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GeezerVison is showing babbageastronomy.blogspot.com — Charles Babbage's Lectures On Astronomy Thursday, 10 July 2025Table of Contents
Babbage's
Lectures On Astronomy
Given at The Royal Institution, 1815
Wednesday, 9 July 2025Charles Babbage at the Royal Institution: An Analytical Account of his 1815 LecturesI. Introduction: A Young Mathematician on the London StageIn 1815, as London celebrated the final victory at Waterloo, a 23-year-old Charles Babbage was launching a very different kind of campaign—an intellectual insurgency aimed at the heart of the British scientific establishment. His lecture series at the Royal Institution that year was far more than a simple academic exercise; it was a calculated, public-facing assault on the state of English mathematics and the first major strategic step in a career that would eventually lead to the conception of the modern computer. Babbage in 1815: The Ambitious GraduateBorn into the family of a wealthy banker, Charles Babbage (1791-1871) possessed the financial independence that defined the "gentleman scientist" of the era, allowing him to pursue his intellectual passions without the immediate need for professional income.[1, 2] His time at Cambridge University, first at Trinity College and then at Peterhouse, from which he graduated in 1814, was marked by profound frustration.[1, 2] He found the mathematical curriculum stagnant, stubbornly adhering to Isaac Newton's cumbersome "dot" notation for calculus while ignoring the more powerful and elegant Leibnizian "d" notation used on the Continent.[2, 3] This dissatisfaction was not passive. In 1812, Babbage, along with fellow undergraduates John Herschel and George Peacock, founded the Analytical Society.[2, 4] Their mission, as Babbage cheekily put it, was to promote "the principles of pure D-ism in opposition to the Dotage of the university".[3, 5] This society was the first manifestation of Babbage's lifelong role as a reformer and polemicist. Upon graduating and moving to London with his new wife, Georgiana Whitmore, in 1815, Babbage was not seeking a conventional job but a platform.[3, 6] He immediately immersed himself in the city's vibrant scientific scene, looking for a way to carry his mathematical crusade beyond the cloistered walls of Cambridge.[3, 7] The Royal Institution: London's Premier Scientific TheatreThe perfect stage for Babbage's ambitions was the Royal Institution (RI) on Albemarle Street. Founded in 1799, its purpose was the popular dissemination of scientific knowledge and new technologies to an educated public.[8, 9] In the preceding decade, it had been transformed by the spectacular lectures of Humphry Davy into London's premier scientific venue, a place where reputations were forged and discoveries announced.[10, 11] For a young, fiercely ambitious mathematician like Babbage, securing a lecture series at the RI was an unparalleled opportunity. It allowed him to bypass the conservative academic hierarchy and broadcast his reformist agenda directly to an influential audience of London's social, political, and intellectual elite. The 1815 lectures were, in essence, a public marketing campaign for a new brand of British mathematics, with Babbage himself as its chief evangelist. II. The Royal Institution and the Economy of Knowledge in Regency LondonTo understand the context and significance of Charles Babbage's 1815 appearance, it is essential to analyze the structure of the Royal Institution's public engagements and the unique economy of reputation in which it operated. Babbage's lectures did not occur in a vacuum but fit within a specific, albeit informal, category of the RI's programming. A Taxonomy of RI LecturesIn the early 19th century, the Royal Institution hosted several distinct types of lectures, each with its own purpose and prestige:
The Currency of ReputationFor a "gentleman scientist" of independent means like Babbage, the primary currency was not financial but intellectual and social capital.[1] An appearance at the Royal Institution was a reward in itself, conferring a level of legitimacy and visibility that was difficult to achieve elsewhere. The audience was a powerful cross-section of society, including potential patrons, influential figures, and members of other learned societies. Success on the RI's stage could directly pave the way for further accolades. In Babbage's case, the 1815 lectures were a clear success in this regard; just one year later, in 1816, he was elected a Fellow of the prestigious Royal Society.