Chapter XII (2)

(2_b_² - 4_b_ _a_ + (8/3)_a_³) / (2_b_ _a_ - 2_a_²) =
(_b_² - 2_b_ _a_ + (4/3)_a_²) / (_b_ - _a_) =
((_b_ - _a_)² + (1/3)_a_²) / (_b_ - _a_) =
_b_ - _a_ + ((2/3)_a_²) / (_b_ - _a_),

which represents the distance of the level M N from the result
of all the horizontal pressure against the circumference, which
distance exceeds D C, and consequently the direction of the
result passes from below the centre C of the wheel to a distance
from the said centre, which is = ((1/3)_a_²)/(_b_ - _a_).

If this distance be multiplied by the result of all the
horizontal pressure, that is, by 2_a_.(_b_ - _a_); there is
obtained (2/3)_a_³ for the momentum of the force which tends to
make the wheel revolve from L towards O. This being established,
it is known that the force which causes the half of the wheel
F L G to revolve vertically to the top (calling _g_ the specific
gravity of the wheel) is = (1 - _g_) F C O L, and which force
passes through the center of gravity of F L O. And consequently
the gravity of any circular segment divided by the half of the
radius, is distant from the centre of the circle by a quantity
equal to the twelfth of the cube of the chord divided by the
segment; and therefore the centre of gravity of the semicircle
F C O L, will be distant from the centre C by the quantity
(1/12)8_a_³/(E C O L) = (2/3)_a_³/(E C O L). Consequently the
momentum of this force tending to make the wheel revolve from O
towards L will

be = (2/3_a_³)/(E C O L) . (1 - _g_)(E C O L) = 2/3(1 - _g_)_a_³.

But moreover a certain momentum will be derived from the other
half F Q O of the wheel, which being out of the water, tends by
its own weight downwards with a force = _g_ . (E C O Q) = _g_ .
(E C O L), which multiplied by the distance (2/1_a_³)/(E C O L)
of the centre of gravity of the semicircle F Q O from the centre
of the wheel gives as a momentum of force tending to turn the
wheel from O to L the quantity 2/3_g_ _a_³. Thus the whole
momentum to make the wheel turn from O to L, will be 2/3(1 -
_g_)_a_³, + 2/3_g_ _a_³ = 2/3_a_³, that is to say the same that
is found to turn the wheel in the opposite direction, viz., from
L to O, and thence the wheel remains perfectly motionless.

3. Cor. I. If the wheel were specifically heavier than the water,
one would not be able to conceive in that case any motion from L
to O, as seemed probable in the former supposition. Since, then,
the momentum of the force, which turns vertically downwards the
portion of the wheel F C O L, and tends to make it revolve from L
to O is = 2/3(_g_ - 1)_a_³ to which momentum should be added a
certain portion of the horizontal pressure, that is to say 2/3,
and thus is obtained the whole momentum 2/3_g_ _a_³, tending
to cause the wheel to turn from L to O; and to which momentum
precisely, is equal such of the weight of the half F C O Q as
tends to give to the wheel a contrary revolution, that is, from O
to L.

3. Cor. II. If the wheel in place of being a circular plane were
a zone bounded by two concentric peripheries (Fig. 3), then
from the sum of the horizontal pressure of the water against
the exterior periphery should be taken the sum of the opposite
horizontal pressure against the other interior semi-periphery
of the zone. So calling _a_ the greater radius of the zone, and
λ its breadth, the sum of the first horizontal pressure is =
2_a_(_b_ - _a_) and the sum of the second = 2(_a_ - λ)(_b_ - λ) -
(_a_ - λ) = 2(_a_ - λ)(_b_ - _a_). Then subtract the latter from
the former and there remains 2(_b_ - _a_)λ for the sum of the
whole pressure, which acts upon the zone (_sic_) of the half of
the wheel immersed in the fluid in a direction tending from the
outside to the interior of the wheel.

Moreover the sum of the momenta of all the horizontal pressure on
the exterior circumference relatively to the level

M N is = 2_b_ _a_ - 4_b_ _a_ + 8/3_a_³.

And similarly the sum of the momenta of the horizontal pressure
opposite, on the interior semi-circumference, relatively to the
given level is = 2(_b_ - λ)² - (_a_ - λ) - 4(_b_ - λ) × (_a_ -
λ)² + 8/3(_a_ - λ)³.

Subtracting this sum from the preceding, there remains the sum
of the momenta acting on the zone of the half-wheel from the
exterior to the interior = 2_b_² _a_ - 4_b_ _a_² + 8/3_a_³ -
2(_b_ - λ)² (_a_ - λ) + 4(_b_ - λ) (_a_ - λ)² - 8/3(_a_ - λ)³ -
2_b_² λ - 4_b_ _a_ λ + 4_a_² λ - 2_a_ λ² + 2/3λ³ = 2λ (_b_(_b_
- _a_) - _b_ _a_ + 2_a_² - _a_λ + 1/3λ²) = 2λ ((_b_ - _a_)(_b_
- _a_) + _a_² - _a_λ + 1/3λ²) Then dividing this sum of the
momenta by the sum of the pressure there will be 2λ(((_b_ -
_a_)(_b_ - _a_) + _a_² - _a_λ + 1/3λ²)/(2λ(_b_ - _a_))) = _b_
+ _p_ (_a_(_a_² - _a_λ + 1/3λ²)/(_b_ - _a_)) the distance of
the center of the pressure from the level of the fluid, that
is, to the distance of the result of all the pressure from that
level. From this it is evident that the center of pressure falls
under the center of the wheel, C, to the distance (_a_² - _a_λ +
1/3λ²)/(_b_ - _a_) .

