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30 and 32, Tab. 3. It is further shown
by this circumstance, namely, that every substance is destroyed, or
at least materially changed, by strong and powerful fire and heat:
whence it is clear that tumult and confusion are occasioned by heat,
together with a violent motion in the internal parts of bodies; and
this gradually tends to their dissolution.

What we have said with regard to motion must be thus understood, when
taken as the genus of heat: it must not be thought that heat generates
motion, or motion heat (though in some respects this be true), but
that the very essence of heat, or the substantial self[104] of heat,
is motion and nothing else, limited, however, by certain differences
which we will presently add, after giving some cautions for avoiding
ambiguity.

Sensible heat is relative, and regards man, not universe; and is
rightly held to be merely the effect of heat on animal spirit. It is
even variable in itself, since the same body (in different states of
sensation) excites the feeling of heat and of cold; this is shown by
Inst. 41, Tab. 3.

Nor should we confound the communication of heat or its transitive
nature, by which a body grows warm at the approach of a heated body,
with the form of heat; for heat is one thing and heating another. Heat
can be excited by friction without any previous heating body, and,
therefore, heating is excluded from the form of heat. Even when heat is
excited by the approach of a hot body, this depends not on the form of
heat, but on another more profound and common nature; namely, that of
assimilation and multiplication, about which a separate inquiry must be
made.

The notion of fire is vulgar, and of no assistance; it is merely
compounded of the conjunction of heat and light in any body, as in
ordinary flame and red-hot substances.

Laying aside all ambiguity, therefore, we must lastly consider the true
differences which limit motion and render it the form of heat.

I. The first difference is, that heat is an expansive motion, by which
the body strives to dilate itself, and to occupy a greater space than
before. This difference is principally seen in flame, where the smoke
or thick vapor is clearly dilated and bursts into flame.

It is also shown in all boiling liquids, which swell, rise, and boil
up to the sight, and the process of expansion is urged forward till
they are converted into a much more extended and dilated body than the
liquid itself, such as steam, smoke, or air.

It is also shown in wood and combustibles where exudation sometimes
takes place, and evaporation always.

It is also shown in the melting of metals, which, being very compact,
do not easily swell and dilate, but yet their spirit, when dilated
and desirous of further expansion, forces and urges its thicker parts
into dissolution, and if the heat be pushed still further, reduces a
considerable part of them into a volatile state.

It is also shown in iron or stones, which though not melted or
dissolved, are however softened. The same circumstance takes place in
sticks of wood, which become flexible when a little heated in warm
ashes.

It is most readily observed in air, which instantly and manifestly
expands with a small degree of heat, as in Inst. 38, Tab. 3.

It is also shown in the contrary nature of cold; for cold contracts
and narrows every substance;[105] so that in intense frosts nails fall
out of the wall and brass cracks, and heated glass exposed suddenly to
the cold cracks and breaks. So the air, by a slight degree of cold,
contracts itself, as in Inst. 38, Tab. 3. More will be said of this in
the inquiry into cold.

Nor is it to be wondered at if cold and heat exhibit many common
effects (for which see Inst. 32, Tab. 2), since two differences, of
which we shall presently speak, belong to each nature: although in
the present difference the effects be diametrically opposed to each
other. For heat occasions an expansive and dilating motion, but cold a
contracting and condensing motion.

II. The second difference is a modification of the preceding, namely,
that heat is an expansive motion, tending toward the exterior, but at
the same time bearing the body upward. For there is no doubt that there
be many compound motions, as an arrow or dart, for instance, has both a
rotatory and progressive motion. In the same way the motion of heat is
both expansive and tending upward.

This difference is shown by putting the tongs or poker into the fire.
If placed perpendicularly with the hand above, they soon burn it, but
much less speedily if the hand hold them sloping or from below.

It is also conspicuous in distillations _per descensum_, which men are
wont to employ with delicate flowers, whose scent easily evaporates.
Their industry has devised placing the fire above instead of below,
that it may scorch less; for not only flame but all heat has an upward
tendency.

Let an experiment be made on the contrary nature of cold, whether its
contraction be downward, as the expansion of heat is upward. Take,
therefore, two iron rods or two glass tubes, alike in other respects,
and warm them a little, and place a sponge, dipped in cold water, or
some snow, below the one and above the other. We are of opinion that
the extremities will grow cold in that rod first where it is placed
beneath, as the contrary takes place with regard to heat.

III. The third difference is this; that heat is not a uniform expansive
motion of the whole, but of the small particles of the body; and this
motion being at the same time restrained, repulsed, and reflected,
becomes alternating, perpetually hurrying, striving, struggling, and
irritated by the repercussion, which is the source of the violence of
flame and heat.

But this difference is chiefly shown in flame and boiling liquids,
which always hurry, swell, and subside again in detached parts.

It is also shown in bodies of such hard texture as not to swell or
dilate in bulk, such as red-hot iron, in which the heat is most violent.

It is also shown by the fires burning most briskly in the coldest
weather.

It is also shown by this, that when the air is dilated in the
thermometer uniformly and equably, without any impediment or repulsion,
the heat is not perceptible. In confined draughts also, although they
break out very violently, no remarkable heat is perceived, because
the motion affects the whole, without any alternating motion in the
particles; for which reason try whether flame do not burn more at the
sides than in its centre.

It is also shown in this, that all burning proceeds by the minute pores
of bodies--undermining, penetrating, piercing, and pricking them as if
with an infinite number of needle-points. Hence all strong acids (if
adapted to the body on which they act) exhibit the effects of fire,
from their corroding and pungent nature.

The difference of which we now speak is common also to the nature of
cold, in which the contracting motion is restrained by the resistance
of expansion, as in heat the expansive motion is restrained by the
resistance of contraction.

Whether, therefore, the particles of matter penetrate inward or
outward, the reasoning is the same, though the power be very different,
because we have nothing on earth which is intensely cold.

IV. The fourth difference is a modification of the preceding, namely,
that this stimulating or penetrating motion should be rapid and never
sluggish, and should take place not in the very minutest particles, but
rather in those of some tolerable dimensions.

It is shown by comparing the effects of fire with those of time. Time
dries, consumes, undermines, and reduces to ashes as well as fire, and
perhaps to a much finer degree; but as its motion is very slow, and
attacks very minute particles, no heat is perceived.

It is also shown in a comparison of the dissolution of iron and gold;
for gold is dissolved without the excitement of any heat, but iron with
a vehement excitement of it, although most in the same time, because in
the former the penetration of the separating acid is mild, and gently
insinuates itself, and the particles of gold yield easily, but the
penetration of iron is violent, and attended with some struggle, and
its particles are more obstinate.

It is partially shown, also, in some gangrenes and mortifications of
flesh, which do not excite great heat or pain, from the gentle nature
of the putrefaction.

Let this suffice for a first vintage, or the commencement of the
interpretation of the form of heat by the liberty of the understanding.

From this first vintage the form or true definition of heat (considered
relatively to the universe and not to the sense) is briefly thus--Heat
is an expansive motion restrained, and striving to exert itself in the
smaller particles. [106] The expansion is modified by its tendency to
rise, though expanding toward the exterior; and the effort is modified
by its not being sluggish, but active and somewhat violent.

With regard to the operative definition, the matter is the same. If you
are able to excite a dilating or expansive motion in any natural body,
and so to repress that motion and force it on itself as not to allow
the expansion to proceed equally, but only to be partially exerted and
partially repressed, you will beyond all doubt produce heat, without
any consideration as to whether the body be of earth (or elementary, as
they term it), or imbued with celestial influence, luminous or opaque,
rare or dense, locally expanded or contained within the bounds of its
first dimensions, verging to dissolution or remaining fixed, animal,
vegetable, or mineral, water, or oil, or air, or any other substance
whatever susceptible of such motion. Sensible heat is the same, but
considered relatively to the senses. Let us now proceed to further
helps.

