IMPROVEMENTS IN THE MACHINERY FOR PROPELLING VESSELS AND AERIAL MACHINES BY REACTION, PARTS OF WHICH ARE APPLICABLE TO FORCING FLUIDS FOR OTHER PURPOSES
Year: 1870

page_text: LETTERS PATENT to Richard Boyman Boyman, of Park Hill, Clapham
Park, Surrey, for the Invention of "IMPROVEMENTS IN THE MACHINERY
FOR PROPELLING VESSELS AND AERIAL MACHINES BY REACTION, PARTS OF
WHICH ARE APPLICABLE TO FORCING FLUIDS FOR OTHER PURPOSES."
Sealed the 5th August 1870, and dated the 3rd March 1870.
PROVISIONAL SPECIFICATION left by the said Richard Boyman
Boyman at the Office of the Commissioners of Patents, with his
Petition, on the 3rd March 1870.
I, RICHARD BOYMAN BOYMAN, of Park Hill, Clapham Park, Surrey,
5 do hereby declare the nature of the said Invention for "IMPROVEMENTS
IN THE MACHINERY FOR PROPELLING VESSELS AND AERIAL MACHINES BY REACTION,
PARTS OF WHICH ARE APPLICABLE TO FORCING FLUIDS FOR OTHER PURPOSES," to be
as follows:-
•
1. In so arranging the case and one or two cams of my hydro and
O aero propeller (before patented, as herein-after mentioned,) that the
A

page_text: better and more economical manner than those referred to, as I will now
explain.
By turning to the propellers in the Drawings to which I have referred
it will be seen that some of the entering fluid on the right-hand side
and some of the issuing fluid on the left always remains between the
drum and case of the propeller. It will also be seen that the floats on
the right begin to come out of the drum and act on such internal water
before they begin to propel. And further, that the floats on the left
during and after propulsion cause a wave of motion on the internal water
until the floats are thrust into the drum by the cam or cams. Thus on
both sides of the propeller an internal disturbance of the fluid is produced,
which is not conducive to propulsion, consequently an amount of
internal work and power proportional to such disturbance is wasted.
This waste of power and therefore of fuel I propose to save in this
way,―
1. By making the case on both sides of the drum so close to it as to
leave little or no room for any internal fluid where it is now,
and so
arranging the cam or cams that the floats shall not begin to come out of
the drum until they act on the external water, where it enters for
propulsion, whilst on the other side the floats shall enter the drum when
they have ceased to propel, and thus waste little or no power in internal
work.
2. The three arrangements of the reaction tube referred to at the
beginning hereof are these:-
:―
I. The tube is not extended much if at all beyond the sweep of the
floats at the bottom and sides of the propeller, for the sooner the reaction
water is got rid of the better. In all the Drawings of the Specifications
of the four Patents before mentioned the reaction water is first driven
into the reaction tube, and thence into the open water. In my present
arrangement the reaction water is driven direct into the open water or
nearly so. This enables the tube to be shortened and to be made with
only a slight curve, and it may be that only a slight divergence at either
end will be required for such a tube.
II. The second arrangement of reaction tube is in making it of the
same area throughout, except at the divergence at both ends, with an

page_text: easy curve, and no longer than is necessary for the reaction water to
be first driven into the tube and thence into the open.
III. The third arrangement is in making the tube all round the
propeller and discharging the reaction water at the opposite end to its
entrance. At some part of the circumference the water will pass into
another tube, which will cross the tube where the water enters. The
floats must be so arranged that the entering water may impinge upon
them to help the drum round instead of impinging against the curve of
the tube and retarding the vessel.
The mouth of all these tubes must be towards the bow of the vessel,
and the end towards the stern as nearly level as possible, similar in this
_respect-to-the-reaction tubes in the Specifications and Drawings before
referred to. The floats must be made hollow for the easy entrance and
exit of the water which will be drawn into the slits in the drum as the
floats are sent out and drawn in. This is important and forms part of
my system of hydro-propulsion included in my Letters Patent of the 1st
August 1867, No. 2223, before referred to, page 3, line 17 to 25, and in
my claims, page 29, line 36. And this part I now combine with my
new hydro-propeller invented to prevent the floats doing any internal
work by uselessly agitating the fluid, as before described.
By making the case in halves the floats can be taken out to repair and
to offer no obstruction to the vessel when sailing. Also the whole
propeller can be drawn into the vessel by disconnecting the shaft in a
similar manner to that described in my said Specification of the 1st
of August 1867, No. 2223, Sheet I., Figures 6 and 7, and by having a
water-tight case or box over the whole, a screw for such purpose, and a
sliding door to cut off the water from such case, similar to what is
described in the said Specification, and shewn at Sheet II., Figure 1.
These I combine with my present improvements, and also an arrange-
ment for turning similar to that described in the said Specification, and
shewn at Sheet III., Figures 1 and 2.
My new propellers being enclosed are force pumps even for propelling,
and can therefore be used as pumps for other purposes. I will now
shew how they can be used as fire and bilge pumps to afford the greatest
security against the two greatest dangers of navigation, fire and leaks.
This occurred to me in the first Patent I took out for hydro-propulsion,

page_text: which was in the name of the late James Pedder, dated the 6th of
November 1847, No. 11,946, page 12, line 18.
My new arrangement for this purpose and thereby utilizing the whole
engine power is as follows:-An opening will be made in the vessel
leading from the inside of the reaction tube to the fire hose and bilge
pipe, which will be provided with cocks to turn on and off. A door
outside or sliding valve inside the vessel working through a stuffing box
will close the bow entrance of the reaction tube, when the propeller
will draw the water from the hold and use it for propelling if sufficient.
For fire the bilge cock will be closed and the fire one opened, when by
reversing the engine the water will be drawn in from the end of the
reaction tube, and be used as required. Thus the propelling, fire, leak,
and bilge pumps are combined in one, and the whole engine power
utilized, which cannot be done in any other system than hydro-
propulsion unless by taking on board pumps large enough to absorb the
whole power.
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 27th August 1870.
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 Third day of March, 1870, in the thirty-
third year of Her reign, did, for Herself, Her heirs and successors,
give and grant unto me, the said Richard Boyman Boyman, Her especial
license that I, the said Richard Boyman Boyman, my executors, admi-
nistrators, 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 there-
after 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 Inven-
tion for "IMPROVEMENTS IN THE MACHINERY FOR PROPELLING VESSELS AND
AERIAL MACHINES BY REACTION, PARTS OF WHICH ARE APPLICABLE TO FORCING
FLUIDS FOR OTHER PURPOSES," upon the condition (amongst others) that I,

page_text: the said Richard Boyman Boyman, by an instrument in writing under
my hand and scal, 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 my 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 :-
My
improvements-in-the-machinery-for-reaction-propulsion-depend
upon certain principles and formulæ I have discovered, which must,
I think, be understood before the nature of my said Invention, and in
what manner the same is to be performed, can be understood, especially
as a knowledge of the principles on which it is founded can alone enable
it to be distinguished from all other methods of propulsion.
I can, for instance, find no trace of these principles or of my formulæ
for Impulse propulsion in any work of science or mathematics. The
very names too which I must use, Impulse and Reaction, are not
merely unknown in propulsion but are denied by the first engineers,
mathematicians, and men of science to whom I have submitted my
discovery. I must therefore depart from the usual form of Specification,
suitable enough for a mere mechanical Invention, improved upon one
day and superseded the next, and put on record for all time those
fundamental principles of physics on which my improvements on
reaction propulsion are based. It is necessary also for the improvement
of naval architecture, because the great maritime nations of the world
have been trying for more than a century to find the resistance of
vessels, and the present Admiralty is doing so now, spending public
money in efforts which must necessarily fail like all others because
made on wrong principles. Now my own system, being grounded on
the primary laws of nature, is the ultimate reach and developement of
the science of propulsion both for water and the air, and the only
measure of the resistance of both elements. It will therefore supersede
all other systems and never be itself superseded. This then is the
preamble which I have to establish as the foundation of my Invention.

page_text: THE PRINCIPLES OF THE SCIENCE OF PROPULSION, OF IMPULSE, AND
REACTION.
1. When a fluid moves against a plane of the same area it is what Í
call Impulse. This is shown in Sheet 5, Fig. 2, which is a Drawing of
the arm of the machine, similar to the well-known Barker's mill with
which I made the experiments in 1842 on which my discovery, formulæ,
and Invention are based. I then found that when a jet of steam
impinged against a plane of the same area, as shown in the Drawing,
about one-half of the fluid escaped past the plane, and consequently
carried with it about one-half of its power. Impulse therefore begins
with a loss of about 50 per cent. This I call the law of plane and
fluid action of equal areas. But when the plane was large enough
to arrest the whole jet and deflect it at right angles, as shown in Sheet 5,
Fig. 3, the plane received the full force of the jet. Action and reaction,
or, as I call it, Impulse and Reaction, are then equal and opposite, the
arm of the machine stands still, as shown in the Drawing, and Newton's
law is verified. To obtain this result in practice the plane must be
about 8 or 9 times as large as the area of the impinging fluid.
2. When a fluid issues from a hole it reacts in the opposite direction
with its full force. This I call reaction, and is my principle of pro-
pulsion on water and in the air. The principle is shown in the Drawing
of my experiments in 1842, Sheet 5, Figs. 2 and 3, where the fluid is
seen issuing from the hole in the arm of the machine. I then found
that the force of reaction is about twice the force of impulse against a
plane of the same area, as shown in Fig. 2, but, as I have said, not any
more than impulse when it is against a plane large enough to prevent
any of the fluid escaping past it, as shown in Fig. 3. In 1847 I repeated
these experiments with water and found the same results as with steam,
thus bringing for the first time elastic and inelastic fluids under one and
the same law of dynamics.
3. The mind discovers what the eye but sees. I saw these things in
1842 and 1847, but did not then know the important discovery I had.
made. I had first to learn the means of doing so, of deciphering the great
problem then set me by nature. For the first time since the creation

page_text: the only 2 principles of propulsion possible to man, impulse and reaction,
were then brought together face to face, striving for the mastery for the
propulsion of the world through the twin oceans of air and water.
Nature, as we see in the Drawings, gave the victory to reaction, which
exerted twice the strength of impulse, and so overcame it and prevailed
against it. But it took me more than a quarter of a century at intervals
to understand it. I had first to understand the laws of force and motion,
and to put them into proper formulæ for paddle wheel and screw pro-
pulsion before I could determine the force they exerted on the water.
These I discovered in 1857, which will be given in their place, and the
proof of which will be found in the Specification of my Patent of the
29th May 1866, No. 1497, p. 3 and 4, and p. 20 to 25. I had next to
-discover the-laws, principles, & application of hydro-propulsion to enable
me to determine the resistance of a vessel so propelled.
4. This took me, at intervals, from 1847 to 1857, when I abandoned
hydro-propulsion as I then thought for ever, because I went on the
Newtonian doctrine of the equality of action and reaction as well in
plane and fluid action as in other things. I thus made the resistance of
the vessel R equal to the pressure on the floats P, so that the equation
for equable motion became R=P, a fundamental error which is taught
to this day. Were this true hydro-propulsion would be worthless,
because it has losses of its own from which both paddle wheel and
screw are free.
5. In 1866 the two principles of propulsion, Reaction in the hydraulic
Nautilus, and Impulse in the Volunteer paddle wheel, were tried against
each other, though unconsciously, by the patentee of the Nautilus.
Happening to take up the Engineer of the 13th of April of that year, I
first read of their competitive trials. I was now acquainted with the
laws of hydraulics and hydrodynamics, and also with paddle-wheel pro-
pulsion embodied in appropriate formulæ, without which those trials
would have been as barren of instruction to me as they have been to the
world. I was thus able at once to analyze their performance, and found
what was unintelligible to me for some days. I found, for instance, that
the resistance of the Nautilus, at 8.3 knots an hour, was only about
756 lbs. It followed that the resistance of her competitor the Volunteer,
a vessel of about the same size, form, draught, power, and speed, must
be about the same.

page_text: 6. But by my equation for equable motion, RP, the pressure on the
floats was about 2004 lbs., so that the efficiency of her paddle wheels
was only about 24 per cent. of her indicated power of 80 horses, thus
losing 100-24-76 per cent. of such power. I was for some days
unable to account for so great a loss as (2004-756=) 1248 lbs. to begin
with, because nothing was more solidly established than the Newtonian
doctrine of the equality of action and reaction. It is maintained by all
English and French engineers and naval architects, and will be found in
the works and papers of Tredgold, Barlow, Professor W. J. Macquorn
Rankine of the University of Glasgow, Professer Main of the Royal
Naval College, Portsmouth, Labrousse, Mornay, and others. Moreover
the equation R=P is taught to this day in all the colleges of Europe as
a fundamental principle of paddle wheel and screw propulsion, based on
Newton's third law of motion, the equality of action and reaction.
7. But having proved my analysis of the Nautilus and Volunteer step
by step, and unable to come to any other conclusion than that the
resistance of the Volunteer was (2004-756=) 1248 lbs. less than the
effective pressure on her floats, I thus discovered that Newton's law was
not true in plane and fluid action. Account for it I could not, till deeply
pondering day and night on this strange departure from his universal
law my experiments on action and reaction 24 years before all of a
sudden flashed across my mind like a stream of light, and everything was
made clear to me as if by inspiration.
8. I found in 1842, as I have said, that when a jet of fluid impinges
against a plane of the same area as the fluid one-half of it escapes past
the plane, and therefore cannot impart to it the power due to the fluid
so escaping. Hence there is a loss of about 50 per cent. of the force of
impulse to begin with. When however the plane was 8 or 9 times the
size of the fluid there was no loss of power; but the paddle wheel and
screw cannot be any larger than the water they set in motion. They
are then like my experiment (shown in Sheet 5, Fig. 2) planes of the
same area as the fluid, and so there must be the same loss when a plane
moves against a fluid as when a fluid moves against a plane of the same
area. This then must be the process:-The paddle wheel and screw
impart to the water their whole pressure P, and the whole pressure in
the water so set in motion reacts upon the float; but this is not large
enough to retain all the water, 8 or 9 times the area being required.

page_text: Therefore one-half of the water which so reacts rushes past the floats
towards the bow of the vessel, and thus carries one-half of the engine
power with it. Hence in paddle wheel and screw propulsion there must
be a loss of about 50 per cent. of the power imparted to them to begin.
with, which I then called the loss of primary velocity.
9. But in reaction there is no escape of water, and consequently no
loss at all to begin with. Since then it saves 50 per cent. of the power
at starting, Reaction is the only true principle of mechanical propulsion
on the water and in the air, and will never be superseded, because the
only other principle possible to man, Impulse, loses 50 per cent. of the
power at starting.
10. By-this-inductive generalization-from-mere-abstract-experiments-
in 1842 with a small jet of steam, and not made in reference to pro-
pulsion, I discovered four things-1, the large loss of paddle wheel
and screw propulsion; 2, that Newton's law of the equality of action
and reaction is not in such case practically true; 3, a standard measure
of the resistance of vessels for all time; and, 4, the superiority of reaction
to that of impulse for propulsion.
In this way was verified the following prediction in my letter to the
Reverend J. A. L. Airey, Professor of Mathematics at Merchant Taylors'
School (1866-1851=) 15 years after it was made:- "St. James' Street,
Brighton, March 5th, 1851. I am convinced, for many reasons too
numerous to trouble you with, that the principle of reaction will be
the only method of propulsion on water and in the air, and will never
be superseded. I have been turning my attention to carbonic acid
This pre-
and other self-generating denser gases in lieu of steam."
diction was first published in the Specification of my Patent of the 10th
May 1860, No. 1155, p. 14, line 5, but was not verified until six years
after it was published, and 15 years after it was made.
11. How it was subsequently established, by induction from the ex-
periments of the Nautilus and Folunteer in April 1866, has been here
shown. Now as these were being investigated by the Admiralty
engineers, and some of the first men of science of the day, I thought
my discovery might be made by others, and so, fearing to be deprived
of the thought and labors and expence of a quarter of a century, I
filed, far too hastily, a Provisional Specification on the 29th of May 1866,
No. 1497, "For Improvements in Propelling Vessels by the Reaction of

page_text: Water, and in the Machinery for the Purpose." As this was only a
month after the first idea of the difference between action and reaction
occurred to me, and was based on the memory of experiments 24 years'
before, not made in reference to propulsion, never thought of since, and
apparently erased from my memory, I was unable, all of a sudden, and
in the tumult of mind at so large and unexpected a discovery, to arrange
my ideas on the subject with precision, to give all the mathematical
formulæ correctly, to invent the proper machinery, and to show the
real saving in fuel. My hasty Specification of 1866 is therefore a true
reflex of the confusion of mind, struggling through darkness and disorder
into light and order, which will account for much in that Specification
which I would now omit.

page_text: term of Weisbach's formula for the friction of water in pipes, and this
formula is fully confirmed by experiments in long narrow finely
shaped vessels by the experiments of Morin on the towing of swift
canal boats." And for the reasons given by the learned. doctor at
fol. 25 of his report, he says, at folio 26, such formula "unquestionably
gives a lower limit below which the resistance cannot possibly be."
14. We see therefore that one of the first scientific authorities of our
time relies on the experiments of the first experimental philosophers of
England, France, and Germany, Beaufoy, Morin, and Weisbach, em-
bodied in the formula R=0.01 v2 S. The co-efficient of 0.01 is multi-
plied by the Professor by 1·1 or 1.2, for what he calls "the augmented
_surface." And by this means he makes the resistance of the Banshee
at 16.2 knots an hour=15928 lbs. due to her-surface-S,-and-(22569—
15928=) 6641 lbs. due to driving a wave before her; in all (15928+
6641) 22569 lbs., which is the pressure on her floats. He observes
therefore, at fol. 23 of his report, that "the Banshee may be classed as
respects 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." I shall show, however, that as her resistance
is so small as only 8468 lbs., instead of 22569 lbs., the Banshee must be
above good ordinary steamers.
15. In further opposition to my discovery that R is not equal P
(because, as I say, there is an escape of water and a loss of primary
velocity and power equal to begin with) the Professor thus writes, at
fol. 16 of his report, "The resistance R and slip S (Rs) is the only
possible loss of work connected with the longitudinal motion of the
water. Whatsoever resistance the water opposes to the direct back-
ward horizontal motion of the propelling instrument can only be
a forward pressure of the water upon that instrument, which forward
pressure must in every conceivable propelling apparatus be wholly
transmitted to the ship, as there is no other body to receive it." If by
any means the forward pressure exerted by the water through the
propeller to drive the ship is diminished, precisely to the same extent
is the horizontal resistance of the water to the motion of the propeller
diminished, and the engine (as practical engineers say ") "runs away,"
or increases its speed until those two equal quantities have again
attained an amount corresponding to the pressure of the steam." This,

page_text: however, is an assumption I must be allowed to say, and contrary
to. the fact.
16. Reducing these remarks to their simplest terms the Professor
says, that "if half of the waters escaped past the floats their resistance
would be so reduced that the engine would run away with them; but
as it does not there can be no escape." Now all arguments founded
on assumption must be rejected in limine. I will, however, show the
error in this casc. Motion is power.
Hence half the water could not
escape unless half the power had been expended in giving it motion.
Only half the power, therefore, is left to overcome the resistance of the
vessel. Now the power uselessly expended in giving motion to the
water that escapes, and the power usefully expended in giving motion
to the vessel, make up the whole power, and so leave none to " run
away with the floats."
17. In support however of his argument and of the formula before
given for the resistance of vessels R=f v² S, the Professor sent me a copy
of his paper read on the 27th November 1862, in which he says,
"law which experiment has shown to be at least approximately true is,
"the
that the resistance of vessels varies as the surface of the contact and as
"the square of the velocity of gliding; and its results have been found
"to agree very closely with those of experiment, and have also becn
"used since 1858 by Mr. James R. Napier (the eminent shipbuilder), and
"the author with complete success in practice, to calculate beforehand
"the engine power required to propel vessels at given speeds." In
the investigation of truth no argument is to be received based upon
assumption. I was therefore bound to reject this formula R=fv² S for
the same reason that I rejected the argument of the Professor before
given in para. 15 & 16, namely, that it was assumption. For this
formula assumes three things which are opposed to three laws of
physics 1st. That the resistance of bodies is the same in unconfined
as in confined water. Now it was only in canals, pipes, and channels
that Morin's, Wiesbach's, and Beaufoy's experiments were made, and
from which the co-efficient of friction is taken for the formula for
resistance of vessels. 2. That the resistance encreases with the immersed
surface S. And 3. That the resistance of a plane is equal to the engine
pressure upon it.

