ask, why it is not sufficient for all purposes, and accordingly, why it
does not supersede the move complicated and laborious methods? why every
sailor does not provide himself with a chronometer, instead of finding
his longitude at sea by tedious and oft-repeated calculations, as he is
in the habit of doing? I answer, it is only in a few extraordinary cases
that chronometers have been constructed of such accuracy as to afford
results as exact as those obtained by the other methods, to be described
shortly; and instruments of such perfection are too expensive for
general use among sailors. Indeed, the more common chronometers cost too
much to come within the means of a great majority of sea-faring men.
Moreover, by being transported from place to place, chronometers are
liable to change their _rate_. By the rate of any timepiece is meant its
deviation from perfect accuracy. Thus, if a clock should gain one second
per day, one day with another, and we should find it impossible to bring
it nearer to the truth, we may reckon this as its rate, and allow for it
in our estimate of the time of any particular observation. If the error
was not uniform, but sometimes greater and sometimes less than one
second per day, then the amount of such deviation is called its
"variation from its mean rate." I introduce these minute statements,
(which are more precise than I usually deem necessary,) to show you to
what an astonishing degree of accuracy chronometers have in some
instances been brought. They have been carried from London to Baffin's
Bay, and brought back, after a three years' voyage, and found to have
varied from their mean rate, during the whole time, only a second or
two, while the extreme variation of several chronometers, tried at the
Royal Observatory at Greenwich, never exceeded a second and a half.
Could chronometers always be depended on to such a degree of accuracy as
this, we should hardly desire any thing better for determining the
longitude of different places on the earth. A recent determination of
the longitude of the City Hall in New York, by means of three
chronometers, sent out from London expressly for that purpose, did not
differ from the longitude as found by a solar eclipse (which is one of
the best methods) but a second and a quarter.
_Eclipses of the sun and moon_ furnish the means of ascertaining the
longitude of a place, because the entrance of the moon into the earth's
shadow in a lunar eclipse, and the entrance of the moon upon the disk of
the sun in a solar eclipse, are severally examples of one of those
instantaneous occurrences in the heavens, which afford the means of
comparing the times of different places, and of thus determining their
differences of longitude. Thus, if the commencement of a lunar eclipse
was seen at one place an hour sooner than at another, the two places
would be fifteen degrees apart, in longitude; and if the longitude of
one of the places was known, that of the other would become known also.
The exact instant of the moon's entering into the shadow of the earth,
however, cannot be determined with very great precision, since the moon,
in passing through the earth's penumbra, loses its light gradually, so
that the moment when it leaves the penumbra and enters into the shadow
cannot be very accurately defined. The first contact of the moon with
the sun's disk, in a solar eclipse, or the moment of leaving it,--that
is, the beginning and end of the eclipse,--are instants that can be
determined with much precision, and accordingly they are much relied on
for an accurate determination of the longitude. But, on account of the
complicated and laborious nature of the calculation of the longitude
from an eclipse of the sun, (since the beginning and end are not seen at
different places, at the same moment,) this method of finding the
longitude is not adapted to common use, nor available at sea. It is
useful, however, for determining the longitude of fixed observatories.
The _lunar method of finding the longitude_ is the most refined and
accurate of all the modes practised at sea. The motion of the moon
through the heavens is so rapid, that she perceptibly alters her
distance from any star every minute; consequently, the moment when that
distance is a certain number of degrees and minutes is one of those
instantaneous events, which may be taken advantage of for comparing the
times of different places, and thus determining their difference of
longitude. Now, in a work called the 'Nautical Almanac,' printed in
London, annually, for the use of navigators, the distance of the moon
from the sun by day, or from known fixed stars by night, for every day
and night in the year, is calculated beforehand. If, therefore, a sailor
wishes to ascertain his longitude, he may take with his sextant the
distance of the moon from one of these stars at any time,--suppose nine
o'clock, at night,--and then turn to the 'Nautical Almanac,' and see
_what time it was at Greenwich_ when the distance between the moon and
that star was the same. Let it be twelve o'clock, or three hours in
advance of his time: his longitude, of course, is forty-five degrees
west.
