 1866, and formularized in
1869, her resistance is only 8468 lbs., shown in such Table, column 12.
So small a resistance was at once ignored by the schools. Professor
Rankine maintained that it was "impossible," observing that his formula
"fv³ S” unquestionably gives a lower limit, below which the resistanco
cannot possibly be," as extracted from his paper of 1866 in paragraph 20.
And in support of his other formula R=P, the Professor asserts that
"Rs is the only possible loss of longitudinal work," as shewn in
.paragraph 41.
'
81. Further, one of the oldest and ablest engineering firms wrote to
me in 1868 to the effect that " very careful experiments showed that
I very much underrate the power required to propel a vessel through
the water." This and many other objections being against me and
coming from such high authorities, it seemed but honest to give them
to the public. And so they were duly recorded against. my discovery
of 1866 in my Specification of 1870, p. 19 to 24.
.
82. My object in giving some of these extracts here is to show what
is the present state of the science of fluid resistance, to put on record in
particular that the universal belief is that it is very great, instead of
being comparatively little. For the first theoretical and practical
authorities of Europe make the resistance of the Banshee 22569 against
my 8468 lbs. And certainly a vessel of her size, going at the almost
railway speed of 18.5 miles an hour, and subject to the law that
resistance encreases as the square of the velocity, yet meeting with
so small a resistance as only 8468 lbs. did surprise me. The following
was my remark upon it in my said Specification of 1870, p. 44:-" Here
naval architects have had before them for (1870-1842)=25 years this
admirable vessel, going at the great speed of 18.5 miles an hour, yet

page_text: with so small a resistance as 8468 lbs. as to be almost incredible at that
speed."
83. But it was proper then, as it is now and at all times, simply to
state the facts, and there leave them. For we have to do with the truth
always, and just as we find it, for or against, but with the consequences
never. These are in better hands than ours. And now for a con-
firmation of my present discovery, and that in 1866, for both mutually
support each other, as gratifying as it is unexpected, which shows that
the resistance of the Banshee is so small as 8468 lbs., though declared
to be "impossible" by Dr. Rankine, by another professor, and by the
great engineering firm.
⚫0155 c t v²
84. It is said in paragraphs 15 and 16 that there seemed some
necessary relation between my new formulæ, the displacement formula
R=
lbs., and the midship area formula R= · 6 c a vª lbs., and
these with the impulse formula of 1869 R=18VP lbs. It is said also that
the first two are of no practical value, because the forms of resistance
vary so much that we cannot find the value of the co-efficient c without
experiment with every vessel. This part of my Specification was copied
before it occurred to me that the value of c might be found approximately
by my formula. R SVP lbs. It is then necessary first to show that
3
this formula is absolutely true.
85. The paddle wheel and screw, like any other body in action,
cannot do just as they please, first one thing then another. They
cannot then " vary from 39 to 65 per cent.," as the great leader of the
schools says they do in his paper of the 13th August 1866. Neither
can they make laws for themselves. They must therefore be governed
and controlled by laws as fixed, certain, and unchangeable as the motions
of the heavenly bodies themselves. Now there are only two kinds of
laws which can apply to the paddle wheel and screw, impulse or re-
action; impulse is when a fluid impinges against a plane of the same
area, as in the undershot water wheel; and'e converso where a plane
impinges against a fluid. For the same bodies brought together under
the same circumstances must always produce the same results. Or
there could be none of that certainty, in nature which the reciprocal
action of fluids and solids teaches, no matter which moves against the
other. So much for impulse. Reaction only applies to the issue of water
from a hole.

page_text: the
86. In other words, the laws of impulse apply only to the action of
fluids and solids uninclosed. Those of reaction apply only to the action
of a plane or water enclosed. Consequently, as the paddle wheel and
screw are uninclosed, like the undershot water wheel and screw,
laws of impulse alone govern and control the force of motion and
efficiency of these propellers, which is according to the relative velocities
of propeller and of vessel v. These laws are embodied in my formula
in paragraph 48, provided the escape of water past the propellers
towards the bow of the vessel be only 40 per cent. But if it be
50 per cent., as believed, the resistance would in such case be found by
VP
40
my formula R= lbs., given in my Specification of 1870, paragraph 43.
3 VP
But to be on the safe side and make ☎ the maximum, so as to have
ample power to overcome it, the 40 per cent. formula R
used throughout.
-3 VP
=
lbs. is
87. A law of nature is independent of the experiments of man, and
if they are not in accordance with it they are wrong, just as those
relied on by Professor Rankine for his formula fv³ S feet lbs. are wrong.
Or if such are true, illogical conclusions have been deduced from them.
But it so happens that the formula R = is confirmed by the inde-
pendent analysis of Professor Rankine himself, and the Reverend Pro-
fessor J. A. L. Airey, who observed in "Engineering" of August 1867;
that his investigations were founded on a careful study of the subject
for the last seventeen years." Their analysis, as observed in para-
graph 38, was of the resistance of the hydraulic reaction Nautilus, the
competitive vessel of the paddle wheel Volunteer, and therefore of that
vessel. Also a few months afterwards the same eminent mathematicians
investigated the resistance of the ironclad hydraulic reaction Waterwitch,
the competitive vessel of the Vixen and Viper twin screws, and there-
fore of those vessels also. Their investigations were published in the
> Engineer of 1866, and have never been impugned. Now it was not
till three years afterwards that my impulse formula for paddle wheel
and screw, R =
came into being, and made the resistance of the
Volunteer, Vixen, and Viper about the same as that of the Nautilus
and Waterwitch, found by the Professors by a different process to such
3 formula. Moreover the five vessels referred to arc of different sizes,
lengths, draughts, speed, and horse power, so that a thousand vessels
-3 VP
P

page_text: could not better test my formula. For the laws of the same propeller
can never change.
88. We have then the above formula established (1) on the un-
changeable laws of impulse, (2) by the experimental results of the
five vessels referred to, which it is important to bear in mind are
in accordance with my own experiments of 1842, (3) by the inde-
pendent investigations of eminent mathematicians by a different method
in such. formula. We can therefore now use it with great confidence
for the purpose of finding the co-efficient of general displacement or
resistance. This means the degree in which the normal resistance of ]
a plane 6 is diminished by the general form of the body, and not
merely by the bow, which co-efficient has never yet been found.
89. When it occurred to me in January last that the resistance of
bodies passing through fluids was a question which could only be solved
by the laws of dynamics, and not of friction, as maintained by Dr. 1
Rankine and the schools, it was with no little agitation that the letter of
Mr. Oliver Lang of 1849 was referred to (that mentioned in paragraph 37)
to see if he had sent me the important data of the displacement of his
beautiful vessel the Banshee. It was now plain that it ought to be
almost inconceivably small for so large a vessel, to confirm my discovery 2
that the chief resistance was displacement in one foot lbs. And there
was found the following recorded, 1870-1849=) 21 years ago "dis-
placement 580 tons, area of load water line 3540 feet, area of midship
section 182.5, length between perpendiculars .189, breadth of vessel
27.2;" and in a subsequent letter "length of stem (bow) from midships 2
86.5 feet."
90. We come then to their use 21 years afterwards, preserved
strangely enough from a fire which in 1849 consumed my library,
furniture, and manuscripts, every thing except the above letters and my
book of experiments in 1842. All seemed worthless then, and were 3
worthless, the experiments until 1866, and the letters till now, but from
which such large discoveries have at last come. Such fire then is my
reason for following my discoveries in all their details and relations here;
to show how those of 1866 and the present one mutually confirm each
other. For they are of sufficient importance for the improvement of 3
naval architecture, steam navigation, and the introduction of aerial navi-
gation, to be put beyond the power of man, or the accidents of fire, so

page_text: 189
The agreement in principle between the last two, before either is dealt
with, is 2240 × 580-6874 lbs., and 6×182.5×64-18=7027 lbs. It seems
then to me that these are the necessary relations of harmonious laws,
and not the fortuitous coincidence of incongrous things like these of
Professor Rankine's frictional and dynamic formulæ. For the Table in
paragraph 35, columns 8 and 9, shows an agreement, in the last example
there given, of R=P in lbs. only with R=fv³S in feet lbs. But we must
not force a suitable conclusion which does not come naturally, especially
in science.. We cannot, for instance, equate anything so incongruous as
lbs. and feet. lbs.; they are mathematically wrong, not being of the same
order or of the same powers. Besides, such agreement is more fatal to
both formulæ than even the great difference in the three other examples
in the Table in paragraph 35, for the reasons given in paragraphs 44 to 46.
94. Governed myself by law, and not by experiments or authority,,
however respectable, it was only right, in 1870, to give, in my Specifi-
cation of that year, the resistance of the Banshee, as found by my impulse
formula, though so small as then to seem almost incredible. And
now it.is confirmed by my present discovery and the data of Mr. Olivier
Lang, furnished 21 years ago, a pleasing instance of the truth of law..
We have then to seek some principle as our guide in all things, because
the Great Designer and Constructor of the moral and physical worlds, so
strangely in harmony, has ordained that everything should be governed
by law, and not left to itself, or there would be no certainty for man.
We ought not, therefore, to undertake any matter of moment without
first seeking diligently for the law which underlies it for our guide.
+3VP
95. And it is as true in science as in other things, "Seek and ye shall
find." When, then, we have found our seeking we have simply to record
it and leave it, however incredible, however opposed to the teaching of
the world; for we may be sure that, such is the connexion and mutual
dependence of different branches of science, we ourselves, or some one
after us, will verify what we have found if true. It has been so here.
No one, for five years of my Patent of 1866, would believe it a discovery
that made fluid, resistance so small, only about two-fifths of what it is
made by the schools, as shown in the Table, paragraph 35, and thus
reduced the assumed resistance of the Banshee from 22,569 lbs. to 8468 lbs.,
the Victoria and Albert from 40,616 to 15,231 lbs., and the Hercules
14500 to 17 714. The
;

page_text: wheel and screw to begin with, due to the laws of impulse, discovered in
1866, by induction from my abstract experiments in 1842. Now the
system of reaction, which is my system of propulsion, has no loss at all
to begin with, as discovered in 1842, but not understood till 1866. This
is shown by the formula in paragraph 50, where R=P, pure and simple.
Whilst in the formula for impulse, paragraph 48, R is not equal P, as
maintained by the schools, but only equal SVP, the difference, P.- 8VP,
"
being the loss of paddle wheel and screw propulsion according to the
relative velocities.
97. Confirmed as this now is by the true dynamic laws of resistance.
found by a different process, as shown in paragraphs 14, 15, and 92, we
have one more instance of the calm confidence with which we may trust
ourselves to the order, certainty, and consistency of general laws. For
laws are the embodiment of God, of the universal presence of Him who
made them and maintains them everywhere. Therefore will they never
deceive us, but, true as the needle to the pole, sooner or later lead us
into the haven of our rest where we desire to be. The day of inter-
pretation and of verification is sure to come in due
ourselves or others, and it matters little which.
time, either to
98. The aim and end of science is laws, of mechanics facts. It is.
proper, therefore, to guard against mistaking the nature of the co-
effecient ċ in paragraphs 91 and 92. There will no doubt be found in all.
vessels or aerial machines (for with the folly of ballooning and flying
true science has nothing to do) a certain relation, more or less exact as
the data arc exact, between the displacement resistance and midship
area resistance, both in one foot lbs., as shown in paragraph 93. But
the co-efficient of resistance c for one vessel will not do for another of
different displacement, though the wedge-shaped bow of both be of the
same proportions. There are three reasons for this :—
1. The length of vessel does not encrease in the same proportion aș
the displacement does, and the resistance does not depend entirely.
upon displacement. Hence the length cannot, in short vessels, reduce
the displacement in one foot lbs. sufficiently to make one and the
same co-efficient c reduce the formula R=¨º or 6c a v³, to the
-0155 € w²
',
1
3 VP

page_text: 2. The resistance does not encrease with displacement in length, the
reasons for which have been given in paragraphs 9, 10, and 14. And
3. A small difference in form makes a great difference in results, as
found by my experiments in reaction propulsion. This is confirmed by
the fact that many a naval architect has built two vessels from the
same design, and so alike that he himself can detect no difference in
them, and yet one shall be faster than the other, though under the same
circumstances, as shewn in paragraph 54.
99. The first and second reasons just given are thus verified. The
Banshee is 189 feet long, and displaces 580 tons. The Victoria and
800
2245
--
580
=3.8 times as
9062
2245
Albert is only 189 =1-6 times as long, yet displaces
much water, whilst the Devastation is (300-285=) 15 feet shorter,
yet her estimated displacement, furnished by the Admiralty, is =4
times that of the Victoria and Albert. Now this last vessel confirms
my discovery, that encreased displacement by length does not encrease
resistance. For though she displaces 3.8 times as much water as the
Banshee, she goes nearly one knot faster, yet with less than twice the
indicated power, as shown in the table, paragraph 35, column 2.
100. How much this is opposed to the teaching of Professor Rankine,
in his surface formula R=fv² S feet lbs., has been abundantly shown.
How the same erroneous principle is maintained by Mr. E. J. Reed,
C.B., late Chief Constructor of the Navy for eight years, has also been
shown in paragraphs 30 and 31. In the latter he says, that "the horse
power expended in overcoming the excess of frictional resistance upon
the longer ship is 20167." And this eminent naval architect observes a
few lines before, that "the immersed surface of the longer vessel exceeds
that of the shorter by 14669 square feet." Now the immersed surface
of the Victoria and Albert is =3.39 times that of the Banshee.
12000
8540
101. Nevertheless what is based on reason is confirmed by facts.
Hence my discovery that the chief resistance to bodies passing through
fluids is dynamical and not frictional being conformable to reason is
confirmed by facts. Whilst the doctrine of the schools being opposed
to reason is contradicted by facts. For the very facts sent to refute my
discovery refute their own theory. Because according to the extracts
in paragraph 31, the Victoria and Albert going nearly a knot faster, and
having 3.39 times the immersed frictional surface, ought to have more