[21, 22] III. The 1815 Lecture Series: A ReconstructionWhile the historical record is frustratingly incomplete, a careful synthesis of the available evidence allows for a detailed reconstruction of Babbage's 1815 lecture series, addressing the fundamental questions of who, why, when, and what. Who and Why: The Lecturer's PurposeThe lecturer was Charles Babbage, a 23-year-old mathematical prodigy, recently graduated from Cambridge and eager to make his mark on the London scientific scene.[1, 23] His purpose was twofold. First, he aimed to publicly champion the superiority of continental Leibnizian calculus over the entrenched Newtonian methods, continuing the work of his Analytical Society on a national stage.[3, 5] Second, he sought to establish his own credentials as a leading authority in mathematics and astronomy, thereby building the social and intellectual capital required for a prominent scientific career and for the ambitious, large-scale projects he was already beginning to contemplate.[6, 24] When: Dating and Scheduling the LecturesMultiple sources unequivocally date the lecture series to the year 1815.[3, 21, 25] However, the specific dates—the day and month of each individual lecture—are not present in the available research and are likely lost to history, as the RI's detailed proceedings for this type of guest lecture from such an early period have not survived in accessible archives.[26, 27] Contextual analysis of popular science lectures of the period indicates that astronomy lectures were often a feature of the Lenten season, suggesting a possible timeframe in the spring of 1815, though this remains speculative.[28] What: Reconciling Topics and Reconstructing ContentA central conflict in the secondary sources is the precise topic of the lectures. Some accounts state it was "astronomy," while others claim it was "calculus".[21, 29] | Snippet ID | Source Type | Stated Topic | | :--- | :--- | :--- | | [21] | Wikipedia Article | Astronomy | | [3] | Educational Website | Astronomy | | [22] | Online Article | Astronomy | | [25] | Online Article | Astronomy | | [23] | Biographical Article | Astronomy | | [4] | Commercial Website | Calculus | | [29] | Museum Website | Calculus | Based on his known work and interests at the time, a plausible syllabus for the series can be reconstructed:
IV. The Matter of Remuneration: Gentlemanly Science and Institutional FinancesThe question of how much Charles Babbage was paid for his 1815 lectures can be answered with a high degree of certainty, despite the lack of a direct receipt. The conclusion, drawn from powerful circumstantial evidence, is that he was paid nothing at all. The opportunity to speak was, in itself, the compensation. The Crucial Primary Source: The 1827 LetterThe most definitive piece of evidence comes from an autograph letter written by Babbage himself on April 15, 1827.[20] In it, he details his efforts to arrange a lecture series at the RI for a colleague from Ireland. Babbage notes that he wrote to the RI managers "in such a manner that they might if they chose propose some remuneration for the expense you might be at in bringing the necessary apparatus from Ireland".[20] The RI's response, as relayed by Babbage, is exceptionally revealing: "They however do not seem to have viewed it in that light, but they express a perfect willingness to allow you to give a few lectures on the subject...".[20] This passage demonstrates that even twelve years after Babbage's own lectures, and when prompted by an influential figure, the RI's default position for a guest lecture series was to offer its prestigious platform but not financial remuneration—not even for expenses. A Two-Tiered System of Scientific LaborThis evidence points to a clear, two-tiered financial system at the Royal Institution, one that reflected the semi-professionalized state of science in the Regency era. On one tier were the core, salaried professionals. In 1801, Humphry Davy was appointed Assistant Lecturer at an annual salary of £105 (approximately £10,000 in modern terms) plus accommodation, with the promise of a promotion to a full professorship at £300 per year.[13] This was a professional wage for a man whose life was the Institution. On the other tier were the "gentlemen scientists" like Babbage. These men, often of independent means, pursued science as a calling rather than a career. Babbage's father was a wealthy banker, and upon his death in 1827, Babbage inherited an estate valued at £100,000, a truly vast fortune at the time.[1, 2] For this class of individual, payment for a lecture series would have been secondary to the invaluable currency of reputation, influence, and access to an elite audience. Given the RI's explicit refusal to pay a guest lecturer's expenses in 1827, it is virtually inconceivable that they would have paid a fee to the 23-year-old Babbage in 1815. V. Babbage's Enduring Engagement with the Royal InstitutionThe 1815 lectures were not an isolated event but the beginning of a long and evolving relationship between Charles Babbage and the Royal Institution. His role grew from that of a young, aspiring speaker to an established and influential figure within London's scientific ecosystem. A Friend and Supporter of FaradayBabbage became a correspondent and colleague of Michael Faraday, the RI's greatest asset.