page_text: 1842, that when a fluid moves against a plane of the same area there is
a primary loss of power of about 50 per cent. But he denies any loss at
all when the plane moves against the fluid! Still, against all authority,
all mathematics, all experiments, all experience, I maintained the
simplicity of the laws of the Creator, the unity of principle in diversity
of action, and that things of the same type are governed by the same
laws. Therefore there must be the same reciprocal action between planes
and fluids, no matter which sets the other in motion. But the learned
man maintained the contrary, and referred to his own practical experience
and that of Mr. Napier in shipbuilding in verification. He says, as
before quoted, "that the formula R=fv² S has been used with complete
success in practice to calculate beforehand the engine power required
-to-propel-vessels-at-given-speeds." That-may-be-truc-in-some-cases
as regards the engine power, but not as regards the resistance. For
the formula sometimes makes it more than twice what it is, and no
doubt in this way. Not knowing my discovery, that a plane moving
against a fluid can only utilize one-half of the power expended upon it,
and therefore can only overcome a resistance equal to half of such
power, the Professor has assumed that a plane utilizes all the power.
Consequently, by augmented surface or some other manipulation, the
formula is made to account for the whole engine power, and thus makes
the resistance twice what it is. For since a plane wastes half the power
in letting half the water it sets in motion escape past it towards the bow
of the vessel, the engine power must be doubled to supply such waste.
The formula therefore f² S may be, in some cases, approximately true,
as the Professor says, "to calculate beforehand the engine power required
to propel vessels at given speeds."
But it is not what it is represented
to be, a measure of the resistance of vessels. On the contrary it is
fundamentally wrong, and therefore grievously and detrimentally wrong,
for the improvement of naval architecture, because it makes some
of the best forms of least resistance inferior to worse forms, as the
Professor asserts of the Banshee, and so gives bad models instead of the
best for building vessels for our navy and mercantile marine, a matter of
some national importance I think.
19. How empirical and wrong is the formula of the learned Regius
"

page_text: The experiments of erring man cannot be so exact as the laws of
uncrring God. Any discrepancy therefore between the results deduced
from official data and the laws of impulse discovered by me in August
last (1869), given in cols. 7, 8, 9, and 10, and herein-after explained, are
the errors of experiments, not of the laws. An approximation ncar
enough to determine the laws which govern the experiments is all we
can expect.
(V)2
66
20. It is here proper to point out that up to 1857 I had calculated the
resistance of vessels by the formula then universally adopted and taught
in the schools, R=P= 2 g -w, a, sce Tredgold, by Professor Wool-
house, appendix, p. 59, where the editor says (V-v) Va expresses
-the-whole_amount_of_power exerted," and "the resistance=(V—v)² a.”
At p. 43 and p. 47, 24 experiments are given, made with the different
steamers there mentioned. And Mr. Barlow observes at p. 54, "the
results of the preceeding investigations have been fully borne out by a
very interesting and complete set of experiments made by Mr. Field,
most of which I attended." A table is then given of 30 experiments
made with a paddle wheel of 17.83 ft in diameter. Relying on the
mathematical and experimental researches of so many able men these
gave me a saving of about one-third of the fuel by my system of
hydro-propulsion. But in 1857 I discovered, mathematical analysis,
that all their experiments and formulæ were wrong, and that the true
laws of force and motion were those which I embodied in my formula
(V-v)²
2 g
20 a.
P-2 Va(V-0) = 1100 (1), I being the indicated power, and fengine
friction, about 20 per cent. Unfortunately however I adopted the
Newtonian doctrine of the equality of action and reaction from 1857 to
1866, and made R = P. This encreased the resistance to more than twice
that given by the erroneous formula of the schools, R = P =
Thus my own formula of 1857 took away all my profit, and induced me
to abandon in that year the thought and labor and expense of the 10
previous years, given at intervals to hydro-propulsion. I lost nine years
more before returning to it in 1860, when, as I have said, I discovered,
by induction from my experiments in 1842 that the Newtonian doctrine
of the equality of action and reaction is not practically true in plane and
fluid impulse of equal areas. I have thus lost (10 + 9 =) 19 years of
the best part of my life by the false teaching of the schools.
21. My formula of 1857 for the effective pressure on the paddles or

page_text: screw (not the resistance R but) P=
immutable.
"
1100 (I-S) still remains true and
What I now affirm is, that the resistance of the vessel R
is not equal to P, because of the great escape of water, and conse-
quently of power. The Regius Professor however still maintains my
formula, that R=P, for at p. 5 of his "further additional remarks on
Mr. Boyman Boyman's paper, and on his remarks dated 29th August
1866," which "further remarks" of the Professor is dated the
7th September 1866, he says, the equation of uniform motion is
R=P, as I made it from 1857 to 1866. This too is maintained by
all the authorities I have consulted, and is taught as one of the
fundamental principles of physics. See Tredgold on the Steam Engine
by Professor Woolhouse, appendix, p. 59; the Marine Steam Engine by
Professor Main, of the Royal Naval College, Portsmouth, edition 1849,
p. 272, and 4th edition of 1860, p. 319.
66
22. I was the first to discover in 1866 the discrepancy between the
effective power and the resistance shown in the table, paragraph 19,
cols. 5 and 7. Now the Professor maintains that his formula fv² S, in
col. 6 of that table has been verified by the experience of himself and
Mr. Napier, and he equally maintains that the equation for uniform
motion is R=P" in col. 5. The difference between the two, shewn
in col. 8, cannot be explained by any law of physics, except that which
I have discovered as the ruling power of the paddle wheel and screw,
namely, impulse. Now, just as it is the business of the accountant to
give a true account of every shilling received and spent, so it is the
province of the man of science to give a true account of every pound of
power he receives and spends. He must trace it out, show where it
goes to, and what he gets for it; but this he cannot do until he has
discovered the laws of nature which make some of the power go here, .
some there, and some elsewhere. These laws he must then embody in
algebraic symbols, which must balance to a fraction, making the useful
effect and loss equal the power expended. My formulæ alone do so,
because these alone embody the true laws of plane and fluid impulse of
equal area. One Professor; however, accounts for the discrepancy
between the surface resistance and pressure on the floats a discrepancy
(which is admitted) by the vessel raising a wave. Another by the twin
screws sucking in the water behind, causing a kind of vacuum, and
so practically doubling the resistance." All assumption; but the
B

page_text: sure and certain laws of impulse, which can alone account for the
phenomenon they utterly reject, unable to emancipate their minds from
the false teaching of the schools, the equality of action and reaction in
fluids as well as solids.
23. The Professor is morcover confirmed in his error by experiments
and practice, as he says. Now this teaches us how people are misled
by appearances, the mere shows of things, in science as in life, without
the informing mind to resolve them into their components to show the
connexion of the parts, and to give to each what belongs to it. Facts,
indeed, are the mere dry bones of science, which nothing teach, the
skeletons of unlovely things, requiring always the guidance of a law to
interpret their meaning and classify them. Not merely do they hide
the essence from us, but mislead, by making things seem what they are
not. Thus does the equation for equable motion R=P make the
resistance of vessels more than twice what it is by assuming that R-P
pursuant to the Newtonian doctrine of the equality of action and
reaction. I have however shown in the table, paragraph 19, what
belongs to the resistance, and what to the loss of the propeller.
THE REGIUS PROFESSOR CONFIRMED BY ANOTHER AUTHORITY.
.
24. Disappointed and saddened, after so many years' labour, that one
so eminent as the Professor should reject my discovery as impossible, I
submitted it to a Reverend Professor of mathematics, who had studied
and written more on propulsion than any one known to me, and with
whom I had corresponded on scientific subjects for more than 15
years. We discussed my discovery for more than 2 years, and our
letters would fill a volume. But no one could be more indignant than
this supreme mathematician at a discovery so opposed to the teaching
of the schools. The primal scat of mathematical learning, Cambridge,
knew it not, and therefore it could not be true. The Newtonian doctrine
of the equality of action and reaction in every conceivable case was too
firmly grounded ever to be rooted up. In this wise then the Reverend
Professor wrote on the 13th of March 1867, "I still deny, unhesitatingly
and unequivocally, that there is any such loss as you assign to the
engines, your long paper to the contrary notwithstanding.”
" So much then for your discovery by induction, and proof by deduction,
on which you lay so much stress. I have above shown it to be vitally

page_text: wrong. I am quite convinced myself that this primary loss notion.
will lead you into confusion and trouble, and I cannot be a party to
that."
25. In another letter of the 14th December 1867 the Professor says,
I should be clearly wrong, nay I should be doing you an injustice, if
I were to go along with you in what, as far as my understanding and
grasp of the subject goes, I cannot accept. No one would rejoice
more than myself if you could establish your doctrine and convince
the world. I should be the first to congratulate you. Your reputation
would be great, and it would be unquestionably all your own."
26. In a subsequent letter of the 27th February 1868, the Reverend
Professor says, "You insist that there must be a loss of 50 per cent., a
primary loss as you name it, before you can take stock of anything
for work done, whether in actual propulsion or in ordinary losses.
This loss I believe to be purely imaginary (for I can no way conceive
it), a sort of ignis fatuis. If you can convince the world, as I
have said before, of a primary loss of 50 per cent. of engine power
from the very nature of the action of the paddle wheel and screw, you
will have indeed achieved a great discovery, but it must be all your
own. I cannot possibly have any share in it. The results shown by
such vessels as the Plover and Royal Alfred experimentally condemn'
your theory most effectually to my mind."
27. Here again are actual experiments brought against my inductive
generalization; false experiments I need scarcely say. Let me then
show further how superior is inductive logic to all experiments and
all reasoning, without the light of law as a guide. On the 18th May
1868, the Reverend Professor thus wrote: "I constrained myself to
make a fourth attempt to shew you, on your own premises, that your
views about loss of primary velocity are fallacious, but again to no
purpose. My proof you say is illogical, and based on an assumption,
&c. It is neither illogical nor does it assume anything but your own
premises, taken that I might assume nothing of my own.
The proof.
of your error is complete, if I know what proof means, and I ought to
know proof from assumption, else I have been an imposter all my life
long in the art of reasoning."
. 28. I ventured to point out to the Reverend Professor that my
discovery was necessarily true, being based on sound inductive reasoning
on the laws of physics, the analogies of science, and experimental

page_text: results; and that though I was no mathematician, never having had
a lesson in mathematics, still that discovery and Invention precede
mathematics, which is the mere instrument or machine of thought,
the embodiment only of a diviner and higher power, a deeper and more
original perception of the truth and harmony of things. I also observed
that mathematicians should prove everything, and assume nothing. To
this the Professor replies on the 29th of October 1868, "You are quite
right, mathematicians should prove everything and assume .nothing.
Therefore when asked I have given you proofs again and again, but
instead of pointing out in any one instance where my proofs fail, 1
you summarily toss them aside as no proofs, at all, and call them
ceaseless assumptions. I call this reckless assumption, if not worse.
If you do not see what proof is and what not, I do, else my mathe-
If
matical training from boyhood upwards has been thrown away.
you find, as you most certainly will, that the world will not follow
upon your chariot wheels (as you have so unreasonably expected me to
do) blame the world and yourself for the consequences, and not me."
29. We now come to the fundamental error of the schools, not in
theory but in its application to plane and fluid action of equal areas..
The whole question," I wrote, "like all great questions reduced to the
simplest elements, lies in a nutshell. Prove what you and other
mathematicians assert, that R=P in paddle wheel and screw pro-
pulsion, and my refutation will be complete ;
you cannot.
know it by a higher calculus than the mere mechanical calculus of
figures, the calculus of induction, by which all great discoveries have
been made, by which I made mine, and which never misleads.".
but
I
30. The Reverend Professor thus replied on the 31st of October 1868:
"The formula R=P for the paddle wheel is only the fundamental
principle of action and reaction expressed in symbols applicable to the
case, neither more nor less. It is therefore what physical laws make
it, not I. It wants no proof, indeed it admits of none, unless you
would have a proof of the principle itself. Deny the formula and you
deny the principle, for they are here identical. That you cannot see
this, or, seeing it, are content to put yourself in antagonism to the
first physical principle of all mechanical science is no fault of mine."
31. The Reverend Professor refers to Newton's third law of motion,
which is thus enunciated by its illustrious discoverer:- "Action must
always be equal and contrary to reaction, or the actions of two bodies
-

page_text: "
upon cach other must be equal and directed towards contrary sides.'
Now as all the laws of nature were made and are maintained by the
same Omniscient and Omnipotent Being, one law cannot contradict
another. Newton's law is necessarily true in every conceivable case.
Hence as my law of impulse as the governing power of plane and fluid
action is also necessarily true they cannot clash, nor do they. The
paddle wheel and screw act upon the water with all the force they
receive from the engine, and the water set in motion reacts with the
same force against the floats, and so fulfills Newton's law of the equality
of action and reaction.
32. But now another law no less imperative comes into operation,
which I will call the law of application. This says if you would make
Newton's law as true in practise as it is in theory you must have the
plane impinged upon 8 or 9 times as large as the reacting fluid, in order
to prevent any of the water escaping past it, as shown by my experiments
in 1842, referred to in paragraph I. But since you cannot make the
paddle wheel or screw any larger you cannot prevent such escape. It is
then manifest that if the same amount of force cannot be received by the
plane impinged upon, as by reaction, Newton's law cannot be practically
truc. I cannot therefore understand how these profound mathematicians
could not scc this when pointed out to them. They confound a law of
force with its transmission; the theory of power with its utilization.
God gives the power and the laws which govern it; man has to discover
them and the best means of applying them. Hence the art of science
is economy, simplicity, and efficiency, three essentials which will always
be combined in that machine which utilizes the greatest amount of the
power expended. And this is mine.
THE DICTUM OF THE LORDS OF THE ADMIRALTY.
33. It was my duty to submit to the Admiralty a discovery that
would save so much of the public money in first cost of engines
and in fuel, and give to the Chief Constructor of the Navy an unerring
standard of the resistance of all vessels, and so enable him to select
the forms of least resistances. To prevent therefore more of the public
time and money being wasted in building screw ironclads at about
a quarter of million apiece, only to be superseded by my system

page_text: have the honor to submit for consideration the science of hydro-
propulsion, the only exact science patented since the Patent Laws in
1623, or brought before the Admiralty since its existence. Founded
on the primary laws of nature this system is the ultimate development
and reach of science for propulsion; it will therefore supersede all
other systems and never be itself superseded.' I gave Drawings and
explanations of my experiments in 1842, and established my discovery
on the solid basis of common sense, the laws of physics, the analogies
of science, experimental results, inductive logic, and the two crucial
instances of the power test and area test there explained.
34. These are too remarkable to be omitted here. I found in 1842
that the force of impulse was only half of the force of reaction. There-
fore, I reasoned in 1866, for Impulse to overcome the same resistance as
reaction twice the power must be expended and twice the area to receive
it. If, then, my discovery is true, that there is the same loss when a
plane moves against a fluid as when a fluid moves against a plane of the
same area, I shall find that the power and area of every paddle wheel
and screw vessel in the world is at least twice as great as would be
required by reaction to overcome the same resistance at the same relative
velocities. The official returns of the indicated power of the Volunteer,
Viper, and Vixen, given in the table at paragraph 19, established the
soundness of my first induction as regards twice the power, and this I
called The Power Test. And the measurement of the areas of reaction
of the Nautilus and Waterwitch and of the paddle wheel and screws of
the Volunteer, Viper, and Vixen established the second induction as
regards twice the areas, and this I called "The Area Test." Here then
was the triumph of inductive philosophy. For twice the power and
twice the area cannot exist in the paddle wheel and screw unless they
lose one-half of the power expended upon them, and therefore require
such loss to be made good by double the power and area of propeller to
enable them to overcome the same resistance as reaction.
35. I therefore pointed out in my paper to the Admiralty that there
were the same proportions of power and area in the Waterwitch, Viper,
and Vixen, of nearly 800 h. p., as in the Nautilus and Volunteer of less
than 100, which was conclusive evidence of the universality of the law
of plane and fluid impulse of equal areas as well in propulsion as in my
own experiments in 1842. I gave also a brief Abstract of my labours
and discoveries of (1867-1842) 25 years, shewing by what steps I was

page_text: gradually led to the discovery. But the scientific adviser of the
Admiralty, one of the Professors of the Royal Naval College, Portsmouth,
made short work of it all by directing an official letter to be sent me,
dated the 9th April 1868, informing me that
66 my communication
contained nothing of any value to this department."
36. This is indeed remarkable coming from such a college. Besides
which it may be laid down as a mathematical axiom that equal bodies
in contact must act and react upon each other with equal effect which-
ever body first acts upon the other, a fluid against a plane or a plané
against a fluid; both must necessarily be governed by the same laws.
Whatever then is the useful effect of one must be the useful effect of the
other also. Different they cannot be in the nature of things. There
cannot be one set of laws for a fluid moving against a plane and a totally
different set of laws for the same plane moving against the same fluid.
Therefore a plane moving against a fluid, such as the paddle wheel and
screw, cannot receive and transmit more of the power expended than
a plane moved by a fluid of the same area. Since then this loses about
50 per cent. of the power to begin with, as shown by my experiments of
1842, all plane and fluid action of the same area must do the same. For
the same type the same principle: equal bodies equal effects.
37. Independent however of all such reasoning, my discovery of the
loss of the paddle wheel and screw in 1866 by induction from the loss
of a plane acted upon by a fluid of the same area, as found by my
experiments in 1842, can be established by the unerring logic of a
syllogism.
1. A plane acted upon by a fluid of equal area loses 50 per cent.. of
the power expended upon it.
2. Equal bodies act and react upon each other with equal effect.
The paddle wheel and screw are planes of equal area with the
fluid they act upon.
3. Therefore they lose 50 per cent. of the power expended upon
them.
No reasoning, much less anything so inferior to reason as mathematics,
can answer this logical induction. It is such a necessary truth that the
human mind cannot conceive or understand its opposite.
38. After the Lords of the Admiralty had thus rejected my discovery

page_text: "
I submitted it to one of the oldest and still one of the first engineering
firms in England, the head of which thus wrote on the 19th February
1868 "You should have had an answer sooner had I not wished to think
the matter well over. I am sorry to say that your paper (a copy of
the one sent to the Admiralty) has not convinced me that there is that
great loss of power of which you speak. Much has to be assumed in
your calculations (I never assume anything), "whilst the results
taken from the experiments in the Rattler and Highflyer, which I
enclose, are got at from actual practice. These data were the results
of very careful experiments, and have in actual experience turned out
truc. I assure you in thus giving my opinion I have given much
consideration to the matter, because to do what you state ought to be
done would be of national importance.” And in-another-letter-of-the-
16th March 1868, this gentleman asserts, as a practical man, that I
very much under-rate the power required to propel a vessel through
the water."
86
39. Thus the Regius Professor, the Reverend Professor, the great
engineering firm, and the scientific adviser of the Admiralty, all
independent of one another, deny my discovery, the two first on the
ground of physical and mathematical science, confirmed by experiments,
and the third on the ground of "the results of very careful experiments
which have in actual experience turned out true." Certainly the
experience of the Regius Professor, Mr. Napier to whom he refers for
confirmation, and the great engineering firm are very great. All that
they say then 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 laws must be in harmony with facts.
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; there-
fore I rejected them as lawless and worthless. So did I keep on for years
improving the machinery which is now described in this Specification.
This then is another of those intellectual battles between philosophy and
scholasticism, true theory and false practice which have been going on
from the earliest discovery to this. I have now to explain the laws
I have discovered.