page_text: than four times the resistance of the Banshee, and four times the horse
power to overcome it. Yet the former has not even twice as much as
the latter, as shown in the table, paragraph 35.
102. Something has been said in paragraphs 19, 20, 31, 60, and 75, of
the thousands of experiments, the tens of thousands of pounds, and the
many distinguished men whose labours have been spent in vain on the
resistance of vessels. Mr. John Scott Russell, has too added his own
great abilities and experience to the same subject, as will be found in my
Specification of 1870, p. 34 and 37. "He had been," he said,
66 one of
the deputation which went from the British Association for the Ad-
vancement of Science to the Lords of the Admiralty. They had begged,
with all their might, force, energy, power, and weight, that the Admiralty
would assist them in getting one single experiment with one single
carefully measured ship, of which they would have been able to say her
resistance in going through the water was so many pounds, but the
Lords of the Admiralty did not entertain it."-Engineering, March 26,
1869, p. 218.
103. This extract is given to show the importance attached to this
question, and that the true principles are not understood, even by the
ablest men. If, for instance, the resistance of bodies passing through
fluids depended on the bow alone, then the co-efficient of displacement
of one vessel would do for all others whose bows were of the same pro-
portions. But resistance depends on many things, on the bow, stern,
midship area, displacement, and length. Alter then only one of these
and you alter the general results, just as we should if we altered the
quantity of water in pipes and the form thereof. Any change then in
one of the conditions would necessarily affect the general co-efficient c.
Therefore" one single experiment however exact would only mislead
if applied to any other vessel, except exactly the same in all the several
things that go to make up the general resistance of bodies. For these
reasons this science is the most treacherous and deceptive in the world,
shewn by a century of failures in paragraphs 60, 66, and 75. To deduce
then from model experiments or those on canal boats, referred to in
paragraph 20, that the surface of one form and size will give a formula,
that will do generally for other bodies of different forms, sizes, areas,
and displacements, is to draw illogical deductions from irrevelant facts.
104. But every body in motion of the same form must necessarily be
governed and controlled by the same unvarying laws, and by these alone

page_text: it can exercise its power. We have then only to discover the laws which
govern such unvarying body in motion, whether a cannon ball, paddle
wheel, screw, hydro-propulsion, or water moving a solid, and we have
the exact amount of power which such body is capable of exerting.
When then we apply the power of such unvarying form to overcome the
resistance of vessels we find at once by the fixed laws of such body what
such resistance is, because it cannot be either more or less than the
power that overcomes it.
105. With such application then we are on the solid ground of nature.
For it matters not now what may be the form, size, bow, stern, displace-
ment, length, midship area, speed, smoothness, or foulness of bottom,
fresh or salt water, canal, river, or ocean; because the unvarying form
of propeller governed by unvarying laws, devised for it by the Creator,
can only exert a certain amount of power, therefore can only overcome
just so much resistance, neither more or less. Now my formulæ in
paragraphs 48 and 50 embody the laws, therefore the power which the
paddle wheel and screw impulse and hydro-propulsion reaction can exert
at different relative velocities. It follows that by these laws we can
determine with all required accuracy what is the resistance of every
body so propelled, and at every velocity.
106. These axioms are to my mind necessary truths, founded on those
divine intuitions of the reasoning faculty which have been bestowed on
man to enable him to discern truth from error. But it seems to me
necessary to record them here to refute all future objections, because
my discovery of 1866, founded on these fundamental truths, has been
so positively denied for five years, by so high and honored an authority as
the Regius Professor of the University of Glasgow, and by others of the
schools. It is then desirable to show that his formula R = fv² S feet
lbs., relied on in opposition to my discovery, besides being wrong in
principle, which has been already shown, has two more errors, its.
complexity and uncertainty.
107. The laws of the Creator, as far as they are known to me, are
distinguished by their simplicity, efficiency, certainty, and economy.
But as efficiency and economy, are one we may omit the last word.
Thus everything complicated and uncertain has for 20 years been
rejected by me as untrue somewhere. Now it is hard enough to arrive
at true results by Professor Rankine's formula, as will be seen by the
following extract from his paper in the Mechanics' Magazine of the
'

page_text: 20th September 1861:-" Professor Rankine refers to previous inves-
tigations of the effect of friction in resisting the motion of a ship
through the water; but remarks that those investigations could not be
expected to yield definite results, because in them the velocity of sliding
of the particles of water over the ship's bottom was treated as sensibly
equal to the speed of the ship%; whereas that velocity must vary at
different points of the ship's bottom, in a manner depending on the
positions of those points and the figure of the ship; being on an average
greater than the speed of the ship in a proportion increasing with the
fullness of the ship's lines. He then explains the general nature of the
mathematical processes by which the friction can be determined. Their
results, in the exact form, are very complex; but they can be expressed
approximately for practical purposes by comparitively simple rules.
Examples are given of the application of those rules to experiments by
Mr. J. R. Napicer, the author, and others, on steam ships of very various
sizes, forms, and speed."
108. "Their results in the exact form are very complex," the Professor
observes something of their complexity will be seen in the extract from
Mr. E. J. Reed's paper in paragraph 30. Also in the remarks of Pro-
fessor Haughton in paragraph 33. Now the meaning of "a trodioidal
ribbon and augmented surface" is not certain. It has been shown too,
in paragraph 37, that in the measurement of the Banshee by "a
trodioidal ribbon or augmented surface," or something else, there is a
difference between her builder and the Professor of (5200-3540 =)
1660 square feet. Further, the co-efficient of friction f=012 in the
formula fv S is only for a smooth surface. It must therefore vary for
wood, iron, or copper, smoothness or foulness of bottom and sides. And
this, spread over a surface of many thousand square feet, must affect. the
amount of resistance. Five years therefore before its erroneous principle
was discovered it was rejected by me because not in harmony with the
laws of physics, plane and fluid impulse of equal areas discovered in
1842, the reciprocal actions of fluids and solids, and the 'simplicity and
unity of the laws of nature.
"3 VP
v
109. We can now contrast the simplicity and certainty of a true law
of the Deity, embodied in my formula R= lbs. for paddle wheel
and screw impulse. No "trodioidal ribbon or augmented surface," or
other manipulation or co-efficient of friction or displacement, or form
of bow or stern is here required. The value of Vis found at once from

page_text: SUMMARY OF RESISTANCE.
112. I do not profess to have exhausted in a few months, for my
present discovery was only made in January last, the great scientific
problem of all ages, the resistance of bodies passing through fluids. For
(as shown in paragraphs 17, 19, 20, 22, 31, 33, 60, 66, 75, 76, & 102), this
question has been investigated by some of the most eminent philosophers
and mathematicians from Newton to Rankine, Scott Russell, and Mr.
W. Froude now making experiments by order of the Admiralty. And
he too will as certainly fail in finding the form of least resistance, the
laws which govern it, and the laws for measuring what such resistance
is, as all his able predecessors have failed, for the reasons given in
paragraphs 76, 98, 99, & 103.
113. Now Professor Rankine's two formulæ, R=P lbs. and fo³ S feet lbs.
are as opposed to my present discovery of the form of least resistance,
and the laws which govern it, as to my inductive discovery of 1866, of
the great loss of primary velocity in the paddle wheel and screw. Thus
his high and honored authority and that of others have lost me five-
years of my Patent of 1866, the culmination of the thought and labours
and expenditure of more than a quarter of a century. Since then no one
in the world but myself can refute his formulæ, it seemed to me that
it was right to do so here, that such refutation might be the ever
living witness on behalf of my discoveries. Besides the nation is more
largely interested in this question than myself, because millions of public
money and still more valuable time have already been spent on short
ironclads. Now my object is to put on record the present state of the
science of naval architecture, as shewn in the designs of its first men.
Nothing therefore can show this better than the fact that Mr. E. J.
Reed, C.B., has received an honorarium of £5,000 from the public purse
for his Invention of short ironclads, the best evidence of the satisfaction
of the nation. It is then remarkable that the thought and labours of
all past centuries in naval architecture should have ended at last, and
in the greatest naval nation in the world, in the worst type of vessel
yet introduced into the British navy, and that the nation should be
perfectly satisfied with it.
114. Short ironclads is the worst type of vessel, because short
vessels necessitate deep vessels to bear the required armour, or to
carry the required cargo. Hence their resistance is so great as to make

page_text: them expensive steamers and slow sailers, requiring half a gale of wind
to get any decent speed out of such huge hulks. Thus short and
deep vessels are opposed to the three fundamental principles of least
resistance discovered by me. These are long, shallow, and narrow, tho
last two to reduce midship area resistance and length to give capacity;
but length encreases resistance, according to the principle of surface
friction enunciated by the Regius Professor and the schools, in his
erroneous formula fv S feet lbs. It seemed then required of me to
destroy a formula which is opposed to the true principles of naval
architecture, and would therefore stop all future progress. For it has 1
already, according to Mr. Reed in paragraphs 30 and 31, prevented so
ble a man from introducing long ironclads into our navy.
115. It has therefore been shown that the formula for finding the
esistance of bodies passing through fluids contains three fundamental
rrors in science :-
-
1. It is a merė frictional instead of dynamic formula for a body in
motion.
2. It is a formula in feet lbs. instead of lbs. only and cannot
therefore equate with R=P lbs.
3. It is a formula that is irrespective of the arca of the midship 2
section, as shown by the widely different area in the Table,
though this is the chief cause of fluid resistance.
Further, the above formula is condemned by its complexity and
incertainty, as shown in paragraphs 107 and 108. Also by its making
o economical a vessel as the Banshee "somewhat below good ordinary 2
teamers," as stated in the Professor's paper of the 13th August 1866.
This formula then condemns some of the best principles of naval archi-
ecture, for though the Banshee was built more than 20 years ago wo
have not yet got her superior if her equal in the whole British navy.
116. Nothing has done so much to emasculate the mind and deprive 3
t-of its natural manhood, than the swaddling clothes of authority; the
hilosopher fortunately for mankind will not wear them. He will
nvestigate for himself and believe only sound logical deductions from
acts based on the realities of nature. Some one at the commencement
f steam navigation started with the foolish assumption that there is no 3
ifference in the action of a plane enclosed or uncnclosed, though
he very words show there is a difference. Nevertheless, schoolmen

page_text: maintain there is none, that the whole mass of slippery and mobile fluid
set in motion by an unenclosed plane paddle wheel or screw is driven
astern just as if they were enclosed, whilst some assert that if any
water does escape towards the bow there is no loss of power. Professor
Rankine, for one, maintains that my discovery of the loss of primary
velocity "is impossible" because he says that the resistance R and
residuary velocity S is the only possible loss of longitudinal work," as
shown in paragraph 80; this, however, is contradicted by the theory and
practice of all hydraulic machines in all parts of the world. For every
pump and hydraulic machine, except the paddle wheel and screw, is
enclosed for the sole purpose of preventing that very "loss of horizontal
work" called leakage which the Professor maintains is "impossible."
The logic is remarkable. There is a loss when leakage is reduced to a
minimum by enclosing the plane. This every one admits. But there
is no loss at all when such leakage is increased to a maximum by not
enclosing the plane. Call one a hydraulic machine or pump, and there
is loss of power proportional to leakage. Take its enclosure away and
call it a paddle wheel, and there is then no loss at all. Both push
against water, but a name makes all the difference in the results.
117. Now one of the sublimest departments of the human mind is
the conquest of the winds and waves in their greatest fury by steam.
navigation. Still more sublime will be the navigation of the still and
solemn realms of air. Hence some of the highest interests of man are
concerned in all discoveries which will materially advance the one, and
give the world the other. Since then nothing but my past and present
discoveries can ever do either it may be permitted me for such great
and noble purposes as these to sum up the refutation of the schools, so
that every one strong enough to resist the trammels of authority and
think for himself may see the truth of my discovery of 1866 and this.
For both are in direct opposition to the two formulæ of the schools
R=P lbs. and R=ƒv³ S' feet lbs.
118. Based on the realities of nature my discoveries can never be
refuted except by first refuting six of the fundamental principles of
physics.
1. The law of plano and fluid impulse of equal areas discovered by
me in 1842, whereby a plane impinged upon by a fluid of the same
arca loses 40 or 50 per cent. of the power expended in consequence
of so much of the fluid escaping past the plane unutilized.

page_text: 2. The reciprocal action of fluids and solids, whereby the same bodies
acting upon one another under the same circumstances must always
produce the same results, whether the solid act on the fluid as the
paddle wheel and screw do, or the fluid act on the solid as it does upon
the undershot water wheel and windmill.
.3. That pursuant to such law a vessel in motion meets with the
same resistance as if at rest from the motion of a stream at the same
velocity.
4. That except the paddle wheel and screw, all hydraulic machines
are enclosed, notwithstanding the extra cost, and loss from friction and
valves, solely to prevent the still greater loss by the escape of water past
a simpler and cheaper machine unenclosed.
5. That my two crucial instances (1) area test, and (2) power test of
the truth of my discovery do not exist. These are, that the area of
propeller and horse power of every screw and paddle wheel vessel
in the world from the smallest Thames boat to the Great Eastern
679.6 feet long, are at this moment at least twice as great as the area
and power required to overcome the same resistance at the same
relative velocities by reaction propulsion. This unanswerable evidence
of my discovery is particularly dwelt upon in all my papers and
Specifications of 1866. Paper to the Admiralty in 1867, and Specification
of 1870, p. 22, paragraph 34.
6. That the laws of impulse embodied in my formulæ in paragraph 48
can alone account, not merely for so remarkable a discrepancy as that
between the pressure on the propeller P, and resistance of the vessel R,
shown in the Table, paragraph 35, columns 8 and 12, but also for the
variations in such discrepancy at different relative velocities, as shown
in column 17 of such Table.
"
119. On such realities of nature do my discoveries imperishably rest.
And it will be admitted by every philosopher acquainted with the history
of inductive science that from Columbus and Copernicus to Newton
and Watt no discovery was at its first promulgation ever supported by
a greater weight of positive and exact evidence than mine of 1866. It
was and is, for instance, based on the laws of physics (plane and fluid
impulse of equal areas, and the reciprocal action of fluids and solids); on a
the analogies of science (the undershot water wheel and screw), on official
experiments, those of the five vessels referred to in paragraphs 38 & 39.
And all these are confirmed by the laws of impulse, whose mathematical