Whence multiplying this distance by the result of the pressure,
or by 2λ(_b_ - _a_), we obtain 2λ(_a_² - _a_λ + 1/3λ²) to express
the momentum of the horizontal pressure of the water, directed to
make the wheel turn from L to O.

Now the momentum with which the vertical impulse of the fluid
tends to make the semicircle F C O L turn from O to L (supposing
the wheel not with a simple zone, but with a circular plane) is
= 2/3_a_³. Likewise the momentum of the impulse of the fluid to
cause the internal semicircle V C I G from O to L is - 2/3(_a_
- λ)³. Then taking this second momentum from the first, the
momentum of the zone from the fluid V G I O L F to give the wheel
an impulse from O to L will be = 2/3(_a_³ - (_a_ - λ)³) = 2λ(_a_²
- _a_λ + 1/3λ²) which is precisely the momentum with which the
horizontal pressure of the fluid to impress on the wheel an
impulse in the opposite direction, that is to say from L to O.
Consequently from the pressure of the fluid the wheel cannot
have any motion around its center.

The weight of the wheel itself, by which the half-zone immersed
in the water tends to make the wheel turn from L to O, and the
half which is out of the water, to make it turn in the reverse
direction, such a weight, I say, cannot induce any motion of
rotation, and both halves remain in equilibrium around the center
C.

Article by William Nicholson

William Nicholson was born in London in 1753; died in 1815. He was a scientist of note, and a writer of scientific subjects. In 1797 he established in London and continued publishing until 1814, a periodical entitled "Journal of Natural Philosophy, Chemistry and the Arts," known, however, throughout the civilized world as "Nicholson's Journal."

A Perpetual Motion device of Dr. Conradus Schwiers, in 1790, and the Richard Varley device, in 1797, described at page 132 et seq., ante, had attracted a great deal of attention, and were the occasion of much discussion. A consequent increased interest in the subject of self-moving mechanism was thus created.

Mr. Nicholson, whose scientific attainments were recognized by all, was asked to publish an article on the subject. His article appeared in his publication, "Nicholson's Journal," and is as follows:

_On the Mechanical Projects for Affording a Perpetual Motion_

In consequence of the notice taken of Mr. Varley's attempt to
produce a perpetual motion, I have been requested by several
correspondents to state how far the mechanical scheme for which
Dr. Conrad Schwiers took out a patent in the year 1790, for
the same object may be worthy of attention. I have, on that
occasion, mentioned the difficulties which have prevented any
clear general demonstration of the absurdity of this pursuit
from being produced, though it has not been difficult to show
the fallacy of the individual plans. It does not, indeed, seem
easy to enunciate the scheme itself. What in universal terms is
the thing proposed to be done? Is it to cause a body to act in
such a manner that the reaction shall be greater than the action
itself, and by that means generate force by the accumulation of
the surplus? Or, can the motion communicated be greater than
that lost by the agent? Since these positions are evidently
contrary to the physical axioms called the laws of nature, and
frictions and resistances would speedily destroy all motions of
simple uniformity, it may be presumed that 's Gravesande, who
thought that all the demonstrations of the absurdity of schemes
for perpetual motion contained paralogism, would have stated the
proposition under different terms. But without entering upon this
apparently unprofitable disquisition, it may be useful, as well
as entertaining, to make a few observations on the mechanical
contrivances which depend on a mistaken deduction from the
general theorem respecting the balance, among which that of Dr.
Schwiers must be classed.

There is no doubt but numerous arrangements have been made, and
still are labored at by various individuals, to produce a machine
which shall possess the power of moving itself perpetually,
notwithstanding the inevitable loss by friction and resistance of
the air. Little, however, of these abortive exertions has been
entered upon record. The plans of Bishop Wilkins, the Marquis of
Worcester, and M. Orffyreus, are all which at this time occur to
my recollection.

There is no doubt but the celebrated Wilkins was a man of
learning and ability. His essay towards a real character and a
philosophical language is sufficient to render his name immortal.
Twenty years before the appearance of that work he published
his "Mathematical Magic," namely, in the year 1648, containing
295 pages, small octavo, which, from the number of copies still
in being, I suppose to have been a very popular treatise. It is
in this work that I find, among other contrivances for the same
purpose, a wheel carrying sixteen loaded arms, similar to that
delineated in Fig. 4, plate 15, in which, however, for the sake
of simplicity, I have drawn but six. Each lever, A B C D E F,
is movable through an angle of 45 degrees, by a joint near the
circumference of the wheel, and the inner end or tail of each
is confined by two studs or pins, so that it must either lie in
the direction of a radius, or else in the required position of
obliquity. If the wheel be now supposed to move in the direction
E F, it is evident that the levers A B C D, by hanging in the
oblique position against the antecedent pins, will describe a
less circle in their ascent than when, on the other side, they
come to descend in the positions E F. Hence, it was expected that
the descending weights, having the advantage of a longer lever,
would always predominate. Dr. Wilkins, by referring the weights
to an horizontal diameter, has shown that in his machine they
will not. A popular notion of this result may also be gathered
from the figure, where there are three weights on the ascending
and only two on the descending side; the obliquity of position
giving an advantage in point of number, equal to what the other
side may possess in intensity. Or, if this contrivance were to be
strictly examined, on the supposition that the levers and weights
were indefinitely numerous, the question would be determined by
showing that the circular arcs A K, H I, are in equilibrio with
the arcs A G, G L.