page_text: THE LAWS OF IMPULSE WHICH GOVERN THE ACTION OF THE PADDLE
WHEEL AND SCREW; THEIR FORMULE. FORMULE FOR RE
ACTION. FORMULE FOR NUMBER OF REVOLUTIONS OF ENGINES AND
PROPELLERS. PRESENT STATE OF THE SCIENCE OF RESISTANCE
OF VESSELS; AND FORMULE FOR FINDING IT.
:
40. My experiments on action and reaction from which my discovery
of the loss of the paddle wheel and screw was deduced having been
made (1870-1842=) 28 years ago, and not in reference to propulsion,
I am unable to say at this distance of time of the loss of primary velocity
in 1842 was 50 or 40 per cent. I have therefore framed 2 sets of
formulæ, one for a loss of 50, the other of 40 per cent., the latter being
about the loss of the undershot water wheel, which is the type and
principle of the paddle wheel.
When I made the discovery referred to it was only as planes of equal
area with the water which the paddle wheel and screw set in motion at
moorings, for my experiments in 1842 were not made with an impulse
wheel nor at different relative velocities, but simply against a plane at
moorings, that is, stationery. When, however, in April 1866 I
generalized the loss of primary velocity to the paddle wheel and
screw I found by my analysis that there was always a residual pheno-
menon, a further loss than 40 or 50 per cent. which my experiments
of 1842 would not account for. It was not then until the 13th of
August of last year (1869) that I discovered, by induction from the
undershot water wheel, that the paddle wheel and screw are governed by
the laws of impulse. I could not then before determine their real loss
at different relative velocities of propeller and vessel. Nor could I find
the true resistance of vessels, of so much importance of the improve-
ment of naval architecture. I knew that by the law of plane and
fluid impulse of equal areas resistance of vessels could not be more
than ; and this I pointed out to the Admiralty in my Paper of 1867.
But the perfect law of impulse which governs the resistance at all
relative velocities, and explained the residual phenomenon found by my
analysis, was the crowning mercy" of my discoveries in 1869.
P
«
41. There are no laws in the world that I know of so curious and
anomalous as those of impulse. I found by-analysis, for-instance, this
contradiction, that as the loss of residuary velocity encreases the gain or

page_text: efficiency encreases until the velocity of the prime mover is twice the
velocity of the body moved, V=2v. And then when is more than
2 the gain or efficiency decreases as the loss of residuary velocity
encreases. It follows, therefore, that the maximum efficiency is when
V=2v. I then found that if with these' relative velocities the escape
of water be 50 per cent. the loss of primary velocity, the useful effect,
and loss of residuary velocity are all equal. None is before or after
the other, yet have they 3 different names, and are 3 different things,
as their names show; and in one and the same body. Here then, if
permissible to point out the fact, we have a trinity in unity in physics
never before discovered, shewing that harmony and analogy between the
spiritual, moral, and physical worlds which it has been my delight for
many years to search into, and to which I owe so much.
42. The Laws of Impulse and Reaction are essentially different, because
in Impulse there is a large escape of primary velocity, and in reaction
none. Therefore they require different formulæ to embody their different
laws. But both arise from the same source, the fundamental laws of
force and motion embodied in my formula of 1857
(I-f).
P=V²−v²+(V−v)² a=2 Va (V−v)=1100 (1-5)= 2 PE
V+0
This is the effective pressure which the engine exerts on the paddle
wheel, screw, and area of reaction, and which the paddle wheel and
screw exert on the water, but not on the vessel as reaction docs. This
will be seen by the following formulæ, which, being unknown at the
great seat of mathematical learning, Cambridge, I venture to call for
distinction

page_text: where U=R v. This is given for convenience of calculating, 2g=w
for salt water being eliminated throughout.
44. The symbols mean as follows:-P is the effective pressure on the
paddle wheel or screw; I is the indicated power; f, the engine and axle
friction, which I take at 20 per cent. of the indicated power; V is the
mean velocity of the paddle wheel or screw in feet per second, and that
of the vessel; a is the effective area of propeller, the inclined blades of
the screw being reduced to a square area like the paddle wheel, for
simplicity of formula and to show clearer the principles of impulse;
PE is the actual power expended on the propeller after such deduction
of 20 per cent; R is the resistance in lbs.; Uis the useful effect, or clear
work done in propelling the vessel; L is the gross loss, 1st, of the
primary velocity 1, and 2nd, of the residuary velocity 4; E is the
modulus of efficiency of the paddle wheel and screw according to
their relative velocities; and IE is the indicated efficiency, assuming
20 per cent. of the indicated power to be consumed in friction.
All the formulæ, except P, R, and E, are in feet Ibs. per second,
which divided by 550 will give the nett effective horse power required to
overcome the given resistance at different relative velocities.

page_text: the efficiency encreases as the loss of residuary velocity encreases, until
V=2v. Now as this is the maximum efficiency it is manifest that wo
cannot depart from it (by making more than 2 v) except by encreasing
the loss of residuary velocity. Since then the efficiency now decreases
as this loss encreases, we require a formula which will embody this
variation of the law of impulse, that is, a formula which makes the
efficiency depend on the loss of residuary velocity. This we get from
my formulæ for reaction propulsion herein-after given. For instance,
though for impulse R is not equal to P for reaction, it is
A velocity of paddle wheel or screw more than 2 has never existed,
and will never exist, so that the last two formulæ are more curious than
useful. It is, however, necessary in discovering a new law of physics to
explain it in all its bearings.
49. I know no law so interesting as that of impulse, so anomalous and
curious. Nothing can better establish the present state of the dynamics
of propulsion. For the great aim of engineers is to make the loss of
ԱՏԵՂ Ա. IS, However, necessary in discovering a new law of physics to
explain it in all its bearings.
49. I know no law so interesting as that of impulse, so anomalous and
curious. Nothing can better establish the present state of the dynamics
of propulsion. For the great aim of engineers is to make the loss of

page_text: Banshee but every paddle wheel and screw vessel in the world is at this
moment encumbered with hugh paddle wheels and screws, the cause
sometimes of their foundering, for no other purpose than to waste power
and fuel by setting a large body of water in motion to escape past them
unutilized. And strange indeed it is that not one of the many scientific
mathematicians, naval architects, and engineers, from the time of Watt
to Brunel, Rankine, and Scott Russell, not only in this country but in
France, distinguished as it is by the illustrious Poncelet and so many
eminent theorists, surpassing strange I think it is that none should
have discovered the laws of paddle wheel and screw propulsion, here
enunciated for the first time and shown to be so wrongly applied. As a
science indeed it is so without law, both in theory and practice, and
so contrary to law as to be in the same state in the latter end of
the 19th century as physical science was previous to the age of
Galileo in the middle of the 16th century.
53. We now come to the laws of my own system of propulsion, and
since these also were discovered and proved by me, I venture to call
them by my name for distinction, to show what formulæ I go by
in applying my machinery and calculating the power, efficiency, &
loss.
V+0
per cent. of the indicated power approxi- 3
mately given for convenience of calculating, where U=R v.
54. We see that in reaction RP pure and simple, because there is
no escape of water to begin with, as in impulse. We see also by
comparing the formula for P for impulse, paragraph 43, with reaction,
paragraph 53, that both start from one and the same source, the 3

page_text: fundamental laws of force and motion embodied in the formula P=2Va
(v). But then they separate. For impulse has 2 losses, primary
and residuary velocity, shown in the formula for L, paragraph 43, whilst
reaction has only one loss, that of residuary velocity, shown in its formula
for L, paragraph 53. But besides the great loss of primary velocity
in Impulse under the best circumstances (when F=2v). This law of
maximum effect is very unfavorable in application. Even with V=2v
the indicated efficiency would be only =32 per cent. But for high
speeds, like those from Holyhead, Dover, and Folkestone, the Victoria
and Albert, the Banshee, Hercules, and other first-class steamers
a velocity of propeller of twice that of the vessel is economically
impracticable.
48 V
55. For even with the present velocities of propellor and direct acting
engines the rapid reciprocation of pistons of large powers has been found
so injurious in the United States that their government has introduced
gearing into her war vessels to drive the engines at less speed to enable
them to work longer than those connected directly with the screw. But
gearing entails loss of power from friction, and the teeth of the wheels
are liable to injury. Thus for maximum effect (and that only 32 per cent.
the law of Impulse renders it necessary to have a much higher velocity
of piston than at present, the limit of which is already reached in great
powers. Or else gearing which consumes power or a larger diameter of
screw, part of which would then be out of water exposed to shot.
56. Now the law of physics for reaction on my system is as favorable
for maximum effect as the law of Impulse is unfavorable. For the
less V, that is, the nearer vis to V (not as in impulse, the further vis
from up to 2v), the greater the efficiency. Thus the greatest powers
can be connected direct to my hydro-propellers, and work with a
comfortable velocity of pistons, as will be seen by the following
57. FORMULE FOR NUMBER OF REVOLUTIONS OF ENGINES AND
REACTION PROPELLERS.
After setting out several cams to get good angles for the floats to
be moved into the drum I found that a proper diameter of propeller
would be about 8.5 times the projection of the float. This I take at
15 feet for so large a vessel as the Hercules of 8500 indicated power.
Hence the diameter of propeller for mean velocity of float, by which I do
not mean the drum, but the diameter from the top of the case to the bottom

page_text: whole thing is so indifferent to me that I can hardly bring myself to
go on with it, so fatal to me has been the teaching of the schools.
60. I have also shewn that the Regius Professor, the Reverend Professor,
one of the first Cambridge mathematicians, and others, still insist on this
fatal error, even when pointed out to them. Inseparably connected-
therefore as my Invention is with the true resistance of vessels, it is, I
think, incumbent on me to put on record the present state of the science
of resistance, especially as I can only in this way show the novelty of
my formulæ and Invention, and their practical value,
61. The art of naval architecture and aerial navigation is to get the
form of least resistance to a.body passing through a fluid, that it may be
propelled at the least expenditure of power, weight of engines, boilers,
water, and fuel. But such form never can be found until we know
the resistance of some given body of large size used in navigation.
The illustrious Newton devised a formula for such a body, but his
equation is so complicated and the form. found from it so erroneous in
some cases that it is never used. The difficulties surrounding the
subject are in some degree entered into by Herschel in his Natural
Philosophy of 1831, p. 180, where he says, In what relates to the
We can include our
motion of fluids we are completely at a loss.
problems in algebraic equations, and we can demonstrate that they
contain the solutions, but the equations themselves are so intractable
and present such insuperable difficulties that they often leave us quite
as much in the dark as before. But even were these difficulties
overcome recourse to experiments must still be had to establish the
data on which particular applications are to depend."
62. Now recourse to experiments has been again and again had for a
century, and are still going on at this moment, for the purpose of finding
the resistance of fluids to bodies passing through them. The Admiralty
are conducting. those for water through Mr. .W. Froude, and the
Aeronautical Society of Great Britain (whose President is the philosophic
Duke of Argyll, author of "The Reign of Law,") are conducting those
for air. Both however will be a waste of thought and time and money.
For only by my method of first finding the laws of physics that govern
the action of the propeller which overcomes the resistance, can it be found
with any degree of accuracy. This physical truth I ought, I think, to
establish here, to save further. waste of thought, time, and money, and
especially as my Invention depends upon it.

page_text: 63. A. former neighbour of mine, the late Mr. Henry Beaufoy, printed
with rare munificence at his own private press, bought for the purpose,
the laborious and costly experiments of his munificent father, Colonel
Mark Beaufoy. Mr. Beaufoy gave me a copy of their great work,
"Nautical and Hydraulic Experiments," published in 1834, to assist me
in my pursuits; and at page XXXII. the editor observes, "The united
experiments made by the English and Swedish philosophers have not
cost so little as £50,000 sterling." Some idea of the number of these
experiments may be got from the fact that in the first volume they take
up 688 pages of large quarto. But these are considered so unreliable in
practice that the British Association for the Advancement of Science
_appointed_a_committee_of_scientific men in 1863 to make further
experiments. The result of their labors is thus stated in the Mechanics'
Magazine of August 28th, 1868, p. 172, "Professor Rankine then read
the report of the committee on the performances of steam ships, which
stated that the committee had collected a great deal of information
with regard to the performances of upwards of 350 vessels which were
being prepared, and would shortly be published in a tabular form with
the Transactions of the Association. It had been the duty of the
committee only to collect such data, and not to form any practical
conclusion therefrom."
Ի
64. As unreliable as all Beaufoy's experiments were the years of
research and experiments of this committee, though made with all the
appliances of modern science and by the most advanced men of science of
our day. This will be best seen by the following remarks of one of its
members: "Mr. Scott Russell said he was a member of the Steam
Performance Committee for the purpose of collecting valuable infor-
mation upon the subject. They made an enormous collection of data
which when threshed out yielded a great deal of chaff and very little
corn. There was one thing which the British Association had not
done, but which he thought this institution might do. He had been
one of the deputation which went from the British Association 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 exact experiment with one single carefully
measured ship of which they would have been able to say her
resistance on going through the water was so many pounds, but the
Lords of the Admiralty did not entertain it."-Engineering, March 26th,
1869,
P. 218.

page_text: 65. In 1868 a still larger committee was appointed by the British
Association to report on the state of existing knowledge on the resistance
and stability of ships. Their report was prepared by Mr. C. W. Merri-
field, F.R.S., Principal of the Royal School of Naval Architecture and
Marine Engineering, and was read before the British Association. In
our exhaustive report, published in Engineering of the 21st of August
1868, and 27th August 1869, the Principal refers to the experiments
of Euler, D'Alembert, Chapman, Bossut, Beaufoy, Reach, Professor
Rankine, Scott Russell, M. Dupuy de Lorne (Chief Constructor of the
Imperial Navy of France), and others on the resistance of ships, and
observes:"We have had many theories on the subjects, but the illus-
trious authors of them express themselves as thoroughly dissatisfied
with the basis on which they rest. We may then sum up the results
in the broad statement that there exists no generally recognized theory
or rule for calculating the resistance of a ship. Many such rules
have been put forth, but they do not agree in their form or in their
result."
66. The committer therefore appointed a deputation to wait on the
Lords of the Admiralty to request that "some experiments on fluid
resistance should be made with a ship of considerable size and fine
form in deep inland water free from. ground swell, such as may be
found in Norway and on the west coast of Scotland." To this appli-
cation the Lords of the Admiralty thus replied:-" Admiralty, S.W.,
9th February 1870. Sir,With reference to your letter of the 28th
September 1869, I am commanded by my Lords Commissioners of the
Admiralty to inform you that after full consideration they are unable
to give a general assent to the proposal of your committee to conduct
experiments upon Her Majesty's ships in the fiords of Norway or on
the inland waters of the west of Scotland; but my Lords have been
pleased to sanction certain experiments upon models to be conducted by
Mr. Froude, a member of the committee, and will cause the results of
those experiments to be communicated when complete to the Institution
of Naval Architects, the British Association, and such other professional
bodies as to my Lords may seem desirable. I am, sir, your obedient
servant, (Signed) Vernon Lushington. C.W. Merrifield, Esq., F.R.S.,.