This method requires more skill and accuracy than are possessed by the
majority of seafaring men; but, when practised with the requisite degree
of skill, its results are very satisfactory. Captain Basil Hall, one of
the most scientific commanders in the British navy, relates the
following incident, to show the excellence of this method. He sailed
from San Blas, on the west coast of Mexico, and, after a voyage of eight
thousand miles, occupying eighty-nine days, arrived off Rio de Janeiro,
having, in this interval, passed through the Pacific Ocean, rounded Cape
Horn, and crossed the South Atlantic, without making any land, or even
seeing a single sail, with the exception of an American whaler off Cape
Horn. When within a week's sail of Rio, he set seriously about
determining, by lunar observations, the precise line of the ship's
course, and its situation at a determinate moment; and having
ascertained this within from five to ten miles, ran the rest of the way
by those more ready and compendious methods, known to navigators, which
can be safely employed for short trips between one known point and
another, but which cannot be trusted in long voyages, where the moon is
the only sure guide. They steered towards Rio Janeiro for some days
after taking the lunars, and, having arrived within fifteen or twenty
miles of the coast, they hove to, at four in the morning, till the day
should break, and then bore up, proceeding cautiously, on account of a
thick fog which enveloped them. As this cleared away, they had the
satisfaction of seeing the great Sugar-Loaf Rock, which stands on one
side of the harbor's mouth, so nearly right ahead, that they had not to
alter their course above a point, in order to hit the entrance of the
harbor. This was the first land they had seen for three months, after
crossing so many seas, and being set backwards and forwards by
innumerable currents and foul winds. The effect on all on board was
electric; and the admiration of the sailors was unbounded. Indeed, what
could be more admirable than that a man on the deck of a vessel, by
measuring the distance between the moon and a star, with a little
instrument which he held in his hand, could determine his exact place on
the earth's surface in the midst of a vast ocean, after having traversed
it in all directions, for three months, crossing his track many times,
and all the while out of sight of land?
The lunar method of finding the longitude could never have been
susceptible of sufficient accuracy, had not the motions of the moon,
with all their irregularities, been studied and investigated by the most
laborious and profound researches. Hence Newton, while wrapt in those
meditations which, to superficial minds, would perhaps have appeared
rather curious than useful, inasmuch as they respected distant bodies of
the universe which seemed to have little connexion with the affairs of
this world, was laboring night and day for the benefit of the sailor and
the merchant. He was guiding the vessel of the one, and securing the
merchandise of the other; and thus he contributed a large share to
promote the happiness of his fellow-men, not only in exalting the powers
of the human intellect, but also in preserving the lives and fortunes of
those engaged in navigation and commerce. Principles in science are
rules in art; and the philosopher who is engaged in the investigation of
these principles, although his pursuits may be thought less practically
useful than those of the artisan who carries out those principles into
real life, yet, without the knowledge of the principles, the rules would
have never been known. Studies, therefore, the most abstruse, are, when
viewed as furnishing rules to act, often productive of the highest
practical utility.
Since the _tides_ are occasioned by the influence of the sun and moon, I
will conclude this Letter with a few remarks on this curious phenomenon.
By the tides are meant the alternate rising and falling of the waters of
the ocean. Its greatest and least elevations are called _high and low
water_; its rising and falling are called _flood and ebb_; and the
extraordinary high and low tides that occur twice every month are called
_spring and neap tides_. It is high or low tide on opposite sides of the
globe at the same time. If, for example, we have high water at noon, it
is also high water to those who live on the meridian below us, where it
is midnight. In like manner, low water occurs simultaneously on opposite
sides of the meridian. The average amount of the tides for the whole
globe is about two and a half feet; but their actual height at different
places is very various, sometimes being scarcely perceptible, and
sometimes rising to sixty or seventy feet. At the same place, also, the
phenomena of the tides are very different at different times. In the Bay
of Fundy, where the tide rises seventy feet, it comes in a mighty wave,
seen thirty miles off, and roaring with a loud noise. At the mouth of
the Severn, in England, the flood comes up in one head about ten feet
high, bringing certain destruction to any small craft that has been
unfortunately left by the ebbing waters on the flats and as it passes
the mouth of the Avon, it sends up that small river a vast body of
water, rising, at Bristol, forty or fifty feet.