[19, 34] In 1824, Babbage was among the influential supporters who backed Faraday's election as a Fellow of the Royal Society, a significant act of collegiality and patronage that helped secure Faraday's position in the scientific establishment.[35] A Facilitator and Power BrokerThe 1827 letter arranging a lecture for a colleague shows Babbage in a new light.[20] By this time, he was no longer a young man seeking a stage, but an established power broker who could lend his name and influence to help others gain access to the RI's prestigious platform. He had become part of the institutional machinery he once sought to impress. The Social Hub: Babbage's SoiréesWhile not official RI events, Babbage's own famed Saturday night soirées, held at his Dorset Street home during the 1830s and 1840s, mirrored the RI's function as a social and intellectual nexus.[1, 36] These events brought together a dazzling mix of scientists, artists, politicians, and socialites to discuss the latest inventions and ideas. Famously, Babbage would often display a working portion of his Difference Engine at these gatherings, adopting and personalizing the RI's model of combining scientific demonstration with elite social engagement.[36] The following timeline illustrates Babbage's rapid integration and ascent within the key scientific institutions of his day, placing the 1815 lectures in their proper context as a critical early milestone. | Year | Activity | Institution(s) Involved | Significance | | :--- | :--- | :--- | :--- | | 1812 | Co-founds the Analytical Society | Cambridge University | Begins his campaign for mathematical reform.[2, 30] | | 1815 | Delivers lecture series | Royal Institution | Establishes public profile in London; promotes new calculus.[3, 21] | | 1816 | Elected Fellow | Royal Society | Gains official recognition from the scientific establishment.[21, 22] | | 1820 | Co-founds the Astronomical Society | Royal Astronomical Society | Institutionalizes his interest in astronomical calculation.[23] | | 1822 | Announces the Difference Engine | Royal Astronomical Society | Begins his life's major work on mechanical computation.[23, 32] | | 1824 | Supports Faraday's election | Royal Society | Acts as a patron and established figure.[35] | | 1827 | Facilitates lectures for a colleague | Royal Institution | Demonstrates his influence and role as a broker.[20] | | 1828 | Appointed Lucasian Professor | Cambridge University | Reaches the pinnacle of academic mathematics, though he never lectured.[7, 22] | | 1834 | Co-founds the Statistical Society | Statistical Society | Expands his institutional influence into new fields.[7, 30] | VI. Conclusion: The Lectures as a Foundation for a Revolutionary CareerThe evidence provides a clear and detailed picture. In 1815, the 23-year-old Charles Babbage delivered an unpaid series of lectures at the Royal Institution on the topic of Mathematical Astronomy. His primary motivation was to promote the superiority of continental calculus and to establish his own scientific reputation in London. These lectures were a resounding success, not in monetary terms, but in the far more valuable currency of intellectual and social capital. This early success was a foundational element for the revolutionary work that followed. The reputation and network Babbage began to build with activities like the 1815 lectures were essential prerequisites for his later, more audacious projects. The credibility he established as a public man of science was vital when he approached the British government for funding for his Difference Engine, a project that would ultimately receive the formidable sum of £17,500.[32] Furthermore, the intellectual themes of his lectures—the demand for error-free calculation and the critique of human fallibility in producing astronomical tables—were the direct precursors to the work that would consume his life.[24, 31] While the 1815 lectures may seem a minor footnote when compared to the grandeur of the Difference and Analytical Engines, they were a formative and necessary first step. They mark Babbage's crucial transition from a student radical to a public intellectual, laying the social and philosophical groundwork for a career that would ultimately, though not in his own lifetime, change the world and cement his legacy as the "Father of the Computer".[23]
Monday, 11 November 2013Lecture 12: Beyond the Solar SystemLecture 12Beyond the Solar System*
[script
of lecture missing]
* Note:
conjectured title of lecture.