page_text: relations are in exact accordance with all the observed phenomena,
which are, as before observed, the varying losses at different relative
velocities shown in the Table in column 17.
120. In my opinion therefore those who are teachers in Israel, and
are in authority, should no more depart from the close logical rules of
philosophic and scientific investigation, than our judges should depart
from the strict rules of legal evidence. This doctrine was so clearly laid
down in my paper to the Admiralty of 1867, that it may be of service
to science and the public to record it here. It was observed at page 26
of that paper," the conduct of the human understanding in considering
all new discoveries has been well defined by the greatest reasoner,
philosopher, discoverer, astronomer, geometer, and mathematician ever
combined in one man, Newton the illustrious, who thus speaks in his
Optics"-As in mathematics, so in natural philosophy, the investigation
of difficult things by the method of analysis ought ever to precede the
method of composition. This analysis consists in making experiments
and observations, and in drawing general conclusions from them by
induction, and of admitting of no. objections against the conclusions,
but such as are taken from (true) experiments or other certain truths.
121. In short, facts and their meaning is the sum and substance of
philosophy. Every fact has its meaning. Is it a true fact, and what
is its sure meaning? Only so were Newton's, my own, and all inductive
discoveries ever made. For, following his principles, in 1842 were
made my abstract experiments," and in 1866 my "observations" of the
experiments conducted by the Admiralty officials with the Nautilus,
Volunteer, Waterwitch, Vixen, and Viper. Then it was that " gencral
conclusions were drawn by induction" from my experiments in 1842 to
those of 1866. And so was made my discovery of the loss of primary
velocity in the paddle wheel and screw, as shown in the Table,
column 13.
66"
122. And lastly, it was observed in my said paper to the Admiralty,
"that with the exception of these abstract experiments in 1842, all
"the facts and data in support of my discovery are furnished by the
Admiralty officials and others, not one by me. Therefore the facts
" themselves cannot be doubted. Mine only is the reasoning upon
them, deducing therefrom in strict logical order one universal law
"of physics for all time; the inferiority, as before observed, of plane
"and fluid impulse, and the superiority of reaction for propulsion for
-66

page_text: "both elements." Now when one person supplies the theory, and others
independent of each other and ignorant of it, furnish the data and facts
which agree with it in all its variations; when such theory accounts
both for the primary and residuary phenomena, and when no other
law can do so; then we have the highest evidence in support of the
discovery to which mere human capacity can reach. Yet has it been
denied for five years by virtue of an empirical formula R=fv² S' feet lbs.
which is opposed to the fundamental principles of natural philosophy
which support mine; inductive philosophy, the laws of physics, the
analogies of science, experimental results of the five vessels referred to,
and mathematical analysis; a formula which is wrong in principle,
form, and fact, as shown in paragraphs 29, 44 to 48, 60 to 65, 119,
and elsewhere.
"both elements." Now when one person supplies the theory, and others
independent of each other and ignorant of it, furnish the data and facts
which agree with it in all its variations; when such theory accounts
both for the primary and residuary phenomena, and when no other
law can do so; then we have the highest evidence in support of the
discovery to which mere human capacity can reach. Yet has it been
denied for five years by virtue of an empirical formula R=fv² S feet lbs.
which is opposed to the fundamental principles of natural philosophy
which support mine; inductive philosophy, the laws of physics, the
analogies of. science, experimental results of the five vessels referred to,
and mathematical analysis; a formula which is wrong in principle,
form, and fact, as shown in paragraphs 29, 44 to 48, 60 to 65, 119,
and elsewhere.
PART IV.
SAVING BY MY DISCOVERIES OF THE FORM OF LEAST RESISTANCE,
AND REACTION PROPULSION, AND DESCRIPTION OF MACHINERY.
123. The superiority of mental science to experimental, the least
intellectual and therefore lowest grade of science, having been shewn
in the detection of wrong experiments, or wrong deductions from true
ones, we can now show the advantages of my discoveries. We will
take the Hercules for comparison, because her world renowned designer,
Mr. E. J. Reed, C.B., has declared her to be his "representative vessel,"
and because the whole scientific press are unanimous in her praise. She
is 325 feet long, 59 broad, has a mean draught of 24.8 feet, and at 14.7
knots an hour exerted an indicated power of 8528 horses. My type :
of fighting ship will have at least the same defensive and more offensive
power, because she will draw (24.82—13.43=) 11.39 feet less. We have
then to find the saving in fuel, and consequently in cost of engines of
the new type, compared with the most advanced state of steam navigation
science of our time.
124. The speed of the Hercules was 14.7 knots = 1.688×14.7=
24 82 feet a second. This be 10 per cent. less than the mean
°
velocity of her screw =
24.82 x 10
100-10
-
-2-75 feet a second. Hence V=24-82+
2.75=27.58 nearly. Deduct 20 per cent. for engine and shaft friction
from her indicated power of 8528, then by my formula of 1857 the a
1100 (IS). 1100 x (8528-1705.6)
cffective pressure on her screw was P=110
143218.3 lbs. This then is her huge resistance as maintained by
+
27 58+24.82
=

page_text: 100-15
1465 x 15 =259 h. p. Therefore the gross indicated power required for
my fighting ship will be 977+259+1465=2701. Hence the saving on
the Hercules will be
68 per cent. on vessels of such deep
draught.
8528-2701 x 100
8528
==
128. We now see the importance of my present discovery of the form
of least resistance, whereby the resistance of bodies passing through
fluids can be so much reduced to begin with; for, notwithstanding the
extravagant allowance of 40 per cent. for the losses of my system, the
saving still comes out so large as 68 per cent. for these reasons:―The
paddle wheel and screw, as shewn before, begin with a loss of primary
velocity due to the water slipping past the floats, and which is the only
true slip; this alone amounts to (P-R) v feet lbs., where R=" .3 VP
lbs.
as given in the formula, para. 48. There is also the further loss of the
whole pressure P, which runs away in the residuary velocity shown in
my formula of 1857 =P (=) feet lbs., para. 48. Now the engine
power must not only be sufficient to make good both these losses, but
also its own friction of 20 per cent. upon such losses as well as on the
useful effect Rv feet lbs., in which again the greater R the greater
the power and engine friction required.
129. In my system of reaction there is also the loss of the whole :
resistance R in the residuary velocity, but no loss from slip, for here
there is no slip, which is the loss of primary velocity. Still as my loss is
R() feet lbs. we see how important is any discovery in naval
architecture which will reduce R to a minimum to begin with, because
not only is R lost in reaction as well as in impulse, but there is the
further loss upon R due to my reaction propellers, and then a further
loss of 20 per cent. for engine friction upon such propellers, as well as
on the whole power expended.
130. As regards the area of reaction and of propellers, their diameter,
and number of revolutions for the above fighting ship. At the same a
speed as the "Hercules," 14° 7 knots an hour =14.7x1-688=24-82 feet
a second. Let the mean velocity of my propellers V=1.5 v=1.5×24.82
=37.23 feet, say 37.5 feet a second. Then the resistance being 25861 lbs.
as found in para. 126, the area of reaction and of the floats will be,―
a
R
25861
DARD
25861
27.2 square feet nearly 3

page_text: 27.2
131. It is proposed to have two reaction propellers, one on each side
of the keel, as shown in the Drawing, Sheet 1. The propellers will be
either the box-cam propeller, shewn in Sheet 2, Figures 2 and 3; the
cam propeller in Sheet 3; the centrifugal propeller shown in Sheet 4,
Figures 1 & 2; or the roller propeller, Fig. 3. Hence area of reaction and
floats required for each propeller = = 13.6 square feet. If then
the projection of float through the ship be 2 feet the breadth of each
propeller will be 6.8 feet. This in the bottom of the ship 59 feet
wide will be amply protected from shot or shell, wreck of spars, sails,
or other screw entanglements which sent to the bottom the "Prince,"
laden with important clothing and stores during the Crimean War, and
many another vessel with her crew.
13.6
2
1
132. The number of revolutions depends on the weight of engines.
The economy and convenience of high-pressure steam are best known
to those who have studied it most. But the present marine engines
have only a mean steam pressure of about 25 lbs., when locomotives
safely carry many millions of persons every year in all parts of the
world at a boiler pressure of 150 lbs. So small a pressure as 25 lbs. in
marine engines necessitates huge, costly, and heavy engines and boilers
for navigation, where space, lightness, and simplicity are far more
necessary than on land. For weight increases draught, this resistance,
and this again requires more weight of engine power and fucl to
overcome. Such a system then is too unsound and costly to last.
2729
2
19.1 V
19°1 x 37.5
70
133. It is therefore proposed to have locomotive boilers, engines,
surface condensation, and a mean steam pressure of 100 lbs. on the
pistons. Now the indicated power of each pair of propeller engines
will be only =1364.5 horses. Hence such light weights can very
well run at 70 revolutions a minute. The diameters of propellers
therefore will be d =
-= 10.23 feet. Hence with 2 fect
projection of floats the actual diameter for mean velocity of floats will.
be (2+10-23=) 12-23 feet. When the application of my system is
confined to a particular diameter of propeller the number of revolutions
corresponding thereto will be n = 1-2 per minute, d being the actual
diameter required to give a mean velocity of V.
19-1 V
134. Swift despatch boats are the messengers of safety, the heralds

page_text: therefore show that the speed of vessels like the "Victoria and Albert"
can be doubled with only about double the indicated power, but with
not much more than the same consumption of fuel between given
places. This will be thought impossible in days of such advanced
science as our own by those who know that, by the laws of the squares
and cubes, the resistance becomes four times and the power to overcome
it must be eight times what they are at only half the speed.
Thus by
the formulæ and doctrine of Professor Rankine, Main, and the schools
the resistance of the "Victoria and Albert" being 40616 lbs., as shown
in para. 35, and her indicated power 2980, to increase her speed from 17
to 34 knots an hour would require ✓✓
=23,840
h. p. More, in fact, because so great an encrease as eight times her
present engines, boilers, water, and fuel would so encrease their weight,
and her immersion, as to add materially to her present resistance to
begin with. In short any such railway speed would be impracticable
were the doctrine of the schools true.
==
2980 x 34³ 2980 x 39304
173
4913
135. Her present resistance at 17 knots is however only 15231 lbs.
by my formula, as given in the Table, para. 35. But by my present
discovery the resistance of bodies passing through fluids is inversely as
their length, provided displacement, bow, and stern be kept the same, a
as explained in paras. 11 and 12. Therefore, by doubling the length of
the "Victoria and Albert," her resistance would be only,

page_text: engine friction; in all 1.5 of 3490 = 2326 h.
P. . Also for untried
machinery, to be on the safe side, add 15 per cent. as in para. 127.
= 616 h. p. Hence the gross indicated power
This comes to
required will be
3490 x 15
100-15
:
3490+2326+616-6432 horses.
137. Thus by increasing the power from 2980, what it is now at
17 knots, to a little more than double (even with the unlikely losses of
40 per cent. for my system) science can now give vessels of the capacity
of the "Victoria and Albert" at the railway speed of 34 knots which are
about 34×1-15=39 miles an hour. But by the two formulæ of Pro-
fessor Rankine and the schools, R=P lbs. and R=fv³ S feet lbs., eight
times the power would be required to double the speed of such a vessel.
This would come to (8×2980 =) 23840 h. p. as shewn in para. 134.
Hence there is a saving of (23840-6432=) 17408 h. p., by combining
my discovery of reaction propulsion, patented in May 1866, and March
1870, with my present discovery of the laws and form of least resistance.
138. By doubling the velocity we halve the time. Now the distance
between Folkestone and Boulogne is about 29 miles, and the average
speed of the present passage boats is 15 miles an hour, and the passage
across about 2 hours. If then we take the average speed of vessels,
designed and propelled according to my discoveries at only 30 miles an
hour, the horrible agony of the sea-unknown to me-would be endured
for only half the time it is now, and in a vessel of 600 feet long and
40 broad, and therefore with less rolling, pitching, and heaving. If too
the indicated power be double what it is now, the cost of fuel, which
is the chief thing in steam navigation, will be about the same, whilst
the wear and tear of engines, stokers, and men will be only half what
it is now.
139. The great cry of the age is speed and more speed at sea. We
can then now greatly reduce the time and ocean horrors of international
communication with the Continent, the United States, and.our Colonies,
and admirably adapted in its application is my principle of reaction to
give what the age wants. Because the area of reaction and of propeller
is inversely as the square of the speed. Consequently the greater the
speed the more convenient the application. For example, the area of
reaction and propeller floats for such vessel referred to at 34 knots an
hour 57.392 feet a second would be,

page_text: 19.8
square feet nearly. If then the projection of floats be 2 feet the breadth
of each propeller will be = 2×2=4·82, say 5 feet; small indeed for a
vessel 600 feet long and 40 broad. The number of revolutions and
diameter of propellers will be best determined by the kind of engine,
and by convenience, and these can be found by the formula in
para. 133.
600
140. The draught being inversely as the length such a vessel will have
a mean draught of 15 × 800 -7.5 feet, which is 9-7.5= 1.5 foot less
than the Banshee. But then my vessel will be (40-27·17=) 12.3 feet
broader. Now one of my aims has been to get stability without
resistance, which is done by my stability planes shown in Sheet 1,,
Figures 1, 2, 3, letters d, d, and as indicated in my Provisional Specifi-.
cation. Were, however, the resistance of bodies passing through fluids
due to the whole immersed surface in feet lbs., as taught by Professor
Rankine, and adopted by the late Chief Constructor of the Navy, as
shown in paras. 30 and 31, such Invention of mine would increase the
resistance in proportion to the whole frictional surface S in the Pro-
fessor's formula R=foS feet lbs., and consequently be worthless.
DESCRIPTION OF THE SHIP OF MY INVENTION & MACHINERY OF
REACTION PROPULSION.
141. Sheet No. 1, Figure 1, is a side view of the ship showing the:
general arrangement of the fighting, propelling, and steering apparatus,
and their relative positions fore and aft and above and below the water
line; Figure 2 is a deck plan; Figure 3 is a plan of the hold showing
the general arrangement of the propelling and steering apparatus, and,
their relative positions with respect to the line of keel and ends of the
ship; Figure 4 is an end view of the same; Figure 5 is a longitudinal
section through the engine room on line A, B; Figures 3 and 6 are cross
sections through the engine room on line C, D, Figure 3.
}
142. The centre or midship. portion a is raised well out of the water,.
and carries one turret 6 for two guns, whilst the ends of the ship c;.
which are both alike to prevent turning, have no freeboard but are
flush with the water line. The object is to reduce weight, draught, and
resistance with a small target for the enemy's shot and action of the
wind and waves. The ship is also shown with a flat bottom for shallow
water, and has stability planes d standing out from the sides to check