Tides are caused by the unequal attractions of the sun and moon upon
different parts of the earth. Suppose the projectile force by which the
earth is carried forward in her orbit to be suspended, and the earth to
fall towards one of these bodies,--the moon, for example,--in
consequence of their mutual attraction. Then, if all parts of the earth
fell equally towards the moon, no derangement of its different parts
would result, any more than of the particles of a drop of water, in its
descent to the ground. But if one part fell faster than another, the
different portions would evidently be separated from each other. Now,
this is precisely what takes place with respect to the earth, in its
fall towards the moon. The portions of the earth in the hemisphere next
to the moon, on account of being nearer to the centre of attraction,
fall faster than those in the opposite hemisphere, and consequently
leave them behind. The solid earth, on account of its cohesion, cannot
obey this impulse, since all its different portions constitute one mass,
which is acted on in the same manner as though it were all collected in
the centre; but the waters on the surface, moving freely under this
impulse, endeavor to desert the solid mass and fall towards the moon.
For a similar reason, the waters in the opposite hemisphere, falling
less towards the moon than the solid earth does, are left behind, or
appear to rise.
[Illustration Fig. 46.]
But if the moon draws the waters of the earth into an oval form towards
herself, raising them simultaneously on the opposite sides of the earth,
they must obviously be drawn away from the intermediate parts of the
earth, where it must at the same time be low water. Thus, in Fig. 46,
the moon, M, raises the waters beneath itself at Z and N, at which
places it is high water, but at the same time depresses the waters at H
and R, at which places it is low water. Hence, the interval between the
high and low tide, on successive days, is about fifty minutes,
corresponding to the progress of the moon in her orbit from west to
east, which causes her to come to the meridian about fifty minutes later
every day. There occurs, however, an intermediate tide, when the moon is
on the lower meridian, so that the interval between two high tides is
about twelve hours, and twenty-five minutes.
Were it not for the impediments which prevent the force from producing
its full effects, we might expect to see the great tide-wave, as the
elevated crest is called, always directly beneath the moon, attending it
regularly around the globe. But the inertia of the waters prevents their
instantly obeying the moon's attraction, and the friction of the waters
on the bottom of the ocean still further retards its progress. It is
not, therefore, until several hours (differing at different places)
after the moon has passed the meridian of a place, that it is high tide
at that place.
The _sun_ has an action similar to that of the moon, but only _one
third_ as great. On account of the great mass of the sun, compared with
that of the moon, we might suppose that his action in raising the tides
would be greater than the moon's; but the nearness of the moon to the
earth more than compensates for the sun's greater quantity of matter.
As, however, wrong views are frequently entertained on this subject, let
us endeavor to form a correct idea of the advantage which the moon
derives from her proximity. It is not that her actual amount of
attraction is thus rendered greater than that of the sun; but it is that
her attraction for the _different parts_ of the earth is very unequal,
while that of the sun is nearly uniform. It is the _inequality_ of this
action, and not the absolute force, that produces the tides. The sun
being ninety-five millions of miles from the earth, while the diameter
of the earth is only one twelve thousandth part of this distance, the
effects of the sun's attraction will be nearly the same on all parts of
the earth, and therefore will not, as was explained of the moon, tend to
separate the waters from the earth on the nearest side, or the earth
from the waters on the remotest side, but in a degree proportionally
smaller. But the diameter of the earth is one thirtieth the distance of
the moon, and therefore the moon acts with considerably greater power on
one part of the earth than on another.