The simplest method of examining any scheme of this kind with
weights, consists in inquiring whether the perpendicular ascents
and descents would be performed with equal masses in equal times.
If so, there will be no preponderance, and, consequently, no
motion. This is clearly the case with the contrivance before us.

The Marquis of Worcester, who will ever be remembered as the
inventor of the steam engine, has described a perpetual motion in
the fifty-sixth number of his "Century of Inventions," published
in the year 1655, and since reprinted in 1767 by the Foulis's at
Glasgow. His words were as follows:

"To provide and make, that all the weights of the descending side
of a wheel shall be perpetually further from the center than
those of the mounting side, and yet equal in number and heft to
the one side as the other. A most incredible thing if not seen,
but tried before the late King (of blessed memory) in the Tower
by my directions, two extraordinary ambassadors accompanying his
Majesty, and the Duke of Richmond and Duke Hamilton, with most of
the Court attending him. The wheel was fourteen feet over, and
forty weights of fifty pounds apiece. Sir William Balfour, then
Lieutenant of the Tower, can justify it with several others. They
all saw that no sooner these great weights passed the diameter
line of the lower side, but they hung a foot further from the
center; nor no sooner passed the diameter line of the upper side,
but they hung a foot nearer. Be pleased to judge the consequence."

Desaguliers, in his "Course of Experimental Philosophy," Vol.
I, page 185, has quoted this passage, and given a sketch of a
pretended self-moving wheel, similar to Fig. 5, plate 15, as
resembling the contrivance mentioned by the Marquis of Worcester.
The description of this last engineer agrees, however, somewhat
better with the contrivance Fig. 4. It must, of course, be a
mistake in terms, when he says the weight receded from the center
at the lower diameter and approached towards it at the upper:
the contrary being, in fact, necessary to afford any hope of
success; and accordingly in the quotation it is so stated. I am,
therefore, disposed to think that Fig. 5 represents the wheel
of Orffyreus at Hesse Cassel, much talked of about the year
1720, and which probably was made to revolve, during the time
of exhibition, by some concealed apparatus. It consists of a
number of cells or partitions, distinguished by the letters of
the alphabet, which are made between the interior and exterior
surfaces of two concentric cylinders. The partitions being
placed obliquely with respect to the radius, a cylindrical or
spherical weight placed on each, it is seen from the figure,
that these weights will lie against the inner surface of the
larger cylinder whenever the outer end of the bottom partition
of any cell is lowest; and, on the contrary, when that extremity
is highest, the weight will rest on the surface of the interior
cylinder. Let the wheel be made to revolve in the direction
A B C; the weights in C D E F G H I being close to the external
circle, and the weights K L M A B close to the inner, for the
reasons last mentioned. As the cell B descends, its weight
will likewise run out, at the same time that the weight in
the cell I will run in in consequence of its partition being
elevated. By the continuation of this process, since all the
weights on the descending side pass down at a greater distance
from the center, while those of the ascending side rise for a
considerable part of their ascent at a less distance from the
same point, it is concluded that the wheel will continue to
maintain its motion. On this, however, it is to be remarked that
the perpendicular ascent and descent are alike, both in measure
and in time of performance; and that the familiar examination,
even to those who know little of such subjects, is sufficient
to show that the preponderance is not quite so palpable as at
first it appears. For the weights G and F, H and E, I and D
are evidently in equilibrio, because at the same horizontal
distance from the center; and if the favorable supposition that
the weight B has already run out be admitted, it will then
remain a question whether these two exterior weights, B and C,
can preponderate over the four inner weights, K L M A. The more
accurate examination of this particular contrivance will lead to
the following theorem: In two concentric circles, if tangents be
drawn at the extreme points of a diameter of the smaller, and
continued till they intersect the larger, the common center of
gravity of the arc of the greater circle included between the
tangents and of the half periphery of the smaller circle on the
opposite side of the diameter, will be the common center of the
circles. If, therefore, the balls were indefinitely numerous and
small, the supposed effective parts of the wheel (Fig. 5) would
be in equilibrio, as well as the parts beneath the horizontal
tangent of the inner circle.

Fig. 6 represents the contrivance of Dr. Schwiers, which, in
a periodical publication, in other particulars respectable,
has been said to continue in motion for weeks and even months
together. There is not the smallest probability that it should
continue in motion for half a minute, or nearly as long as
a simple wheel would retain part of its first impulse. The
external circle denotes a wheel carrying a number of buckets,
A B I L, etc. C represents a toothed wheel, on the same axis
which drives a pinion D; and this last drives another pinion
E upon the axis of a lanthorn, or wheel intended to work a
chain-pump with the same number of buckets as in the larger wheel
A B I. The lanthorn G is made of such a size as to receive the
buckets _a b i l_ with a due velocity. K represents a gutter
through which a metallic ball, contained in the bucket _m_, may
run and lodge itself in the bucket A of the wheel. Each of the
buckets of the wheel, B I L M, which are below the gutter, is
supplied with a metallic ball, and so likewise are the ascending
buckets, _a b i l m_, of the chain-pump. As the pump supplies
the wheel, it is again supplied at M, where the balls fall into
its ascending buckets. Now, it is presumed that the balls in the
wheel I suppose on account of their distance from the center of
motion, will descend with more than sufficient force to raise
those on the chain, and, consequently, that the motion will be
perpetual.