XXI. After our tables of first review, our rejection or exclusive
table, and the first vintage derived from them, we must advance to the
remaining helps of the understanding with regard to the interpretation
of nature, and a true and perfect induction, in offering which we
will take the examples of cold and heat where tables are necessary,
but where fewer instances are required we will go through a variety
of others, so as neither to confound investigation nor to narrow our
doctrine.

In the first place, therefore, we will treat of prerogative
instances;[107] 2. Of the supports of induction; 3. Of the correction
of induction; 4. Of varying the investigation according to the
nature of the subject; 5. Of the prerogative natures with respect to
investigation, or of what should be the first or last objects of our
research; 6. Of the limits of investigation, or a synopsis of all
natures that exist in the universe; 7. Of the application to practical
purposes, or of what relates to man; 8. Of the preparations for
investigation; 9. And lastly, of the ascending and descending scale of
axioms. [108]

XXII. Among the prerogative instances we will first mention solitary
instances. Solitary instances are those which exhibit the required
nature in subjects that have nothing in common with any other subject
than the nature in question, or which do not exhibit the required
nature in subjects resembling others in every respect except that
of the nature in question; for these instances manifestly remove
prolixity, and accelerate and confirm exclusion, so that a few of them
are of as much avail as many.

For instance, let the inquiry be the nature of color. Prisms,
crystalline gems, which yield colors not only internally but on the
wall, dews, etc. , are solitary instances; for they have nothing in
common with the fixed colors in flowers and colored gems, metals,
woods, etc. , except the color itself. Hence we easily deduce that
color is nothing but a modification of the image of the incident and
absorbed light, occasioned in the former case by the different degrees
of incidence, in the latter by the various textures and forms of
bodies. [109] These are solitary instances as regards similitude.

Again, in the same inquiry the distinct veins of white and black in
marble, and the variegated colors of flowers of the same species, are
solitary instances; for the black and white of marble, and the spots of
white and purple in the flowers of the stock, agree in every respect
but that of color. Thence we easily deduce that color has not much to
do with the intrinsic natures of any body, but depends only on the
coarser and as it were mechanical arrangement of the parts. These are
solitary instances as regards difference. We call them both solitary or
wild, to borrow a word from the astronomers.

XXIII. In the second rank of prerogative instances we will consider
migrating instances. In these the required nature passes toward
generation, having no previous existence, or toward corruption, having
first existed. In each of these divisions, therefore, the instances
are always twofold, or rather it is one instance, first in motion or
on its passage, and then brought to the opposite conclusion. These
instances not only hasten and confirm exclusion, but also reduce
affirmation, or the form itself, to a narrow compass; for the form
must be something conferred by this migration, or, on the contrary,
removed and destroyed by it; and although all exclusion advances
affirmation, yet this takes place more directly in the same than in
different subjects; but if the form (as it is quite clear from what
has been advanced) exhibit itself in one subject, it leads to all. The
more simple the migration is, the more valuable is the instance. These
migrating instances are, moreover, very useful in practice, for since
they manifest the form, coupled with that which causes or destroys it,
they point out the right practice in some subjects, and thence there
is an easy transition to those with which they are most allied. There
is, however, a degree of danger which demands caution, namely, lest
they should refer the form too much to its efficient cause, and imbue,
or at least tinge, the understanding with a false notion of the form
from the appearance of such cause, which is never more than a vehicle
or conveyance of the form. This may easily be remedied by a proper
application of exclusion.

Let us then give an example of a migrating instance. Let whiteness be
the required nature. An instance which passes toward generation is
glass in its entire and in its powdered state, or water in its natural
state, and when agitated to froth; for glass when entire, and water in
its natural state, are transparent and not white, but powdered glass
and the froth of water are white and not transparent. We must inquire,
therefore, what has happened to the glass or water in the course of
this migration; for it is manifest that the form of whiteness is
conveyed and introduced by the bruising of the glass and the agitation
of the water; but nothing is found to have been introduced but a
diminishing of the parts of the glass and water and the insertion
of air. Yet this is no slight progress toward discovering the form
of whiteness, namely, that two bodies, in themselves more or less
transparent (as air and water, or air and glass), when brought into
contact in minute portions, exhibit whiteness from the unequal
refraction of the rays of light.

But here we must also give an example of the danger and caution of
which we spoke; for instance, it will readily occur to an understanding
perverted by efficients, that air is always necessary for producing the
form of whiteness, or that whiteness is only generated by transparent
bodies, which suppositions are both false, and proved to be so by
many exclusions; nay, it will rather appear (without any particular
regard to air or the like), that all bodies which are even in such of
their parts as affect the sight exhibit transparency, those which are
uneven and of simple texture whiteness, those which are uneven and of
compound but regular texture all the other colors except black, but
those which are uneven and of a compound irregular and confused texture
exhibit blackness. An example has been given, therefore, of an instance
migrating toward generation in the required nature of whiteness. An
instance migrating toward corruption in the same nature is that of
dissolving froth or snow, for they lose their whiteness and assume the
transparency of water in its pure state without air.

Nor should we by any means omit to state, that under migrating
instances we must comprehend not only those which pass toward
generation and destruction, but also those which pass toward increase
or decrease, for they, too, assist in the discovery of the form, as is
clear from our definition of a form and the Table of Degrees. Hence
paper, which is white when dry, is less white when moistened (from
the exclusion of air and admission of water), and tends more to
transparency. The reason is the same as in the above instances. [110]

XXIV. In the third rank of prerogative instances we will class
conspicuous instances, of which we spoke in our first vintage of the
form of heat, and which we are also wont to call coruscations, or free
and predominant instances. They are such as show the required nature
in its bare substantial shape, and at its height or greatest degree
of power, emancipated and free from all impediments, or at least
overcoming, suppressing, and restraining them by the strength of its
qualities; for since every body is susceptible of many united forms of
natures in the concrete, the consequence is that they mutually deaden,
depress, break, and confine each other, and the individual forms are
obscured. But there are some subjects in which the required nature
exists in its full vigor rather than in others, either from the absence
of any impediment, or the predominance of its quality. Such instances
are eminently conspicuous. But even in these care must be taken, and
the hastiness of the understanding checked, for whatever makes a show
of the form, and forces it forward, is to be suspected, and recourse
must be had to severe and diligent exclusion.

For example, let heat be the required nature. The thermometer is a
conspicuous instance of the expansive motion, which (as has been
observed) constitutes the chief part of the form of heat; for although
flame clearly exhibits expansion, yet from its being extinguished every
moment, it does not exhibit the progress of expansion. Boiling water
again, from its rapid conversion into vapor, does not so well exhibit
the expansion of water in its own shape, while red-hot iron and the
like are so far from showing this progress, that, on the contrary, the
expansion itself is scarcely evident to the senses, on account of its
spirit being repressed and weakened by the compact and coarse particles
which subdue and restrain it. But the thermometer strikingly exhibits
the expansion of the air as being evident and progressive, durable and
not transitory. [111]

Take another example. Let the required nature be weight. Quicksilver
is a conspicuous instance of weight; for it is far heavier than any
other substance except gold, which is not much heavier, and it is a
better instance than gold for the purpose of indicating the form of
weight; for gold is solid and consistent, which qualities must be
referred to density, but quicksilver is liquid and teeming with spirit,
yet much heavier than the diamond and other substances considered to
be most solid; whence it is shown that the form of gravity or weight
predominates only in the quantity of matter, and not in the close
fitting of it. [112]

XXV. In the fourth rank of prerogative instances we will class
clandestine instances, which we are also wont to call twilight
instances; they are as it were opposed to the conspicuous instances,
for they show the required nature in its lowest state of efficacy, and
as it were its cradle and first rudiments, making an effort and a sort
of first attempt, but concealed and subdued by a contrary nature. Such
instances are, however, of great importance in discovering forms, for
as the conspicuous tend easily to differences, so do the clandestine
best lead to genera, that is, to those common natures of which the
required natures are only the limits.