As the sun and moon both contribute to produce the tides, and as they
sometimes act together and sometimes in opposition to each other, so
corresponding variations occur in the height of the tide. The _spring
tides_, or those which rise to an unusual height twice a month, are
produced by the sun and moon's acting together; and the _neap tides_, or
those which are unusually low twice a month, are produced by the sun and
moon's acting in opposition to each other. The spring tides occur at the
syzygies: the neap tides at the quadratures. At the time of new moon,
the sun and moon both being on the same side of the earth, and acting
upon it in the same line, their actions conspire, and the sun may be
considered as adding so much to the force of the moon. We have already
seen how the moon contributes to raise a tide on the opposite side of
the earth. But the sun, as well as the moon, raises its own tide-wave,
which at new moon coincides with the lunar tide-wave. This will be plain
on inspecting the diagram, Fig. 47, on page 220, where S represents the
sun, C, the moon in conjunction, O, the moon in opposition, and Z, N,
the tide-wave. Since the sun and moon severally raise a tide-wave, and
the two here coincide, it is evident that a peculiarly high tide must
occur when the two bodies are in conjunction, or at new moon. At full
moon, also, the two luminaries conspire in the same way to raise the
tide; for we must recollect that each body contributes to raise a tide
on the opposite side. Thus, when the sun is at S and the moon at O, the
sun draws the waters on the side next to it away from the earth, and
the moon draws the earth away from the waters on that side; their united
actions, therefore, conspire, and an unusually high tide is the result.
On the side next to O, the two forces likewise conspire: for while the
moon draws the waters away from the earth, the sun draws the earth away
from the waters. In both cases an unusually low tide is produced; for
the more the water is elevated at Z and N, the more it will be depressed
at H and R, the places of low tide.
[Illustration Fig. 47.]
Twice a month, also, namely, at the quadratures of the moon, the tides
neither rise so high nor fall so low as at other times, because then the
sun and moon act against each other. Thus, in Fig. 48, while F tends to
raise the water at Z, S tends to depress it, and consequently the high
tide is less than usual. Again, while F tends to depress the water at R,
S tends to elevate it, and therefore the low tide is less than usual.
Hence the difference between high and low water is only half as great at
neap as at spring tide. In the diagrams, the elevation and depression of
the waters is represented, for the sake of illustration, as far greater
than it really is; for you must recollect that the average height of the
tides for the whole globe is only about two and a half feet, a quantity
so small, in comparison with the diameter of the earth, that were the
due proportions preserved in the figures, the effect would be wholly
insensible.
[Illustration Fig. 48.]
The variations of distance in the sun are not great enough to influence
the tides very materially, but the variations in the moon's distances
have a striking effect. The tides which happen, when the moon is in
perigee, are considerably greater than when she is in apogee; and if she
happens to be in perigee at the time of the syzygies, the spring tides
are unusually high.
The motion of the tide-wave is not a _progressive_ motion, but a mere
undulation, and is to be carefully distinguished from the currents to
which it gives rise. If the ocean completely covered the earth, the sun
and moon being in the equator, the tide-wave would travel at the same
rate as the earth revolves on its axis. Indeed, the correct way of
conceiving of the tide-wave, is to consider the moon at rest, and the
earth, in its rotation from west to east, as bringing successive
portions of water under the moon, which portions being elevated
successively, at the same rate as the earth revolves on its axis, have a
relative motion westward, at the same rate.
The tides of rivers, narrow bays, and shores far from the main body of
the ocean, are not produced in those places by the direct action of the
sun and moon, but are subordinate waves propagated from the great
tide-wave, and are called _derivative_ tides, while those raised
directly by the sun and moon are called _primitive_ tides.
[Illustration Fig. 49.]
The velocity with which the tide moves will depend on various
circumstances, but principally on the depth, and probably on the
regularity, of the channel. If the depth is nearly uniform the tides
will be regular; but if some parts of the channel are deep while others
are shallow, the waters will be detained by the greater friction of the
shallow places, and the tides will be irregular. The direction, also, of
the derivative tide may be totally different from that of the primitive.
Thus, in Fig. 49, if the great tide-wave, moving from east to west, is
represented by the lines 1, 2, 3, 4, the derivative tide, which is
propagated up a river or bay, will be represented by the lines 3, 4, 5,
6, 7. Advancing faster in the channel than next the bank, the tides will
lag behind towards the shores, and the tide-wave will take the form of
curves, as represented in the diagram.