page_text: their archives, where I show (at p. 3, paragraph 11) that "this great
question of resistance unsolved till now was now solved." And again in
p. 4, paragraph 15, p. 5, paragraph 16, p. 6, paragraph 21, and p. 8,
paragraphs 28 to 36. The answer to this was, as I have said, that "it
contained nothing of any value to this department." Having then in
their possession the great question of resistance solved, and in the only
way in which it ever can be solved, by the fixed and unerring laws of
plane and fluid impulse of equal areas, which govern the propeller that
overcomes the resistance, the same department is now spending the
public money in the same kind of experiments which have failed for a
hundred years, some of which, as Beaufoy tells us, "have not cost so
little as £50,000 sterling." Such then is the novelty of my method of
finding the resistance of vessels. For even when pointed out and proved
by inductive generalization of the laws of physics discovered in 1842,
plane and fluid impulse of equal areas, it was rejected by the Lords of
the Admiralty as "of no value to this department."
68. Nothing however can be of less value to that department than the
experiments now making. For it is unphilosophic to try experiments
with models in one water, and from them infer the resistance of large.
vessels of all forms, sizes, depths, speeds, and in all waters; but far 1
more unphilosophic would it be to infer the power of all horses from
experiments on perambulators. Yet from these petty model resistances
the
power or modulus of the paddle wheel, screw, and therefore of my
and all other propellers will be inferred. The resistance of even the
same vessel depends upon the water in which it is propelled. Some 2
experiments are reported in the Times of the 13th October 1869, which,
establish the fact. They were made on the Suez Canal and signed
"Daniel A. Lange, Director and Representative of the Suez Canal Com-
pany, from which the following is an extract:-"The last question
to determine was the loss of speed incurred by a vessel navigating in 3
the canal compared with the open sea in smooth water. It was found
that the loss of speed, owing to the more confined water area of the
canal, amounted to one-fourth, using of course the same power in
both cases.' This confirms my remark in para. 17 of one of the
fundamental errors of the formula fr°S adduced to refute my discovery. 3
"
69. As regards models I have shown that the most extensive and costly
experiments ever made with models, those of Beaufoy, are no longer
relied on. Mr. Merrifield, the Principal of the Royal Naval School of

page_text: Naval Architecture, thus confirms the fact in his report before referred
to "It unfortunately happens that no trustworthy comparison can be
drawn from small to large models." This is further confirmed by the
experience of Mr. John Scott Russell, the discoverer of the wave line
form of vessel and builder of the Great Eastern, the largest ship in the
world.
70. The following is taken from Engineering of the 29th of April last,
1870, containing a report of a meeting of the Institution of Naval
Architects. "The Chairman (Mr. J. Scott Russell, F.R.S.) said, that
some time since the Institution had expressed the desire of having
experiments made by the Admiralty upon full-sized vessels, for the
purpose of ascertaining the amount of direct absolute force necessary to
drive a fully-sized ship at a certain speed. The Admiralty had not
chosen to reply favourably to the request, but had shown its good will
to the science of naval architecture by giving Mr. Froude, a dis-
tinguished contributor to the transactions of the Institution, a sum of
money to enable him to make an interesting series of small experiments
upon models. He did not mean to announce that experiments upon
very small models furnished safe or accurate data for experiments upon
large ships. Experiments upon small models. in a canal were doubtless
extremely useful in their way, but the results would not be sufficiently
reliable as to authorise their application to large vessels in the open sea.
He warned them not to expect such a thing,, or they would be doomed
to disappointment. He had himself taken the trouble to make ex-
periments upon 120 small models, extending; in one case from. 24 inches
to 12 feet in length, and in another case from 30 to 60 feet long.. The
one valuable result of all his experiments upon small model, that he was
led by an examination of the curious results to make experiments. of
quite another kind upon the large scale, and he had arrived at the con-
clusion, from the graduated series of models, that the two cases were
so far removed from each other, as to any practical ratio,. that the
experiments upon the small scale were only useful as suggesting what.
should be done in the converse case.. Therefore, although. Mr.. Froude.
would no doubt have the pleasure of making, a number of beautiful
and interesting experiments upon the models; they would not furnish
reliable data for a full-sized sea-going vessel. He would state what his.
own experience had been. He had. made an experiment upon Sir Isaac

page_text: Newton's form of least resistance on a small scale, and had found it
marvellously successful; but when he tried the same thing in a ship of
100 feet long Sir Isaac Newton's form of the solid of least resistance
appeared to be the form of the solid of greatest resistance. He would
give another instance. He knew a ship 180 feet long of the ordinary
shape of the time, and with 100 horse power, and he said to himself, "I
will build a ship of the same length and the same beam, and I will put
60 horse power in her, but I will make her of that form which appears to
be the form of least resistance, which ought to make her as fast as the
other vessel of 100 horse power; the two vessels shall run together on
the same station for 12 months, and we shall then have a tolerable
notion which_of_the_two_is_the_fastest." He did not know whether they
were prepared for the result, but it was very curious. The fine bowed
vessel was much the slowest in shallow water, and much the fastest in
deep water. In the smooth water of the river the large power was much
the slowest, and in the rough water of the deep sea much the fastest,
That was in direct
and the rougher the water the better in proportion.
contradiction to the experiments which he had made on a small scale,
and confirmed what he had stated as to the difference between the two
cases. He then had four ships to build, all of the same size, with the
same engines and of the same horse power. They were 212 feet long,
36 feet beam, and 400 horse power, a very respectable experiment. Ho
constructed them with those little differences between their shapes which
nobody but a shipbuilder would be able to recognize. One was with the
sharpest and the fullest bow; the second a little fuller and a little finer
bow the next fuller, and the bow finer; and the fourth still fuller and
the bow still finer; in fact fullness and fineness of bow running inversely.
In these four vessels there was a difference of two knots an hour between
the two extremes."
71. No writer that I am acquainted with combines more theoretical
knowledge with practical experience than Mr. Scott Russell; or las
written better standard works on shipbuilding. This gentleman, then,
confirms what Herschel says in his Natural Philosophy on "the in-
superable difficulties of dynamical inquiry in what relates to the
motion of fluids and their resistance to motion, referred to in
paragraph 61. We see also that the resistance of vessels so large as
212 feet long and 400 h.p. is no guide to the resistance of even the same

page_text: vessel in different water, much less to other vessels. We may be sure,
therefore, that the mere model experiments being now conducted by
the Admiralty will only end in the same disappointment as all others
have done
THE SUPERIORITY OF SOUND INDUCTION OVER EXPERIMENTS UNGUIDED
BY LAW. FUNDAMENTAL ERRORS. EFFICIENCY OF PROPELLERS
AND EFFICIENCY OF VESSELS. FORMULE FOR RESISTANCE.
72. I have now shown what is the present state of physical science in
one of its sublimest developments,, the conquest of the wind and waves;
and how earnestly desired by the scientific world of steam navigation is
some standard of the resistance of vessels. The Admiralty, I have
shown in paragraph 64, was implored "to assist the Committee in
getting only one single exact experiment with one single carefully
measured ship, of which they would be able to say her resistance on
going through the water was so many pounds."
73. But now, instead of having the resistance of only one vessel, we
have the means of finding the resistance of all, and with unerring
exactness. Observe then what I wish to record here, lest I have no
other opportunity of doing so, the supreme power of induction from the
fixed laws of nature over all experiments not guided by law; though
thousands upon thousands have been made to discover the resistance of
vessels, and thousands upon thousands. of pounds so. wasted, Beaufoy's
alone costing, not so little as £50,000." Experiments, as I have said,
were made by me in 1842. with a minute jet of steam, minute, because
by my formula the velocity of steam at 120 lbs.. pressure above the
atmosphere is V = 146-128/ B+14·7·log. n = 3174 feet a second ;. con-
W
sequently the steam would soon run out of even a locomotive boiler
were the area of the jet half an inch in diameter. These experiments
were not even made in reference to propulsion, or to the resistanco
of vessels, but in connection with Mr. James Pilbrow's. injet steam.
wheel, which I patented in 1842. That went at once to the limbo. of
abortive schemes and everything. connected with it.. The experiments.
on action and reaction alone remained of any use.. But. they made.no.
impression upon us, nor on the late Mr. Brunel, to whom we showed
them, and others. They continued dormant in. the mind, whatever that
is, for (1866-1842) 24 years, apparently erased from it, because never

page_text: thought of once during this quarter of a century. But in 1866 these
experiments were called from their long sleep by some flash of thought
and instantly led to the 3 greatest discoveries in steam navigation
since its introduction. 1st. The great loss of paddle wheel and screw
propulsion. 2nd. That reaction is the only true principle of mechanical
propulsion in water and in the air, and will never be superseded. And
3rd. That the resistance of vessels cannot be more than one half of thic
pressure on the paddles R = 2.
P
74. But, as I have said in paragraph 40, I found that in all the paddle
wheels and screws I analysed there was always a residual phenomenon
which the mere law of plane and fluid impulse would not account for.
This further loss I put down to shock, although I could not so make it
mathematically. It was then, as I have said, that on the 13th of August
låst year (1869) I discovered by induction from the undershot water
wheel that the laws which govern the action of the paddle wheel and
screw were those of impulse. These laws I put into appropriate formula
to show the useful pressure and effect of such propellers at different relative
velocities given in paragraphs 43 and 45. And then I had the satis-
faction of finding that not only did these formulæ account for the
residual phenomena referred to, but that they were also an unerring
standard of the resistance of vessels of all lengths, breadths, forms, sizes,
draughts, and speeds, and in all waters in this wise.
75. It is manifest that the resistance of vessel cannot be greater than
the power that overcomes it. Also that the power cannot be greater
than the propeller can transmit. Now every propeller like every other
body in motion is governed by certain fixed laws by which it can
transmit so much power and no more. We have then only to find out
the laws of physics which govern the propeller and determine how much
power it can transmit, and we know at once the resistance of the vessel
to which it is applied. Now the power of machines is called the modulus
of efficiency, and this being fixed by the laws which govern it is an
invariable quantity. In other words no machine can under any
circumstances exceed its normal modulus.
76. The Regius Professor however, referred to in paragraph 12, asserts
at fol. 28 of his report of 1866 against my discovery, that "ordinary
existing steamers use from 39 to 65 per cent. and lose from 61 to 35
per cent. of their indicated power." Moreover Professor Rankine, one
of the first scientific authorities of our time, author of many standard

page_text: works, and of European reputation, gives, at p. 550 of his work, "The
Steam Engine and other Prime Movers, an investigation of "The
efficiency of propellers," and at p. 552 observes that "the efficiency of
the propeller (a pair of plate iron feathering paddles was found to be
78." I have however shown by my formula E at paragraph 45 that
if the loss of primary velocity be only 40 per cent. the efficiency of
the best feathering paddles at the same relative velocities as Professor
Rankine takes (V= 1.25v) is only E= = 333. Now this is not
half the efficiency which Professor Rankine inakes the paddle wheel and
screw, and from actual experiments, as he says clsewhere, on the Admiral
paddle and an ironclad screw vessel.
6 V
77. Here then are two more fundamental errors of the first men of
science of our time contained in paragraph 76, 1st., that the efficiency of
the paddle wheel and screw varies from 39 to 65 per cent., and 2nd, that
it reaches 78 per cent. Now there is one efficiency of vessels and
another of propellers, both distinct from each other. The efficiency of
vessels varies because their forms vary, which explains the phenomena
pointed out by Mr. Scott Russell in paragraph 70, also why all the usual
methods to find a standard of resistance for vessels have failed and must
always fail. We cannot get from one form of vessel a standard of
resistance for other forms. But we can from a plane because the form
never varies. Hence the efficiency of the paddle wheel and screw never
varies at the same relative velocities, much more does it vary from 39
to 78 per cent., as laid down by the schools. For it is one of the funda-
mental laws of the Creator that the same bodies acting upon one another
under the same circumstances must always produce the same effects.
All inductive generalization relies upon this universal law, and so alone
new discoveries are made.
78. It was only relying on this law that I discovered as I have said by
induction from experiments of 1842 and formularized in August 1869,
an unerring standard of the resistance of vessels. I knew, for instance,
that what a fluid would do against a plane of the same area a planc
would do against a fluid, and that what one plane would do against water
or air another similar plane would. So with screws of similar form, and
so with reaction propulsion of different kinds. We have then only to
find the modulus of each to know the modulus of all of the same type

page_text: applied in the same way. This law then brings us back to the principle
laid down in paragragh 75, that the resistance of vessels cannot be more
than the modulus of the propeller that overcomes it.
'
79. We have then in the formulæ in paragraphs 43, 45, and 53 the
modulus of the paddle wheel, screw, and reaction propulsion, at all
relative velocities, pursuant to exact and unchanging laws. Whatever
therefore be the form, size, length, breadth, depth, or speed of vessel, in
canal, river, or ocean, if that vessel be propelled by paddle wheel or
screw, and if the loss of primary velocity be 50 per cent., its resistance
111
R3VP
3 x 27.3 x 143514.9
24.82
=47,356 lbs.

page_text: 83. Now I need not say how important it is for the improvement of
naval architecture, as a guide to the form of least resistance and as the
first step to aerial navigation, to know that a body of a given size and
form, like the Banshee, going through the water at a speed of 18.5 miles
an hour encounters a resistance of only 8468 lbs. instead of 22569 3 lbs.,
and that a still larger body meets with a resistance of only 47356 instead
of 143514 9. But the importance of such a discovery is increased by
the fact that much cheaper engines and of less weight, with boilers and
water of less weight and stowage, and much less fuel also with less
weight and stowage, will propel the same vessel at the same speed:
Now less weight is less immersion, and less immersion is less resistance,
and less resistance is less power to overcome it. Therefore to save in
one thing is to save in all.
84. I venture to think then that, as life is so uncertain, and there is
only myself who can explain these things and refute the lawless dogmas
of the schools, it was incumbent on me to do so here, and so preserve for
all time the present state of the science of propulsion and resistance of
vessels. Moreover the application of my present Invention, the area of
reaction, the size of the propellers, the horse power, loss and efficiency,
are all based on my discovery of the resistance of vessels. And this, as
I have said, is in opposition to the Newtonian doctrine of the equality
of action and reaction which makes R=P, maintained as I have shown
by all naval architects, engincers, and mathematicians, and taught in
schools and colleges "as one of the first physical principles of all
mechanical science," to use the words of the Reverend Professor in.
paragraph. 30, who so teaches his classes and wrongly.
S5. We have now an unerring method of finding the resistance of
every variety of steamer, from the lumbering tug, canal boat, river and
swift continental passenger vessel to the huge leviathans of iron which
stem the ocean. We can therefore select the naval architect who is the
most consummate master of his art, and for the first time make a true.
scientific comparison of the efficiency of different vessels, and so reach the
solid of least resistance. As this is of importance for the improvement.
of the naval architecture of the first naval power in the world I will take
the Banshee, built in 1848 by Mr. Oliver Lang, and compare with her
the Vixen and Viper, built by the Admiralty in 1866. The following.
data are from official returns :-

page_text: the Vixen and Viper were built only 4 years ago by the Admiralty, with
all the acquired experience of naval science since the Banshee.
89. I have now shown in my formula for E, paragraphs 43, 45, and
53, that the efficiency. of the paddle wheel, screw, and reaction pro-
pulsion is an invariable quantity (at the same relative velocities) to
whatever vessel applied. And necessarily so, because pursuant to the
fixed laws of an unvarying form known and formularised. I have also
shown that the efficiency of vessels greatly varies with their ever varying
form, in consequence of which all the experiments for a hundred years
and now being continued by the Admiralty have failed to find the true
resistance of vessels. But now we have in my discovery of the means of
finding their true resistance a standard to go by, and can therefore, by
comparing the efficiency of different vessels in the manner pointed out,
solve at last the insoluble problem of the solid of least resistance, which,
as shown in paragraph 70, even Newton failed to do. Naval architects
too will at last get the merit due to their superior science.
90. This is deemed impossible, but nothing is impossible except what
is opposed to the laws of nature. These however are so favourable as to
make aërial navigation certain. There is, for instance, such harmony
and therefore simplicity in the laws of the Creator that we cannot
navigate one fluid on any other principles, by any other application, or
by any other laws and formulæ, than those by which we navigate
another fluid. The air is a fluid, like water, but lighter, that is all. It
follows that the laws of dynamics and resistance which apply to one
fluid must necessarily apply to the other also. And if the laws, the
application of them, therefore by precisely the same machinery and in
the same way. To try then to turn man into a flying animal who was
made a walking and a sitting one, and to confine the navigation of the
air, that boundless gift to all mankind, merely to those strong enough-to
move winged machinery and to make human life dependent on its.
mechanism never breaking; all this is not the aim of the philosopher
but the wild dream of the poet, or empiric, unacquainted with the
elementary principles of physics and the analogies and harmony of
science. It is not therefore, as Bacon says in his Valerius Terminus
(here misleading men) that "there is no proceeding in Invention of
knowledge but by similitude." We must no more imitate the birds

page_text: resistance of vessels does not depend upon the immersed surface, as
maintained by the same learned man in paragraphs 13 and 17, and also
more strongly in the following extract from his Report of 1866 against
my discovery:-"It is well established," he says at fol. 20, "by direct
experiment (and not merely by inference from indicator diagrams) that
the resistances of similarly 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.”
92. It would be hard to say how many millions of tons of coal and of
money the first fundamental error has wasted since the introduction of
steam navigation. For had it been known 50 years ago that the
Newtonian doctrine is not practically true in propulsion, and that the
paddle wheel and screw begin in consequence with a loss of 50 per cent.
of power and of fuel, reaction propulsion had long ago been discovered.
But there are more false facts in the world than false theories. I have
shown in para. 20 how experiments even by eminent mathematicians and
engineers conducted without any laws as a guide have led to the most
crroneous conclusions, and how seriously they have affected me by
delaying my system of reaction propulsion for (1866-1847) nearly twenty
years. Now these "direct experiments" of the Professor are equally
erroneous. The laws of fluid resistance are directly the reverse to those-
he lays down. All my own analysis of the resistance of vessels show
that instead of its encreasing with the immersed surface, as the Regius
Professor asserts, it decreases. And this anomalous physical law is
confirmed by the following extract from p. XXIV. of Beaufoy's great
work, "Nautical and Hydraulic Experiments." 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" (therefore of its immersed
surface) "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."
93. Now however important it may be for the improvement of naval
architecture to establish this remarkable physical law, it is still more
important for aërial navigation, because the surface of friction surrounded
by air is so great. I have shown, for instance, in the Specification of

page_text: my Patent of the 12th of December 1866, No. 3262, p. 39 and 42, that
for the conveyance of 200 persons and 56 lbs. of luggage each the aerial
machine (a double cone with intermediate cylinder) must be 1303 feet
long and 195.5 feet in diameter, and that the surface of friction is
506,025 square feet. There are no data to show within what limits the
resistance to motion decreases as the length of surface increases. I
cannot therefore frame a formula to find the minimum resistance, but
I can to find the maximum resistance beyond which it cannot be, and
this is all we want at present to convince men of science of the certainty
of aerial navigation.
3 VP
=
3 x 35 87 x 40616
28 696
94. I have taken the Victoria and Albert, Her Majesty's paddle wheel
_yacht,-as-my-guide-because-I-have-exact data, which are these:-
Length, 300 feet; breadth, 40 feet; draught, 14 feet; immersed surface,
12000 square feet; indicated power, 2980; speed, 17 knots. Now her
resistance by my impulse formula =
=15231 lbs.
For aerial resistance take the density of a cubic foot of air (at 46°)
at 07859 lbs., which is (078159=) 816-64 times lighter than sea water.
From these data we get a co-efficient of resistance of 1 square foot of
surface at one mile an hour of a form not inferior to that of Her
Majesty's yacht. This is c= 0000040S, but for convenience and certainty
we will encrease it to 000005.
64
95. We thus get the formula of resistance for acrial navigation
R=000005 S. m²,
where S is the surface in square feet surrounded by air, and m miles
an hour. This co-efficient is about one-half of what I made it in my
Specification of 1866, No. 3262, p. 38, because I then took the Banshee
as my guide, and in deference to a distinguished mathematician assumed
her resistance to be nearly twice what I made it. But I will be true to
my own laws and my own formulæ because I know them to be right.
96. Now whilst the surface of my vast aerial machine is not
506025
12000
2=43 times more than that of the Victoria and Albert, the density
of resistance is 07859-816.64 times less. Thus it is that we get a
resistance almost incredibly small compared with general belief. For
instance, the maximum resistance of such a machine as I have described,
with its 200 passengers and luggage at 30 miles an hour, would be
only = 000005 S m²=·000005 × 506025 × 30=2277-1125 lbs. This
however is based on the most unfavourable assumption, which is on