The deception in this contrivance has much less seduction than
in the two foregoing, because it is more easily referred to the
simple lever. This, like the others, exhibits no prospect of
success, when tried by the simple consideration of the quality
of the ascent and descent in the whole time of the rotation
of a single ball. It may also be shown from the principles of
wheel-work, which are familiar to artisans, that whatever is
gained by the excess of the diameter of the great wheel beyond
that of the wheel C, is again lost by the excess of the lanthorn
A beyond the pinion E.

The fundamental proposition of the simple lever or balance,
that equal bodies at an equal distance from the fulcrum will
equiponderate, but that at unequal distances the most remote
will descend, has, in these and numberless other instances, led
mechanical workmen and speculators to pursue this fruitless
inquiry with labor and expense often ill-afforded, and with a
degree of anxiety and infatuation which can hardly be conceived
by those who have never suffered the pain of hope long deferred.
For this reason chiefly, it has appeared desirable and useful
to treat the subject in a familiar way without descending to
those expressions of contempt, which ignorance, harmless to all
but itself, is surely not entitled to. If such reasoners were
well convinced that the power of a machine is to be estimated
by the excess of motion referred to the perpendicular, without
any regard to the apparent center of the machine, and that
in machines very little compounded it is possible to produce
effects directly contrary to the rule which is true of the simple
lever, they would probably renounce many flattering projects,
grounded only on the supposition of its universality. Desaguliers
contrived an apparatus in which two equal weights may be placed
at any distance whatever from the center of motion, and still
continue in equilibrio. Fig. 3 represents this instrument. A D
denotes a balance with equal arms, and E F another of the same
dimensions. These move on the centers B and C, and are connected
by the inflexible rods A E and D F; the motion being left free
by means of joints at the corners. Across the rods A D, E F, are
fixed two bars, I K, L M. Now, it is unnecessary to show that the
weight G will describe exactly the same line or circular arc,
when the levers are moved into the position _a d f e_, or any
other position, as it would have described in case it had been
suspended at A, or K, or E; and that it is of no consequence in
this respect at what part of the line A E or I K it be fixed.
The same observations are true of the weight H on the other
side. And accordingly it is found that these equal weights may
be suspended anywhere on the lines I K and L M without altering
their equilibrium.

By this contrivance it is most evidently proved to those who
are totally unacquainted with the theory, that weights do not
preponderate in compound engines on account of their distance
from the center. Several contrivances may be made to the same
effect. The following combination of wheel-work presented
itself to me as one which would most probably be mistaken for a
perpetual motion. (Fig. 2, plate 15.) The five circles represent
the same number of wheels of equal diameter and number of teeth,
acting together. The middle wheel A is fixed between two upright
pillars, so that it cannot revolve. The other four wheels are
pinned in a frame H I, in which they can revolve, and through
which the axis of A likewise passes. From the extremity of the
axis of D, and also of _d_, proceed the horizontal levers H K and
I L, which are equal, and point in the same direction parallel
to the plane of the wheels. At the extremity of these arms hang
the equal weights P and _p_. Let it now be imagined that the
end I of the frame is depressed, the wheel B will turn round by
the reaction of the fixed wheel A in the same direction as H I,
and it will make one revolution in the same time relative to
the frame, or two with regard to absolute space, by reason of
its being carried round. The action of B upon D will produce a
rotation relative to the frame in the opposite direction during
the same time. Instead, therefore, of two revolutions like the
wheel B, this wheel D, with regard to absolute space, will not
revolve at all, and in every position of the apparatus the arm
I L will continue horizontal, and point the same way. For similar
reasons the arm H K will retain its position. Consequently, it is
seen that the descending weight will move at a great horizontal
distance from the center N, while the ascending weight rises
very near that center. But there will, not on this account,
be a perpetual motion: for the action of the levers H K and
I L upon the frame H I, by means of the toothed wheels, will,
in the detail, be found precisely alike, and in the general
consideration of the motions of P and _p_, the opposite motions
in the circle E F G will be accurately the same.

It has always been considered as essential to a perpetual motion
that it should be derived from some energy which is not supposed
to vary in its intensity. Such are the inertia, the gravity or
magnetism of bodies. For an occasional or periodical variation of
intensity in any force is evidently productive of motion, which
requires only to be accumulated or applied, and the apparatus
for applying it cannot be considered as a machine for perpetual
motion. Neither in strictness can any machine whose motion is
derived from the rotation of the earth, and the consequent change
of seasons and rotation of events, be so considered, because
it does not generate, but only communicates. The perpetual
flow of rivers; the vicissitudes of the tides; the constant,
periodical and variable winds; the expansions and contractions
of air, mercury, or other fluids, by daily or other changes of
temperature; the differences of expansions in metals, by the
same change; the rise and fall of the mercury in the barometer;
the hygrometric changes in the remains of organized beings, and
every other mutation which continually happens around us, may be
applied to give motion to mills, clocks, and other engines, which
may be contrived to endure as long as the apparatus retains its
figure.