Lecture 11: On CometsLecture 11
On Comets
Besides the planets which perform
their revolutions in orbits nearly circular and which almost always remain
within our view or at least within the
reach of our telescopes there is another species of bodies which only present
themselves to our view at short and distant intervals, which shine with
splendour for a time and then retire into the depths of the heavens. These have
been usually called comets and are distinguished from either stars by a long
train of light which usually accompanies them and which is always situated in a
direction opposite to the Sun and which diminishes in lustre as it recedes from
the body of the comet.
Of all parts of philosophy that
which was the latest to receive solid improvement was undoubtedly the theory of
comets. The stars were considered as meteors little different from the
exhalations and luminous appearances which we sometimes behold in the
atmosphere. Some philosophers as Apollonius, Seneca and many of the
Pythagoreans had more correct notions on this subject but these seeds of truth
were extinguished by a weight of prejudice and by the authority of the
Aristotelian school.
From this
opinion it unfortunately happened that the ancients were very careless in
making and transmitting to us observations on these phenomena and we have now
only to regret they were so little enlightened on this subject since from the
want of materials with which they might have supplied us the decision of some
of the most interesting questions of physical astronomy will probably be
postponed some centuries.
Until the time of Tycho Brahe we
find concerning comets but few reasonable conjectures. This celebrated observer
began to open the eyes of astronomers to the real nature of these bodies by an important discovery. He demonstrated
from the smallness of the parallax of these bodies that they are much more
distant from our Earth than the Moon is. He even endeavoured to represent their
course by supposing them to move in an orbit round the Sun. This however we
should observe was an hypothesis purely astronomical and he by no means supposed
that they were planets of a peculiar nature revolving round the Sun. This
discovery of Tycho [Brahe] was confirmed by the observations of various
astronomers of his time. And at the commencement of the 17th century it
received new illustrations from Galileo and Kepler.
It was
natural as soon as Men were undeceived respecting the situations of these
bodies for Men to endeavour to submit their motions to calculations. Tycho
[Brahe] had set the example and Kepler soon followed it; this celebrated astronomer
imagined he could represent their motions by supposing that they moved in a
straight line. He was obliged however to acknowledge that they did not move
uniformly in this line. This circumstance ought naturally to have led him to
consider their path as curved. But being unwilling to give up the straight line
he was obliged to admit an acceleration and retardment in different parts of
it. It is singular that Kepler who was in other matters so clear sighted, who
possessed a genius peculiarly calculated to penetrate into those causes which
contribute to the order, the harmony and the magnificence of the universe,
should have been little better acquainted with the nature of these stars than
the herd of mankind. He confined himself to supposing that they were new
productions of Nature similar to the meteors which sometimes appear in our
atmosphere.
The
supposition that comets move in a straight line was for a long time the
favourite hypothesis among astronomers. The positions of the comet which appeared
in 1665 were calculated by this method and it had caused some surprise that the
results were not far distant from the truth. We shall however presently see the
reasons of this coincidence. It was however from Cassini that this hypothesis
derived its greatest celebrity. He applied it to the comet which appeared in
1652 and also to several others and his results were sufficiently near the
truth to convince many that he had arrived at the true explanation. It must
however be observed that his hypothesis would not satisfy distant observations
on the same comet and that to a great number of them it was utterly
inapplicable. It will naturally be enquired how it could happen that from a
false hypothesis so many observations should be satisfied as to produce for it
a considerable reputation for several years. The answer to this question is not
difficult. Comets according to more modern observations are found to move in
flattened ellipses. In some cases these ovals are so much elongated that they
approach very nearly in some parts to the nature of a parabola. A parabola is a
curve composed of two branches which at a short distance from the summit
approach very much to straight lines. From this circumstance a comet if seen in
one part of its orbit will seem to be moving in a straight line. A comet when
it is approaching the Sun gradually disappears in its rays and after being hid
during some time is seen moving from the Sun. This can not be reconciled with
the hypothesis of Cassini and in fact he made a singular mistake respecting the
comet of 1680-81. All those who supposed the comet to move in a straight line
imagined that there were two different comets which moved in straight lines
passing very near the body of the Sun, whereas in fact it was one and the same
comet which only disappeared from being lost in the Sun's rays and again became
visible in its recess from that body.