page_text: 'rolling. The false keel e is to protect the hydro-propellers f and the
rudders g. The ship is divided into water-tight compartments by bulk-
heads h, and horizontal planes to cut off the water and to prevent coals
or goods beneath from shifting when the ship rolls. The end com-
partments communicate with the next compartment by water-tight
doors i, which are to be closed in case of damage to that part of the
ship, and those compartments communicate with the raised portion of
the ship by hatchways, the combings of which should be carried up
considerably above the water line, which is level with the lower deck.
143. The boilers ; are placed in the centre of the ship. The funnel
passes through the middle of the turret for protection, and the gun
carriages are fitted on opposite sides of it. The hydro-propellers ƒ (of
the centrifugal type) and reaction tubes are fitted to slide inside of an
'outer case in the ship, so that by means of screws they can be drawn
inside the ship for sailing or repair, when the opening in the ship's
bottom is to be closed by the sliding doors k. These hydro-propellers
äre each driven by a pair of high-pressure surface condensing engines,
in which it is proposed to use steam of an average pressure of 100 lbs.
per square inch.
144. From the main steam pipes supplying the engines smaller pipes
are carried to a pair of high-pressure surface condensing engines m at
either end of the ship. These are to work steering hydro-propellers n,'
which are placed across each end of the ship to keep the bows turned'
to the enemy to present the least mark to their shot. When these
strike at an angle and against double armour at the bows they will not
often do much mischief. Such steerers will also be useful for ramming
or avoiding it, and for navigating among rocks and shoals.
145. The rudders g at either end of the ship are fitted to work in
openings in the false keel before mentioned, and are of great length and
small depth. The rudder shafts or posts o pass through stuffing boxes
to the inside of the ship, and their upper ends turn in bearings fixed to
the under side of the deck above them. The tillers p are fixed just
below the deck, and the tiller ropes or chains q are led along beneath
the. .deck until they reach the centre compartment, when they turn
over the pulleys and pass up through the lower deck to the steering
wheels 8.
"
146. From the point where the tiller chains leave the end com-
Lam
in share the lower deck they are enclosed in³

page_text: water-tight tubes t, so that should one compartment become full of
water it will not flow into the next compartment by the holes the said
chains pass through. Either rudder may be fixed in its central position
when required by the screw u, which passes through a stuffing box in
the bottom of the ship, and forces a cramp or inverted Y piece over
the back of the rudder which has previously been placed in its central
position.
147. Such is my Invention to carry out the general principles of
my discovery of the laws and form of least resistance consistent with
capacity and offensive and defensive powers. Should it be found in
practice that the weight of water which may be occasionally on the
submerged parts at the water line, in Sheet I., is disadvantageous, such
parts may be raised just high enough to prevent such weight of water,
and be covered over with a convex or angular deck.
148. It is said in my Provisional Specification to the effect that it
is doubtful if such very long ships as will best carry out my present
Invention could be propelled and turned conveniently with the present.
screw, single or double, that I therefore combined with such Invention
my former Invention of reaction propulsion described in my Speci-
fication of the 3rd March 1870, No. 623. The following then is the
description of such Invention, which I now combine with my said ship
to propel it by reaction.
149. Sheet 2, Figure 1 is a transverse, and Figure 2 a longitudinal
section of a propeller with ten floats, each opposite one being connected
by a pair of rods n, that the centrifugal force of the float not in action
may reduce the friction of the roller in the cam attached to the float
in action, the connecting rods n being sufficiently strong to take the
strain. Hence the friction pressure of the rollers on the cams is only
that due to the resultant centrifugal force. Holes are made in the
shaft g for the connecting rods to pass through, the shaft being enlarged
to prevent the holes weakening it. This arrangement I call the box
cam, because the floats a are worked by a cam b enclosed in a box or
case by the false' partition o. In this way communication between the
cam and the sea is prevented, which permits the rollers to be greased.
Water leakage from the drum into the chamber p is drawn off by the
engine pump through the pipe ġ. The rigidity of the drum is obtained
by making of a very strong section the ring.r, which is fastened to the

page_text: '
angle iron d, and together with the latter is fastened to the slotted
arms e, which radiate from the bosses fon the shaft g.
150. Figures 3, 4, and 5 of the same Sheet 2 represent (on an enlarged
scale) a front view, end view, and sectional plan of two opposite con-
necting floats, with the arrangement of framework for carrying the cam
rollers rendered necessary by the box cam arrangement. Each float
consists of a strong steel frame a, the lower part which acts upon
the water being fitted with wood 6. This woodwork is incased in
sheet steel c² on both sides to combine strength and lightness. The
arm d¹ carrying the cam roller is forged all in one with the framing at
the top, and is winged out as shewn to prevent it springing. The space
between the arm and the float is left for the false partition which
encloses the cam, and also for the ring of the drum. Figures 6 and 7
of this same Sheet 2 are enlarged views of the disconnecting apparatus
between the engine and hydro-propeller, as shewn in Figure 2. is a
strong disc forged in one piece with the engine shaft. Another diso j¹
is securely keyed on the propeller shaft containing a pin k¹, which fits
into a corresponding slot in the disc 2. When the propellers want
repairing, or it is desired to use sails only, and to lift the propeller into
the ship, the engines are slowly turned round until the centre of the pin
is in the vertical line through the axis of the drum; the slot i will then
allow the pin to be lifted out of it, and the propeller can be raised.
151. Sheet 3, Figures 1 and 2, are respectively a transverse and
longitudinal section of a reaction propeller, with opposite floats con-
nected, similar to Figures 1 and 2, Sheet 2, but worked by an external
cam. In this propeller the bottom of the ship is gradually inclined up
to the point j, where the floats a are drawn into the drum to prevent
them churning the water. The upper portion of the cam e³, which
descends some distance below the periphery of the drum (consequent
upon having the floats connected), is completely covered by the angle
iron d and annular plate f¹ to prevent water in the cam escaping into
the drum. As the water is enclosed in the cam, and as the distance
between the rollers is lessened at the top, there would be a tendency to
· compress the water in the cam. This is obviated by the cam being made
deeper or wider than the rollers to leave a free passage g for the water
between the rollers and the cam. The floats are drawn in and driven
out by the upper curved portion of the cam at e³, so that the lower part
of the cam at h¹ (between the ends of the tube and the point j, where the

page_text: ..bottom of the ship is brought up) is increased in width to prevent the
rollers touching it. The radial movement is communicated through
the connecting rods n to the opposite float. Figures 3 and 4 of this
same Sheet 3 are enlarged views of a portion of one of the floats of the
reaction propeller shown in Figures 1 and 2, the construction of which
is similar to that shown in Figures 3, 4, and 5 of Sheet 2.
In this case
the cam roller is pinned direct on the end of the float without the
intervention of an arm, as the cam 'in which it revolves is not enclosed.
152. Figure 5 of this same Sheet 3 shows a transverse section of a
similar reaction propeller to that in Figure 1, Sheet 2, fitted with screws
for drawing the propeller into the case for repairs, or when it is required
to use sails, and also with various valves and passages for turning the
propeller into a bilge or fire pump. The screws pass through stuffing
'boxes in the case, and are worked by worms in the shaft & gearing into
the worm wheels m³, which latter are keyed on the screw spindles k³.
The lower and screwed ends of these spindles work in nuts attached to
the propeller, and so raise or lower it as required, When raised the
opening in the bottom of the ship is covered by the slides m³, worked by
the screw spindles n³, upon which worm wheels are keyed gearing into
the worms o², which are worked through the tooth wheels by the hand
wheel q². The passages &³ (which run up on each side of the propeller)
are for the delivery of the water to any part of the ship when the hydro-
propeller is used as a fire pump, and are about the same sectional area
as the reaction tube. The valves are for closing either end of the
reaction tube when the propeller is used as a fire or bilge pump, and are
actuated by the screw spindles u³ working through water-tight stuffing
boxes v³ on tubes &³. On these screw spindles are keyed worm wheels w³
gearing into worms, and worked by a handle at the side of the tube.
The sea valves ³ in the bottom of the ship are for opening commu-
nication between the passages 8 and the reaction tube / when the
valves are down, and are worked by the hand fly wheel y' and
gearing Z³ which actuate the valve spindles.
153. The bilge valves a³ are for opening communication between the
valves and the lower valve chambers of the passages »³; these valves are
actuated in the same manner as the valves . The fire valves 6³ open
and close communication between the passages 8³ and the valve chamber
below. When it is desired to use the propeller as a fire pump, should
the ship be going ahead, the after valve x is opened, the after valve {*

page_text: is lowered till it meets the reaction tube, and the fire valve 63 is opened.
The propeller will then force water through the after passage s³ to any
desired part of the ship. When the propeller is required to pump water
from the bilge, should the ship be going ahead, the forward valve a³ in
the bottom of the ship is opened, the forward valve t is lowered, and
the forward bilge valve a³ is opened. The propeller will then draw the
water from the bilge by suction and propel the vessel by reaction at
the other end of the reaction tube if the power and bilge or leakage be
sufficient for the purpose. Should the ship be going astern when either
the fire or the bilge pump is required the opposite set of valves must.
be used. Grease cups are fixed on the propeller case, with jointed.
tubes d³ to adapt them to the raising and lowering of the propellers and
their reaction tubes and communicate with the rollers and cams.
154. Sheet 4, Figures 1 and 2, represent a transverse and longitudinal
section of a mechanical equivalent for the saving cams and rollers,
described in my said Specification of 1870, p. 3 and 53, para. p. 79,
line 19, and elsewhere. Such mechanical equivalent I call the centri-
fugal reaction propeller. The floats a are not moved in and out of a
drum as in the other reaction propellers, but are rigidly fixed to the
propeller shaft. The principle of action is that of a centrifugal pump,
but instead of the feed water entering in the middle it enters the reaction
tube in front atƒ³ the same way as in my other reaction tubes and for
the same objects. These are, 1st, that the entering water may press
against the floats in the direction of their motion to help them to over-
come the statical pressure of the external water at their back, and 2nd,
to enable the floats to have the benefit of the velocity of the vessel..
This they would not have if the water entered in the middle as it does in'
the centrifugal pump in Her Majesty's ironclad "Waterwitch," thereby
consuming considerable power. Now the two objects just mentioned,
combined in a short, slightly curved, and divergent reaction tube, and
the saving cam to prevent loss of internal work, are the fundamental
principles of my system of reaction propulsion. When the water enters
at fs, Sheet 4, it passes through the openings in the floats g³, and so
prevents a vacuum being formed between the floats when the water is
thrown off by centrifugal force for reaction at ³. Sides ³, ³, fixed to
the floats revolve with them to prevent water friction at the sides of the
case. To reduce the water friction in the case sides are fixed to the
floats and revolve with them, as shown in Sheet 4, Figure 2. The
leakage between these sides and case can be drawn out as shown at j³,

page_text: before explained in Sheet 3, Figures 2 and 3, at q. The reaction pro-
peller shown in Sheet 4, Figure I., is in the ship, that is, the projection
of the floats is flush with the bottom if acting vertically, or with the
sides if placed horizontally. The bottom or side is therefore gradually
sloped towards the floats, and gradually sloped from them about 1.5 in
15 feet or so for the gradual entrance and exit of the propelling water.
155. Figure 3, in the same Sheet 4, shows one of my reaction pro-
pellers with a differently formed reaction tube similar to that in my
said Specification of 1870, Sheet I., Figure 2, letters k, k. The difference
between this and my other reaction tubes shown in the other Drawings
is this, the bottom of the tube in Figure 3 is continued with the sides
thereof so that all the water set in motion by the floats must come out
together at the divergent exit. This form makes a complete tube. All
the others are incomplete tubes by a part of the bottom of the tube being
cut off, so that the reaction water at such part is driven at once into the
open. But the sides of the incomplete tubes are as complete as if they
were perfect tubes, like that shewn in Sheet 4, Figure 3. Part of the
bottom of the incomplete tube is cut off to prevent the loss of vis viva
in the complete tube, should any such loss be there found by waters of
different velocities due to different velocities of the floats mixing together
in the complete tube before they can be expelled for reaction. The prin-
ciples of fluid action on which the complete and incomplete tube were
devised are more fully explained in my Provisional Specification of 1870,
page 3, line 16 to 33, and page 79, paragraph 148. In that Specification
the incomplete tube is called direct reaction, because the propelling
water is driven directly into the open. It is scarcely necessary to say
that all my propellers are enclosed, as partly shewn in Sheet 4, Figure 3.
156. My Inventions shown in Sheets 2, 3, & 4, and the above
description of them, are not new, per se, being taken from my said
Specification of 1870, but they have never before been applied to any
such ship as that of my present Invention. They are therefore a new
combination for the purpose of propelling it, and without which it is
doubtful if my present Invention can can be made completely useful to

page_text: 1866 and 1870, a philosophic and not a mere mechanical Invention.
Both therefore are different to any Inventions patented since the Patent
Laws of 1623, so far as my own researches have gone. Such Inventions
therefore require a different Specification to mechanical Inventions..
For a philosophic Invention is one that is founded on the previous
discovery of some new law of nature or the discovery that a known
law applies to something new and useful to which it was never applied
before.
158. Thus the discovery of laws leads to new inventions to make such
laws useful to mankind, but inventions never lead to the discovery of
laws, because the lower cannot lead to the higher. If then a philosophic
invention is reduced to the simplest organization which can be devised
for making a law of nature useful to the world, it can never be either
superseded or improved. For in the noble aphorism of the prince of
philosophers, "Homo naturæ minister et interpres, tantum facit et
intelligit, quantum de naturæ ordine re vel mente observaverit; nec
amplius scit aut potest." This is divinest human insight on record,
especially as it was made in the infancy of science. Since then man
cannot go beyond the laws of nature in his inventions, and laws are
the foundations of science, it is necessary to explain the laws which he
has discovered and his invention embodies, so clearly as to be under-
stood. He must therefore point out the distinction between the old
and new laws, as much as between old and new inventions; for new
laws can best interpret and explain new inventions founded upon them.
These then are 'the principles which have guided me in preparing this
Specification.
159. Mere mechanical inventions on the other hand, not being based
on the laws of nature, have not attached to them any adjunct, and
therefore do not admit of any other explanation than the Invention itself."
Subject to change, they are invented one day, improved upon the.next,
and superseded by something better. Such are bows and arrows, smooth
bore guns, locks, mail travelling, and a thousand more mechanical
contrivances. In short the history of Inventions is the history of
improvement and change; but the history of discovery is that of per-
manence, for the discovery of a law of nature once made is made for.
ever; it is neither superseded, lost, or forgotten, like mere mechanical
devices, and some of the secrets of manufacture.. Now as labour in all
things is. proportional to their endurance,. it follows that the labour of:

page_text: discovery the labour of everlasting laws-is far greater than the
labour of invention. At any rate (1871-1842=) 29 years of the best
part of my life have been passed at intervals in making the discoveries
contained in this Specification and those of 1870, p. 75 to 79.
160. Their combined novelty and utility are best seen in the saving
of 68 per cent. in my fighting ships in paragraph 127, and the still
greater saving in my despatch boats in paragraph 137. For it is main-
tained by the formulæ of the Regius Professor of the University of
Glasgow, by Professor the Reverend Robert Main, of the Royal Naval
College, Portsmouth, and by the other eminent authorities mentioned
in para. 34, that there is nothing at all to be saved in propulsion.
For no propeller can do more than transmit the whole pressure P to
the vessel to overcome its resistance R, and none can ever be invented
more simple than the paddle wheel and screw. That such transmission,
of the whole pressure P is maintained in their "equation for equable
`motion R=P will be seen in such paragraph 34.
I
161. This too is maintained by Professor Rankine, even when his
attention is particularly called to the fact that such equation is contrary
to the two fundamental laws of physics before referred to, (1) the
reciprocal action of fluids and solids, and (2) that man being imperfect
cannot make a perfect machine, one that shall transmit all the pres-
sure P to the working elements of such machine.. Still the learned.
Doctor maintains in his paper of the 13th of August 1866, in my
possession, that these are my errors, inasmuch as "the pressure must,
in every conceivable propelling apparatus, be wholly transmitted to the :
ship, and that the slip R S (called residuary velocity by me) is the
only possible loss of work connected with the longitudinal motion of
the water."
162. Not only does this doctrine of the schools shut the door against:
every conceivable improvement in propulsion, for the reasons given in
paragraph 160, but makes all other systems than the paddle wheel and
screw as much more expensive as they are less simple than these pro-,
pellers. If then the losses of my system be 25 per cent. it will be just.
so much more expensive in engine power and fuel than the paddle wheel
or screw. It has however been shewn that when combined with my
present Invention of the form of least. resistance the saving will be.
about 68 per cent. instead of a loss of 25 per cent. This then it is
.