Mr. Nicholson's article, published above, shows, if nothing else had ever shown, the fact that he was endowed with a real scientific mind. It also shows what is still most interesting--that his mind anticipated and that he had a subconscious conception of the principle of Conservation of Energy.

In 1824 and 1825 there was published in London a mechanical journal called "The Artisan"; or "Mechanic's Instructor." In one of the issues the following occurred on the subject of Perpetual Motion:

Perpetual motion is a motion which is supplied and renewed from
itself without the intervention of any external cause: to find
a perpetual motion, or to construct a machine which shall have
such a motion, is a subject which has engaged the attention of
mathematicians for more than 2,000 years; though none perhaps
have prosecuted it with so much zeal and hopes of ultimate
success as some of the speculative philosophers of the present
age.

Infinite are the schemes, designs, plans, engines, wheels, etc.,
to which this longed-for perpetual motion has given birth;
and it would not only be endless but ridiculous to attempt to
give a detail of them all, especially as none of them deserve
particular mention, since they have all equally proved abortive;
and it would rather partake of the nature of an affront than a
compliment, to distinguish the pretenders of this discovery, as
the very attempting of the thing conveys a very unfavorable idea
of the mental powers of the operator.

For among all the laws of matter and motion, we know of none
which seems to afford any principle or foundation for such an
effect. Action and reaction are allowed to be ever equal; and a
body which gives any quantity of motion to another, always loses
just so much of its own; but, under the present state of things,
the resistance of the air, and the friction of the parts of
machines, necessarily retard every motion.

To keep the motion going on, therefore, there must either be a
supply from some foreign cause, which, in a perpetual motion, is
excluded.

Or, all resistance from the friction of the parts of matter must
be removed; which necessarily implies a change in the nature of
things.

For by the second law of motion the changes made in the motions
of bodies are always proportional to the impressed moving force,
and are produced in the same direction with it; no motion, then,
can be communicated to any engine, greater than that of the first
force impressed.

But, on our earth, all motion is performed in a resisting fluid,
namely, the atmosphere, and must, therefore, of necessity, be
retarded; consequently, a considerable quantity of its motion
will be spent on the medium. Nor is there any engine or machine
wherein all friction can be avoided; there being in nature no
such thing as exact smoothness or perfect congruity; the manner
of the cohesion of the parts of bodies, the small proportion
which the solid matter bears to the vacuities between them, and
the nature of those constituent particles not admitting it.

Friction, therefore, will also, in time, sensibly diminish the
impressed or communicated force; so that a perpetual motion can
never follow, unless the communicated force be so much greater
than the generating force as to supply the diminution occasioned
by all these causes; but the generating force cannot communicate
a greater degree of motion than it had itself. Therefore, the
whole affair of finding a perpetual motion comes to this, viz.,
to make a weight heavier than itself, or an elastic force
greater than itself; or, there must be some method of gaining a
force equivalent to what is lost by the artful disposition and
combination of the mechanical powers: to this last point then,
all endeavors are to be directed; but how, or by what means such
a force can be gained, is still a mystery!

The multiplication of powers or forces avails nothing; for what
is gained in power is lost in time; so that the quantity of
motion still remains the same.

The whole science of mechanics cannot really make a little power
equal or superior to a larger; and wherever a less power is found
in equilibrio with a greater--as, for example, twenty-five pounds
with one hundred--it is a kind of deception of the sense; for
the equilibrium is not strictly between one hundred pounds and
twenty-five pounds moving (or disposed to move) four times as
fast as the one hundred pounds.

A power of ten pounds moving with ten times the velocity of one
hundred pounds would have equalled the one hundred in the same
manner; and the same may be said of all the possible products
equal to one hundred: but there must still be one hundred pounds
of power on each side, whatever way they may be taken, whether in
matter or in velocity.

This is an inviolable law of nature; by which nothing is left to
art, but the choice of the several combinations that may produce
the same effects.

The only interest that we can take in the projects which have
been tried for procuring a perpetual motion must arise from the
opportunity that they afford of observing the weakness of human
reason.

For a better instance of this can scarcely be supplied than to
see a man spending whole years in the pursuit of an object,
which a single week's application to sober philosophy would have
convinced him was unattainable.

But for the satisfaction of those who may not be convinced of the
impossibility of attaining this grand object, we shall add a few
observations on the subject of a still more practical nature than
the above.

The most satisfactory confutation of the notion of the
possibility of a perpetual motion is derived from the
consideration of the properties of the center of gravity; it is
only necessary to examine whether it will begin to descend or
ascend when the machine moves, or whether it will remain at rest.
If it be so placed that it must either remain at rest or ascend,
it is clear, from the laws of equilibrium, that no motion derived
from gravitation can take place; if it may descend, it must
either continue to descend forever with a finite velocity, which
is impossible, or it must first descend and then ascend with a
vibratory motion, and then the case will be reducible to that of
a pendulum, where it is obvious that no new motion is generated,
and that the friction and resistance of the air must soon destroy
the original motion.