It is
remarkable that the ellipse which this comet really described is very much
elongated so that its two sides approach nearly to straight lines. And it was
principally from the accuracy of his predictions relating to this comet that
Cassini astonished the world and extended the credit of this theory. But the
triumph of this hypothesis was only caused by a fortunate coincidence of circumstances.
It was therefore transient and soon gave place to another incomparably more
accurate. In fact notwithstanding the theory of Cassini it was soon discovered
that the paths of comets are not straight lines, but that they are curved and
that the concave part is directed towards the Sun.
Helvetius recognised this fact and
Dr. Hooke demonstrated it. He says that we must positively reject the testimony
of observation. It is in contradiction to this. Helvetius imagined comets to be
eruptions projected from the body of the Sun or even from the planets.
"If" said he, "we project a body from the surface of the Earth
it will describe a parabola. Therefore" said he, "these bodies which
are projected from the Sun or planets will also describe parabolas." As to
the physical construction of these bodies he imagined them to be nothing more
than a collection of vapours collected in the atmospheres of the planets which
gradually rose higher and higher till at last they were projected from them and
moved in different curves according to the velocities they had acquired.
Such was
the state of the theory of comets when the celebrated one of 1680 made its
appearance. It was first accurately observed in Saxony on the 4th November. It
was then moving with increasing velocity towards the Sun. About the 30th it
moved at the rate of 5 degrees in a day and shortly after it disappeared. About
22nd December it reappeared moving very swiftly from the Sun and its velocity
gradually diminished until the middle of March 1681 when it was no longer
visible. On its return from the Sun it had a tail or train of light extending
70 degrees, that is it reached much more than one third of the heavens. It was
proved that these two [appearances] were the same comet from the resemblance of
the solid nucleus which presented the same appearance before and after its
passage near the Sun, and also from the direction of its course which was the
same. But the strongest proof was that the calculations which Newton made
respecting this comet and which were founded on this supposition agreed
accurately with observation.
It was a
fortunate circumstance for the progress of Astronomy that the Earth was in a
favourable situation to see both the access of this comet to the Sun and also
its recess from that body. Without this accidental circumstance the true system
of the cometary motions might not perhaps have appeared for a long time. But
this singular coincidence hastened its discovery.
The first outline of the true
cometary theory came from Germany. A clergyman named Doerfell, the minister of
a small village, had observed the comet with much care. He is an astronomer
very little known and has not received that credit which was due to [him for]
the manner in which he treated a subject which was at that time both new and
difficult. Doerfell proved that the comet which receded from the Sun was the
same as the one which had approached it a short time before. He showed that it
moved in a parabola having the Sun in its focus. He ascertained the distance at
which it passed from the Sun. All these circumstances were published in 1681,
but the language in which it was written and probably the little reputation of
the author caused it to be neglected, and it was not noticed until long after
Newton had established the same truths by other methods.
The
anticipation of one of the discoveries of our great countryman does not however
in the least denigrate from his glory. It was with Doerfell an astronomical
hypothesis, but with Newton it was a physical truth, a branch of his general
system. In fact it was impossible for our astronomer after having established
the gravitation of the planets towards the Sun and recognising as he did with
the astronomers of his time that comets are not the transient meteor of a
moment, not to suppose them governed by the same laws which regulate the other
bodies of the System. It was therefore necessary to suppose revolving in very
eccentric ellipses to account for their not being constantly visible. But
Newton still further demonstrated the truth of his method by applying them to
the determination of the path of the comet of 1680 and it is remarkable by what
accuracy his calculations of the position of the comet agreed with the
observations of Flamsteed. The greatest difference only amounted to two minutes
of a degree.