As an example, let consistency, or that which confines itself, be
the required nature, the opposite of which is a liquid or flowing
state. The clandestine instances are such as exhibit some weak and low
degree of consistency in fluids, as a water bubble, which is a sort
of consistent and bounded pellicle formed out of the substance of the
water. So eaves’ droppings, if there be enough water to follow them,
draw themselves out into a thin thread, not to break the continuity
of the water, but if there be not enough to follow, the water forms
itself into a round drop, which is the best form to prevent a breach
of continuity; and at the moment the thread ceases, and the water
begins to fall in drops, the thread of water recoils upward to avoid
such a breach. Nay, in metals, which when melted are liquid but more
tenacious, the melted drops often recoil and are suspended. There is
something similar in the instance of the child’s looking-glass, which
little boys will sometimes form of spittle between rushes, and where
the same pellicle of water is observable; and still more in that other
amusement of children, when they take some water rendered a little
more tenacious by soap, and inflate it with a pipe, forming the water
into a sort of castle of bubbles, which assumes such consistency, by
the interposition of the air, as to admit of being thrown some little
distance without bursting. The best example is that of froth and snow,
which assume such consistency as almost to admit of being cut, although
composed of air and water, both liquids. All these circumstances
clearly show that the terms liquid and consistent are merely vulgar
notions adapted to the sense, and that in reality all bodies have a
tendency to avoid a breach of continuity, faint and weak in bodies
composed of homogeneous parts (as is the case with liquids), but more
vivid and powerful in those composed of heterogeneous parts, because
the approach of heterogeneous matter binds bodies together, while the
insinuation of homogeneous matter loosens and relaxes them.

Again, to take another example, let the required nature be attraction
or the cohesion of bodies. The most remarkable conspicuous instance
with regard to its form is the magnet. The contrary nature to
attraction is non-attraction, though in a similar substance. Thus
iron does not attract iron, lead lead, wood wood, nor water water.
But the clandestine instance is that of the magnet armed with iron,
or rather that of iron in the magnet so armed. For its nature is such
that the magnet when armed does not attract iron more powerfully at
any given distance than when unarmed; but if the iron be brought in
contact with the armed magnet, the latter will sustain a much greater
weight than the simple magnet, from the resemblance of substance in the
two portions of iron, a quality altogether clandestine and hidden in
the iron until the magnet was introduced. It is manifest, therefore,
that the form of cohesion is something which is vivid and robust in
the magnet, and hidden and weak in the iron. It is to be observed,
also, that small wooden arrows without an iron point, when discharged
from large mortars, penetrate further into wooden substances (such
as the ribs of ships or the like), than the same arrows pointed with
iron,[113] owing to the similarity of substance, though this quality
was previously latent in the wood. Again, although in the mass air does
not appear to attract air, nor water water, yet when one bubble is
brought near another, they are both more readily dissolved, from the
tendency to contact of the water with the water, and the air with the
air. [114] These clandestine instances (which are, as has been observed,
of the most important service) are principally to be observed in small
portions of bodies, for the larger masses observe more universal and
general forms, as will be mentioned in its proper place. [115]

XXVI. In the fifth rank of prerogative instances we will class
constitutive instances, which we are wont also to call collective
instances. They constitute a species or lesser form, as it were, of the
required nature. For since the real forms (which are always convertible
with the given nature) lie at some depth, and are not easily
discovered, the necessity of the case and the infirmity of the human
understanding require that the particular forms, which collect certain
groups of instances (but by no means all) into some common notion,
should not be neglected, but most diligently observed. For whatever
unites nature, even imperfectly, opens the way to the discovery of the
form. The instances, therefore, which are serviceable in this respect
are of no mean power, but endowed with some degree of prerogative.

Here, nevertheless, great care must be taken that, after the discovery
of several of these particular forms, and the establishing of certain
partitions or divisions of the required nature derived from them, the
human understanding do not at once rest satisfied, without preparing
for the investigation of the great or leading form, and taking it for
granted that nature is compound and divided from its very root, despise
and reject any further union as a point of superfluous refinement, and
tending to mere abstraction.

For instance, let the required nature be memory, or that which
excites and assists memory. The constitutive instances are order or
distribution, which manifestly assists memory: topics or commonplaces
in artificial memory, which may be either places in their literal
sense, as a gate, a corner, a window, and the like, or familiar persons
and marks, or anything else (provided it be arranged in a determinate
order), as animals, plants, and words, letters, characters, historical
persons, and the like, of which, however, some are more convenient than
others. All these commonplaces materially assist memory, and raise it
far above its natural strength. Verse, too, is recollected and learned
more easily than prose. From this group of three instances--order,
the commonplaces of artificial memory, and verses--is constituted
one species of aid for the memory,[116] which may be well termed a
separation from infinity. For when a man strives to recollect or recall
anything to memory, without a preconceived notion or perception of
the object of his search, he inquires about, and labors, and turns
from point to point, as if involved in infinity. But if he have any
preconceived notion, this infinity is separated off, and the range of
his memory is brought within closer limits. In the three instances
given above, the preconceived notion is clear and determined. In the
first, it must be something that agrees with order; in the second, an
image which has some relation or agreement with the fixed commonplaces;
in the third, words which fall into a verse: and thus infinity is
divided off. Other instances will offer another species, namely,
that whatever brings the intellect into contact with something that
strikes the sense (the principal point of artificial memory), assists
the memory. Others again offer another species, namely, whatever
excites an impression by any powerful passion, as fear, shame, wonder,
delight, assists the memory. Other instances will afford another
species: thus those impressions remain most fixed in the memory which
are taken from the mind when clear and least occupied by preceding
or succeeding notions, such as the things we learn in childhood, or
imagine before sleep, and the first time of any circumstance happening.
Other instances afford the following species: namely, that a multitude
of circumstances or handles assist the memory, such as writing in
paragraphs, reading aloud, or recitation. Lastly, other instances
afford still another species: thus the things we anticipate, and which
rouse our attention, are more easily remembered than transient events;
as if you read any work twenty times over, you will not learn it by
heart so readily as if you were to read it but ten times, trying each
time to repeat it, and when your memory fails you looking into the
book. There are, therefore, six lesser forms, as it were, of things
which assist the memory: namely--1, the separation of infinity; 2, the
connection of the mind with the senses; 3, the impression in strong
passion; 4, the impression on the mind when pure; 5, the multitude of
handles; 6, anticipation.