page_text: the length of the Victoria and Albert, which is only 300 feet long.
How much less the resistance would be for a length of 1303 feet, the
length of the Aerial, I cannot say; but less it would be pursuant to the
law of physics now established, which not merely makes the resistance
inversely as the length of surface, but "exceedingly diminishes it," as
shown in paragraph 92.
97. If then we can overcome by steam navigation the resistance of
two fluids, wind and water, we can assuredly overcome the resistance of
only one, and that 816 times lighter than the other, especially as this is
only 2277 lbs., even if the addition of a cylinder in the middle of my
2 cones should not diminish its resistance. Since, however, a law of
physics is invariable, I believe that the resistance of a well shaped machine
will be "exceedingly diminished," as well in one fluid as in another. But
even if it be not, steam navigation can no more compete with aërial
navigation than sailing vessels can with steam. For the resistance of
the Victoria and Albert at 17 knots =17x1 1507=19.56 miles an
hour was 15231 lbs. Hence at the same speed as the Aerial 30 miles
an hour, and speed is now the chief aim of science, her resistance would
be about 15231 ×
= 15231 x 2.3523 = 35829 lbs.
19.562 15231 x 382.59
Taking = 1.5 the effective h. p. required would be
1100
30'
900
3682.9
1.5
R (V+v)
1100
-
35829 × (60+44) =3582 9. To this add 25 per cent. for my losses, and to
the sum 20 per cent. for engine friction, making together =2388.6,
and the indicated power required would be about (2388 6+3582.9=)
5971 5 horses, even by my system, and nearly twice as much by the
paddle wheel or screw:
98. For aerial navigation at 30 miles an hour =30×1 467-44 feet
a second, and a convenient area of propeller and of reaction, the mean
velocity of the floats must be about 3 v=3×44=132 feet per second.
The force of reaction would then be about 2 F (V-º)=28.4 lbs. per square
816.64
R
-
2277
F 28-4
=80.2 square
foot. Consequently the area required would be
feet, which divided into four propellers will be convenient enough.
2277 x (132+44)
R(V+v). =
1100
1100
= 364 3. To
The effective horse power would be
this add 25 per cent. for the losses of my system, and to the sum
864-3
1.5
=242.86.
20 per cent. for engine friction; these together would be
Hence the gross indicated power required would be about (242.86+
364.3) 607.16, instead of 597.1.5, the power required to drive the.
D

page_text: fluids is evidently the first step to aerial navigation, because it shows us
how small such resistance.is. We have certainty at last; we know what
we have to overcome in navigating the air, and we know that we can
overcome it. Were however the Newtonian doctrine practically true in
paddle wheel and screw propulsion, that R=P, the resistance of our
aerial machine would be nearly three times as great and the engines
nearly three times as powerful to overcome it. Now much more weight
of engines, boilers, water, and propellers might be so difficult to sustain
in air as to make all the difference between the practicability of aerial
navigation or not. A small resistance then, however good for steam
navigation, is. better for navigating the still and solemn regions of the
air, showing how one discovery leads to another, because all nature is
connected together by that great scientific Being whose master mind is
over all his works, the divine qualities of which we read in their per-
fection, harmony, and fitness for man's use. On this I must needs speak,
because only by so believing and relying have I made my discoveries, and
continued a large expenditure of time and money in opposition to the
authority and experiments of the Regius Professor, the Reverend Pro-
fessor, the Royal Naval School Professor, and eminent engineer referred
to in paragraph 12 to 17, 20, 24 to 33, 33 to 36, 38 to 40, and 76 to
79. So inferior therefore are mathematics, practice, and experiments to
inductive philosophy.
100. I cannot then help pointing out here the adaptation of the means
of God to the ends of man. All has been given that he wants for his
use and advancement to some far higher sphere on earth, and to which he
will assuredly reach, for the improvements of the past repeat themselves
in the present and indicate the future. Why man cannot discover all.

page_text: at once forms no part of my philosophy to inquire into; for who can
inquire into the mind of God! It may be, as the wise of old tells us in
his proverbial philosophy, "It is the glory of God to conceal a thing,
but the honor of kings is to search out a matter." As I have said, all
we want we have, and intellect to discover more when we want it. Beasts
and birds, and fish, and flowers, and fruits whose seed is in itself, each
after his kind (the philosophy of nature beyond mere man to think of
thousands of years ago in the primal ignorance of the world), exhaustless
supplies of water, wood, coal, iron, tin, copper, and a thousand other
things put by in the great storehouse of the earth by His economical
hand who wastes nothing that he has made; laid out countless ages ago,
ready for man's sustenance and use when he should be created and
want them.
101. But besides these materials for his comfort man has not been left
without a guide in all his spiritual and physical requirements, even for
his convenience. It was, for instance, necessary for him to know two
things-1st. The force of all bodies in motion, of the wind and water
that turn his windmills and water wheels, of the steam and paddle wheel
and screw that propel him against winds and waves, and even of his
instruments of destruction, the cannon ball, the greatest force on earth.
2nd. It was also necessary for man to know the resistance of bodies
passing through a fluid, in order to discover the form of least resistance,
that he might navigate the ocean and the air with all possible speed, at
the least cost, and with the least incumbrance of weight. Now nothing
but divine laws could give man the knowledge of these two things, the
force of motion and resistance, both of which are found only in the laws
of gravitation, silent, unseen, intangible.
102. Finding some years ago that I could be sure of nothing in
propulsion without first being sure of the force of motion, and finding
so many authorities differing, I had to discover what it is. The con-
tradictory theories of Newton, Leibnitz, and others will be found in
the Specification of my Patent of the 29th of May 1866, No. 1497,
p. 15, line 30, to p. 17. And my proof that the force of motion = 20,
172
29
g
w, deduced from
and that the working force is equal to half. that =
the laws of gravitation, will be found at p. 20 to p. 25 of such Specification.
Now this proof is the foundation of all my formulæ in paragraph 42,
43, 45, and 53, for the force of motion of the paddle wheel and screw
D 2

page_text: impulse and water reaction, also of the resistance of fluids.
Because as
I have said no resistance can be greater than the power that overcomes
it, nor can the power be greater than the laws which govern it.
103. Only then in the laws of the Creator, those of gravitation which
tells us of the force of motion, and in the laws of impulse which tell us
how such force is disposed of, can we find any standard for the resistance
of vessels in water or in air. For I have shown in para. 59 to 70 how
man left to his own devices without the light of divine laws to guide
him can do nothing; how for a hundred years and more he has tried
experiment after experiment and wasted tens of thousands of pounds on
the resistance of fluids, and how the Admiralty is still doing so, certain
of nothing but failure like all their predecessors, because-they-will-not-
go to the laws of their Great Teacher for instruction and guidance.
Having now explained and established the laws which govern the
action of the paddle wheel and screw, of the resistance of vessels, and
reaction propulsion, and given the formulæ for all, I will describe the
machinery of my system.of propulsion for water and air.
•
.
DESCRIPTION OF MACHINERY. MECHANICAL EQUIVALENTS. APPLICA-
TION ΤΟ THE IRONCLAD HERCULES. SAVING BY MY SYSTEM.
HYDRO-PROPULSION UNIVERSALLY CONDEMNED. MORE EXPERI-
MENTAL ERRORS. SUPERIORITY OF INDUCTION. ABSTRACT OF
DISCOVERIES FROM 1842 TO 1870. DIFFERENCE BETWEEN MY
PRESENT AND FORMER INVENTIONS OF REACTION PROPULSION.
CLAIMS.
104. Sheet I., Figs. 1, 2, 3, 4, and 5 are transverse sections of various
forms of reaction propellers worked by cams; Fig. 6 is a longitudinal
section of the propeller shewn in Fig. 5. The last two I call the box
cam.
Sheet 2, Figs. 1 and 2 are mechanical equivalents for the cam and
rollers, being transverse sections of two forms of reaction propellers
worked by eccentrics; Fig. 3, in the same Sheet 2, is a longitudinal
section of the propeller shewn in Fig. 1; Figs. 4 and 5, in the same
Sheet, are enlarged views of one of the eccentrics of the reaction
propeller shewn in Fig. 2; Fig. 6 is a sectional plan of the reaction
propeller tube on the line A, B.

page_text: Sheet 3, Figs. 1, 2, and 3 are enlarged views of one of the floats of
the reaction propeller shewn in Figs. 5 and 6, Sheet I.; Fig. 4, in the
same Sheet 3, is a transverse section of reaction propeller similar to
that shewn in Fig. 5, Sheet I., with a modified arrangement of canr and
float; Fig. 5 is a longitudinal section of the same; Figs. 6 and 7 are
enlarged views of portions of one of the floats of reaction propeller
shown in Figs. 4 and 5; Figs. 8 and 9 are enlarged views of dis-
connecting apparatus between the engine and reaction propeller shewn
in Fig. 6, Sheet. 2.
Sheet 4, Fig. 1 is another mechanical equivalent for the cam and
rollers, being a transverse section of reaction propeller with floats
worked by a stationary crank; Fig. 2 is a longitudinal section of the
same; Fig. 3 is a longitudinal section of reaction propeller applied as
a fire pump, with horizontal engines attached for working the same;
Fig. 4 is a plan of fire pump showing the propeller pump in section;
Fig. 5 shows two forms of cams and rollers for drawing in the floats at
different angles.
Sheet 5 shows reaction propeller and engine attached applied to a
ship of the size of the Hercules, with a method of turning the propeller
into a fire and bilge pump.
Sheet 6, Figs. 1 and 2 show respectively a plan and transverse section
of ship, seen in Sheet 5.
Sheet 7 is another mechanical equivalent for the cam and rollers-
Here the floats are fixed to the boss like an ordinary paddle wheel, yet do
no internal work in the case, being, in this respect, on the same principle
as most of the other reaction propellers, except Fig. I., Sheet I., which
does internal work in the case.
105. This Fig. (I., Sheet I.) is given to show it to show the unsound
principle of all my former reaction propellers now superseded by my
present improvements. For internal useless work is there done by the
floats on the water between the drum and case by every float in turn,
and also on both sides from S to j, thereby wasting power and con-
sequently fuel. But as a description in other respects will do for some
of the other propellers I will explain it. Fig. I. shows a transverse
section of a reaction propeller with ten floats a, a, a, a, &c. worked by
an internal cam 6 by which the rollers draw the floats within the drum.
To make the periphery of the drum c rigid (the sides being cut away to
admit the passage of the rollers) a strong wrought-iron ring is attached

page_text: to the angle iron d, and together with the latter is fastened to the
slotted arm e.. The arms radiate from a solid boss f which is keyed to
the shaft g, and the arms are further tied together and stiffened by a
eircular plate . The space i between the plate and the angle iron
besides allowing for the passage of the rollers also allows what water
may leak into the drum to flow out into the enclosing case, and thence
into the bilge of the vessel.
Fig. 2 of the same Sheet I. represents a transverse section of a re-
action propeller with sixteen floats a, a, a, a, &c. worked by an external
cam b. This cam is so arranged that the rollers draw the floats within
the periphery c of the drum so as to do no internal work, as is done in
Fig. 1. The periphery of the drum is made perfectly rigid in the same
manner as that described for the drum in Fig. 1. The wrought-iron
ring, and angle iron d are made sufficiently wide to cover the cam, thus
preventing the water contained in it from escaping into the drum. The
circular plate forming the side of the drum can be made very large
in this propeller, thus adding to the strength of the drum, while there
is still sufficient passage at i for the water that may leak into the drum
to escape.
Fig. 3 of the same Sheet I. shows a transverse section of a reaction
propeller with ten floats a, a, a, &c. and rollers worked by an external
cam b in the reaction tube k. In this propeller also the bottom of the
ship is brought close up to the point j, where the floats are drawn within
the drum, thus preventing the churning of the water, which is internal
work. This drum has in addition to the external cam 6 a small internal
cam in which rollers run attached to the inner edge of the floats.
The object of this small cam is to prevent the friction of the centrifugal
force of the floats from being thrown upon the external cam b. The
latter cam is made sufficiently wide to prevent the rollers touching it
while they are within the drum, also whilst the floats are propelling
the water through the reaction tube, for then the centrifugal force is
communicated to the internal cam 7. But the external cam band rollers
draw, the floats in and out of the drum. The small internal cam / is
made at these parts sufficiently wide to prevent the interior rollers
touching it while the outer rollers are being actuated by the external
cam. Thus when the rollers of the internal cam arrive at its enlarged
part the rollers of the external cam arrive at its narrowed part. Hence
the floats are always under the control of either the external or internal

page_text: cam.. The drum is made perfectly rigid by a strong ring secured as in
the former case to the angle iron d; also by the ring of plate iron m,
which takes the strain. carried in the former. described reaction propeller
by the circular wrought-iron plate h..
Fig. 4 of the same Sheet I. is a transverse section of a reaction pro-
peller with ten floats and rollers, a, a, a, a, &c. worked by an internal
cam b. This propeller also has the bottom of the ship brought up to
the point j, where the floats are drawn within the drum to prevent
internal work in churning the water. In this propeller the friction due
to the centrifugal force of the floats is to some extent prevent being
communicated to the cams by the floats being linked together by a pair
of rods n. By this means the centrifugal force of one float acts in
opposition to the centrifugal force of the one connected to it, the con-
necting rods being made sufficiently strong to take the strain. It
follows that the-friction pressure of the rollers on the cams is only that
due to the resultant centrifugal force due to the propelling float
describing a larger circle. Holes are made in the shaft for the con-
necting rods to pass through, the shaft being enlarged to prevent the
holes weakening it. Rigidity is given to the drum by a strong wrought-
iron ring attached to the angle-iron d; and also by the circular plate h.
Figs. 5 and 6 of the same Slicet I..arc cnlarged. transverse and longi-
tudinal sections of the aft reaction propellers shewn in Sheets 5 and 6.
This propeller has ten floats, cach opposite one being connected by
rods n, n, &c., as described in Fig. 4. This improvement I call the box
cam, because the floats a, a, a, &c. are worked by a cam b enclosed in a
box or case, by the false partition o. Thus communication between the
cam and the sea is prevented, which permits the rollers to be greased.
Water leakage from the drum into this chamber p-is drawn off by the
engine pump through the pipe q. The rigidity of the drum is obtained
by making the ring r, which is fastened. to. the angle iron d, of a very
strong section. In this arrangement of cam a modified form in the
framework of the float is necessary, which is shewn in Sheet 3, and will
be hereafter described...
106. Sheet 2, Figs. 1 and 3 are transverse and longitudinal sections of
a reaction propeller, the floats of which are worked by eccentrics, as
mechanical equivalents for the cams and rollers.. The action of the
eccentric is such that the floats are always moving radially, cither
towards or from the centre of the drum. For the sake of reducing

page_text: t
the diameter of the eccentrics the floats are not drawn within the
periphery of the drum until they reach the point j. Here then is a
partial churning of the water during the passage of the float from the
points to the point j, which, being internal work, is one objection to
this form of mechanical equivalent. These floats are actuated by the
eccentric straps t working side by side on a fixed eccentric w which is
bolted to the outer case v. Each float has a separate eccentric strap on
each side of the drum, the arms of which straps are jointed to pro-
jecting studs x from the sides of the floats a. Thus as the drum
revolves, carrying with it the floats and their eccentric straps, the
necessary motion is given by the fixed eccentric. From the action of
the eccentric the floats, after_entering-the-reaction-tube, still continue
to be slightly pushed out, until they reach the mid or vertical position in
the tube, and, after passing this position, the contrary action takes place.
This deviation of the floats from the true concentric passage is slight,
and is further reduced by gradually contracting the passage from the
centre to the ends, making it follow an intermediate position between
the true concentric passage and the path which the ends of the floats
describe. The passage is thus made to take an intermediate course, so
as to diminish the small difference between the areas of the tube at the
centre and the ends; also to reduce the small loss occasioned by the floats
not accurately fitting the bottom of the tube.
Fig. 2 of the same Sheet 2 is a transverse section of propeller with
floats worked by an eccentric, in the manner described for the propeller
in Figs. 1 and 3. In this propeller the eccentric is increased in diameter,
that the floats may be drawn quicker into the drum; that the bottom of
the ship may be gradually sloped up to the point j, where the floats are
drawn in, to prevent churning of the water. The number of floats is
increased to fifteen, to reduce to a minimum the contraction of the
passage consequent on the unequal projection of the float.
Figs. 4 and 5 of the same Sheet 2 are enlarged views of one of the
eccentric straps of the propeller shown in Fig. 2. The eccentric strap
is recessed on its inner edge y to a sufficient depth to admit the in-
troduction of small steel friction rollers z. These, as the eccentric strap
is carried round by the floats, revolve on the chilled surface of the
eccentric u to reduce friction. Fig. 6 is a sectional plan of reaction
tube on the line A, B, showing the divergency given to the side of the
tubes, similar divergencies being given to all, the reaction tubes..