The comet
of 1680 was remarkable for the long period of its revolution, which is 575
years, and also for its near approach to the Sun. According to Newton it
approached so near as to be distant from that body only the ?th part of the
distance of the Earth from the Sun. It must therefore have experienced a heat
26,000 times greater than we ever receive from the Sun's rays and if to obtain
a more elevated point of comparison it is compared to that of red hot iron it
will be found that this comet must have been 2,000 times hotter. From this it
appears that the comet must have been composed of very solid matter not to be
dissipated by such an intense heat and this affords a new proof of the
permanence of these bodies.
Newton conjectured that this comet
as well as others which like it revolve round our Sun approximate continually
to this body at each revolution and that the[y] ultimate[ly] fall into it, for
the purpose of supplying the loss to which it is continually subject by the emission
of particles of light. But this is purely a matter of conjecture and must not
be ranked with the astronomical discoveries of Newton, but which are not the
less solidly established whatever may be the fate of these conjectures.
With
respect to the tails of comets there have been various opinions. It is almost
needless to refute that entertained by most of the ancients and by some few of
the moderns. They conceived that the tails of comets arose from the refraction
of the rays of light through the nucleus of the comet but this is contradicted
by the fact that the nuclei of comets are evidently opaque. Kepler once
maintained this opinion but in his subsequent writing he gave it up. He then
attributed their tails to their atmospheres and to the evaporation of the more
volatile parts caused by the heat of the Sun. This is nearly the opinion which
Newton embraced and he compared the tails of comets to the smoke which follows
a burning body in rapid motion. Such was the most probable explanation of the
cause of the tails of comets before De Mairan. This eminent philosopher to whom
we are indebted for an explanation of the aurora borealis conjectured with some
degree of probability that the tails of comets are formed by the matter of the
solar atmosphere which these bodies attract to themselves on their approach to
their nearest distance from the Sun, and to account for their tails always
appearing on the opposite side to the Sun he supposes that this is the effect
of the impulsion of the rays of light. There are some circumstances which
render this explanation at least probable. It may be remarked that comets do
not begin to exhibit a tail until they have approached nearer the Sun than the
semidiameter of the earth's orbit and this is supposed to be about half the
extent of the Sun's atmosphere. Those comets on the contrary which have not
approached so near to the Sun such as those which appeared in the years 1585,
1718, 1729 etc. have been seen without any tail. The ingenious work of De
Mairan in which he establishes this opinion contains several other proofs by
which this opinion is establish
ed. These
appendages to cometary bodies present various appearances according to the
positions in which they are perceived. If a comet is moving in a direction
nearly at right angles to the path of our Earth it will appear to have a tail
in the direction opposite to the Sun, but if the comet is moving almost
directly towards us or directly from us it will appear to be surrounded with a
nebulosity, and in particular cases is said to be bearded.
After Newton no one contributed more
to the improvements of this branch of Astronomy than Dr. Halley. This learned
astronomer presented to the Royal Society in 1705 a treatise on Comets in which
he applies the principles taught by Newton to the determination of the orbits
of comets and he formed tables of their motions similar to those of the
planets. Towards the conclusion however he gave other methods of his own on the
more accurate supposition of their revolving in ellipses. This was the most
valuable and interesting part of the curious communication of the author.