page_text: believed is sufficient evidence of the novelty and utility of my discoveries
and Inventions, which patentees are required to show.
163. Closed too is the door against all further improvement in naval
architecture by the Professor's surface resistance formula R=fo³ $
feet lbs., and adopted by the late Chief Constructor of the Navy,
referred to in paragraphs 30 and 31. For by my discovery the form of
least resistance and greatest capacity is narrowness, shallowness, and
length. But by the doctrine of the schools, length cannot be got
without increased surface, and consequent resistance. This is shown in
the example of the "Victoria and Albert," in the Table, paragraph 35,
which Professor Rankine himself selected to illustrate his formula fv³ S.
For he there shows that the assumed resistance is by surface equal to
the assumed resistance by the pressure on the paddle P; consequently
that length does not decrease resistance, even with the same displace-
ment. It has however been shown in paragraph 135, that the resistance
of this vessel at the same speed, even when double her present length, is
only 7615.5, instead of 40616 lbs., which the Professor makes it, as shown
in the Table, paragraph 35.
15231-7615.5
15281
164. The actual resistance of this vessel, as she now is, is 15231 lbs. ;
but by my present discovery and Invention it will be only 7615-5 lbs.
This then is a saving of
× 100 =) 50 per cent. of power
merely in the form of ships, independent of my saving by reaction
propulsion. Now such saving of 50 per cent. in steam power is a saving
of 50 per cent. in wind power, and consequently in sails, masts, spars,
and men to manage them. Such then is the novelty and utility of
my present discovery and Invention in naval architecture for sailing
vessels.
165. Besides the saving in fuel of 68 per cent. in paragraph 127, the
novelty and utility of such Invention for men-of-war will be further seen
by the following extract from one of the first scientific journals of the
day, "The Engineer" of August or September last :- "It may be taken
* for granted that we do not possess a single ironclad which cannot be
penetrated at short range by the improved 35-ton, or even by the
"25-ton gun. It may also be taken for granted that we cannot put on
any thicker armour than we use now, unless we leave large portions of
"the ship unprotected, or make her of colossal proportions." Now the
Drawing in Sheet I. shows that if my fighting ship be 600 feet long; she
will be thus divided: 200 feet only for the freeboard, deck, and turret,
66.
$6

page_text: 200 for the bow, and 200 for the stern. Thus she need never turn, and
the water will close in gradually as she moves, to prevent bow resistance;
pursuant to the principles enunciated in paragraph 13. The breadth will
remain the same as that of the "Hercules," 59 feet. She is now 325 feet
long; thus the weight of armour on her freeboard of (325-200=) 125
feet can be added to increase the defensive power of the 200 feet of free-
board of my fighting ship. This will double the resistance if it be as
the square of the thickness. Hence with twice the resisting power of
the part exposed there will be only 200 feet exposed on each side to
shot, shell, winds and waves, instead of 325 feet. This is about (2×14×
125 =) 3500 square feet less. So far then as regards the greater
defensive powers of my ship over the "Hercules," "the representative
ship" of the late Chief Constructor of the Navy. Her offensive powers
will be greater, because with twice the resisting power, and drawing
only about 15 or 16 feet, instead of 24.8, she can get nearer to a fort,
which is what British seamen like best, short, sharp, and decisive.
166. My discoveries will therefore revive the good old days of British
valour and seamanship, by giving England all she wants to revive them,
vessels that can fight at close quarters, and sail round the world faster
and with less men than she could ever do before, as shown in para-
graph 164. But England has no such fleets now, only a fleet of short
and deep ironclads, drawing such great depth of water, and having in
consequence such great resistance, that they can neither steam long nor
sail well. They cannot in consequence adequately defend her shores,
colonies, or commerce.
167. The greater safety of my ships is also in their favor. A ship is
a lever, rising and falling upon its centre as a fulcrum, where, in con-
sequence, the least motion is. The screw of the Hercules is of the
ridiculous size of 23.5 feet in diameter, and weighs 23 tons 10 cwt., and
with its shaft 4/7 tons 10 cwt. hangs at the end of the ship on a leverage
of half its length = 162 feet. When therefore the armour clad monster
of the deep, heavily laden with its scaly hide to the depth of. 24 feet or
more, is slowly climbing up the steep glassy side of some mountain wave
this heavy weight at the stern must tend to drag it down. If in this
perilous position a wave of many tons fall upon the stern deck, such
additional weight may just give the.turn against the ship, by preventing
the bow getting the stern up again. She must then go down stern
foremost, as the ill fated Captain was seen to do with five hundred brave
་་

page_text: men on board, and four hundred thousand pounds of public money.
When too on the crest of a wave the bow and stern, heavily loaded with
freeboard, anchors, chain cables, and screw, must tend to make the ship
rise and fall like boys on a see-saw of 325 feet long, and so pitch and
roll horribly.
168. None of these dangers exist in my Inventions, either for fighting
ships or for mercantile purposes. The chief weights are distributed
about the middle of the ship, where they can be best borne, and best
balance the long bow and stern, and so prevent pitching. For neither
of these is loaded with freeboard, anchors, cables, or screw, whilst the
same weight as the Hercules will have a bearing on the water of .600
feet, instead of only 325. My propellers are not only at the bottom of
the ship, but protrude two feet through it. They will therefore always
have a firm grip on the water, which the screw cannot always have.
Thus every now and then they race, spin, clank, and jerk most un-
pleasantly. Water-tight divisions of a hundred feet or so, both of bow
and stern, will be covered over with coal to the height of six or eight
feet. Over that will be an iron deck, that water may supply the place
of the coal as it is consumed, the iron above it being to prevent the
water shifting when the ship rolls. These contrivances and the keel,
which may be deep, thick, and heavy, will act as a balance of 600 feet
long at the bottom, to keep upright the deck and freeboard of 200, and
the turret of only 40 feet. We can thus have the two fundamental
principles of sound naval architecture, heavy bottoms and light tops, and
so combine a greater degree of stability and safety than can be now
obtained either in turret or sailing ships.
169. Pursuant to that harmony and fitness of creation which are seen
most by those who observe most, the advantages which belong to sound
principles are as apparent as the disadvantages which belong to false prin-
ciples. We have shown in paragraph 167 what is the effect of hanging a
screw weighing 23 tons at the end of a lever of 162 feet when crawling
up a wave, or when upon the crest of it. The screw has however two
other evils; (1), besides beginning with a loss of about 50 per cent, of
engine power, it wastes more power and injures the ship by shaking it;
and (2), it is of no other use than for propelling. The top of the screw
works in water so near the surface as to be frequently fouled to the loss
of ship, cargo, and crew. It has a top pressure of only about 3 x64 18
=192 lbs. per square foot, whilst the bottom works. beneath a pressure
,

page_text: .
of 24x64 18=1540 lbs. per square foot. This produces an irregularity
of action which shakes the ship, injures it, and consumes power in
proportion to the work in the shake. In the event of leaks or fire, so
huge and ponderous a machine as screw or paddle wheel is useless.
Extra pumps and engines are therefore necessary, and these are but
petty affairs compared with the whole engine power.
170. All this is reversed in my system. The propellers always work
under the same pressure, and always in deep water, and therefore with
such smooth and easy motion as cannot shake the ship or race as the
screw does when pitching. And the very tube which is necessary for
reaction forms the best protection for the floats which work in them
against getting fouled and the shocks of the sea, if there be any 10 or
16 feet deep. These floats and tubes protruding only two feet into the
water, are by a few turns of the screw wheels (shown in Sheet 3) easily
raised two feet, and the ship built according to my present discovery is
turned at once into a first-class sailing vessel. But this cannot be done
with a screw of 23.5 feet in diameter. Then again the hydro-propellers
are the best possible security against the greatest dangers of navigation,
leaks and fire; for the propellers themselves are pumps, and being
large enough to absorb the whole engine power for propelling must also
absorb it for leaks and fire; they can also discharge speedily the water
ballast or water let in to encrease the draught to reduce the mark
for fighting.
171. If then such system of naval architecture and propulsion saved
no fuel instead of 68 per cent. it must in time supersede both paddle
wheel and screw. But it has been rejected for five years by the schools,
and was declared in 1868 by the Admiralty, under the advice of their
scientific adviser, "to be of no value to this department." It is manifest
therefore that there is mental blindness as well as colour blindness; for
even eminent mathematicians and men of science deservedly in repute :
and above the littleness of professional jealousy have been so long
accustomed to look at things only in one light, and that a wrong one,
that they now seem incapable of so adjusting the focus of their mind as
to see things in their true light..
PLANE AND FLUID ACTION, FALSE PHILOSOPHY, CONCLUDING
REMARKS, AND CLAIMS.
'

page_text: Admiralty would not believe in my discovery and formula R=
lbs.,
which made the resistance of bodies passing through fluids so small.
Seeing this, and that there was no hope of introducing my system of
reaction propulsion, and that my Patent of 1866 was running out, it was
necessary to discover the laws and form of least resistance to confirm
and so introduce my previous discovery, knowing that one law of nature
cannot be opposed to another law; and never did man constrain himself
more to make a discovery, or with more continuous effort persevere till
it was made.
173. It is however strange that the one of 1866 should be rejected by
the schools, since apparently they do not understand the nature of plane
and fluid action, judging by the doctrine enunciated by the learned Pro-
fessor in paragraph 161, for in another part of the same paper of 1866
in my possession the learned man observes, "That the forward pressure
must in every conceivable propelling apparatus be wholly transmitted to
the ship, as there is no other body to receive it." This is another
assumption at variance with the fact, because the body of water behind'
the float receives part of the forward pressure as it escapes from the
float, pursuant to the well-known law, the line of least resistance. It'
seems desirable therefore to establish this fact, which can only be done
by explaining the nature of plane and fluid action, and so give one more
proof of my past and present discovery, each of which confirms the
other, as shown in paragraph 93.
•
174. When the paddle wheel and screw are at rest they are crowded
up to their edges with particles of water; these are slippery and mobile,
and therefore sensitive to the slightest action of force; as soon then as
they are pressed against by the irresistible power of many horses all the'
water must go somewhere. The particles which are round the edges
being incompressible and unconfined necessarily slip and pour over on
all sides. And this is the only true slip =(P-R) v feet lbs., for that
which is called slip is the loss of residuary velocity = P (-) feet lbs..
Such slippery direction the particles of water at the edges are con-
strained to take pursuant to the law of the line of least resistance;-
whereby all bodies in motion, from lightning to a cannon ball,, are-
compelled to go where they are resisted. least. This place in the paddle
wheel and screw is at the unconfined edges; hence the particles of water
slip and rush over them into the little hollows and eddies on the other
t
J

page_text: side of the floats, where the pressure is least, which is towards the bow.
Now as there can be no motion without power, and all motion unim-
parted is power lost, such escape of water is power lost.
175. But a mass of water equal the whole area of the float or screw
blades is acted upon at the same instant, set in motion all at once, and 5
nothing first. Consequently the mass in the middle is not allowed by
the irresistible push of the float to wait until the water on all sides of it
has escaped over the unconfined edges. Therefore the middle portion of
This then is the only part that
the water set in motion is driven astern.
can react upon the propeller and push the vessel on. All the rest of the 1
water set in motion reacts past the float as it slips over it on all sides, and
is wasted, simply because it is not confined to prevent its escape as it is
in pumps and every other hydraulic machine except the paddle wheel
and screw. When therefore the Regius Professor and the schools
contend against any such escape in these propellers as "impossible” and 1
say "there is no other body to receive the pressure but the ship," they
are contending against the natural and necessary action of planes and
fluids, against the laws of nature, also against facts, as shown in the
great loss of power in the Volunteer, Vixen, and Viper.
. 176. As regards the quantity of water, and consequently of power, that 2
does so escape. This was found to be from 40 to 50 per cent. by my
experiments with a jet of steam in 1842 and with water in 1847 against a
plane of the same area, as explained in my Specification of 1870, page 7,
and shewn in the Drawing thereof, Sheet 5, Figure 2. Therefore, by
induction and by the law of the reciprocal action of fluids and solids, 2
there must necessarily be the same loss when a plane moves against a
fluid as when a fluid against a plane. And this inductive discovery of
the loss of paddle wheel and screw in 1866 was in that year confirmed by
official experiments with the Nautilus and Volunteer, and Waterwitch,
Vixen, and Viper, as shown in paragraph 38. The last three ironclads 3
have also been for five years and still are running every day or so before
the eyes of the schools. But they do not see who have such power and
authority with the Admiralty and the public that the difference between
the pressure on the screws and the resistance of these vessels does entail
the loss in the Table, paragraph 35, column 13, in conformity with the 3
natural action of an uninclosed plane before explained.
177. It would be incredible, if not true, that notwithstanding the high
praise given to the Baconian philosophy for three centuries, especially