One of the most common fallacies by which the superficial
projectors of machines for obtaining a perpetual motion have
been deluded, has arisen from imagining that any number of
weights ascending by a certain path on one side of the center of
motion, and descending on the other at a greater distance, must
cause a constant preponderance on the side of the descent; and
for this purpose weights have been made to slide or roll along
grooves or planes, which lead them to a more remote part of the
wheel, from whence they return as they ascend, as represented in
the following figure: Or they have been fixed on hinges which
allow them to fall over at a certain point so as to become more
distant from the center; but it will appear on the inspection
of such a machine that although some of the weights are more
distant from the center than others, yet there is always a
proportionally smaller number of them on that side on which they
have the greater power; so that these circumstances precisely
counterbalance each other.

We have heard it proposed to attach hollow arms to a wheel by
joints or hinges at the circumference, and to fill these arms
with quicksilver or small balls instead of the plan represented
by the above figure; but though we have never heard of it having
been tried, we are perfectly convinced that it would end as all
other attempts have done; that is, in a total failure.

The Possibility of Perpetual Motion Asserted

The enthusiastic earnestness with which the subject of Perpetual Motion was formerly discussed is illustrated by the fact that the Holy Scriptures were dragged in to support arguments on the proposition.

The following is a verbatim copy of an article published in an English scientific magazine in 1829:

"Notice to Perpetual Motion Seekers."--The following is a literal
copy of a communication which we have received under this head.
We publish it for the benefit of all concerned: "Perpetual Motion
Seekers! see Coloss., ch. ii., v. 8--'Beware lest any man spoil
you, through philosophy and vain deceit, after the tradition of
men, after the rudiments of the world.' Ye are making the words
of God of none effect by your traditions in publishing these
things to the world. How can such toys and baubles as these be
perpetual? See Malachi, ch. iv., v. 1--'For behold the day cometh
that shall burn as an oven; and all the proud, yea, all that do
wickedly, shall be as stubble.' Here is the end of them. I, the
undersigned, have to inform the public, the model for making
perpetual motion is to be found in that too much neglected book
of models, the Bible. I called upon the Lord, and he showed it
to me. I said, 'Lord, shall I show this unto them? This was the
answer to me: See Isaiah, ch. xli., v. 29--'Behold, they are all
vanity; their works are nothing.' I said, 'Lord, be pleased to
show me some more about it.' 'Bring forth your strong reasons,
saith the King of Jacob.'--Isaiah, ch. xli., v. 21. This was the
answer: See Isaiah, ch. xli., v. 14--'Fear not, thou worm Jacob.
* * Behold, I will make thee a new sharp threshing instrument
having teeth; thou shalt thresh the mountains, and beat them
small, and shall make the hills as chaff.' See also Jeremiah,
ch. vii., v. 9--'The wise men are ashamed; they are dismayed and
taken,' etc. See also Jeremiah, ch. ix., v. 12--'Who is the wise
man that may understand this?' If there is not a wise and learned
man who can show this, there is a deaf and unlearned man that
will, by the blessing of God, set it forth to you. I am that deaf
and unlearned man, George Lovatt, Stafford.

"P. S.--Mr. Editor: I have told you what I was commanded to do.
See Ezekiel, ch. iii., v. 4 to the end. Now, see thou forget it
not; let those models which come from the Word of God have the
first place.--Joshua, ch. xxiv., v. 15."

John Bernoulli's Dissertation on Perpetual Motion

John Bernoulli was born in 1667, and died in 1748. He belonged to the famous Belgian family bearing the name. His family seems to have been peculiarly prolific in men of great genius for mathematics and science. Almost any encyclopedia with any pretense for thoroughness will mention and give the sketch of the life of from five to nine members of the Bernoulli family.

John Bernoulli possessed perhaps the greatest genius of any bearing the name for pure mathematics and pure mechanics. He was a contemporary of such men as Leibnitz, Euler and Newton, a co-laborer with the two former, but never conceded the merits of Newton. He was of a peculiar disposition, of intense likes and dislikes and among his peculiarities it may be mentioned that he harbored an unreasonable hatred toward a worthy and deserving son.

In 1742 he wrote a work entitled "Dissertation on Effervescence and Fermentation." To this work he added an appendix entitled "Concerning Artificial Perpetual Motion." The appendix translated into English and as published by Dircks, is as follows:

Scarcely had I finished this dissertation, when, attentively
considering the nature of precipitation and secretion, briefly
explained in the last pages, there accidentally occurred to me
a mode of constructing, by means of some continually flowing
liquid, the much-talked of and long-desired Perpetual Artificial
Motion; and this as a completion to my work, on account of the
affinity of the subject, I now propose for the consideration of
the learned.

No one need be told how eagerly for a length of time this same
Perpetual Motion has been sought after by the most celebrated
men, how ardently desired; what indeed have they not contrived?
To what expense have they not gone? How many machines have they
not constructed? But all in vain.