He
calculated the orbits of the comets and formed them into a table in order to
compare them. By this means he had the satisfaction of verifying the opinion of
those who supposed these stars [were] subject to periodical return. In fact
from the inspection of the tables he found that the comets which appeared in
1531, 1607 and 1682 had very nearly the same orbit and the
intervals between their appearances were nearly 75 years. From this he
concluded with a very high degree of probability that it was one and the same
comet whose period of revolution is about 75 years. He found that the
inclination of all the three orbits was about 18 degrees and that, if the mean
distance of the Earth be supposed to be 100, then the least distance of the
comet of 1531 was 57, that of 1607 was 58 and that of 1682 was 58. This
difference is very small when we consider the imperfection of practical
astronomy at the time the observations on which these calculations were made
depended.
These
were strong reasons for presuming on the identity of the three comets but
further circumstances rendered it still more probable. In counting back from
1531 75 or 76 years we find other comets. Thus in the years 1546, 1380 and 1305
[also in 1230, 1155, 1080 and 1006] there appeared other comets. In fact no
astronomer has transmitted to us observations by which we may determine
decisively their orbits, but by comparing their appearance and motions as
transmitted to us by historians with those of the comet we are considering and
allowing for the different positions of the Earth Dr. Halley found they agreed
very well. Thus assured of its revolution in 75 years he ventured to predict
its return in the year 1758 or 59. This is the first prediction that was ever
made of the appearance of a comet and it is well known that it was justified by
the event. Dr. Halley remarked that the comet observed in 1661 by Helvetius and
that of 1532 seen by Appianus were the same. Had this been the case it ought to
have returned in 1780 or 81. This however was not the case. By comparing his
tables of the orbits of comets Dr. Halley conjectured that the brilliant comet
of 1680 had reappeared several time at the distance of 575 years.
He
founded this opinion on the following circumstances that in the year 1106 there
occurred a beautiful comet whose description much resembled that of 1680. In
the year 531 a similar one appeared, and in the year 46 before the Christian
era appeared that prodigious comet so celebrated by historians and which
followed so nearly the death of Julius Caesar.
But Dr. Halley went still further in
continuing to retrograde 575 years at each step: he found that this same comet must
have appeared very nearly at the time of the universal deluge, and he formed
the bold conjecture that this was the secondary cause made use of to produce
that horrible catastrophe. This body was accompanied by a tail of prodigious
extent which according to Newton consisted of vapours raised by the solar heat.
Halley supposed that the Earth might have passed through this and that by the
effect of gravity these vapours would have fallen on its surface and thus
produce the immense body of water by which our globe was inundated. The
celebrated Whiston has supported this explanation of the deluge with much
ingenuity and seems by his zeal to have acquired the title of its author
although it was undoubtedly Halley's. It may be observed that it is scarcely probable
that such an effect would result from our globe passing through the tail of a
comet. Vapours rarefied to such a degree as these must be even if they exceeded
our globe many times in volume would form but an inconsiderable quantity of
water insufficient for the ravages of which the traces still remain. It would
be easy to prove this from considering what has been demonstrated by Newton
that a cubic inch of air would if carried to the distance of the Earth's
semidiameter from its surface be rarefied to such a degree as to fill the whole
space from the Sun to the orbit of Saturn.
This same
comet has been employed by another celebrated writer to explain another point
of history. He conjectured that this same comet appeared about the time of
Ogyges and that it gave rise to the singular phenomenon which has been
mentioned by historians with astonishment. They relate that 40 years before the
deluge of Ogyges, the planet Venus was seen to quit its ordinary course and to
be accompanied by a long train of light. Upon which the learned writer observes
that in the infancy of Astronomy men might easily mistake a comet just
disengaging itself from the sun's rays for the planet Venus quitting her usual
course and accompanied by a long tail. But so many other comets might have
given rise to this mistake that we can unfortunately determine nothing certain
as to the date of this deluge from such a circumstance.
Since the period of Dr. Halley much
more extensive tables have been formed. It appears from them that there are
nearly as many whose motion is retrograde as there as ones whose motion is
direct, and it also appears that their orbits are inclined to the ecliptic at
every possible angle. This is another and powerful argument if any further one
were wanted against the theory of vortices.
It may
also be remarked that the greater number of comets descend towards the Sun
within the Earth's orbit. Of the 35 whose orbits were calculated by La Caille
there were only six whose least distance from the Sun exceeded the mean distance
of the Earth from that body.