On account of the retarding influence of shoals, and an uneven, indented
coast, the tide-wave travels more slowly along the shores of an island
than in the neighboring sea, assuming convex figures at a little
distance from the island, and on opposite sides of it. These convex
lines sometimes meet, and become blended in such a way, as to create
singular anomalies in a sea much broken by islands, as well as on coasts
indented with numerous bays and rivers. Peculiar phenomena are also
produced, when the tide flows in at opposite extremities of a reef or
island, as into the two opposite ends of Long-Island Sound. In certain
cases, a tide-wave is forced into a narrow arm of the sea, and produces
very remarkable tides. The tides of the Bay of Fundy (the highest in the
world) are ascribed to this cause. The tides on the coast of North
America are derived from the great tide-wave of the South Atlantic,
which runs steadily northward along the coast to the mouth of the Bay of
Fundy, where it meets the northern tide-wave flowing in the opposite
direction. This accumulated wave being forced into the narrow space
occupied by the Bay, produces the remarkable tide of that place.
The largest lakes and inland seas have no perceptible tides. This is
asserted by all writers respecting the Caspian and Euxine; and the same
is found to be true of the largest of the North-American lakes, Lake
Superior. Although these several tracts of water appear large, when
taken by themselves, yet they occupy but small portions of the surface
of the globe, as will appear evident from the delineation of them on the
artificial globe. Now, we must recollect that the primitive tides are
produced by the _unequal_ action of the sun and moon upon the different
parts of the earth; and that it is only at points whose distance from
each other bears a considerable ratio to the whole distance of the sun
or moon, that the inequality of action becomes manifest. The space
required to make the effect sensible is larger than either of these
tracts of water. It is obvious, also, that they have no opportunity to
be subject to a derivative tide.
Although all must admit that the tides have _some connexion_ with the
sun and the moon, yet there are so many seeming anomalies, which at
first appear irreconcilable with the theory of gravitation, that some
are unwilling to admit the explanation given by this theory. Thus, the
height of the tide is so various, that at some places on the earth there
is scarcely any tide at all, while at other places it rises to seventy
feet. The time of occurrence is also at many places wholly unconformable
to the motions of the moon, as is required by the theory, being low
water where it should be high water; or, instead of appearing just
beneath the moon, as the theory would lead us to expect, following it at
the distance of six, ten, or even fifteen, hours; and finally, the moon
sometimes appears to have no part at all in producing the tide, but it
happens uniformly at noon and midnight, (as is said to be the case at
the Society Islands,) and therefore seems wholly dependent on the sun.
Notwithstanding these seeming inconsistencies with the law of universal
gravitation, to which the explanation of the tides is referred, the
correspondence of the tides to the motions of the sun and moon, in
obedience to the law of attraction, is in general such as to warrant the
application of that law to them, while in a great majority of the cases
which appear to be exceptions to the operation of that law, local causes
and impediments have been discovered, which modified or overruled the
uniform operation of the law of gravitation. Thus it does not disprove
the reality of the existence of a force which carries bodies near the
surface of the earth towards its centre, that we see them sometimes
compelled, by the operation of local causes, to move in the opposite
direction. A ball shot from a cannon is still subject to the law of
gravitation, although, for a certain time, in obedience to the impulse
given it, it may proceed in a line contrary to that in which gravity
alone would carry it. The fact that water may be made to run up hill
does not disprove the fact that it usually runs down hill by the force
of gravity, or that it is still subject to this force, although, from
the action of modifying or superior forces, it may be proceeding in a
direction contrary to that given by gravity. Indeed, those who have
studied the doctrine of the tides most profoundly consider them as
affording a striking and palpable exhibition of the truth of the
doctrine of universal gravitation.
FOOTNOTE:
[11] The exact longitude of the City Hall, in the city of New York, is
4h. 56m. 33.5s.
LETTER XX.
PLANETS.--MERCURY AND VENUS.
"First, Mercury, amidst full tides of light,
Rolls next the sun, through his small circle bright;
Our earth would blaze beneath so fierce a ray,
And all its marble mountains melt away.
Fair Venus next fulfils her larger round,
With softer beams, and milder glory crowned;
Friend to mankind, she glitters from afar,
Now the bright evening, now the morning, star."--_Baker._