The secret desire of this Perpetual Motion still perplexes and
torments many, and excites their minds to such a degree that we
see the ears and minds of learned men carried away by it; yet
many philosophers reject the idea, unanimously asserting that
Perpetual Motion cannot be communicated and cannot be invented;
which opinion is nevertheless not of any weight, seeing that they
rashly judge that no one should be listened to who boasts of
having found out such a thing; and their reasons (as I confess)
do not suffice to convince me; for I do not hesitate to assert
not only that Perpetual Motion may be discovered, but that it has
now actually been discovered, as will be confessed by any one
who reads these lines; and what is this labor to many? does not
Nature herself (who is never said not to operate by mechanical
laws) indicate Perpetual Motion to be possible? To recall but one
instance, what is the constant flux and reflux of the rivers and
seas but Perpetual Motion? Does it not all belong to Mechanics?
Therefore, you must confess that it does not exceed the limits of
mechanical laws, and is not impossible; what then hinders that
following Nature in this, we should be able perfectly to imitate
her? as indeed I shall so conclude, by declaring to these the
possibility of Perpetual Motion and the manner of obtaining it;
and lest thou come to an adverse conclusion, or regard it as a
Titanic enterprise, I pray that thou mayest first well weigh the
thing, or, if it so please thee, put its truth to the test of
experience.

First of all the following must be premised:

1. If there are two fluids of different density, the weights of
which respectively are in the ratio G to L; the altitudes of
cylinders of equal weight, and having the same base, will be in
the ratio L to G.

2. Therefore, if the altitude A C of one fluid contained in the
vessel A D to be the altitude E F of the other fluid contained in
an open tube, as L to D; the fluids so placed will remain at rest.

3. Therefore, if A C to E F be in a greater ratio than L to
G, the fluid in the tube will ascend; or if the tube be not
sufficiently long, the fluid will escape by the orifice E. (These
are proved by Hydrostatics.)

4. It is possible to have two fluids of different gravity, which
are capable of being mixed one with the other.

5. It is possible to have a filter, strainer or other separator,
by means of which the lighter fluid may be separated from the
heavier.

_Construction_

These being pre-supposed, I construct Perpetual Motion in the
following manner:

Let two fluids of different gravity and capable of mixing
together (which is possible by Hyp. 4) be taken in any
quantities, in equal quantities, if desired; let the ratios of
their gravities be first determined, which suppose as G to L, the
heavier to the lighter; and being mixed, let a vessel, A D, be
filled to A.

This having been done, let a tube be taken, open at both ends
E F; and of such a length that A C : E F > 2 L : G + L; and
the orifice F stopped, or rather filled with a filter or some
substance separating the lighter fluid from the heavier (as is
possible also by Hyp. 5); when the tube filled in this manner
with fluid is immersed to the bottom of the vessel C D; I say
that the fluid will continually ascend by the orifice of the tube
F, and by the orifice E will fall into the fluid below.

_Demonstration_

Because the orifice of the tube F is occupied by a filter (by
Constr.) which separates the lighter fluid from the heavier;
it follows, that if the tube be immersed to the bottom of
the vessel, the fluid lighter by itself, which is mixed with
the heavier fluid, must ascend in the tube, and as it will
ascend above the surface of the surrounding fluid as A C :
E F = 2 L : G + L : which is (by Const.) A C : E F > 2 L :
G + L, it necessarily follows (by Hyp. 3) that the lighter
liquid, through the orifice E, will fall in the vessel below;
there it again mixes with the heavier (by Hyp. 4); and then,
penetrating the filter, ascends again into the tube, and escapes
by the upper orifice. So, therefore, the flow is continued
perpetually.--Q. E. D.

_Corollary_

Hence a reason may easily be given, why water from the depths of
the ocean, ascending into the summits of the mountains, bursts
from them in the form of rivers and flows again into the ocean;
so does Nature offer to us the spectacle of perpetual motion.

Hence I say, they do not well explain who allege that the water
ascends to these heights through the pores of the earth, as a
fluid ascends in narrow tubes above the surface of the fluid
surrounding; for if such were the explanation of the thing, they
would never be able to demonstrate it; for the water so raised
to a height from the bosom of the earth, falls again, whereas
we see that the fluid in these narrow tubes, although slightly
elevated above the surrounding surface, never issues from their
orifices and falls into the fluid below. The following is then
the more feasible explanation. It is known that water in which
much salt is held in solution is heavier than fresh water; now
sea-water, as is sufficiently evident from the taste, contains
many saline particles; consequently it is heavier than spring or
river water; so that it is credible that the earth acts like a
filter through the pores of which only fresh water can pass, the
saline particles being left behind, and this increases the weight
of the water; the fresh water must ascend much higher on account
of the immense profundity of the ocean, as it is forced to the
highest peaks of the mountains by the presence of the sea-water;
and thence, not being able to ascend any higher, it falls in
rivers.

P. Christopher Scheiner

That an earnest belief in the possibility of Perpetual Motion has not been confined entirely to scientific tyros and enthusiastic dreamers, is sufficiently attested by the fact that a respectable number of eminent scientists, many of whom had done great service in their scientific labors, have believed in such possibility.

Among these is to be mentioned P. Christopher Scheiner, a German, born 1575, and died 1650. He was a mechanic of note; in his day made valuable additions to what was known of light and optics, invented the Pantagraph, discovered solar spots, besides benefiting mankind by many other distinguished fruits of his genius.

The subject of Perpetual Motion claimed some of his attention. He wrote in defense of its possibility. The substance of what he said, translated into English, is as follows:

Let the centre of the universe then, or of gravity, be A, and the
gnomon A B C, of which the extremity A is pierced and traversed
by an axis going through the centre of the world, so that it may
turn and revolve freely and easily around the said centre; to
the other extremity of the gnomon, C, let a phial full of water
be attached.