Again, for example’s sake, let the required nature be taste or the
power of tasting. The following instances are constitutive: 1. Those
who do not smell, but are deprived by nature of that sense, do not
perceive or distinguish rancid or putrid food by their taste, nor
garlic from roses, and the like. 2. Again, those whose nostrils are
obstructed by accident (such as a cold) do not distinguish any putrid
or rancid matter from anything sprinkled with rose-water. 3. If those
who suffer from a cold blow their noses violently at the very moment
in which they have anything fetid or perfumed in their mouth, or on
their palate, they instantly have a clear perception of the fetor or
perfume. These instances afford and constitute this species or division
of taste, namely, that it is in part nothing else than an internal
smelling, passing and descending through the upper passages of the
nostrils to the mouth and palate. But, on the other hand, those whose
power of smelling is deficient or obstructed, perceive what is salt,
sweet, pungent, acid, rough, and bitter, and the like, as well as any
one else: so that the taste is clearly something compounded of the
internal smelling, and an exquisite species of touch which we will not
here discuss.

Again, as another example, let the required nature be the communication
of quality, without intermixture of substance. The instance of light
will afford or constitute one species of communication, heat and
the magnet another. For the communication of light is momentary and
immediately arrested upon the removal of the original light. But heat,
and the magnetic force, when once transmitted to or excited in another
body, remain fixed for a considerable time after the removal of the
source.

In fine, the prerogative of constitutive instances is considerable,
for they materially assist the definitions (especially in detail) and
the divisions or partitions of natures, concerning which Plato has
well said, “He who can properly define and divide is to be considered
a god. ”[117]

XXVII. In the sixth rank of prerogative instances we will place similar
or proportionate instances, which we are also wont to call physical
parallels, or resemblances. They are such as exhibit the resemblances
and connection of things, not in minor forms (as the constitutive do),
but at once in the concrete. They are, therefore, as it were, the first
and lowest steps toward the union of nature; nor do they immediately
establish any axiom, but merely indicate and observe a certain relation
of bodies to each other. But although they be not of much assistance
in discovering forms, yet they are of great advantage in disclosing
the frame of parts of the universe, upon whose members they practice
a species of anatomy, and thence occasionally lead us gently on to
sublime and noble axioms, especially such as relate to the construction
of the world, rather than to simple natures and forms.

As an example, take the following similar instances: a mirror and the
eye; the formation of the ear, and places which return an echo. From
such similarity, besides observing the resemblance (which is useful
for many purposes), it is easy to collect and form this axiom. That
the organs of the senses, and bodies which produce reflections to the
senses, are of a similar nature. Again, the understanding once informed
of this, rises easily to a higher and nobler axiom; namely, that the
only distinction between sensitive and inanimate bodies, in those
points in which they agree and sympathize, is this: in the former,
animal spirit is added to the arrangement of the body, in the latter it
is wanting. So that there might be as many senses in animals as there
are points of agreement with inanimate bodies, if the animated body
were perforated, so as to allow the spirit to have access to the limb
properly disposed for action, as a fit organ. And, on the other hand,
there are, without doubt, as many motions in an inanimate as there are
senses in the animated body, though the animal spirit be absent. There
must, however, be many more motions in inanimate bodies than senses in
the animated, from the small number of organs of sense. A very plain
example of this is afforded by pains. For, as animals are liable to
many kinds and various descriptions of pains (such as those of burning,
of intense cold, of pricking, squeezing, stretching, and the like),
so is it most certain, that the same circumstances, as far as motion
is concerned, happen to inanimate bodies, such as wood or stone when
burned, frozen, pricked, cut, bent, bruised, and the like; although
there be no sensation, owing to the absence of animal spirit.

Again, wonderful as it may appear, the roots and branches of trees
are similar instances. For every vegetable swells and throws out its
constituent parts toward the circumference, both upward and downward.
And there is no difference between the roots and branches, except that
the root is buried in the earth, and the branches are exposed to the
air and sun. For if one take a young and vigorous shoot, and bend it
down to a small portion of loose earth, although it be not fixed to
the ground, yet will it immediately produce a root, and not a branch.
And, _vice versâ_, if earth be placed above, and so forced down with a
stone or any hard substance, as to confine the plant and prevent its
branching upward, it will throw out branches into the air downward.
The gums of trees, and most rock gems, are similar instances; for both
of them are exudations and filtered juices, derived in the former
instance from trees, in the latter from stones; the brightness and
clearness of both arising from a delicate and accurate filtering. For
nearly the same reason, the hair of animals is less beautiful and vivid
in its color than the plumage of most birds, because the juices are
less delicately filtered through the skin than through the quills.

The scrotum of males and matrix of females are also similar instances;
so that the noble formation which constitutes the difference of the
sexes appears to differ only as to the one being internal and the other
external; a greater degree of heat causing the genitals to protrude in
the male, while the heat of the female being too weak to effect this,
they are retained internally.

The fins of fishes and the feet of quadrupeds, or the feet and wings of
birds, are similar instances; to which Aristotle adds the four folds in
the motion of serpents;[118] so that in the formation of the universe,
the motion of animals appears to be chiefly effected by four joints or
bendings.

The teeth of land animals, and the beaks of birds, are similar
instances, whence it is clear, that in all perfect animals there is a
determination of some hard substance toward the mouth.

Again, the resemblance and conformity of man to an inverted plant
is not absurd. For the head is the root of the nerves and animal
faculties, and the seminal parts are the lowest, not including the
extremities of the legs and arms. But in the plant, the root (which
resembles the head) is regularly placed in the lowest, and the seeds in
the highest part. [119]

Lastly, we must particularly recommend and suggest, that man’s present
industry in the investigation and compilation of natural history be
entirely changed, and directed to the reverse of the present system.
For it has hitherto been active and curious in noting the variety of
things, and explaining the accurate differences of animals, vegetables,
and minerals, most of which are the mere sport of nature, rather
than of any real utility as concerns the sciences. Pursuits of this
nature are certainly agreeable, and sometimes of practical advantage,
but contribute little or nothing to the thorough investigation of
nature. Our labor must therefore be directed toward inquiring into and
observing resemblances and analogies, both in the whole and its parts,
for they unite nature, and lay the foundation of the sciences.

Here, however, a severe and rigorous caution must be observed, that we
only consider as similar and proportionate instances, those which (as
we first observed) point out physical resemblances; that is, real and
substantial resemblances, deeply founded in nature, and not casual and
superficial, much less superstitious or curious; such as those which
are constantly put forward by the writers on natural magic (the most
idle of men, and who are scarcely fit to be named in connection with
such serious matters as we now treat of), who, with much vanity and
folly, describe, and sometimes too, invent, unmeaning resemblances and
sympathies.

But leaving such to themselves, similar instances are not to be
neglected, in the greater portions of the world’s conformation; such
as Africa and the Peruvian continent, which reaches to the Straits of
Magellan; both of which possess a similar isthmus and similar capes, a
circumstance not to be attributed to mere accident.

Again, the New and Old World are both of them broad and expanded toward
the north, and narrow and pointed toward the south.

Again, we have very remarkable similar instances in the intense cold,
toward the middle regions (as it is termed) of the air, and the violent
fires which are often found to burst from subterraneous spots, the
similarity consisting in both being ends and extremes; the extreme of
the nature of cold, for instance, is toward the boundary of heaven,
and that of the nature of heat toward the centre of the earth, by a
similar species of opposition or rejection of the contrary nature.