page_text: by the discriminating Macaulay, the false philosophy of Aristotle is
followed, if not taught, in our day. The schoolmen start with the
assumption that R=P. It is pointed out that such an hypothesis is
contrary to common sense, that an uninclosed plane can drive astern all
the water it sets in motion, as if it was inclosed, like all other hydraulic
machines. They then resort to another assumption to show that this
must be so, namely, that there is no other place for the water to go to,
an assumption contradicted by fact and law, as shown in paragraph 174.
Thus one erroneous assumption is maintained by another.
178. It is next assumed that the resistance of bodies passing through
fluids is proportional to the immersed surface. Since then all resistance
is calculated in one foot lbs., a vessel of 300 feet long passing through
only one foot has by this doctrine a resistance of 300 feet. They then
appeal to facts, but three out of four instances contradict their assump-
tion, and their formula of f S feet lbs. founded upon it, as shewn in
paragraph 35, columns 8 and 9. But insisting, as they do, on their other
lawless formula R=P, they must needs maintain it when called upon
to show why these their two formulæ do not agree; and these are the
reasons taken from their papers of 1866-7 and 1868, in my possession.
179. The Volunteer paddle wheel is not equal to other vessels in
economy of power, but can be propelled by an indicated power of from
55 to 60 instead of from 90 to 100, as stated in the paper of Professor
Rankine, of September 1866, and the "Engineer" of November 2nd,
1866, page 337. The latter mentions the "Nautilus," but it is the same
as the Volunteer, for their resistance is admitted to be about the same,
1074 lbs., as shown by the Professor's formula in the Table, paragraph 35,
column 9. It is also admitted that the pressure on her floats was about
2292 lbs., as shewn in column 8. Now it is manifest that altering the
form of a vessel, and so reducing her resistance in order to reduce her
horse power, cannot alter the laws of nature which the Creator has
ordained to govern and controul her propeller. The per-centage of
loss, therefore, cannot be altered with the same propeller, because that
remains ever an invariable quantity at the same relative velocities of
V and v. If, then, a vessel of the same displacement as the Volunteer
can be propelled by feathering floats with 55 or 60 horse power, the fact
has no application to the observed phenomenon, her loss of power. For
the immutable laws which govern and controul such propeller, and make
P

page_text: its loss of power what it is, cannot be increased or decreased by altering
the form of the vessel it propels. This is a necessary truth.
180. The twin screws of the Vixen and Viper suck the stern water in,
and so practically increase their normal resistance from about 6664 lbs.
in column 9, which is admitted, to about 20542 lbs. in column 8, the
pressure on their screws, which too is admitted. We are thus told that
inclined planes uninclosed have sufficient power to produce a vacuum of
(20542-6664-) 13878 lbs.! For so only can the Reverend Professor
bring the normal resistance of these vessels from 6664 to their assumed
resistance of 20542 lbs., by the scholastic formula R=P.
181. If, however, these open screws had such powers of suction my
discoveries would still save 68 per cent. of cost of engine and fuel,
because they have no stern to suck. But it so happens that there is
the same small efficiency and consequent great loss in the radial paddle
wheel the Volunteer, and in the feathering paddle wheels Banshee, and in
the Victoria and Albert, as shown in the Table, paragraph 35, column 18.
What little difference there is simply due to the difference and laws
of relative velocities. These propellers, again, have nothing before them
to suck. This distinguished mathematician, however, says in one of
his printed papers that he "had studied the subject of propulsion for
seventeen years. Unfortunately for the advancement of science he had
bound his fine mathematical intellect with the fetters of authority, and
could not break them. How he had committed himself to this false
formula R=P, and how angry he was with me for disturbing the repose
of the schools with my heretical doctrines, will be somewhat seen in my
Specification of 1870, page 18, paragraph 24, to page 21, though that is
but a very small part of our correspondence on the subject.
182. We now come to the beautifully formed vessel the Banshee.
She is, however, declared by the Regius Professor to bc, "as regards
economy of power somewhat below good ordinary steamers, probably
because of her being driven at a speed a little exceeding the limit suited
to her length." Thus her normal resistance of 11148 lbs., in column 9,
is forced up to the pressure on her paddle of 22569 lbs. in column 8,
merely to support the same erroneous formula, R=P lbs. In other
words, with her fine prow of 86 feet long, she drives a wave before her,
or does something else which is equivalent to an additional resistance
of (22569-11148=) 11421 lbs.

page_text: 183. The Victoria and Albert is the last of the examples in the Table.
She is (300-189)= 111 feet longer than the Banshee, (15-8.8=) 6.2
feet deeper, and (40·3-27.2=) 13-1 feet, broader. Thus it so happens
that she has just enough immersed surface to make the two false formulæ
agree, fv's feet lbs. and R=P lbs., as shown in the Table, paragraph 35,
columns 8 and 9. But this is a forced agreement, not a natural one,
because, as observed before, these formulæ are of a different order and of
different powers, one being feet lbs. and the other lbs. simply, and so
never can be equal to one another. This vessel, however, is pronounced
by the Regius Professor Rankine to be " as regards economy of power
exceptionally good," whilst serious faults are found with all the others,
even with the fairy-like Banshee, one of the most beautiful specimens
of naval architecture, for no other reason, apparently, than that they
do not support either of the formulæ of the schools, R=P lbs. and
R=fv's feet lbs.
184. There is not, perhaps, in the history of science from the dark
ages to our own, a more remarkable instance than this of the wrong
method of investigating the phenomena of nature and tracing them
to their vera causa. For it has been shown in paragraphs 177 and
178, that some of the first theoretical and practical writers and pro-
fessors of our time on the science of naval architecture, propulsion,
and resistance, begin their enquiries into my discovery with the pre-
conceived notion that fluid resistance is R=P lbs., and fv² S feet lbs.
They then appeal to facts to support their assumption, those given
in the Table in paragraph 35, and when the remarkable discrepancy
between their theories and facts are brought to their notice by me, the
only one to discover it, they resort to other assumptions as lawless and
untenable as their theories, as shown in paragraphs 177 to 184.
185. Thus unable themselves to rest on the firm realities of nature
they will not let me do so, but reject everything that supports me,
though my doctrine is the only true resistance of bodies passing
through fluids discovered since the creation. It is remarkable too what
it is they do reject. The law of physics (plane and fluid action of equal
areas discovered in 1842) and the inductive generalization of that law
in 1866 to all planes and fluids, and consequently to the paddle wheel
and screw. They reject too one of the fundamental laws of natural
philosophy, the reciprocal action of fluids and solids, which necessarily
gives the same results, whichever moves the other, and consequently

page_text: confirms my induction of 1866. This law did indeed seem to have
some effect for a time on Professor Rankine in 1866, as will be seen by
an extract from his paper in paragraph 26. But unfortunately for
science and for me he preferred the fallible and incongrous experiments
of man to the infallible and harmonious laws of God. The analogies
and harmonies of science were equally rejected, in this case the under-
shot water wheel and windmill, the congeners of the paddle wheel and
screw; which show that things of the same type are necessarily governed
by the same laws, and therefore subject to the same losses. Then again
were ignored the two remarkable crucial instances of the truth of my
inductive discovery in 1866, namely, the power test and area test,
explained in my Specification of 1870, page 22. Even official experi-
mental results, the five vessels referred to in paragraph 38, were
explained away, as shown in paragraphs 177 to 184.
186. Now the resistance of the first two examples given in the Table
was found by Professor Rankine himself and other distinguished mathe-
maticians, by different methods to mine, as shown in paragraph 87.
These then agreeing with my discovery in 1866 ought to have con-
vinced them with the laws of physics and other proofs referred to in
paragraph 185. They do therefore reject a mass of evidenco all dove-
tailing in from my experiments in 1842 to those of Admiralty officials
in 1866, which had it undergone judicial examination in that year,
would have saved several millions of public money on screw vessels
and short ironclads, six years of still more important time, and as many
`years of my valuable Patent.
187. Such serious results then may justify me in remarking that it
is a far higher power to think and reason in letters than in figures, so
that the former should be taught more than the latter. For those
mathematics that produce no fruit themselves, and destroy it when
produced by others, are more prejudicial than beneficial to the com-
munity. If then knowledge is power, wisdom is wealth, without which
power soon comes to an end. It seems to me then that above all Greek
or Latin, or mathematics, the best education a man can receivo or give
himself, as that which is most useful to him in life, that will turn to
the best account whatever sphere he is in. And this seems to me
to be (1) to learn to see things as they really are, not as they seem to
be or as he wishes them to be, or as they are said to be; (2) to draw
right conclusions from facts and arguments; (3) to be governed by the

page_text: evidence in all things, for everything is a simple question of evidence,
however improbable it seem; and (4) in all scientific enquiries to go
by the Baconian method, which seeks for the laws of nature to interpret
the phenomena of nature, since these her laws alone can produce.
Different indeed is the false philosophy of Aristotle, which assumes
what does not exist, then tries to make facts fit in with the assumption,
and when they will not resorts to other assumptions equally groundless,
as shown in paragraphs 177 to 184.
188. There is perhaps no department of human knowledge which
has been more gone over again and again, and by some of the first
mathematicians and scientific minds, from the illustrious Watt to
Brunel, Rankine, Scott Russell, Maundslay and Field, Penn, Laird,
Napier, and others, than steam navigation. In these days then of
advanced science, when everything has been ransacked for further pro-
gress, what can be more improbable than the discovery that from 66 to
70 per cent. of the first cost of engines and fuel can be saved? Especially
too when the first authorities have examined the theory, and deny it
in the most positive terms as 'impossible," and contrary to the first
physical principles of all mechanical science," as shown in paragraphs
19, 20, 22, 41, and in my Specification of 1870, page 19 to 21.
56
•
189. For it is maintained by the schools that there is nothing
whatever to be saved, as shewn in the surface formula fv² S' feet lbs. in
paragraphs 33 and 57, R=P lbs. in paragraph 34, and in the short iron-
clads of Mr. Reed in paragraphs 30, 31, and 101, who is pronounced to
be "the first naval constructor in the world." Yet is my doctrine true,
deduced with no little pain of thought and patience from the eternal laws
of physics. It is a then a mere question of evidence, like everything
else. But rejected by professors of mathematics and others in authority,
who will have nothing to do with the thing, it becomes necessary to
appeal to the general public, whose intellect ever in advance of the
schools has introduced all the discoveries they rejected, and will mine.
For this purpose it seemed right to enunciate the true principles of
philosophy in paragraph 187 which, with the one laid down by Newton
in paragraph 120, will enable all who follow them unerringly to discern
the truth or detect the falsehood of this and other things.
'
190. Do not then be fettered by authority, but go by principles, for
some principle underlies all things. Judge then for yourself in all
things, and reject. not the light of science for the darkness of science,

page_text: the philosophy of Bacon for that of Aristotle. For there is only one
true method of discovery in the world, and never can be any other; that
which guided the enquiries of the highest and noblest intellects that
ever glorified and elevated humanity, that method which has made them
the greatest benefactors of their race until man shall be no more here.
It is the philosophy of Columbus, Copernicus, Galileo, Torricelli, Kepler,
Bacon, Newton, Watt, and other illustrious men, the philosophy of
common sense, truth, discovery, progress. The aim and end of it is to
reduce the apparent tangle and complexity of a multitude of laws to a
few simple primary truths, from which all else proceed. This it does by
discerning the analogies and harmonies of things apparently different,
the connexion and fitness of all creation, the necessary relations which
the mind of man has to his Maker, and to all nature; whereby he is able
to conquer and subdue her greatest powers, by a greater power than any
single power that she has. Such philosophy is therefore the philosophy
of order, classification, exactness, certainty, simplicity, utility; showing
how all things in creation are linked together by a unity of principle in
diversity of action.
191. Now the object of this divine philosophy, unconsciously or con-
sciously, is to teach mankind that only one and the same Law Maker
could by any possibility have made such infinite variety of things, from
greatest to least, from ponderous suns to smallest grain of sand, from
man to insect, all governed by exact and certain laws, without one
contradicting or interfering with another, all having certain relations
with one another, and all working harmoniously together for prógress
and for good. Something of the harmony of these laws has been shewn
in the four new laws of the resistance of bodies passing through fluids,
given in paragraph 93, and that for aërial navigation in paragraph 110.
And such is the unity of principle in diversity of action which has led to
my discoveries, that these laws of resistance, the formulæ of impulse
and reaction in paragraphs 48 and 50, the undershot water wheel,
windmill, paddle wheel, screw, the stability of vessels, the flow of rivers,
and going up hill or down hill; all these are governed by one simple
primary law of gravitation, that which unites our earth with the
ponderous orbs of Heaven, and the grains of sand on the sea shore with
.one another.
192. How opposed is the doctrine of the schools to this pure simplicity

page_text: they can only do by maintaining complexity instead of simplicity;
namely, that for so petty a purpose as paddle wheel and screw pro-
pulsion, the Creator has ordained two distinct sets of laws, (1), that a
plane shall lose fifty per cent. of power when a fluid moves against it;
and (2), another set of laws that the same plane shall lose none at all
when it moves against the same fluid. For they admit my experiments
in 1842, which discovered the former, but deny its application to the
latter. They thus maintain two distinct laws of plane and fluid action,
but which have no existence in nature.
193. In maintaining too the formula R = P, the schools make no
difference in useful effect between the impact of clastic solids and that
of inelastic solids and fluids. They maintain that when an uninclosed
plane acts against a mobile fluid like water, the whole primary vis viva
of the water =P is fully imparted to the unconfined, wet, and slippery
plane; because, it is assumed, that there is no other body to receive the
pressure, as shewn in paragraph 173, and reputed in paragraph 174.
But that is not true in the paddle wheel and screw is true in my system
of reaction propulsion. For it will be seen, in Sheets 2, 3, and 4, that
by enclosing the plane and water acted upon, the whole effective engine
power is concentrated upon, and must pass through, only four or five feet
of tube, and consequently must drive the whole mass of water astern, save
perhaps a little leakage, purposely allowed to prevent the parts touching,
and wear and friction. But with an uninclosed plane the whole sides
are opened for leakage. Yet professors maintain that this push against
slippery and yielding water transfers all the power to the ship it pushes
on; consequently as much as if the paddle were toothed wheels pushing
against tooth rails.
194. Thus the formulæ R=P involves (1) the denial of a fundamenta
principle of mechanics, the essential difference between the action of
solids and fluids; and (2) one of the fundamental principles of physics,
the reciprocal action of fluids and solids. For it is not necessary to
confine the action of solids to get the maximum effect, but it is fluids,
shown in all the fluid machines of the world actuated by artificial power,
steam, air, or water. Therefore by the analogy and harmony of things,'
as well as by facts, the paddle wheel and screw should be confined
also to prevent the waste of power by their working in unconfined
water.