The weight C will turn around the centre A and will first come
to D, thence to E, thence to F and G; then it will return to C,
having described a complete circle, C D E F G; then it will again
move to D, E, F, etc., and so perpetually, since there is no
reason for its stopping in any point of the circle rather than in
another.

That indeed the weight C affixed to the gnomon will move from C
to D, is proved by daily experience, by which it is established
that a gnomon so contrived and placed erect on any flat space,
will not be able to stand, but the arm B C, C preponderating,
will move towards D.

It may in the second place be proved, that if, on the other hand,
another arm B G be added to the gnomon, equal in weight and
similar to the other, the whole G B C A will remain motionless
in equilibrium; therefore the arm B G being taken away and
equilibrium being destroyed, the arm B C must move in the
opposite direction.

The above, from Scheiner, called forth the following from Schott, who was also an eminent mathematician:

Whether there could be a perpetual artificial motion around the
centre of the earth?

We have treated this question in our Hydraulico-pneumatic
Mechanics, Part 2, Class 2, Machine 13, not however universally,
but only in one particular case, that of the Gnomon of Scheiner.
For P. Christopher Scheiner, in "Mathematical Disquisitions,"
in Number XV., Corollary 4, asserts Perpetual Artificial Motion
not to be repugnant to Nature, and attempts to prove it in the
following manner. Let a gnomon of a certain weight A B C be
suspended around A, the centre of the universe, and bound to the
beam D F, which is supported by the columns D F and E G and turns
at the pole D or E; or let it be fixed at the poles, but the
gnomon revolving at A.

These being the conditions, I say that the gnomon A B C will
revolve from C to H and towards I, thence will return to C,
thence to H as before, and so on perpetually. The cause of this
continual motion is the forcible suspension; for the whole gnomon
preponderates in C on account of the perpendicular tangent B A;
which effect becomes more marked if a globe of iron S be supposed
suspended at C. As therefore the whole of this mass, as well
from the supports of the balance as from the momentary diameter,
hangs suspended at C, and the vertex A, on account of the firm
beam D E, cannot fall from the centre of the universe; it comes
to pass that all points as well of the globe S, as of the gnomon
A B C, with a continual motion turn round A; but because, by the
line B A in the fixed point A, they are held from falling to the
centre; therefore the greatest force of that tendency is exerted
in the line B, and induces it to inclination; which inclination
on account of the continuous solidity of the gnomon cannot be
at all abated, so that the whole impetus is exerted either at
the point A about the movable beam or at the movable poles of
the beam D and E; which poles being free in their sockets D and
E, abandon themselves to the motion of Nature, and thus do not
in any wise hinder a perpetual circular motion. What indeed is
self-evident in this, reason confirms, and daily experience in
statics manifests. For if a short gnomon stand either on the
terrestrial superficies M N, O P, or Q R; it will always fall
towards the part C, or N, by the preponderating portion M K C;
which is manifested in daily experiments.

Thence it is evident that if the gnomon were entire, the force
which it exerts at N would pass into the line B A still hanging
over the centre. And this is one argument. The other is from
the contrary. For if an equal and similar gnomon were attached
towards the part D, then the whole mass hanging on its centre
would remain in equilibrium and there would be no motion;
consequently the one half being taken away, the other would
necessarily move according to the laws and experience of statics.
If the shortened gnomon M B C N were bound only to the point M,
the rest being left free, it would certainly revolve, and in the
same case, the point C would describe almost a semicircular arc
till, coming down to a perpendicular position, it would there
remain.

Now as the force of the entire gnomon falls in the vertex A,
there would be an entire and perpetual revolution around A. Much
more would this be the case if on the centre C stood either the
small curve A C L A or the larger one A K C, or finally the globe
S alone, hanging from two iron rods A B and B C, or from one
arc, A N C. From this, therefore, it may be demonstrated that a
perpetual circular motion is possible.

In 1825, the following was contributed to and published in "Mechanics' Magazine." We are unable to give the name of the contributor, but he writes in encouragement of Perpetual Motion. The gist of his article is as follows:

We can now, however, soar above the clouds, explore the depths of
the ocean, and skim over its surface. * * * And be it remembered
that we owe these and many other advantages to a few persevering
individuals who were, in all probability, stigmatized as
chimerical visionaries by those who seem to have an unconquerable
propensity to condemn everything above the level of their own
understanding.

If by perpetual motion nothing more is meant than the putting
in motion some of the most durable substances with which we
are acquainted, in such a manner as to ensure a continuance of
motion as long as those substances will resist the effects of
time and friction, I do not despair of seeing it accomplished.
* * * [He thinks there is] reasonable ground to hope that the
time is not far distant when even this impossibility must yield
to persevering ingenuity. In the present state of public opinion
with regard to its practicability, it would be looked upon as an
empty boast, were I to assert that the discovery is already made.

T. H. Pasley

T. H. Pasley in 1824, contributed an article to "Mechanics' Magazine," asserting the possibility of Perpetual Motion. The following excerpts give the substance of his article:

I feel no hesitation in standing up in support of this grand
desideratum,--this almost forsaken friend of science,--whether
the thing be practicable or not.

On the contrary, "Persevere" should be every one's advice; to do
so, or discontinue, every one's own pleasure. And why should the
impossibility of anything be pronounced unless it be established
wherein the limits of possibility consist?