Lastly, in the axioms of the sciences, there is a similarity of
instances worthy of observation. Thus the rhetorical trope which is
called surprise, is similar to that of music termed the declining of
a cadence. Again--the mathematical postulate, that things which are
equal to the same are equal to one another, is similar to the form of
the syllogism in logic, which unites things agreeing in the middle
term. [120] Lastly, a certain degree of sagacity in collecting and
searching for physical points of similarity, is very useful in many
respects. [121]

XXVIII. In the seventh rank of prerogative instances, we will place
singular instances, which we are also wont to call irregular or
heteroclite (to borrow a term from the grammarians). They are such
as exhibit bodies in the concrete, of an apparently extravagant and
separate nature, agreeing but little with other things of the same
species. For, while the similar instances resemble each other, those
we now speak of are only like themselves. Their use is much the same
with that of clandestine instances: they bring out and unite nature,
and discover genera or common natures, which must afterward be limited
by real differences. Nor should we desist from inquiry, until the
properties and qualities of those things, which may be deemed miracles,
as it were, of nature, be reduced to, and comprehended in, some form or
certain law; so that all irregularity or singularity may be found to
depend on some common form; and the miracle only consists in accurate
differences, degree, and rare coincidence, not in the species itself.
Man’s meditation proceeds no further at present, than just to consider
things of this kind as the secrets and vast efforts of nature, without
an assignable cause, and, as it were, exceptions to general rules.

As examples of singular instances, we have the sun and moon among
the heavenly bodies; the magnet among minerals; quicksilver among
metals; the elephant among quadrupeds; the venereal sensation among
the different kinds of touch; the scent of sporting dogs among those
of smell. The letter S, too, is considered by the grammarians as sui
generis, from its easily uniting with double or triple consonants,
which no other letter will. These instances are of great value, because
they excite and keep alive inquiry, and correct an understanding
depraved by habit and the common course of things.

XXIX. In the eighth rank of prerogative instances, we will place
deviating instances, such as the errors of nature, or strange and
monstrous objects, in which nature deviates and turns from her
ordinary course. For the errors of nature differ from singular
instances, inasmuch as the latter are the miracles of species, the
former of individuals. Their use is much the same, for they rectify the
understanding in opposition to habit, and reveal common forms. For with
regard to these, also, we must not desist from inquiry, till we discern
the cause of the deviation. The cause does not, however, in such cases
rise to a regular form, but only to the latent process toward such a
form. For he who is acquainted with the paths of nature, will more
readily observe her deviations; and, _vice versâ_, he who has learned
her deviations will be able more accurately to describe her paths.

They differ again from singular instances, by being much more apt for
practice and the operative branch. For it would be very difficult to
generate new species, but less so to vary known species, and thus
produce many rare and unusual results. [122] The passage from the
miracles of nature to those of art is easy; for if nature be once
seized in her variations, and the cause be manifest, it will be easy to
lead her by art to such deviation as she was at first led to by chance;
and not only to that but others, since deviations on the one side
lead and open the way to others in every direction. Of this we do not
require any examples, since they are so abundant. For a compilation, or
particular natural history, must be made of all monsters and prodigious
births of nature; of everything, in short, which is new, rare and
unusual in nature. This should be done with a rigorous selection, so as
to be worthy of credit. Those are most to be suspected which depend
upon superstition, as the prodigies of Livy, and those perhaps, but
little less, which are found in the works of writers on natural magic,
or even alchemy, and the like; for such men, as it were, are the very
suitors and lovers of fables; but our instances should be derived from
some grave and credible history, and faithful narration.

XXX. In the ninth rank of prerogative instances, we will place
bordering instances, which we are also wont to term participants. They
are such as exhibit those species of bodies which appear to be composed
of two species, or to be the rudiments between the one and the other.
They may well be classed with the singular or heteroclite instances;
for in the whole system of things, they are rare and extraordinary. Yet
from their dignity, they must be treated of and classed separately,
for they point out admirably the order and constitution of things, and
suggest the causes of the number and quality of the more common species
in the universe, leading the understanding from that which is, to that
which is possible.

We have examples of them in moss, which is something between
putrescence and a plant;[123] in some comets, which hold a place
between stars and ignited meteors; in flying fishes, between fishes and
birds; and in bats, between birds and quadrupeds. [124] Again,

Simia quam similis turpissima bestia nobis.

We have also biformed fœtus, mingled species and the like.

XXXI. In the tenth rank of prerogative instances, we will place the
instances of power, or the fasces (to borrow a term from the insignia
of empire), which we are also wont to call the wit or hands of man.
These are such works as are most noble and perfect, and, as it were,
the masterpieces in every art. For since our principal object is to
make nature subservient to the state and wants of man, it becomes us
well to note and enumerate the works, which have long since been in the
power of man, especially those which are most polished and perfect:
because the passage from these to new and hitherto undiscovered
works, is more easy and feasible. For if any one, after an attentive
contemplation of such works as are extant, be willing to push forward
in his design with alacrity and vigor, he will undoubtedly either
advance them, or turn them to something within their immediate reach,
or even apply and transfer them to some more noble purpose.

Nor is this all: for as the understanding is elevated and raised by
rare and unusual works of nature, to investigate and discover the forms
which include them also, so is the same effect frequently produced by
the excellent and wonderful works of art; and even to a greater degree,
because the mode of effecting and constructing the miracles of art is
generally plain, while that of effecting the miracles of nature is more
obscure. Great care, however, must be taken, that they do not depress
the understanding, and fix it, as it were, to earth.

For there is some danger, lest the understanding should be astonished
and chained down, and as it were bewitched, by such works of art, as
appear to be the very summit and pinnacle of human industry, so as not
to become familiar with them, but rather to suppose that nothing of
the kind can be accomplished, unless the same means be employed, with
perhaps a little more diligence, and more accurate preparation.

Now, on the contrary, it may be stated as a fact, that the ways and
means hitherto discovered and observed, of effecting any matter or
work, are for the most part of little value, and that all really
efficient power depends, and is really to be deduced from the sources
of forms, none of which have yet been discovered.

Thus (as we have before observed), had any one meditated on ballistic
machines, and battering rams, as they were used by the ancients,
whatever application he might have exerted, and though he might have
consumed a whole life in the pursuit, yet would he never have hit upon
the invention of flaming engines, acting by means of gunpowder; nor
would any person, who had made woollen manufactories and cotton the
subject of his observation and reflection, have ever discovered thereby
the nature of the silkworm or of silk.

Hence all the most noble discoveries have (if you observe) come to
light, not by any gradual improvement and extension of the arts, but
merely by chance; while nothing imitates or anticipates chance (which
is wont to act at intervals of ages) but the invention of forms.

There is no necessity for adducing any particular examples of these
instances, since they are abundant. The plan to be pursued is this:
all the mechanical, and even the liberal arts (as far as they are
practical), should be visited and thoroughly examined, and thence there
should be formed a compilation or particular history of the great
masterpieces, or most finished works in each, as well as of the mode
of carrying them into effect.

Nor do we confine the diligence to be used in such a compilation to the
leading works and secrets only of every art, and such as excite wonder;
for wonder is engendered by rarity, since that which is rare, although
it be compounded of ordinary natures, always begets wonder.

On the contrary, that which is really wonderful, from some specific
difference distinguishing it from other species, is carelessly
observed, if it be but familiar. Yet the singular instances of art
should be observed no less than those of nature, which we have before
spoken of: and as in the latter we have classed the sun, the moon, the
magnet, and the like, all of them most familiar to us, but yet in their
nature singular, so should we proceed with the singular instances of
art.

For example: paper, a very common substance, is a singular instance
of art; for if you consider the subject attentively, you will find
that artificial substances are either woven by straight and transverse
lines, as silk, woollen, or linen cloth, and the like; or coagulated
from concrete juices, such as brick, earthenware, glass, enamel,
porcelain and the like, which admit of a polish if they be compact, but
if not, become hard without being polished; all which latter substances
are brittle, and not adherent or tenacious. On the contrary, paper is
a tenacious substance, which can be cut and torn, so as to resemble
and almost rival the skin of any animal, or the leaf of vegetables,
and the like works of nature; being neither brittle like glass, nor
woven like cloth, but having fibres and not distinct threads, just as
natural substances, so that scarcely anything similar can be found
among artificial substances, and it is absolutely singular. And in
artificial works we should certainly prefer those which approach the
nearest to an imitation of nature, or, on the other hand, powerfully
govern and change her course.