page_text: 195. Again and again have these fundamental principles and those
in paragraph 185 been pressed upon the schools, but to no purpose.
It is then the old old story, as sad as it is old, the long intellectual
battle of philosophy against scholasticism, which has been waged from
the dawn of civilization to the present. Philosophy is progress, the
divine light of the world; scholasticism its extinguisher, the repre-
sentative of the old order of things, the opponent of the new. Thus
it is, and by adopting the false philosophy of Aristotle, as shewn in
paragraph 184, scholasticism has discovered nothing, invented nothing,
improved nothing, encouraged nothing, but has opposed everything.
Conscientious men, but narrowed by routine, no class has wasted more
of the intellectual force and time and money of the nation. I remember
the introduction of feathering paddle wheels, surface condensation,
superheated steam, the screw, iron vessels, twin screws, and turret ships.
Each in turn was kept out of the navy for years. And now my
discoveries also. Although then the labour of invention is nothing to
the labour of discovery, harder far is the labour of introduction.
196. None indeed know but the unfortunate discoverer or inventor
what all this is, the heart weariness, the wear and tear of brain, the
irritation of mind, the waste of intellectual power, the saddest waste of
all, because it is the source of all other power, the only crown of
immortality. How earnestly, how continuously, how patiently for five
years have been my efforts to have with me the leaders of the schools of
science, mathematics, naval architecture, and engineering they best know.
My papers to them show it, fifty-nine quarto pages to one Professor in 2
1866, besides correspondence since, still more to another Professor from
May 1866 to October 1868, and thirty printed folio pages to the Lords
of the Admiralty in 1867, but all of no use. Sick then and weary of
contention for long years, let me be excused for this one last effort for
the reception of my discoveries, full of repetitions it may be from 3
inability to revise it. It is put in all forms and in all shapes for different
minds, for many minds many ways, that haply some of these ways may
convert some. For the sweat of thought and of brain, the toils and
expenditure of (1871-1842=) 29 years at intervals, the best part of
man's life, are not easily relinquished, though rejected by the schools.
197. Let me too interest the general public in this subject by showing
that it is more a national than a private question. It was said in the
3

page_text: Civil Engineer and Architects' Journal some years ago that about ten
millions of tons of coals were annually consumed in this country for
steam navigation only. We export largely for the same purpose, and
the consumption and exportation have since increased, and will go on
increasing. For the quickness and certainty of steam, even with its
present weight and waste, are fast superseding sailing vessels. Now my
discoveries will save at least half of the consumption of fuel, and as
many millions sterling every year for ever. Hence will they save three
times the number of tons of human force every year, with all its various
forco generating materials, food, drink, and clothing. For these millions
of coals pass through at least three hands from the seam to the furnaces
of steamers, which therefore consume three times as many millions of
tons of human force. What acres then of grass and manure, what herds
of sheep, what droves of oxen, what fields of wheat and barley, planta-
tions of hops, rivers of beer, shiploads of tea, sugar, and tobacco are
now burnt up and wasted in their correlative labour of supplying the
furnaces of the steamers of the world from false principles of naval
architecture and propulsion!
198. Thus every infringement of the laws of the Creator, moral or
physical, entails their proportionate punishment; here in the waste of
the produce of the earth, of human labor, and of human life. Now only
my discoveries of the small resistance of bodies passing through fluids
and of reaction propulsion to save the waste of the paddle wheel and
scrow can prevent this waste and at the same time materially increase
the speed of ocean navigation, as shown in paragraphs 127 and 134
to 137, and extend man's dominion over nature by giving him a new
world to navigate, the boundless realms of air.
199. Further, there should be no mistake about our navy; yet the
national delusion is as great respecting it now as that of France was
last year about her army, which led to her dismemberment and to per-
petual taxes on three hundred millions sterling added to her national
debt. The Times of the 20th ultimo only expresses the universal belief
when it speaks of "our magnificent ironclad fleet, in which Mr. Reed
feels justly a parental interest." Yet it is unfortunately designed at
variance with the fundamental principles of fluid resistance explained in
these pages; shown by the fact that vessels so short and so deep have
such great resistance that they can neither steam long nor sail well, and
that the true principles of naval construction and propulsion will save

page_text: from 60 to 70 per cent. of the cost of engines and fuel, as shown in
paragraph 127.
200. Until then my discoveries are adopted England can never have
a navy that is adequate to her many wants, more than those of all
Europe together, the protection of her coasts, colonies, and commerce;
never have a fleet whose resistance will be so reduced as to turn it into
a first-class sailing fleet, to teach our sailors their olden superiority of
seamanship, and save the expenses of coals, make steaming the exception
as it ought to be, and not the rule as it is. But now our navy is con-
structed primarily as a steam navy, yet is unable to steam at full speed
more than two or three days from a coaling station, and unable to sail
much better than hulks, so deep is their draught and consequent
resistance; requiring therefore an enormous press of canvas, and half
a gale of wind.
201. The Admiralty are fully aware of the importance of having the
best designs for ships that human ingenuity can devise, and for this
purpose appointed last year a committee of sixteen of the first men of
science of our day, the chief of whom is Professor Rankine, nulli
secundus, if not primus in orbis, in this department of science. But
as shown in these pages (recorded here for national purposes to be
safe from the accidents of fire and the opposition of the schools), until
their two formulæ ƒv³ S feet lbs. and R=P lbs. are rejected no material
progress can be made in naval architecture, as shewn in paragraphs
30, 31, 57, 66, and 126. For the same doctrine and formulæ of the learned
professors which declare my discovery of 1866 to be impossible, in
paragraphs 160, 161, and 173, must necessarily deny my present one,
which confirms the former. Because both of them make the resistance
of bodies passing through fluids only about two-fifths of what it is made
by the formula R=P lbs., as shown in the Table; because too the
formula R=fv² S feet lbs. makes the resistance portional to the im-
mersed surface. If this were true it would for all time prevent any
reduction of the resistance of bodies passing through fluids, and con-
sequently of cost of engines and fuel, as shewn in paragraphs 57, 126,
and 136.
202. There is another fundamental error of the Regius Professor
Rankine and the schools which has not yet been pointed out. This is,
that the efficiency of the paddle wheel and screw encreases as the loss
of residuary velocity-by them called slip-decrcases. This erroneous
.

page_text: doctrine is shewn by the Professor's formula in column 16 of the Table
in paragraph 35. Also in the following extract from an editorial article
in the Engineer of November 2nd, 1866, page 339:-"It is a well-
"known fact that to make the area of water acted upon by the propeller
66
"
as large as practicable consisistently with the dimensions and form of
" vessel is favorable to economy of power." The contrary being the
fact, as regards the paddle wheel, screw, and oar, is a further con-
firmation of one of my doctrines, that there are more false facts in
the world than false theories; also of what is said in my Specification
of 1870, paragraph 39:-"All the authorities say can only be met by
a far diviner and higher power, the unerring logic of sound induction.
Practice may err, true theory never." For here again practice has
erred through immeasurable years, from the first canoe rowed by the
savage to that which is considered the perfection of economical pro-
pulsion in the present day, the Oxford and Cambridge boats, and steam
navigation, shown by the erroneous formula R=P. For, by the theory
of plane and fluid action of equal areas, and of impulse at different
relative velocities, the efficiency of the paddle wheel, screw, and oar
(not reaction, which is my principle) increases as the loss of residuary
velocity (called slip) increases, until 7=2v. This anomalous fact is
the necessary consequence of that law of fluid force which entails a
loss to begin with of 40 or 50 per cent., by acting on a plane of the
same area. Or (by the reciprocal action of solids and fluids) by a plane
acting on a fluid of the same area, as discovered by me in 1866, by
induction from my experiments in 1842, and formularized in 1869, as
shown in paragraph 50.
203. Pursuant to the erroneous doctrine of the schools, shown by
the formula in column 16 of the Table, the practice of all engineers,
not of England only but of the world, has been and is to this day to
encumber steam vessels with the largest paddle wheels and screws
convenience will permit, under the mistaken notion stated in the
Engineer, that to make the area of water acted upon as large as
practicable is favorable to economy of power." In other words the
less the loss of residuary velocity called slip (-) the greater the
efficiency. But as the fact is the reverse this practice entails some of
the worst evils of steam navigation, cumbersome propellers, unnecessary
cost of engines, weight, and waste of fuel. For example, the diameter
of the screw of the Hercules gives an area = (7854 × 23-53 =) 433-73
66

page_text: square feet, whilst the area of my propellers, and for a more effective
fighting ship at the same speed, is only 27.2 square feet, as shewn in
paragraph 130, whilst the saving is 68 per cent., as shewn in para-
.graph 127.
204. Now it is well known that screws generally have less loss of
residuary velocity (slip) than paddle wheels, some screws having no
slip at all, as the schools say; hence the Vixen screw, in the Table,
paragraph 35, ought by their formula to show the greatest indicated
efficiency, but it comes out the worst, as shown in column 18. This
then further refutes the prevailing doctrine, and verifies my discovery,
.that the efficiency of the paddle wheel and screw increases as the loss
of residuary velocity (called slip) encreases until =2 v; these relative
velocities however nowhere exist in practice. Observe too in column 18
of the Table that the indicated efficiency of the Volunteer is greater than
that of the Banshee and Victoria and Albert. This is because the loss
of residuary velocity of the Volunteer is greater, in other words the
laws of impulse being here more observed they more than make up for
the Volunteer having a radial paddle wheel, instead of a feathering
one, which the two other vessels have, and which is somewhat more
economical than the radial wheel.
205. This Specification is written for the advancement of learning,
and therefore for the benefit of mankind, and not merely for a class.
Rejected by those who are considered the great leaders in steam navi-
gation it is necessary to make the general public thoroughly understand
my discoveries, for till they do they cannot be saved the money spent
in screw vessels, engines, and fuel since 1865 and 1867. Nor can the
nation have a navy fit to cope with the navies of foreign powers more
discriminating than our own. Let the public then bear in mind that
the facts which confirm my discoveries and those just mentioned in
paragraph 204 are none of mine.
206. With what particularity they were collected has been stated in
paragrap 37.
Neither these facts nor the laws of nature, nor tho
principles of naval architecture are modified in any degree to fit in
with my own conceptions. Nor do my discoveries need any make-ups
or make-shifts, such as sucking in water in the Vixen screw, and raising
waves in the Banshee paddle wheel required to make one wrong formula
fv S feet lbs. agree with another wrong formúla R=P lbs. only,
as shown in paragraphs 23, 26, 29, and 178 to 180. On the contrary

page_text: the facts supplied to me by the Admiralty in June last, and all the other
facts, are the necessary evolution of divine laws which compel those
facts to come out as they do, and not otherwise. They are then beyond
the power of feeble man to alter. Moreover, the indicated power of
all the vessels is checked by the diameter of the cylinders, steam
pressure, vacuum stroke, and number of revolutions.
207. The speed of the vessel ø found by the log can also be checked,
near enough for all practical purposes, by the mean velocity of the
propeller V, which the universal practice is to make about 1.25 v only
on the erroneous principle explained in paragraph 203. Now the value
of V is obtained with exactness in every vessel, by the mean diameter
of propeller and number of revolutions
per minute; which may be thus
found V=0523 d n feet per second. Hence v=8V, and this pro-
portion is verified by the relative velocities of the Banshee and Victoria
and Albert in columns 14 and 15 of the Table.
•
208. The object of all this is to shew the public that there is no room
for material errors so far as the facts are concerned; because (1) the.
facts furnished by the Admiralty and others are checked in other ways;
(2) because such facts are overuled by the laws of the Supreme Law
Maker, and are therefore compelled to be what they are, and not other-
wise. Thus we come to the crowning proof of my discoveries of 1866,
and the present one, which mutually confirm each other; and it is this,
when one person furnishes the theory, and different persons unknown
to each supply all the facts which support it, in all its natural rela-
tions (different efficiencies at different relative velocities, as shown in
the Table), when they do this without knowing what such theory is, we,
have the most convincing proof of a new discovery which human reason
can ever reach.
209. Whewell's History of the Inductive Sciences and the Philosophy
of Discovery do not record a more comforting and encouraging instance
of the harmony, certainty, and unity of the general laws of the Creator.
The philosophic Master of Trinity would have rejoiced, and minds like
his will rejoice, in this further triumph of the inductive philosophy over
unphilosophic mathematics, over the false experiments and practice of
the world, and over the dogmatism of the schools; the present, then, is
one of many precursors in the past. And so irrefutable a proof of my
discovery was dwelt upon in all my papers, and especially in my printed
paper to the Admiralty of 1867, page 28, beginning "It is proper to.