page_text: 107. Sheet 3, Figs. 1, 2, and 3 represent (on an enlarged scale) a
front view, end view, and sectional plan of two opposite connected floats
for the reaction propeller shewn in the box cam, Sheet I., Figs. 5 and 6.
Each float consists of a strong steel frame a', the lower part, which acts
upon the water) being filled in with wood b'. This woodwork is incased
in sheet steel c¹ 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 shown, 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. This cam will be
clearly seen on referring to the box cam, Fig. 5 and 6, Sheet I.
Figs. 4 and 5 of the same Sheet 3 are respectively a transverse and
longitudinal section of a reaction propeller with opposite floats con-
nected, and worked by an external cam. In this propeller the bottom
of the ship is gradually inclined up to the point j, where the floats are
drawn into the drum to prevent them churning the water. The upper
portion of the cam e', which descends some distance below the periphery
of the drum (consequent upon having the floats connected), is com-
pletely covered by the angle iron d and annular plate f¹ to prevent
water in the cam escaping into the drum; this plate also increases the
strength of 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 frec
passage 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 e¹,
so that the lower part of the cam at ¹ (between the ends of the tube and
the point where the bottom of the ship is brought up) is increased in
width to prevent the rollers touching it. The radial movement is com-
municated through the connecting rods n, n, to the opposite float.
Fig. 6 and 7 of the same Sheet 3 are enlarged views of a portion of
one of the floats of the reaction propeller shown in Fig. 4 and 5, the
construction of which is similar to that shown in Fig. 1, 2, and 3. In
this case the cam roller is pinned direct on the end of the float without
the intervention of an arm, as the cam h¹ in which it revolves is not
enclosed.
Fio S and 9 of the same Sheet 3 are enlarged views of the dis-

page_text: in Sheet I., Fig. 6. In Sheet 3, ¹ is a strong disc forged in one pieco
with the engine shaft. Another disc j¹ securely keyed on the pro-
peller shaft containing a pin k¹, which fits into a corresponding, slot in
the disc ¹. 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.
108. Sheet 4, Figs. 1 and 2 arc a transverse and longitudinal section
of a reaction propeller with fifteen floats a, a, &c. worked by a stationary
crank m², as another mechanical equivalent for the cams and rollers..
Each float has a separate link n' on each side of the drum; one end of
which is jointed to a projecting stud a from the end of the float; the
other end is jointed to the pin o¹ of the stationary crank m². This
crank is forged in one piece with the shaft p', which passes through the
trunnions carrying the drum. On these trunnions are keyed the
engine cranks, these latter being at right angles to assist each other
over the dead points. The bearings s³ on the case are provided with
stuffing boxes to prevent water leaking into the ship. Since from the
action of the links n' all communication between the propeller shaft and
the trunnions q¹ is cut off, the whole strain is conveyed through the sides
and periphery of the false ends of the drum, which are strengthened for
this purpose.
The trunnion has a disc t' and radial arms u¹ forged in the solid with
which are securely fastened to the false ends or sides of the. drum.
These trunnions q' as they revolve would necessarily cause the crank
shaft p¹ to revolve also; but, as it is desired to keep this stationary, a.
train of wheelwork is employed in the following manner:-A wheel
is securely keyed to the shaft p¹, and gearing with this is an inter-
mediate wheel w' running loose on a stud fixed in the crank. On the
crank pin of this crank is a third wheel x¹ gearing into the inter-
mediate wheel ¹. This wheel x is fastened to a small connecting
rody to prevent it revolving. Hence as the crank r¹ itself revolves
the intermediate wheel w¹ is caused to revolve round the wheel v¹ fixet
to the small crank shaft p¹, thus preventing any rotatory movement of
the wheel, that being securely locked by the loose and fixed wheels w¹
and x¹. The smaller ends of the connecting rods y¹ are jointed to a
crank of equal throw with the engine crank, these cranks being con-

page_text: nected by a shaft carried by the bearings ', which are bolted to the
framework of the case. Thus the connecting rod y¹ is always horizontal,
preventing any rotatory movement of the wheel x¹, as this would give
a corresponding movement to the wheel v', which would be detrimental
to the proper working of the floats.
Fig. 5 of the same Sheet 4 is a reaction propeller 16 feet from the top
of the case to the projection of floats, which is 1.5 feet, and there are
16 floats. Two forms of cams are given. The outer or dotted cam
shows that if the projection of float be kept at 1.5 feet, as in the other
propellers, and if they enter the drum at the same distance from the
outside of the vessel as the others, which is 3.75 feet, the cam becomes
more favorable for the rollers to act in, in proportion to the encrease of
the diameter and to the number of floats of the propeller. This cam
and the side or bottom of the vessel are shown in dotted lines, and
would be better still if a box cam, as shown in Sheet I., Figs. 5 and 6.
The much sharper cam in Sheet 4, Figure 5, is given to show that
with the same propeller as that just described the floats may be made
to enter the drum almost as vertically as a feathering paddle wheel of
the same diameter (16 feet, and can also can be drawn into the drum at
a distance of only 2.5 feet from the outside of the vessel.
Fig. 3 of the same Sheet 4 is a longitudinal section of a propeller
constructed to be used as a fire pump with horizontal engines attached
for driving it, and Fig. 4 is a plan of the same with the propeller pump
in section. The floats a, a, a, &c. are eight in number, and are con-
nected together by the rods n, and worked by an external cam b. The
water is drawn in at the bottom of the tube a², and is discharged in a
continuous stream through the nozzle b. Toothed wheels cs are keyed
upon the propeller shaft gearing into pinions d³, which are keyed
to the crank shaft of the two engines f², ft. The gearing is
shewn in this case to suit the size and speed of the propeller, but
with a smaller propeller worked at a higher speed the gearing can
be dispensed with. The propeller case y³ inclosing the drum is
securely bolted to the bed plate h³ upon which the horizontal engines
are fixed, thus making the whole strong and compact.
109. Sheets 5 and 6 show my reaction propellers with engines attached
for a ship of the size of the ironclad Hercules of 8500 indicated power
with her present screw.
Three of my propellers are shown working

page_text: vertically through the bottom of the ship into 3 reaction tubes. These
are so arranged as to be drawn into the ship with the propellers for
repair on sailing. The forward propeller is placed across the keel, and
worked by a pair of engines, one on each side, while the after ones
are placed sufficiently far apart to prevent their reaction water entering
into the tube of the forward propeller should that be objectionable, also
to admit of the introduction of a larger pair of engines between the two
propellers for working them. They are driven by the engine shaft &
passing through stuffing boxes in the water-tight cases, in which work
the drum and floats. The disconnecting apparatus seen within the case
has been already shewn and described in Sheet 3, Figs. 8 and 9.
When-required to use sails only or to be repaired the propellers can
be drawn into the cases by the screws k², which pass through stuffing
boxes in the case, and are worked by worms & gearing into the toothed
wheels m², which latter are keyed to the screw spindles k³. The
opening in the bottom of the ship is then covered by slides m² worked
by the screw spindles n², upon which worm wheels are keyed gearing
into the worms o². The latter are keyed upon the shaft p³, and are
worked by the hand wheels q² through the toothed wheels 22. The
forward reaction propeller is fitted with valves, by which it can be
converted into a fire or bilge pump. The passages s³, s², 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
of about the same sectional area as the reaction tube. . The valves t², t,
are for closing cither end of the reaction tube when the propeller is
used as a fire or bilge pump, and are actuated by screw spindles u², u²,
working through water-tight stuffing boxes 62, 62, on the tubes s², s³...
On these screw spindles are keyed the worm wheels w², w³, gearing
into worms and worked by a handle at the side of the tube. The sca
valves x, x, in the bottom of the ship are for opening communication
between the passages 82, 82, and the reaction tube when the
valves, t, are down, and are worked by the hand fly wheels y
and gearing, which actuate the valve spindles. The bilge valves
a³, a³, are for opening a communication between the bilge and the
lower valve chamber of the passages, &². These valves are actuated
in the same manner as the valves (2, 1. The fire valves 6³, 63, open and
close communication between the passages &², 8, and the valve chamber
below. When it is desired to use the propeller as a fire pump, should

page_text: the ship be going ahead, the two after valves, ², are opened, the
after valve is lowered till it meets the reaction tube, and the fire
valve is opened; the propeller will then force water through the
passage 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 two forward valves x', x³, in the bottom of the ship are 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 ahead when either the fire or bilge pump is required,
the opposite set of valves must be used. Grease cups are fixed on
the propeller case with jointed tubes to adapt them to the raising and
lowering of the propellers and their reaction tubes, and communicate
with the rollers and cams.
AS REGARDS THE SEVERAL CAMS.-Each side of the small cam. I,
Sheet I., Fig. 3, the upper part of the cam b, b, Figs. 4 and 5 of the same
Sheet, and the lower part of the cam 7', Sheet 3, Fig. 4, are all blind
cams. That is, they are made at those parts so large that the rollers
may not touch, because the floats are not worked at those parts.
AS REGARDS THE ANGLES OF THE CAMS AT WHICH THE ROLLERS WORK
THE FLOATS.—The limiting angle of resistance of brass upon iron is 9°6′,
and the coefficient of friction 16, "the surfaces still retaining a little
unctuousness." -Moseley's Engineering and Architecture, 1855, p. 157.
Now even the worst part of the angle of my box cam (Sheet I., Figs. 5
and 6) is as favourable as about 50°, and this, not so bad as the dead
point of a single crank, is passed over in a very small fraction of a
second, and with the full momentum of the heavy propeller.
110. Sheet 7 represents a transverse and longitudinal section of
another variety of mechanical equivalent for the saving cams and rollers.
The floats a, 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 principale 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 at f³ in 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 overcome the statical pressure of
the external water at their back; and 2nd, to enable the floats to have the

page_text: 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 iron clad 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 are the fundamental
principles of my system of propulsion.
111. When the water enters at f³, Sheet 7, 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, 23, fixed to the floats revolve with them to
prevent water friction at the sides of the case. A few words are
necessary on this form of centrifugal float, or it will be condemned by
all men of science acquainted with the subject.
112. In the Great Exhibition of 1851 experiments were made by
Canon, then Professor, Moseley, and General Morin, on centrifugal
pumps, when they found that the modulus of a pump with radial floats
like mine was as low as 24. But with arms curved backwards in the
direction of a tangent to the circumference, as shown in Sheet 7, Fig. 3,
the modulus was as high as 68. The small modulus of the radial floats
was because they discharged the water with the vis viva of the centri-
fugal velocity of the floats remaining in it. The power expended in
producing this vis viva was therefore thrown away. The much higher
modulus of the curved floats was because the velocity of the water
due to their backward curve was about equal to its velocity due to
their forward motion. Thus the water was discharged nearly in a state
of rest, consequently no power was consumed in the cistern of discharge,
but only in the suction pipe, case, and float channels; this came to
about (100-68=) 32 per cent.
113. But to deliver the water in a state of rest in reaction propulsion
would require an unwieldy impracticable size of propeller and reaction
tube. We must therefore discharge the water with some vis viva in it,
which I call residuary velocity V-v. I have therefore shown a Drawing
of the radial float, because too it is simpler and will I think back better
than the curved float. This however looks so well on paper that I have
given a sketch of it in Sheet 7, Fig. 3, where the same letters refer to
the same things as in Fig. I. in the same Sheet. To reduce the water
friction in the case sides are fixed to the floats in both these mechanical
equivalents and revolve with them, as shown in Sheet 7, Figs. 2.

page_text: The leakage between these sides and case can be drawn out, as shown
at 3, and before explained in Sheet I., Figs. 5 and 6, at q.
114. The reaction propeller shown in Sheet 7, Fig. I., is wholly in
the ship, horizontally at the sides or vertically at the bottom. The
curve of the reaction tube only projects and not the floats as in the other
applications. The side or bottom of the ship is therefore gradually
sloped from the entrance and exit of the water down to the ship's side
again, about 15 in 15 feet or so. The depth of the float is here 1.5 feet,
as in the other Drawings.
115. All my reaction tubes are on the same principle, except Figs. 1
and 2 in Sheet I. Still I prefer the bottom of the tube being made a
little longer, as shown in Sheet 7, though the water friction be somewhat
encreased, because there an angle of about 48° drawn from the circum-
ference of the descending float intersects the bottom of the tube, and so
makes sure that none of the feed water can be driven past the bottom
of the tube into the open, which would react on the descending float,
and cause proportionate retardation and loss of power.
APPLICATION TO A STEAMER OF THE SIZE OF THE IRONCLAD HERCULES.
-
116. Her maximum speed was 14.7 knots an hour =14.7×1.688=
24.82 feet a second = v. By the laws of impulse explained in para. 41,
and embodied in my formulæ at para. 43, the less the residuary velocity
V (improperly called slip) the greater the loss, and consequently the
less the resistance of the paddle wheel and screw. But engineers
believing the contrary encumber their vessels with huge screws to
make the slip as small as possible, the loss and inconvenience of which
is shown in para. 51 and 52. Now some screws it is said revolve at less
speed than that of the vessel called negative slip; but the average mean
velocity of screws is not, I am told, 10 per cent. more than the speed of
the vessel. We will then make the mean velocity of the screw of the
Hercules 10 per cent. more. Hence we must add to v
which will make V=2.482+24 82-27 3 feet a second.
24.82 × 10
100
=2.482,
117. At these relative velocities her indicated power was 8500 h. p.;
allow 20 per cent. for engine friction =
6500 × 20
100
=1700 h. p.; then by
my formulæ of 1857, given in para. 42, the effective pressure on her
screw was
D.
1100 (-) 1100 x (8500-1700)
10-14.01.

page_text: 4452
-
system would be 8500–4452 × 100
=90.9 per cent. This, however, is not the
whole gain.
For engines, boilers, water, and fuel of only 4452 h. p.
would be so much lighter than for 8500, as would to some extent reduce
the immersion, and so diminish the resistance and power to overcome it.
The diameter of propellers being 12.75 feet, and their mean velocity
37 23 feet a second, the number of revolutions of engines would be
=55 8 a minute.
12
19.7 V 19 1 x 37 23
12.75
The effective h. p. required for propulsion being 2671·4 (paragraph 120)
that required for each propeller would be 1-890.47 h. p.
2671.4
3
120 16 x 100
890.47
Conse-
quently the losses of my system are
13.5, say 14 per cent.
This is exclusive of loss of vis viva of feed water at entrance of the tube,
if any there be. I have reduced it to a minimum by making the
entrance divergent. This form I find as follows:-Let d the diameter
of reaction tube, and c the co-efficient =1.274, then the diameter of
divergence will be about c d =1.274d; and the distance from the true
area of reaction tube to the divergence will be about 1. This approxi-
mation I apply also to find the divergence of my steam jet equivalent
E

page_text: (VII.) Leakage. I prefer loss from leakage to friction, because
friction in a rotary machine not only entails loss of power but unequal
wear, and because also leakage allows for errors of adjustment. I take
the interstice of leakage at 2 of an inch, and make the leakage of each
propeller including the stop water (which is that part which almost
touches the drum as it revolves) 40 feet long.
-
1
=20×2×40=10= of a square foot. Or thus
1666 square feet. The area of reaction of each
.
square feet. Therefore loss of leakage is
.1'666 × 100
17.083
.. area of leakage
05.05 x 40 x 1224
144 =144=
propeller tube 17.083
=97, say 1 per cent.
124. I do not explain the symbols of the different formulæ, because
I do not go by them. I give them to show that no labour has been
spared to arrive at some results of the losses of my system, and that in
allowing so much as 25 per cent., as in paragraph 120, I have made them
(25-14 ) 11 per cent. more than they come to by the formulæ ; and
even these, applied as they are to my excessive data, give too large
results. The loss of 14 per cent. is calculated on my box cam, Sheet I.,
Figs. 5 and 6. Though the mechanical equivalent propeller in Sheet 7
has no cams and rollers, and no floats moved in and out of a drum, the
friction of the mass of water round so large a circumference and at the
sides of the case would, I think, exceed the losses of the box cam, were
it not for the sides to the floats, which move with them. The dotted
lines in Fig. 3, in Sheet 7, show a piece of iron on each side to prevent
the water entering between the fixed and revolving sides.
125. As practical men object to cams and rollers I must point out
the admirable working of my reaction propeller, which will as much

page_text: 500 lbs., making no more than 500 lbs. for each cam and roller for even
so great an ironclad as the Hercules. And, lastly, the whole effective
engine power is concentrated in the reaction tube of about eight feet
long. There it must all enter, and except friction all come out again, in
the velocity imparted to the ship and residuary velocity in the waste
water, for there is nowhere else that the power can go to.
HYDRO-PROPULSION UNIVERSALLY CONDEMNED.
more
127. Instead of giving many extracts I must content myself by
merely referring to different scientific journals in which it is declared to
be hopeless. This is in-the-Engineer-and-Engineering from April 1866
to the 4th January 1867. An eminent scientific writer in the former
says at p. 15, third column,-"In marine propulsion there really
appears to be little or no room for great improvement, or
accurately no present possibility of effecting it. The Waterwitch
represents the most abnormal effort which has been made to introduce a
new system of propulsion, and the result has been a total failure." Nor
"En-
can I resist one more extract from another scientific journal
gineering, of the 5th July 1867, to put on record the present state of
the science of propulsion. Only three years ago the Editor says, at p. 7,―
"In what direction are we to look for further improvement ?
"
As for the water jets we have specific evidence to go upon, and this
evidence is against them. First, by whatever means the jets are
produced they must of necessity have a considerable 'slip,' and while
this is now known to be four or five fold greater than that of the screw
it is hardly likely, even with the most refined improvements, that this
But
slip can ever be brought down to less than that of the screw.
beyond this view of the case the jets involve a special loss of effect
peculiar to themselves. In the case of ordinary paddle or screw engines
the whole effective pressure of the steam, less the friction of the
machinery, is transferred to the propeller. In the case of the water jets
a very much smaller proportion of the effective pressure is utilised.
128. Such is the scientific darkness of our day, even in this our day of
light, which we may call for distinction "the age of science," for I have
shown in para. 41, and in my formulæ in paragraph 45 and 53, and by
the example in paragraph 51 and 52, that this extract is just the reverse
of the laws of physics which govern the action of paddle wheel and
screw impulse, and jet or hydro-propulsion reaction.