Again, in these instances which we term the wit and hands of man,
charms and conjuring should not be altogether despised, for although
mere amusements, and of little use, yet they may afford considerable
information.

Lastly, superstition and magic (in its common acceptation) are not to
be entirely omitted; for although they be overwhelmed by a mass of lies
and fables, yet some investigation should be made, to see if there be
really any latent natural operation in them; as in fascination, and the
fortifying of the imagination, the sympathy of distant objects, the
transmission of impressions from spirit to spirit no less than from
body to body, and the like.

XXXII. From the foregoing remarks, it is clear that the last five
species of instances (the similar, singular, deviating and bordering
instances, and those of power) should not be reserved for the
investigation of any given nature, as the preceding and many of the
succeeding instances must, but a collection of them should be made at
once, in the style of a particular history, so that they may arrange
the matter which enters the understanding, and correct its depraved
habit, for it is necessarily imbued, corrupted, perverted and distorted
by daily and habitual impressions.

They are to be used, therefore, as a preparative, for the purpose of
rectifying and purifying the understanding; for whatever withdraws it
from habit, levels and planes down its surface for the reception of the
dry and pure light of true notions.

These instances, moreover, level and prepare the way for the operative
branch, as we will mention in its proper place when speaking of the
practical deductions.

XXXIII. In the eleventh rank of prerogative instances we will place
accompanying and hostile instances. These are such as exhibit any body
or concrete, where the required nature is constantly found, as an
inseparable companion, or, on the contrary, where the required nature
is constantly avoided, and excluded from attendance, as an enemy. From
these instances may be formed certain and universal propositions,
either affirmative or negative; the subject of which will be the
concrete body, and the predicate the required nature. For particular
propositions are by no means fixed, when the required nature is found
to fluctuate and change in the concrete, either approaching and
acquired, or receding and laid aside. Hence particular propositions
have no great prerogative, except in the case of migration, of which we
have spoken above. Yet such particular propositions are of great use,
when compared with the universal, as will be mentioned in its proper
place. Nor do we require absolute affirmation or negation, even in
universal propositions, for if the exceptions be singular or rare, it
is sufficient for our purpose.

The use of accompanying instances is to narrow the affirmative of
form; for as it is narrowed by the migrating instances, where the form
must necessarily be something communicated or destroyed by the act of
migration, so it is narrowed by accompanying instances, where the form
must necessarily be something which enters into the concretion of the
body, or, on the contrary, is repugnant to it; and one who is well
acquainted with the constitution or formation of the body, will not be
far from bringing to light the form of the required nature.

For example: let the required nature be heat. Flame is an accompanying
instance; for in water, air, stone, metal, and many other substances,
heat is variable, and can approach or retire; but all flame is hot,
so that heat always accompanies the concretion of flame. We have no
hostile instance of heat; for the senses are unacquainted with the
interior of the earth, and there is no concretion of any known body
which is not susceptible of heat.

Again, let solidity be the required nature. Air is a hostile instance;
for metals may be liquid or solid, so may glass; even water may become
solid by congelation, but air cannot become solid or lose its fluidity.

With regard to these instances of fixed propositions, there are
two points to be observed, which are of importance. First, that
if there be no universal affirmative or negative, it be carefully
noted as not existing. Thus, in heat, we have observed that there
exists no universal negative, in such substances, at least, as have
come to our knowledge. Again, if the required nature be eternity or
incorruptibility, we have no universal affirmative within our sphere,
for these qualities cannot be predicated of any bodies below the
heavens, or above the interior of the earth. Secondly, to our general
propositions as to any concrete, whether affirmative or negative, we
should subjoin the concretes which appear to approach nearest to the
non-existing substances; such as the most gentle or least-burning
flames in heat, or gold in incorruptibility, since it approaches
nearest to it. For they all serve to show the limit of existence and
non-existence, and circumscribe forms, so that they cannot wander
beyond the conditions of matter.

XXXIV. In the twelfth rank of prerogative instances, we will class
those subjunctive instances, of which we spoke in the last aphorism,
and which we are also wont to call instances of extremity or limits;
for they are not only serviceable when subjoined to fixed propositions,
but also of themselves and from their own nature. They indicate with
sufficient precision the real divisions of nature, and measures of
things, and the “how far” nature effects or allows of anything, and
her passage thence to something else. Such are gold in weight, iron in
hardness, the whale in the size of animals, the dog in smell, the flame
of gunpowder in rapid expansion, and others of a like nature. Nor are
we to pass over the extremes in defect, as well as in abundance, as
spirits of wine in weight, the touchstone in softness, the worms upon
the skin in the size of animals, and the like.

XXXV. In the thirteenth rank of prerogative instances we will place
those of alliance or union. They are such as mingle and unite natures
held to be heterogeneous, and observed and marked as such in received
classifications.

These instances show that the operation and effect, which is considered
peculiar to some one of such heterogeneous natures, may also be
attributed to another nature styled heterogeneous, so as to prove that
the difference of the natures is not real nor essential, but a mere
modification of a common nature. They are very serviceable, therefore,
in elevating and carrying on the mind, from differences to genera,
and in removing those phantoms and images of things, which meet it in
disguise in concrete substances.

For example: let the required nature be heat. The classification
of heat into three kinds, that of the celestial bodies, that of
animals, and that of fire, appears to be settled and admitted; and
these kinds of heat, especially one of them compared with the other
two, are supposed to be different, and clearly heterogeneous in
their essence and species, or specific nature, since the heat of the
heavenly bodies and of animals generates and cherishes, while that of
fire corrupts and destroys. We have an instance of alliance, then,
in a very common experiment, that of a vine branch admitted into a
building where there is a constant fire, by which the grapes ripen a
whole month sooner than in the air; so that fruit upon the tree can
be ripened by fire, although this appear the peculiar effect of the
sun. From this beginning, therefore, the understanding rejects all
essential difference, and easily ascends to the investigation of the
real differences between the heat of the sun and that of fire, by which
their operation is rendered dissimilar, although they partake of a
common nature.