page_text: observe." There it is shown that the only experiment of my own was
made (1871-1842=) 29 years ago, a mere abstract experiment with a
small jet of steam against an immovable plane, and not even in refer-
ence to propulsion. Still a discovery so firmly established was rejected as
"impossible" by one Professor, and by another by such singular reason-
ing as is preserved from oblivion in my Specification of 1870, page 18
to 21. Rejected too it has been for five years, for such a heterogenuous
mass of loose and illogical assumptions as are recorded in these pages.
One is, as stated in paragraph 180, that the twin screws of the Vixen
and Viper are such voracious sucking fish of the stern water as to
produce a vacuum of 13878 lbs. But as this curious kind of reasoning
will not do for a paddle wheel steamer, we must have something quite
different for the Banshee. Now she is only 27.2 feet broad, yét has
a bow 86.5 feet long, nearly half her whole length. Yet we are told
that she "is somewhat below good ordinary steamers, being driven at
a speed a little exceeding the limit due to her length."
210. We are then left to the only inference open, that instead of
cutting through the water and gently and gracefully turning it to the
right hand and to the left, at the least expenditure of power, as the fact
must necessarily be (shown by her small displacement and resistance),
this beautifully fine bow does like some square packing case keep up
a huge wave before it. Now her maximum resistance is only 8468 lbs.,
but we will assume it to be 11148 lbs., as made by the formula ƒ v³ S
feet lbs; her draught is 8.8 feet; her fine bow therefore must throw
up a wave as high as this to increase her resistance from 11148 lbs. to
22569 lbs. Lawless assumptions must necessarily lead to impossible
sequences to which even able men are compelled who reject the solid
realities of nature for their own groundless theories. Taking then her
maximum resistance (though denied by me) we have (22569-11148=)
11421 lbs. more power expended. It must therefore go somewhere and
be accounted for somehow%; how the schools account for it has been
shown. What a weary and thankless task then is that of discovery,
though it has done more than any other mere human labour for the
civilization of the world, to advance mankind to some higher and nobler.
sphere of being here, as it is still doing, the chief source of their
safety, their comfort, and their convenience by sea and land. Yet has
discovery and Invention ever been the hardest and painfullest work to
introduce, the least honoured and worst requited of all the travail of
man's soul.

page_text: The
211. It is perhaps desirable before specifying my claims to show how
the principle of my discovery and Invention may be varied.
principle is to reduce midship area displacement, which encrcases
resistance, and to get displacement (which is capacity) in length, because
this does not increase resistance. We will then call the turret deck
the fighting deck, and the bow and stern flush with the water or nearly
so the sailing deck. If now we reduce the fighting deck to fifty, or
say to one hundred feet, we shall save the weight of armour of one
hundred feet long on each side required to make invulnerable the height
between the water line and the fighting deck. There will then be
a saving in such weight in the Hercules (325-100-) 225 feet long.
This will perhaps be more than is sufficient to surround the whole
sailing deck with a light steel freeboard strong enough to resist winds
and waves, but not shot or shell. We shall then have 500 feet long
of sailing and walking deck, besides the 100 feet of fighting deck. Now
100 feet or so of such freeboard at each end may be covered over,
especially in continental boats, for berths or otherwise.
212. The freeboard or bulwarks and masts and sails would of course
be as liable to injury in action as in the old centuries of England's
triumphs on the sea. But the enemy would not waste powder and shot
and time in destroying what would be of no service to him; for were
the whole bulwarks of the sailing deck swept away the steamer would
remain as safe, as is shown in Sheet 1, Figure 1. The vital and moving
parts would still remain uninjured, and the wreck of masts, spars, and
sails could not get into a tube of only two feet deep underneath the
vessel in which my propellers work, secure alike from storms, shocks, or
fouling.
213. The object of keeping the sailing deck so low is twofold: (1) to
save the weight of invulnerable armour between the water line and
a higher deck; (2) to save 500 feet of such space on each side from.
being riddled or stove in by shot and shell, which would destroy many
brave men and let in so much water when rolling as might become
dangerous, and which led to many prizes being destroyed at Trafalgar.
For the same reasons even the fighting deck may be lowered to the level
of the sailing deck either with an invulnerable freeboard for a hundred
feet or so, or with only a light freeboard like the sailing deck. High and
strong iron turrets for hatchways and ventilation may also be inserted
in the decks where required. In such an Invention is combined an

page_text: excellent fighting and sailing ship, and with great economy of steam
and wind power beyond anything yet known in science; a combination
which has been declared to be impossible.
214. 1. I claim constructing steam and sailing vessels as herein-
before described and shown in the Drawings in Sheet I., varied as
in paragraphs 211 to 214, though only fighting ships will require a
turret.
2. Constructing sea-going steam and sailing vessels thirty or more
times as long as their draught, and twelve or more times as long
as their broadest part, which last proportions apply to aërial machines.
3. Constructing the bow of such bodies four and a half or more times
as long as their broadest part, and the stern also. But in deference to
men's prejudices the Drawings in Sheet I. do not give these proportions
nor those in claim 2.
4. Attaching stability planes to all sea-going vessels that would be
dangerous without them, which planes are shown in Sheet I., letters d, d,
the width of which may be reduced by extending them the whole length
of vessel.
]
215. These claims are to carry out the laws and form of least resist- 2
ance with the greatest capacity and defensive power as discovered and
invented by me. The object is to reduce the resistance of bodies passing
through fluids, and consequently the cost and weight of engine, boilers,
water, and fuel in steamers, and of wind power, sails, and men in sailing
vessels as herein-before explained.
216. In the description of my Inventions the roller propeller in Sheet 4,
Figure 3, has been omitted. The roller floats and cams are mechanical
equivalents for my saving cam and floats described in my Specification of
1870, No. 623, pages 3, 79, and 82, paragraph 155, to page 83, paragraph
156. But such floats are not equivalents for my reaction tubes in 3
Sheets 1, 2, 3, and 4, for which there are no equivalents. Longitudinal
openings are made in each partition a, a, through which the water
will enter into the drum space d, d, with the velocity of the vessel ",
and give a pressure due thereto = lbs. If then the mean velocity
of the roller floats in Figure 3, or centrifugal floats in Figure I., be 3
about -1.35 v, the pressure in the drum due to will exceed that

page_text: of reaction for velocities of vessel exceeding 10 feet a second. Now as
the pressure of reaction is, under such circumstances, not only less than
that due to v, but is also upon a much smaller area of reaction than
that of the midship sections, it is plain that the bow must very greatly
reduce the resistance of bodies passing through fluids, very likely nine
or ten times, with long bows. It is my belief, for reasons too long to
explain here, that the modulas of efficiency of my system of propulsion
will exceed that of any machine in the world on land or water, that is,
that it will utilize more of the power expended upon it. The loss of
residuary velocity cannot fairly be included, because no other machine
is subject to the same loss.
217. It grooves be made on each side of the receptacles, as shewn by
the letters 9, 9, the drum water will flow down to the spaces 1, 1, and
prevent their taking away any of the propelling water. The openings
from the receptacles into the drum is to prevent the formation of a
vacuum as the rollers come out, and to prevent them as they go in
squeezing the water past the side of the rollers up which the water
would be forced to fill the vacuum that would be made without such
openings, which therefore save no little power. The roller floats may be
hollow & either roll on the cam m, by centrifugal force kept out, or
may have pulleys n at their ends working in the cam o. Figure 4 of
the same Sheet 4 shows a longitudinal view of one of the roller floats
with the cam pulleys n attached.
218. As this Specification treatise is being written in the country, and
sent to town to be engrossed, it is beyond my power now to soften
expressions or to omit repetitions, though it is only by keeping on
hammering that we can drive in the nail. Hence this exposition of
new laws, and their practical application for the improvement of the
British navy, steam navigation, and aërial locomotion may take some-
what longer to read. But their importance may perhaps excuse such
long efforts to make my discoveries clearly understood by the general
public; for I have failed to do so for five years by the schools; and
only one favorable report would have enabled me to introduce my
Invention of 1866; for capitalists are in plenty, but this is too big
a thing for my means. If then this Specification take two or three
G

page_text: hours to read, it has taken me twenty-nine years at intervals to write,
and at present to no purpose. Such labours in any other intellectual
field would have given a higher place, and more certain heritage.
219. For nothing but my experiments in 1842, and subsequent studies
in the same direction, could have led to the discovery of the form of
least resistance and its laws in January last, sought after from the
days of Newton to our own, as before shown. The public have now
before them the present state of the science of naval architecture in
short ironclads, and of steam navigation in its three different branches,.
each of which is governed by its own peculiar laws:-1, the heart of
the machine, which is the steam engine; 2, its body, which is the ship;
and 3, its legs, which are the propellers.
220. The steam engine, as everybody knows, is governed by the laws
of elastic fluids. But for navigation it is in the infancy of science.
The perfection of machinery it may be, but it combines the three worst
qualities which a marine engine can have, weight, space, and cost.
The present type of marine engine and boiler is therefore doomed to
give place to tlie locomotive type, as shown in Sheet I., The next
branch, the ship, is no doubt all that strength can make it, the strength
of the forge, steam hammer, and rolling mills; but high art has had
no hand in devising so ugly a fleet as ours. For if it be allowable to
quote from myself, some ten years ago, "the useful and the beautiful
are one. Taught then by the philosophy of harmony how beautiful
forms are combined with fitness and efficiency, we may be sure that
whenever we see ugliness we see the want of fitness for its purpose,
and consequently imperfection, inefficiency, and waste.
$
221. Pure science therefore repudiates short ironclads, the ugliest,
costliest monsters of the deep, each a palace in expense, without its
beauty and utility. For it has been shown how opposed they are to the
true laws of fluid resistance here enunciated. They are the only herma-
phrodites of the seas, neither one thing nor the other, steamers nor sailers;
for they can neither steam long, nor sail well. Nor nature, nor science
ever produced such monsters; only man left to his own lawless devices
could do that. Yet were they pronounced by high authority only a few
months ago “the type of science and of strength." Such then is the
science of the naval architecture of our age.

page_text: 222. We now come to the legs; the screw is the worst transmitter
of fluid power of all known machines. It wastes millions of pounds
sterling every year in different parts of the world in millions of tons
of coals, as before shown. This is wasting millions of tons of the sun's
heat and forests of past times garnered up through myriads of ages by
the Provident Father for man's use. But besides all this, a monstrous
weight of many tons, and 23 feet in diameter, hangs at the stern of the
ship at great leverage, every now and then bobbing up and down at
sea, like a bad swimmer. It is therefore necessarily dangerous and
inefficient, whilst even strong wooden vessels cannot stand its shakings.
223. Such is that wasteful machine whose noise and jerks and
clanking make men and women who have crossed the Atlantic sick to
think of; but which the first mathematicians and men of science of
our time declare to be incapable of economical improvement. Because
they say R=P lbs. But the philosophy of science teaches us that an
imperfect machine must necessarily be a wasteful one as it is here shewn
to be; whilst the smooth, easy, and noiseless motion of my Inven-
tion are conducive to economy; for noise, jerks, and waste, and silence,
smoothness, and economy, are co-relative and inseparable.
224. Another test of the truth of my discovery in 1866, and of the
present one has only just occurred to me, but want of time and area of
midship section prevent me working the principle out. Were the bow
of a vessel cut off, the same area of impulse as that of midship area would
be required to propel it, if the force of impulse were obtained by the
same velocity as that of the vessel v. What then we want to know
is, how much the bow of a body passing through a fluid reduces the
normal efficiency of a plane, which we have taken throughout at its
maximum = 6 a.
225. Take the resistance of one of the vessels which has been found by
reaction, of which there. is no dispute by any one. These are the
Nautilus and other competitive vessels before-mentioned. Let then, R=
the resistance so formed; 4 the area of midship section; a that of
reaction for simplicity (not of impulse) to overcome R; and the
velocity of vessel. Then a = and C=6, the co-efficient of diminished
resistance caused by the bow of every vessel whose resistance R is first
found. When therefore all the data are correct, this bow co-efficient,
it seems to me, ought to be more or less in harmony with the dis-
R

page_text: placement and area co-efficient of every vessel whose co-efficients are
found by the methods given in paragraphs 91 and 93.
226. In such case there will be five things in harmony with one
another which do not at first seem to be connected, or their relations
would no doubt have been discovered by those who have written most on
ship building, resistance, and propulsion. It is however no matter if
it be found that the bow co-efficient is not in harmony with the four
formulæ given in paragraph 93. Because I know that, though I stand
alone against the world, and against the most renowned mathematicians,
naval architects, and engineers, deservedly eminent and respected, still
my discoveries are founded on the laws of nature, and are therefore
like them imperishable.
227. It may save misconception to observe, that so great a saving as
68 per cent. over the Hercules as shewn in paragraph 127, and double
the speed of the Victoria and Albert with but little more fucl, as shown
in paragraphs 136 and 137, can only be effected where the draught or
breadth can be sufficiently reduced either with or without my stability
planes. The saving then by my present discovery is a varying one.
But by the one in 1866, that reaction is the only true principle of
propulsion in air and water, the saving is unvarying. Because the
loss of the paddle wheel and screw, also discovered in that year, is
unvarying and immutable, as shown by my formulæ in paragraph 48.
228. If then my system of reaction be applied to any vessel in any
water, canal, river, or ocean, to the slowest tug, swiftest vessel, or
lumbering ironclad, such Invention at the same relative velocities will
save the same first cost of engines and fuel per cent. in all, whatever
the horse power. And this saving cannot be made prior to experiments
less than 47 per cent. as shown in my Specification of 1870, No. 623,
p. 64, paragraph 121. It is then no presumption to say, that this.and my
present discovery will do as much for steam navigation, where economy
and speed are so much wanted, as Watt did for the steam engine.
They will also be a guide to the Admiralty naval architects and engineers
of the world for designing vessels and for propelling them, not only
now but for all time. Having therefore the laws of nature to go by
in both, they will have a certainty of results beyond any which the
present distinguished committee on designs of ships can give. No future
reference therefore will be required, nor ever-varying designs, all morc

page_text: or less imperfect and wasteful in engines and fuel, because more or less
a departure from the fundamental laws of the Creator. My discoveries
will therefore save the Admiralty no little anxiety, and the nation no
little loss of time and money.
•
229. I do therefore commit these discoveries, being rejected by the
schools, to the present and future generations, especially to the leaders of
thought, the large and liberal philosophic mind which belongs to no
school or class, and is therefore ever open to the reception of all truth,
come from what quarter it may. For what was true in my paper to
the Admiralty in 1867 is now, and ever will be, although declared to
"contain nothing of any value to this department." The preamble
then of that document may fitly conclude the exposition of the laws
of this the last discovery that will be made by me in this life. For
it is "the crowning mercy" of Him from whom [cometh down] every
good and perfect gift, to the most unlearned and feeblest agents some-
times given," for the common benefit of all; grateful also for such
termination of the thought and labours of twenty-nine years. Altering
then a word or two to include the present discovery, which so remarkably
confirms the former one, the preamble proved in that paper of 1867,
but rejected, was this," Founded on the primary laws of nature,
my discoveries are the ultimate developement and reach of science
"for naval architecture, aerial navigation, and propulsion. They,
"will therefore supersede all other systems, and never be themselves
superseded." Laus Deo.
66
66
In witness whereof, I, the said Richard Boyman Boyman, have
hereunto set my hand and seal, this Ninth day of October One