page_text: 129. And yet one more extract, because from a scientific writer of
European reputation. It is from p. 161 of the Engineer of the 23rd of
August 1867. The distinguished professor says "We need scarcely
remind our readers that the merits of the Waterwitch system of water
propulsion have formed matter for keen discussion in mathematical and
engineering circles. The questions raised appear abstrusc, principally
because we lack minute and accurate experimental data on which to base
our calculations. Water propulsion, though old as an Invention, is very
novel in that it has only recently received much attention from men able
to grapple with its theory or undergone anything like a fair practical
test of its capabilities. At this moment very little has been decided as
to the actual value of the scheme, and it is perfectly certain that the
best arrangements for applying it in practice have yet to be designed.
That it can ever prove under any circumstances as cconomical as the
paddle or screw is to the last degree doubtful."
130. How interesting and instructive all this will be by and by I need
scarcely say, marking as it does the present state of physical science in
one of its grandest departments, steam navigation. For not only do I
compete in economy with the paddle wheel and screw, but have shown
in paragraph 121 a saving of 47.6 per cent. on the last labors of
Hercules, the chief constructor of the navy.
131. Hydro-propulsion is moreover condemned most by those who
have considered it most, as will be seen by the following extracts from
the report of a first-class professor of mathematics, dated the 9th of May
1865, entitled "Impracticability of Hydro-propulsion regarded as an
Economical Scheme." After several sheets of mathematical analysis,
which would be true enough if his premises were, the professor observes,
"This shows that excepting for a comparatively small excess of U over v,
i.e., for a small slip, hydro-propulsion is an extravagant waste of power.
But for small slip the nozzles must be large for a given resistance, and
on this account alone hydro-propulsion, if it is to be made an economical
as paddles, will be found to be impracticable, because the requisite pipes,
pumps, and appliances would be too large, would, in fact, take up no
small portion of the vessel below the water line. And what then would
become of the space for freight, stowage, cabins, &c., &c."
132. Some more pages of figures follow, and then this-" Hence,
under the most favorable circumstances, U being taken as low as
33.93 for the Banshee, hydro-propulsion from its very nature involves

page_text: greater loss than paddles with the same slip." The Professor then
concludes his paper with the following list of terrifying difficulties:-
"It is for those who advocate the scheme of hydro-propulsion to devise
a convenient arrangement for such large pipes, pumps, &c. If they
place them inside the vessel they must seriously curtail the room for
stowage, cabins, &c. If outside, they will incur all the disadvantages
of paddles, somewhat smaller indeed, but working in closed boxes,
partly if not wholly under the water line, thereby involving a greatly
encreased resistance to motion through the water, besides additional
encumbrances that paddles are free from, whilst in either case the
unavoidable loss of power as compared with the paddle system still
remains as an insuperable objection."
133. Such is the mature opinion of a first class mathematician of this
new science, "founded," as the Professor told the public in one of his
scientific papers in August 1867, “founded on a careful study of the
subject for the last seventeen years." A discoverer then need be of
the stern stuff of a Columbus, for the first European authorities tell me
my discovery is "impossible," and the first authority on hydro-pro-
pulsion that "the machinery of pumps and pipes would be a serious
encumbrance, and the unavoidable loss of power an insuperable
objection." The facts, however, are the other way, as will be seen by
comparing my system of hydro-propulsion with the paddle wheel
Banshee, the vessel which the Professor has himself chosen for my
refutation.

page_text: 154. As to the machinery of large pipes, pumps, and appliances
being a serious encumbrance," there are none such, for they are much
smaller than her present paddle wheels. Then as regards economy,
allowing 25 per cent. for my losses and 20 per cent. for engine friction,
the indicated power required to propel the Banshee by my system of
hydro-propulsion will be about 521 5+347-7-869-2, instead of 1566,
her indicated power at the same speed. So that instead of the
unavoidable loss of power as an insuperable objection," according
to the imaginative professor, there would be a saving of
44.5 per cent.
**
1566-869.2 × 100
1566
Here the saving is less than in the screw Hercules, which was
47.6 per cent., shown in paragraph 121, because the loss of residuary
velocity in the Hercules was less than in the paddle wheel Banshee. We
see therefore how in practice the anomalous laws of impulse assert them-
selves by making the efficiency of the Hercules less as the loss of
residuary velocity is less, and the efficiency of the Banshee more as the
loss of residuary velocity is more, a strange contradiction. But these
results confirm the laws of impulse and the formulæ which embody
them in paragraph 45, formulæ discovered by the analysis of thought,
and not from experiments, which teach nothing.
135. I have now shown the novelty as well of my discovery of the
inferiority of paddle wheel and screw impulse to reaction as of my.
Invention to apply such discovery. This is done by the denial of both
by the first scientific mathematicians of the day, those who have most
studied both. I think, however, that I should give another instance of
the denial of the principle of reaction, because based on direct experi-
ments, and because of a Patent application so nearly like mine as to
deceive many. I refer to a Patent of Captain C. R. Simpson, R.N., for
"Improvements in Apparatus for Propelling Vessels," dated the 20th
July 1865, No. 1890. This, however, is (1865-1847=) 18 years after
my first Patent for hydro-propulsion in the name of James Pedder, who
died in 1849 or 50.
136. I first heard of Captain Simpson's Patent in the Engineer of the
12th July 1867, containing a paper read by the gallant captain before
the Royal United Service Institution. He refers to his "experiments
to ascertain which of the two modes of application would be preferable,
the floats acting in the external water or in a tube. These experiments

page_text: he says, "practically shewed the greatly superior resistance offered to
the action of the floats by the external water," (which is impulse, and
the system he has patented) "to that offered by water in a tube," which
is reaction and my system. Captain Simpson gives his reasons for
prefering the external water to a tube, which are necessarily erroneous,
or he would have made my discovery of the loss of primary velocity.
He then observes, "And hence I argue that the size of the propellers
and their floats being equal the propeller acting on the external water
must give a far higher speed with a given power than the propeller
acting in the through passage." The contrary, however, is the fact, as
shewn by my formulæ in paragraph 43, 45, and 53. The captain further
says, "All the internal propellers of equal size with external ones must
fail in the primary object of speed." I have however shown in para-
graph 133 that the contrary is the fact, that my internal propellers of
only =) of the area of the Banshee's external ones will drive her at
the same speed of 18.5 miles an hour, with only 869.2 indicated power,
and consequently much faster with her present indicated power of 1566.
716
49-2
-
137. Remarkable indeed are the errors of experiments without the
light of law to guide and teach. Captain Simpson further observes,
"The best propeller will be the one that combines within itself the good
qualities of both internal and external systems, and this is the principle
upon which his propeller is constructed." But the truth of science
constrains me to say that he combines the worst qualities of both. For
the loss of the paddle wheel and screw is in the principle impulse, not in
the machinery, whilst the loss of hydro-propulsion is in the machinery
and not in the principle reaction. Now Captain Simpson combines the
cams, the rollers, the moveable floats, the drums, the sides, all the
machinery of reaction with the principle of impulse. Thus combining
the losses of both he combines the worst qualities of both.
138. No one can explain all this but myself because no one knows
anything about it. One engineering firm indeed asserted that Captain
Simpson's application and mine were identical until I explained the
difference. This shows how necessary it is to do so here to save disputes
and time hereafter. I showed them, for instance, by his claims and
Drawings, that his system was nothing more than a method of putting
the paddle wheel underneath the vessel instead of at the side. For the
principle of "external propellers" is the same, impulse, put it where
you will. Moreover, it cannot be turned into a force pump by a mero

page_text: Boyman's Improvements in Propelling Vessels and Aërial Machines.
end valve like mine, shown in Sheets 5 and 6. A mere cam none can
claim any more than any other old mechanical motion. Now Captain
Simpson's cam is not combined with an internal propeller and reaction
tube but with an external propeller, which he says he prefers, and which
alone he claims. Applications follow principles to carry them out.
Thus our applications are as different as our principles.
139. THE POWER AND CERTAINTY OF INDUCTION.
We hear a great deal about "actual experiments refuting theory," and
"again, an ounce of practice is worth a ton of theory." I have morcover
been deluged with experiments with dynamometers in the Rattler
and Highflyer at moorings and running, sent me by an eminent
engineering firm to refute my discovery, and other experiments sent by
another firm for the same purpose. Then there are the remarkable
experiments in paragraph 20; of the Regius Professor in para. 17 and 91;
of the reverend Professor's Plover and Royal Alfred in paragraph 26; and
now Captain Simpson's on the very principle I have discovered and he
has rejected. Let me then say a word in favor of theory based upon law
to show its high superiority over mere experiments based upon nothing.
For I am sick of experiments, lawless and worthless, like all those I have
referred to.
140. No statesman, no general, no historian, no poet, no mathematician
has ever conferred half the blessings on the human race as theory,
inductive generalization, the highest and noblest faculty of the mind.
The world advances only by new discoveries, and these have been made
only by induction. This great power has progressively raised man from
the unclothed and incapable savage to the highest civilization and given
him almost the power of a god, since he has long had dominion over the
winds and waves and will now have over the illimitable regions of the
air. I venture moreover to think that the history of practical science
does not contain a more remarkable instance of the power and certainty
For the one solitary fact of
of inductive philosophy than the present.
my own is the experiment made twenty-eight years ago with the minute
jet of steam referred to in paragraph I., and shown in Sheet 5, Fig. 2.
Nor was this made in reference to propulsion.
141. All the other facts used for inductive generalization from 1842
until now are not mine; mine only is the reasoning which brings them
together and shows how every part is so contrived by the Supreme Being

page_text: 142. For by the power of induction only has been refuted_all_the
mathematics, formulæ, reports, experiments, practice, and arguments of
some of the most renowned scientific mathematicians and engineers of
our time. By it an empirical science has been reduced to an exact one,
the paddle wheel and screw, long relegated from the pale of hydraulic
machines, have been at last classified, have been shown to be merc
uninclosed pumps, to belong to the family of the undershot waterwheel
and windmill, to be governed by the same laws of impulse, and subject
therefore to the same losses. This then is one more instance of the unity
and simplicity of God's laws. By induction again a discovery has been
made which will save many millions of tons of coals every year, man's
most precious substance, of more value than gold or silver or precious
stones, many millions of money, and the wasted labors of thousands of
human beings. It will revolutionize the steam navigation of the world,
open the still untrodden heights of air to man's use and enjoyment, and
be the standard for all time of the resistance of bodies in both elements.
Such then is the power and certainty of inductive logic, reducing the
huge mass of uncertainty and confusion to exact laws embodied in
simple formulæ, according to which all bodies were made to move from
the beginning, and by which they are still governed and controlled.
143. But this power of induction teachès something better than the
order of machines. It is, that all our reasoning would be nothing worth
were it not for the sure foundations on which it rests, and on which
inductive philosophy builds her imperishable superstructures, the har-
mony, simplicity, and certainty of the laws of God. This world is not
then a fortuitous concourse of atoms, thrown together in disorder and
contention to find their different places as they could without arrange-
ment and without laws to keep them in their place. For all nature

page_text: 1859. Discovery that latent heat is latent force, whereby much
treasure may be saved every year in coal, now wasted in latent heat.
See Specification of 1860, No. 1155, pp. 8, 12, 23, 24, 27, 36.
1860. Intermittent reaction propulsion patented in this year, a failure
because of an unknown law to the discovery of which I was led in 1861.
This I called the "Time of Repose of Bodies, or difference in effect
between a long and short impulse with the same amount of force."
Only by this law can a gun be fired a second time, another instance that
Newton's law of the equality of action and reaction is not universally
true in practice.

page_text: V2
W
•
2
1861. Discovery of the proof of the laws of force and motion. I
approach this subject with great diffidence and reluctance for I know
what hard things will be said. Nevertheless no one can alter the facts,
which are briefly these:-The greatest mathematical controversy on
record was in 1780 and 1790, the age of mathematicians, for there have
been none before or after like unto them. It was between Newton and
his followers, and Leibnitz and his, on the force of bodies in motion.
Newton made it equal to the weight and velocity of the body, WV,
Leibnitz equal to the weight and square of the velocity, IV V³.—
Hutton's Philosophical and Mathematical Dictionary, article "Force."
Newton's great authority carried the day, and so far as I can find from
every work and mathematician I have consulted the force of motion has
been handed down as equal W V. · Without knowing what it is, hydro-
propulsion is mere guess work, as in Ruthven's and all other systems,
for the area of reaction cannot otherwise be found. I was therefore
obliged to find out for myself what the force of motion is, which I did
in this year (1861), as shown in my Specification of 1866, No. 1497,
pp. 20 to 24. Neither Newton nor Leibnitz is right. The striking force
of motion is lbs., and its working force through one foot is half
that W. Since, however, mathematicians like these are not likely to
make a mistake it may be that their meaning has been mistaken. But
I know no other facts than those given here, and in Newton's own
"On the Force of Bodies in Motion in the Philosophical
paper,
Transactions for April and May, 1722, No. 391, p. 57. See also Life of
Newton by Sir David Brewster, vol. II., p. 304. Moreover had Herschel
not believed that the force of motion was the weight and simple velocity
of the body, as the illustrious Newton made it, Herschel never would
have written that nothing can be more simple than the highest of all
natural laws, those of force and motion. They are on the contrary the
most complicated and singular of all known laws. Suppose, for instance,
a cannon ball of 100 lbs. is moving with a velocity of 1000 feet a
second, it will not strike in the simple manner supposed, with a force
equal to its weight and velocity only, which is the reasonable sup-
TV 32-2
position, 100 x 1000 = 100,000 lbs., but with a force equal
x 100 = 3,105,500 lbs. Thus, in elastic fluids like steam, the law which
For only 13 349.
governs the force of motion produces grand results.
grains of steam, at a pressure of only 120 lbs. a. a., will strike with a
g
9
V'
1000*

page_text: force of Ds., or more than five hundredweight of iron falling one
foot. If therefore a boiler burst at a pressure of 240 lbs., each square
foot would be hurled through the air with a force of about 46 tons;
accounting for the first time on pure dynamic principles the laws of
force and motion for the destructive effects of boiler explosions. I may
therefore observe that nothing gave me more trouble to find out than
these laws, which were first published in my Specification of 1866,
pp. 20 to 25.
1866. April 13th. In the Engineer of this date appeared the com-
petitive trials between the Nautilus, hydraulic, and Volunteer, paddle
wheel, referred to_in_paragraph-5.-
-
1866. April 29th. Discovery that Newton's third law of motion, the
equality of action and reaction, is not practically true in plane and fluid
action, and consequent discovery of the loss of primary velocity in the
paddle wheel and screw. Verification of my prediction of 1851. See
paragraph 6 to 11, 20, and 30 to 33.
1866. May 29th. First Patent in my own name for reaction
propulsion, No. 1497. I had however taken out a Patent for hydro-
propulsion in the name of the late James Pedder as carly as the 6th of
November 1847, No. 11,946, who died two years afterwards.
1866. December 12th. The discovery of the laws and principles of
Aërial Navigation, and first Patent for it of this date, No. 3262, being the
second Patent in my own name for reaction propulsion. The realization
of reaction in April of this year as the only true principle of propulsion,
led by a single step to its twin application, aërial navigation, the formulæ
and other principles required coming as it were in natural sequence as
though links in a chain that only wanted beginning.
1867. August 1st. Third Patent for reaction propulsion, For Im-
provements in Propelling Vessels and Aërial Conveyances by Reaction,
No. 2223.
1868. June 9th. Fourth Patent for reaction propulsion, Improve-
ments in Aerial Navigation, No. 1881.
1869. August 13th. Discovery by induction from the undershot
water wheel that the laws of impulse govern the action of the paddle
wheel and screw, thus accounting at last for the residual phenomenon

page_text: which so long puzzled me. See paragraph 40; also formulæ for impulse,
paragraph 43 and 45.
1870. March 3rd. Fifth Patent for reaction propulsion. Improvements
in the machinery, principally the saving cam and direct reaction tube
comprised in the present Specification.
146. We are told "not to despise the day of small things, and here
is its illustration. The petty experiment in Sheet 5, Fig. 2, will show
how small a thing was the first link of this long chain, the end of which
has taken the best of my life and my hardest thought and labor to find.
But the mind like all nature, the body or the oak, has its own laws of
growth and development, and very slow they are. To force them is to
weaken them.
AND TUBE.
147. There is a material difference between my present hydro and aero
propeller and reaction tube and those described in the Specifications of
my four Patents referred to in the Provisional Specification. This
difference consists in 7 things.
1. In discovering that the floats of my former reaction propellers did
internal and therefore useless work, as described in the Provisional
Specification, and in designing a cam to prevent it, which I call the
saving cam to distinguish it from all others. This cam is shown in
Sheet I., Figs. 2, 3, 4, 5, and 6; and the cam before patented is shown
in Fig. I. of the same Sheet, where the floats are doing internal work
from S to j at the sides.
148. 2. In discovering a loss of vis viva and consequently of power
in my former reaction tube by the propelling water being driven into
the reaction tube at different velocities of the floats mixing in the tube,
and then being discharged for propelling at one common velocity or
nearly so. In my former reaction tube, Sheet I., Fig. I., some of the
faster particles of water in it must be retarded by the slower moving
mass therc, and so lose a proportionate propelling power. It follows
therefore, as I have said in my Provisional Specification, that "the sooner
the reaction water is got rid of the better." To do this and thereby save
the loss of vis viva I designed a tube, which I call the direct reaction
tube, because the floats discharge the reaction water direct into the open

page_text: for propelling, and not indirectly into it as in my former propellers.
The direct reaction tube has these further advantages:-It can be made
straighter and shorter, which will save further loss from curvature and
friction, as will be seen by comparing all the direct reaction tubes in
Sheet I., Figures 3, 4, 5, and 6, with the indirect reaction tubes in Figs. I.
and 2 of the same Sheet. Fig. I. has two defects, a cam which does
internal work and an indirect reaction tube, both contained in my former
Patents.
149. My present improvements, the saving cam and direct reaction
tube, are the fundamental and essential principles which distinguish my
present hydro and aero propeller and reaction tube from my former ones
and from all other reaction propellers known to me. But there are
other improvements not referred to in my present Provisional Speci-
fication, but which arose out of my saving cam, one of which constitutes
the following third improvement.
150.-3. In connecting the floats of my present propeller to neutralize
to some extent their centrifugal force the object is to reduce the cen-
trifugal pressure of the floats on the rollers and cams, and their
consequent friction, especially in drawing the floats into the drum.
4. In enlarging the case and drum beyond what the projection of
floats would otherwise require to enable them to be connected. It was
this enlargement of the case (which I could not think of four years ago).
which then prevented me carrying out my idea of feathering the floats
of my former hydro-propeller, referred to in my Provisional Specification
of the 29th of May 1866, No. 1497, p. 14, line 25. It will be seen, for
instance, in Sheet I., Fig. 2, annexed hereto that the floats cannot there
be connected because the case is not large enough for them to work in
connected. Nor can the two mechanical equivalents for the saving cam,
shown in Sheets 2 and 4 (Figs. 1 and 2) be used without enlarging the
case for the floats to work in. The drum need not be enlarged but the
case must.
5. In the angle iron to prevent cam leakage into the drum, in what
I call the outer cam, shown in Sheet I., Figs. 2 and 3, and Sheet 3,
Figs. 4 and 5, I came to the angle iron in this way :-In working out
the saving cam internally, that is, near the drum, as seen in Sheet I.,
Fig. 4, I found the angle at which the rollers would have to pull in the
floats so sharp for such inner or drum cam that I designed the outer
cam shewn in Sheet I., Figs. 2, 3, and 5, and Sheet 3, Figs. 4 and 5.