These differences will be found to be four in number. 1. The heat of
the sun is much milder and gentler in degree than that of fire. 2. It
is much more moist in quality, especially as it is transmitted to us
through the air. 3. Which is the chief point, it is very unequal,
advancing and increased at one time, retiring and diminished at
another, which mainly contributes to the generation of bodies. For
Aristotle rightly asserted, that the principal cause of generation and
corruption on the surface of the earth was the oblique path of the sun
in the zodiac, whence its heat becomes very unequal, partly from the
alternation of night and day, partly from the succession of summer and
winter. Yet must he immediately corrupt and pervert his discovery,
by dictating to nature according to his habit, and dogmatically
assigning the cause of generation to the approach of the sun, and
that of corruption to its retreat; while, in fact, each circumstance
indifferently and not respectively contributes both to generation and
corruption; for unequal heat tends to generate and corrupt, as equable
heat does to preserve. 4. The fourth difference between the heat of the
sun and fire is of great consequence; namely, that the sun, gradually,
and for a length of time, insinuates its effects, while those of fire
(urged by the impatience of man) are brought to a termination in a
shorter space of time. But if any one were to pay attention to the
tempering of fire, and reducing it to a more moderate and gentle degree
(which may be done in various ways), and then were to sprinkle and mix
a degree of humidity with it; and, above all, were to imitate the sun
in its inequality; and, lastly, were patiently to suffer some delay
(not such, however, as is proportioned to the effects of the sun,
but more than men usually admit of in those of fire), he would soon
banish the notion of any difference, and would attempt, or equal, or
perhaps sometimes surpass the effect of the sun, by the heat of fire.
A like instance of alliance is that of reviving butterflies, benumbed
and nearly dead from cold, by the gentle warmth of fire; so that fire
is no less able to revive animals than to ripen vegetables. We may
also mention the celebrated invention of Fracastorius, of applying a
pan considerably heated to the head in desperate cases of apoplexy,
which clearly expands the animal spirits, when compressed and almost
extinguished by the humors and obstructions of the brain, and excites
them to action, as the fire would operate on water or air, and in the
result produces life. Eggs are sometimes hatched by the heat of fire,
an exact imitation of animal heat; and there are many instances of the
like nature, so that no one can doubt that the heat of fire, in many
cases, can be modified till it resemble that of the heavenly bodies and
of animals.

Again, let the required natures be motion and rest. There appears to
be a settled classification, grounded on the deepest philosophy, that
natural bodies either revolve, move in a straight line, or stand still
and rest. For there is either motion without limit, or continuance
within a certain limit, or a translation toward a certain limit. The
eternal motion of revolution appears peculiar to the heavenly bodies,
rest to this our globe, and the other bodies (heavy and light, as they
are termed, that is to say, placed out of their natural position) are
borne in a straight line to masses or aggregates which resemble them,
the light toward the heaven, the heavy toward the earth; and all this
is very fine language.

But we have an instance of alliance in low comets, which revolve,
though far below the heavens; and the fiction of Aristotle, of the
comet being fixed to, or necessarily following some star, has been
long since exploded; not only because it is improbable in itself, but
from the evident fact of the discursive and irregular motion of comets
through various parts of the heavens. [125]

Another instance of alliance is that of the motion of air, which
appears to revolve from east to west within the tropics, where the
circles of revolution are the greatest.

The flow and ebb of the sea would perhaps be another instance, if the
water were once found to have a motion of revolution, though slow and
hardly perceptible, from east to west, subject, however, to a reaction
twice a day. If this be so, it is clear that the motion of revolution
is not confined to the celestial bodies, but is shared, also, by air
and water.

Again--the supposed peculiar disposition of light bodies to rise is
rather shaken; and here we may find an instance of alliance in a water
bubble. For if air be placed under water, it rises rapidly toward
the surface by that striking motion (as Democritus terms it) with
which the descending water strikes the air and raises it, not by any
struggle or effort of the air itself; and when it has reached the
surface of the water, it is prevented from ascending any further, by
the slight resistance it meets with in the water, which does not allow
an immediate separation of its parts, so that the tendency of the air
to rise must be very slight.

Again, let the required nature be weight. It is certainly a received
classification, that dense and solid bodies are borne toward the centre
of the earth, and rare and light bodies to the circumference of the
heavens, as their appropriate places. As far as relates to places
(though these things have much weight in the schools), the notion of
there being any determinate place is absurd and puerile. Philosophers
trifle, therefore, when they tell you, that if the earth were
perforated, heavy bodies would stop on their arrival at the centre.
This centre would indeed be an efficacious nothing, or mathematical
point, could it affect bodies or be sought by them, for a body is not
acted upon except by a body. [126] In fact, this tendency to ascend
and descend is either in the conformation of the moving body, or in
its harmony and sympathy with another body. But if any dense and solid
body be found, which does not, however, tend toward the earth, the
classification is at an end. Now, if we allow of Gilbert’s opinion,
that the magnetic power of the earth, in attracting heavy bodies, is
not extended beyond the limit of its peculiar virtue (which operates
always at a fixed distance and no further),[127] and this be proved by
some instance, such an instance will be one of alliance in our present
subject. The nearest approach to it is that of waterspouts, frequently
seen by persons navigating the Atlantic toward either of the Indies.
For the force and mass of the water suddenly effused by waterspouts,
appears to be so considerable, that the water must have been collected
previously, and have remained fixed where it was formed, until it was
afterward forced down by some violent cause, rather than made to fall
by the natural motion of gravity: so that it may be conjectured that
a dense and compact mass, at a great distance from the earth, may be
suspended as the earth itself is, and would not fall, unless forced
down. We do not, however, affirm this as certain. In the meanwhile,
both in this respect and many others, it will readily be seen how
deficient we are in natural history, since we are forced to have
recourse to suppositions for examples, instead of ascertained instances.

Again, let the required nature be the discursive power of the mind.
The classification of human reason and animal instinct appears to be
perfectly correct. Yet there are some instances of the actions of
brutes which seem to show that they, too, can syllogize. Thus it is
related, that a crow, which had nearly perished from thirst in a great
drought, saw some water in the hollow trunk of a tree, but as it was
too narrow for him to get into it, he continued to throw in pebbles,
which made the water rise till he could drink; and it afterward became
a proverb.

Again, let the required nature be vision. The classification
appears real and certain, which considers light as that which is
originally visible, and confers the power of seeing; and color, as
being secondarily visible, and not capable of being seen without
light, so as to appear a mere image or modification of light. Yet
there are instances of alliance in each respect; as in snow when in
great quantities, and in the flame of sulphur; the one being a color
originally and in itself light, the other a light verging toward
color. [128]

XXXVI. In the fourteenth rank of prerogative instances, we will place
the instances of the cross, borrowing our metaphor from the crosses
erected where two roads meet, to point out the different directions.
We are wont also to call them decisive and judicial instances, and in
some cases instances of the oracle and of command. Their nature is as
follows: When in investigating any nature the understanding is, as it
were, balanced, and uncertain to which of two or more natures the cause
of the required nature should be assigned, on account of the frequent
and usual concurrence of several natures, the instances of the cross
show that the union of one nature with the required nature is firm
and indissoluble, while that of the other is unsteady and separable;
by which means the question is decided, and the first is received as
the cause, while the other is dismissed and rejected. Such instances,
therefore, afford great light, and are of great weight, so that the
course of interpretation sometimes terminates, and is completed in
them. Sometimes, however, they are found among the instances already
observed, but they are generally new, being expressly and purposely
sought for and applied, and brought to light only by attentive and
active diligence.

For example: let the required nature be the flow and ebb of the sea,
which is repeated twice a day, at intervals of six hours between each
advance and retreat, with some little difference, agreeing with the
motion of the moon. We have here the following crossways:

This motion must be occasioned either by the advancing and the retiring
of the sea, like water shaken in a basin, which leaves one side while
it washes the other; or by the rising of the sea from the bottom,
and its again subsiding, like boiling water. But a doubt arises, to
which of these causes we should assign the flow and ebb. If the first
assertion be admitted, it follows, that when there is a flood on
one side, there must at the same time be an ebb on another, and the
question therefore is reduced to this. Now Acosta, and some others,
after a diligent inquiry, have observed that the flood tide takes place
on the coast of Florida, and the opposite coasts of Spain and Africa,
at the same time, as does also the ebb; and that there is not, on the
contrary, a flood tide at Florida when there is an ebb on the coasts
of Spain and Africa. Yet if one consider the subject attentively,
this does not prove the necessity of a rising motion, nor refute the
notion of a progressive motion. For the motion may be progressive, and
yet inundate the opposite shores of a channel at the same time; as if
the waters be forced and driven together from some other quarter, for
instance, which takes place in rivers, for they flow and ebb toward
each bank at the same time, yet their motion is clearly progressive,
being that of the waters from the sea entering their mouths. So it may
happen, that the waters coming in a vast body from the eastern Indian
Ocean are driven together, and forced into the channel of the Atlantic,
and therefore inundate both coasts at once. We must inquire, therefore,
if there be any other channel by which the waters can at the same time
sink and ebb; and the Southern Ocean at once suggests itself, which is
not less than the Atlantic, but rather broader and more extensive than
is requisite for this effect.

We at length arrive, then, at an instance of the cross, which is this.
If it be positively discovered, that when the flood sets in toward
the opposite coasts of Florida and Spain in the Atlantic, there is at
the same time a flood tide on the coasts of Peru and the back part
of China, in the Southern Ocean, then assuredly, from this decisive
instance, we must reject the assertion, that the flood and ebb of the
sea, about which we inquire, takes place by progressive motion; for
no other sea or place is left where there can be an ebb. But this may
most easily be learned, by inquiring of the inhabitants of Panama and
Lima (where the two oceans are separated by a narrow isthmus), whether
the flood and ebb takes place on the opposite sides of the isthmus
at the same time, or the reverse. This decision or rejection appears
certain, if it be granted that the earth is fixed; but if the earth
revolves, it may perhaps happen, that from the unequal revolution (as
regards velocity) of the earth and the waters of the sea, there may
be a violent forcing of the waters into a mass, forming the flood,
and a subsequent relaxation of them (when they can no longer bear the
accumulation), forming the ebb. A separate inquiry must be made into
this. Even with this hypothesis, however, it remains equally true, that
there must be an ebb somewhere, at the same time that there is a flood
in another quarter.

Again, let the required nature be the latter of the two motions we
have supposed; namely, that of a rising and subsiding motion, if it
should happen that upon diligent examination the progressive motion
be rejected. We have, then, three ways before us, with regard to this
nature. The motion, by which the waters raise themselves, and again
fall back, in the floods and ebbs, without the addition of any other
water rolled toward them, must take place in one of the three following
ways: Either the supply of water emanates from the interior of the
earth, and returns back again; or there is really no greater quantity
of water, but the same water (without any augmentation of its quantity)
is extended or rarefied, so as to occupy a greater space and dimension,
and again contracts itself; or there is neither an additional supply
nor any extension, but the same waters (with regard to quantity,
density, or rarity) raise themselves and fall from sympathy, by some
magnetic power attracting and calling them up, as it were, from
above. Let us then (passing over the first two motions) reduce the
investigation to the last, and inquire if there be any such elevation
of the water by sympathy or a magnetic force; and it is evident, in the
first place, that the whole mass of water being placed in the trench
or cavity of the sea, cannot be raised at once, because there would
not be enough to cover the bottom, so that if there be any tendency of
this kind in the water to raise itself, yet it would be interrupted
and checked by the cohesion of things, or (as the common expression
is) that there may be no vacuum. The water, therefore, must rise on
one side, and for that reason be diminished and ebb on another. But it
will again necessarily follow that the magnetic power not being able to
operate on the whole, operates most intensely on the centre, so as to
raise the waters there, which, when thus raised successively, desert
and abandon the sides. [129]

We at length arrive, then, at an instance of the cross, which is this:
if it be found that during the ebb the surface of the waters at sea
is more curved and round, from the waters rising in the middle, and
sinking at the sides or coast, and if, during a flood, it be more even
and level, from the waters returning to their former position, then
assuredly, by this decisive instance, the raising of them by a magnetic
force can be admitted; if otherwise, it must be entirely rejected.
It is not difficult to make the experiment (by sounding in straits),
whether the sea be deeper toward the middle in ebbs, than in floods.
But it must be observed, if this be the case, that (contrary to common
opinion) the waters rise in ebbs, and only return to their former
position in floods, so as to bathe and inundate the coast.

Again, let the required nature be the spontaneous motion of revolution,
and particularly, whether the diurnal motion, by which the sun and
stars appear to us to rise and set, be a real motion of revolution in
the heavenly bodies, or only apparent in them, and real in the earth.
There may be an instance of the cross of the following nature. If there
be discovered any motion in the ocean from east to west, though very
languid and weak, and if the same motion be discovered rather more
swift in the air (particularly within the tropics, where it is more
perceptible from the circles being greater). If it be discovered also
in the low comets, and be already quick and powerful in them; if it
be found also in the planets, but so tempered and regulated as to be
slower in those nearest the earth, and quicker in those at the greatest
distance, being quickest of all in the heavens, then the diurnal motion
should certainly be considered as real in the heavens, and that of the
earth must be rejected; for it will be evident that the motion from
east to west is part of the system of the world and universal; since it
is most rapid in the height of the heavens, and gradually grows weaker,
till it stops and is extinguished in rest at the earth.

Again, let the required nature be that other motion of revolution,
so celebrated among astronomers, which is contrary to the diurnal,
namely, from west to east--and which the ancient astronomers assign
to the planets, and even to the starry sphere, but Copernicus and his
followers to the earth also--and let it be examined whether any such
motion be found in nature, or it be rather a fiction and hypothesis
for abridging and facilitating calculation, and for promoting that
fine notion of effecting the heavenly motions by perfect circles; for
there is nothing which proves such a motion in heavenly objects to be
true and real, either in a planet’s not returning in its diurnal motion
to the same point of the starry sphere, or in the pole of the zodiac
being different from that of the world, which two circumstances have
occasioned this notion. For the first phenomenon is well accounted for
by the spheres overtaking or falling behind each other, and the second
by spiral lines; so that the inaccuracy of the return and declination
to the tropics may be rather modifications of the one diurnal motion
than contrary motions, or about different poles. And it is most
certain, if we consider ourselves for a moment as part of the vulgar
(setting aside the fictions of astronomers and the school, who are
wont undeservedly to attack the senses in many respects, and to affect
obscurity), that the apparent motion is such as we have said, a model
of which we have sometimes caused to be represented by wires in a sort
of a machine.

We may take the following instances of the cross upon this subject. If
it be found in any history worthy of credit, that there has existed any
comet, high or low, which has not revolved in manifest harmony (however
irregularly) with the diurnal motion, then we may decide so far as to
allow such a motion to be possible in nature. But if nothing of the
sort be found, it must be suspected, and recourse must be had to other
instances of the cross.

Again, let the required nature be weight or gravity. Heavy and
ponderous bodies must, either of their own nature, tend toward the
centre of the earth by their peculiar formation, or must be attracted
and hurried by the corporeal mass of the earth itself, as being an
assemblage of similar bodies, and be drawn to it by sympathy. But if
the latter be the cause, it follows that the nearer bodies approach to
the earth, the more powerfully and rapidly they must be borne toward
it, and the further they are distant, the more faintly and slowly (as
is the case in magnetic attractions), and that this must happen within
a given distance; so that if they be separated at such a distance from
the earth that the power of the earth cannot act upon them, they will
remain suspended like the earth, and not fall at all. [130]

The following instance of the cross may be adopted. Take a clock moved
by leaden weights,[131] and another by a spring, and let them be set
well together, so that one be neither quicker nor slower than the
other; then let the clock moved by weights be placed on the top of
a very high church, and the other be kept below, and let it be well
observed, if the former move slower than it did, from the diminished
power of the weights. Let the same experiment be made at the bottom
of mines worked to a considerable depth, in order to see whether the
clock move more quickly from the increased power of the weights.