page_text: But the rush of water through these cams on each side into the drum
would cause so much leakage and loss that I found it necessary to cover
the cams inside the case to keep the water in the cams. I then found
that the water at the top of the cam (which I call the blind cam) would
be driven into a smaller space, and therefore I enlarged the blind cams
at those parts to prevent obstruction to the rollers.
151. The first and second improvements, namely, the saving cam
for reaction and direct reaction tube, I believe to be new, because I can
no where find any mention of their principle. Nor have I anywhere
seen the angle iron or enlarged passage in the blind cam in the fifth
improvement. Nor any means of drawing off the water, or lubricating
the cams and rollers in the 6th and 7th improvements. All these there-
fore I believe to be new. But as regards connecting the floats, and
enlarging the case to enable them to be connected, in the 3rd and 4th
improvements, these are not new in themselves, but are new for the
purpose for which they are designed, namely, to save centrifugal pressure
on the rollers and cams and their consequent friction. I found, for
instance, that to prevent the floats doing internal work, the cams must
be set at a much sharper angle than in my former reaction propellers,
which does internal work, as will be seen in Sheet I., Fig. I.
152. Such sharper angle of cam to do no internal work, as shown in
Figs. 2, 3, 4, and 5, of Sheet I., and in Fig. 4 of Sheet 3, necessarily
encreased the roller friction due to the weight of the float. This
I reduced from about 1200 lbs. to about 500 lbs., for each of the
three propellers of an ironclad of the size of the Hercules, by making
the float of the shape shewn in Sheet 3, Figs. 1, 2, and 7, and using
wood covered with steel. Then, finding I could reduce the weight no
F

page_text: these improvements-connection of floats and enlarged case for them to
work in are the natural evolution or development of the principle of
the saving.cam to enable it to be carried out more efficiently, that is,
to do no internal work. Now this cam, of which the connection of
floats is a part, I have explained in my Provisional Specification.
153. But after I had designed these two improvements-connection
of floats and enlarged case-I found that I had 23 years ago myself
patented them, though for different purposes, in the names of James
Pedder, for "Certain Improvements in Steam Engines and Propelling,"
dated the 6th of November 1847, No. 11,946. We did not then think
of centrifugal force, and did not therefore mention it in such Specifi-
cation. The object of connecting the floats at that time was merely to
enable one float to push the other out for propelling, as will be seen in
the Drawing annexed to Pedder's Specification, Sheet 4, Fig. 18.
154. As some evidence of the novelty of the whole seven improve-
ments I may observe, that neither the engineers who made Pedder's
propeller in 1848, nor those connected with it, discovered its defects,
though I tried it in the Albion in 1849, at no little expence. It failed
because of those defects, and which I believe I have alone discovered, and
remedied in the above improvements. For instance, it loses power by
doing internal work; 2, by discharging the propelling water at different
velocities into the same tube, and then into the open; 3, by the
curvature of the tube being unnecessarily great; and, 4, by having no
rollers and proper cams to work the floats. But besides these defects
of the propeller, the system of hydro-propulsion there patented is applied
'contrary to the laws, principles, and formulæ which I have since dis-
covered, in which I pointed out in the Specification of my Patent,
dated the 29th May 1866, No. 1497, p. 41, line 23, to p. 44, line 3.
DIFFERENCE BETWEEN THE PROPELLER AND TUBE.
155. I can nowhere find any distinction made between the reaction
tube and the propeller that moves the water in it; that is, between
machines of motion and machines of principle. But they are distinct,
and require therefore the knowledge of distinct laws to invent.
In

page_text: machines of motion, for instance, we are not left to only one way
of doing the same thing. I have therefore shown 12 propellers, more
or less different, 3 of which are mechanical equivalents for my
saving cam. 1, the eccentric equivalent in Sheet 2; 2, the crank
equivalent in Sheet 4 (Figs. 1 and 2); and 3, the radial and curved
arm equivalent in Sheet 7. All these are for the same purpose as the
saving cam, namely, to do no internal work in the case of the propeller,
as is done in my former one, from S toj at each side, shown in Sheet I.,
Fig. I. Another equivalent occurred to me, a reciprocating three-throw
pump, connected with my reaction tube. But I do not think it
necessary to annex the Drawing, having given other equivalents. These
equivalents verify the remark of the philosophic D'Alembert, "Let us
first find out a thing, and there will be no lack of persons to put it into
shape." The principle discovered, the application follows as a matter of
course.
156. But there is no equivalent for my reaction tube. That is a
machine of principle, like the separate condenser of Watt. It therefore
stands alone, and admits of no improvement. For, like other organisms,
it embodies fundamental principles of nature, which will work properly
only through properly developed organisms. The same soul and intellect
are doubtless given to the savage and idiot as to a Bacon or Newton;
but wanting the properly developed organism to work in, the vis viva of
intelligence and immortality cannot there display their full powers. So
with the vis viva of material power. I used it in 1847 for reaction
propulsion, in the Albion steamer of 35 h. p., but the reaction tube, or
organism in which the power acted was, like that of the savage or cretin,
so imperfectly developed that the power could not work effectively,
The same melancholy exhibition is still seen in Her Majesty's ironclad
Waterwitch, which is the idiot of reaction propulsion, for it cannot
develop two-thirds of the power that passes through it, its organism is
so vile; worse even than mine was in 1847. For whilst its indicated
power is 800, it wastes more than 600. This I pointed out to the Lords
of the Admiralty would be the case, in my paper of 1865, more than a
year before she was tried, but to no purpose. There is my paper, and
there is she; the prediction of science from the knowledge of laws and
its verification. Thus God gives the power, man makes or mars its
efficiency in the construction of his organisms, both of his race and his
invention. He makes the cretin and the Waterwitch.
P 2

page_text: 157. The progressive steps which my organism or reaction tube
was developed will perhaps be best understood by showing that any
departure from its form will affect its normal power. I. If we take away
the divergent entrance a contracted vein in the entering water would be
produced, the water would be drawn into the tube at a greater velocity
than that moving in its larger area, the quicker water would be retarded,
internal work would be done, and a corresponding loss of power would
be entailed. We require then a divergent entrance to prevent all this,
also a divergence at the end of the reaction tube, for the same proper
entrance of the water when the engines and floats are reversed for
backing. 2. If we turn the mouth of the tube up or down, or sideways,
the floats could not get the velocity of the vessel in their favor; there-
fore could not get the full statical pressure of the external water upon
them to overcome such pressure on their other side. But this is
necessary in order to leave the reaction water free to overcome the
resistance of the vessel. Thus any other position of the mouth of the
reaction tube would entail considerable loss of power. 3. If we encrease
the length of the tube we encrease water friction and let the different
velocities of the reaction water mix, and so lose power by both. 4. If
we shorten the tube the descending float would drive some of the water
past the bottom of the tube, which would react on the float, retard it,
and lose power.
5. If we have fewer floats we must encrease the
curvature of the tube, and so lose power, because water in motion
cannot be changed without losing power. And, 6. If we have more
floats we have more friction of the reaction water thrown out from
between them.
'
158. Such then are the principles which a reaction tube must embody,
the non-discovery of which has rendered abortive the efforts of water
propulsion for two centuries, and caused such waste of public money in
the Waterwitch. Thus my reaction tube does for reaction propulsion
on water and in the air what the separate condenser did for the steam
engine; it makes that do which never did before.
There are many
varieties of the steam engine but only one separate condenser. So there
are many varieties of propellers, but only one reaction tube; that is,
only one that will make reaction propulsion an economical and con-
venient application of power. I have shown for instance, twelve varieties
of propellers to set the water in motion, but only one reaction tube to do

page_text: it in.
may.
.
We see therefore that a principle cannot be varied, the auxiliaries
Now as there is some principle to guide us in all things, I venture to
think that in judging of the priority of discoveries and inventions, we
can only go by general principles, and that the philosophy of discovery
and invention teaches us that he who first proves is the first discoverer,
and he who first successfully applies is the first inventor. There seems
no other sure method of determining priority; for he who first does
these things does something no one has done before. Until then it is a
crude idea, the mere foetus of a thought, not a new birth; its laws and
mode of action are unknown; it has no practical existence; it can do
nothing; it is useless to mankind.
159. Approaches more or less near have been made to all great
discoveries, accumulating in some cases for centuries, but these were
not the discoveries themselves; they were but the prognostications, the
gradually increasing shadow of coming events; like faith, the sub-
stance of things hoped for, the evidence of things unseen. For in
discovery and invention the great law of continuity is as observable as in
nature. But the only submerged propeller that I know of, similar
but very inferior to the one patented by me in 1866 and 1867, and
shown in Sheet I., Fig. I., hereto annexed, is the one patented by me in
1847 in the name of the said James Pedder. This propeller has no
saving cam, but it is combined with a reaction tube. This, however,
runs the whole length of the vessel, and has a contraction at both ends.
Such a reaction tube I do not claim. The only other submerged pro-
peller similar to mine now patented with which I am acquainted is
that referred to in Captains Simpson's Patent, in paragraph 135; but that
propeller is not combined with a reaction tube at all, much more with
such a one as mine, shown in Sheet I., and in all the other Sheets. It is
combined with an external propeller, a mere paddle wheel, with moveable
floats working in sides without a bottom; in fact an undershot water
wheel in curbs, governed therefore by the same laws of impulse, and
subject to the same great loss, as before explained. Such a combination
I do not claim. I cannot then find the combination of a saving cam
with a reaction tube of any description except mine. I can now better
explain what my claims are, and I may be permitted to say, as an
amateur, and city man from my youth, and still; that I am not indebted
to book or person, for one suggestion, principle, or law. Theory and

page_text: 160.
CLAIMS.
1st. I claim the saving cam referred to in para. 149, described in para-
graph 147, and shown in all the Drawings, (except in Fig. I., Sheet I.,
which is my old cam,) and the mechanical equivalents before described
and shown in the Drawings, in combination with a reaction tube for
propulsion_of_less_length_than_that_of_the_vessel, _having_an_entrance_
and exit on a line with it.
2. I claim such saving cam, and equivalents before referred to, in
combination with the particular reaction tubes shown in the Drawings.
3. I claim the direct reaction tube referred to in para. 149, described
in paragraph 148, and shown in the Drawings, (except in Figs. 1 and 2
in Sheet I., as the embodiment of the fundamental principles of my
system of reaction propulsion which I have discovered, and explained
in paragraph 157. I claim also such reaction tube in combination with
the saving cam, and its mechanical equivalents, before described and
shown in the Drawings, except in Fig. 1, Sheet I., which is my
former cam.
4. I claim the method of disconnecting the propeller shaft (Sheet 3,
Figs. 8 and 9), and drawing the propeller and reaction tube into the
vessel, and then of preventing the water entering, as herein-before
described and shewn in Sheets 5 and 6. Having before patented this
arrangement in 1867, No. 2223, Sheets 1 and 2, I do not claim it per se,
but in combination with my saving cam and direct reaction tube.
5. I claim also in combination with either and both of these last-
mentioned improvements my new method of using my hydro-propeller
as a fire and bilge pump, in the manner before described and shewn in
the Drawings, Sheet 5, Fig. I.
6. I claim, lastly, the combination, substantially as before described,
of the different parts, areas, and proportions of my new hydro and aero
propeller for reaction propulsion on water and in the air. Also the
manner in which the whole is arranged for propelling, as shown in
Sheets 5, 6, and 7. I do not of course confine myself to the exact
details, for these may be varied by mechanical equivalents.

page_text: 161. Parts of the machinery herein-before described for propelling by
reaction are applicable to forcing fluids for other purposes.
This is
necessarily true, because the principles of propulsion are the principles
of hydraulic machines. For propulsion is pumping, the object being
simply to pump astern all the water set in motion with the least
expenditure of power. Therefore a good propeller a good pump, a bad
propeller a bad pump. Thus the paddle wheel and screw would make
such bad pumps that they are never used for pumping. Now a bad
pump cannot make a good propeller, and as I have shown the paddle
wheel and screw are not good propellers. Having then discovered the
true principles of forcing fluids for propulsion and embodied them in
machinery in harmony with such principles, these must necessarily
apply to other purposes than to steam and aerial navigation. Therefore
I claim the saving cam rollers and floats before described for forcing
fluids, that is, for ships and other pumps, fire and water pressure engines,
also for forcing air into furnaces. I have shown in Sheet 4, Figs. 3 and
1, the arrangement of my saving cam and floats as a fire engine so as to
do no internal work. And if one of the divergent ends of the reaction
tube in Sheet I., Fig. 2., were removed to discharge the water, that would
show one of my hydraulic machines. The floats, which need not be so
many, are there unconnected, because they would move so much slower
than for propelling, and therefore the centrifugal force friction would not
be so material. I need scarcely say that the box cam in Sheet I.,
Figs. 5 & 6, is applicable to hydraulic, pumping, fire, and blowing
162. In my Provisional Specification I referred to three reaction tubes,
two I have described, the direct reaction tube in Sheet I., Figs. 3, 4, 5,
and 6, and the indirect reaction tube in Figs. 1 and 2 of the same Sheet;
as regards the third I do not describe that because when I came to work
it out I found it to be inferior.
163. I have said in my Provisional Specification that "the floats must
be made hollow for the easy entrance and exit of the water which will be
drawn into the slits of the drum as the floats are sent out and drawn in."
And they must be so made when the drum is made as there indicated,

page_text: that is, when the slits or partitions for the floats are continued from one
end of the drum to the other and from the circumference of the drum to
its boss, and the drum is covered in on both sides, for then the water
would have to be forced out of the slits by the floats unless it could
escape through them, and this would entail loss of power and great
pressure and friction on the cams. But when the drum is not so made,
but made as herein described and shewn in the Drawings annexed
hereto, the floats must not be made hollow, or the drum would get full
of water.
164. The improvements in paragraph 150 and mechanical equivalents
-are-not-referred-to-in-my-Provisional-Specification_because_I_had_not
then calculated the centrifugal force friction of the floats; but as I have
said they were the natural sequence or development of my saving cam,
which is comprised in my Provisional Specification; I think therefore
that a fundamental principle, which the saving cam is, being comprised
in the Provisional Specification carries with it its own natural develop-
ment from the same mind, even as the acorn does the oak. For the
principle is the root of the growth, since without the principle there
can be no development, and the principle, as I have said, is embodied
in my Provisional Specification.
165. The tube in Sheet I., Figs. I. and 2, is an indirect reaction tube,
into which the water is first driven at different velocities and mixed
before reacting. It is therefore opposed to the principles on which I
designed the direct reaction tube, which, as I have said, is to prevent
the mixing of different velocitics of water. It is then necessary to
explain why I now claim the saving cam in connection with an indirect
reaction tube.
My discovery in 1866 was that in consequence of the paddle wheel
and screw not being enclosed about half of the water they set in motion
escaped past them unutilized. Now it will be seen in the direct reaction
tube, shown in all the Figures in Sheet I. (except 1 and 2) that the
tube at the bottom of the floats is not continued beyond the lift of the
floats to enclose them there. But I do not think any water will cscape
under them because the one following must always be longer than the
one entering the drum, hence the velocity of the latter must be less;
and the velocity of the water under it more driven by the following
longer float. But should any water escape under the shorter float it will
be arrested and utilized by the longer.

page_text: Suppose however that I am mistaken, this loss of power might be
more than that due to the mixing of the waters in the indirect reaction
tube, shown in Sheet I., Figs I. and 2. This then is why I claim my
saving cam in combination with such an indirect reaction tube.
Writing as this is being copied repetitions and errors will no doubt
be found, but I have carefully examined all the formulæ and Figures
copied for the printer, which have been done with singular accuracy and
alserne
CHO ESCovery and INVENTION
are I think unusual: the first exact science patented since the Patent
Laws in 1623, and one never to be superseded for the navigation of the
ocean and the heavens. The Specification then is in harmony with
its nature, and I venture to think of sufficient importance to mankind
to be established by all the means in my power. For I have shown how
the schools and colleges, and Admiralty professors and engineers of this
generation, those who have the world of science in their hands, the
teaching of the youth of England, and making of engines, both theoretical
and practical, have all risen up against me and condemned me. It
was therefore right to refute them by a higher power than theirs, the
unerring logic of inductive generalization, and of deductive proof, and
now my discoveries are safe. For I know that the supreme public
opinion, above that of any class or sect, which has introduced all the
great discoveries of science against the mere book learning of the
schools will introduce mine. But when in daily use what I have done
will be considered so self-evident or so old that it will be denied to be
any discovery at all, notwithstanding the thought and labour and
expence of 1870-1842=) 28 years. For so it has always been. I
may not then be here to defend my rights, to do what no one else can,
to explain the nature of my discovery, to support it by unanswerable
arguments as I have here by the experimental results of the Vixen,
Viper, and Volunteer, in table at para. 19, and by the crucial
instances in para. 34. Or another fire (which destroyed all I possessed,
even manuscripts in a fire-proof safe, falsely so called) may again reduce
to a black and illegible little heap the huge mass of papers of long
years. I claim therefore the right of defending my rights, nunc pro
tunc, by the extracts I have given from reports, papers, and scientific

page_text: discussions which would else pass away and be forgotten.
For I can
only show the originality of my discoveries by their vehement denial by
the first scientific authorities of our time.
167. But independent of all this I venture to think that the present
discovery makes as great a transition in practical science as Bacon's in
philosophy, since it reduces the empirism of steam navigation and the
resistance of fluids to an exact science, and introduces a new depart-
ment of knowledge, that of aërial navigation. It seems desirable
therefore to explain the present state of the sciences so clearly that
men may know exactly what is old and what is new. Only so indeed
can "the nature of my Invention," that is, the-fundamental-principles,
be clearly understood, and in what respects they differ from the present
system. I have therefore exhausted, as I think, the science of pro-
pulsion, and given a standard for all time of the resistance of bodics
moving in fluids.
168. I have shown, in para. 10, how my prediction of reaction pro-
pulsion in the water and in the air, in 1851, was partly verified by
induction in 1866, and completely in 1869, by discovering that the laws
of impulse governed the action of planes against fluids, as well as fluids
against planes; and thus accounted for the residual phenomenon found
in the paddle wheel and screw referred to in para. 40. I have also
shown in para. 20 how the prediction would have been verified in 1857,
when I discovered the laws and formulæ of paddle wheel propulsion,
had I not unhappily adopted the doctrine of the schools, the equality of
action and reaction in plane and fluid impulse, and so made R=P;
which is still taught, as shown in paragraph 30.
169. It will be seen in such. prediction of 1851, that I ventured to
say, even 19 years ago, that reaction propulsion would never be super-
seded. Now there is no presumption in relying on a primary law of
nature, as the ultima Thule of discovery, beyond which mere man cannot
go. On this point then I will conclude with the highest authority in
philosophy, in noble words indeed, remarkable at all times, still more
remarkable in the dark ages of science three hundred years ago, a sure
guide and consolation in scientific research, one of the very few prose
sentences that can be remembered. Homo, naturæ minister et
interpres, tantum facit et intelligit, quantum de naturæ ordine, re vel
mente observaverit; nec amplius scit, aut potest." A high and noble

page_text: office! How calm, how dignified, how true; nec amplius scit, aut
potest.
In witness whereof, I, the said Richard Boyman Boyman, have
hereunto set my hand and seal, this Twenty-seventh day of
August, One thousand eight hundred and seventy.
R. BOYMAN BOYMAN. (L.S.)