The comets appear to have no fixed
zodiac. On the contrary there is scarcely any constellation in the heavens in
which some comet or other has not been seen. These different positions and the
different inclinations of their orbits do not appear to be the effect of chance
but rather affords cause for admiration. If they had moved in the plane of the
Earth's orbit or very near to it everytime a comet descended towards the Sun or
ascended from it we should be exposed to the danger of a contact, if
unfortunately our globe should at that time be situated at the intersection.
But by means of this inclination it happens that not one of the orbits of
comets yet known cuts that of the Earth. It would indeed be a very curious spectacle
to see a comet pass at the distance of one or two diameters from our globe.
Possibly these might result [in] some physical changes in our little system
which might not be disadvantageous to us. A celebrated naturalist has supposed
we might acquire a new moon and has attributed a similar origin to the one we
possess. It might however be more happy for us to be deprived of this advantage
then to incur the risk of so near a neighbour. Of all the comets which have yet
been observed that of 1680 can approach
nearest to the Earth. Dr. Halley found from calculation that on the 11th
November 1680 at one o'clock it was not further distant from the Earth's orbit
than the Moon is from us. But there would have arisen to us no danger from this
circumstance. It would only have afforded us an opportunity for curious
observations if the Earth had been in a convenient part of her orbit.
It is
true we may not always be so fortunate. According to Whiston this comet [has]
already been the instrument of divine vengeance [and] may at it return involve
us in the burning vapour of its tail, and thus produce a universal
conflagration. We must however always separate these bold and sometimes
fanciful conjectures from the physical theory by which the motions of the
bodies are calculated.
In consequence of the predictions of
Dr. Halley much more attention was paid to the discovery of comets. In the 120
years which elapsed between 1637 to 1757 on 20 had been seen, but in the next
50 years this number was more than tripled. It was observed that the comet
whose return was predicted by Dr. Halley had alternately long and short periods
and it was therefore supposed that it would return about the year 1759, and the
astronomers of the time prepared very diligently to search for it. It was
necessary to calculate the part of the heavens in which it would reappear but
this and the precise time of its return were alike unknown, and this much increased the difficulty of
the search.
The
astronomer Lalande was very ardent in the search and thus assigns his reasons
for it. "It has already appeared" said he "6 times with very
evident marks of identity particularly the last two or three times. There can
therefore be no doubt of its return. Even though astronomers should not observe
it they would nevertheless be convinced of it. It well known to the them that
its little light and immense distance may possibly hide it from our view. But
the public will hardly believe us and they will rank among the number of vague
conjectures this discovery which does so much credit to modern astronomy.
Disputes will again arise; the terrors of the ignorant will continue and 70
years must elapse before we again have an opportunity of removing these
doubts."
The astronomer Messier was actively
employed during 18 months in searching for this comet. This labour was not,
however, unrewarded for in consequence of it he discovered a new comet which he
observed during several months. It was on the 21 June 1759 that he first had
the good fortune of observing the object he was in search of. This day happened
to be very severe and as soon as the stars became visible at sunset he profited
by this circumstance and directed his telescope towards that part of the
heavens in which it was expected to appear. After some time he recognised at
about 7 in the evening a feeble light very similar to the small comet he had
discovered in 1758. He had frequently imagined he had perceived this much
wished for visitor, but he had been deceived by the numerous nebulae which are
scattered in that part of the heavens. After a few observations he found from
its motion that it was the object he was in search of.
Dr.
Halley had observed that the periods of the return of this comet were unequal.
They varied from 75 to upwards of 76 years. He attributed this to the
attraction of the planets. He knew that the motion of Saturn is very sensibly
altered by the attraction of Jupiter and considering that the comet must pass
near Jupiter he imagined this planet might cause the change in its periodical
time. He was not however able to calculate this effect and offered it merely as
a conjecture.
A little before the reappearance of
this comet Clairaut, who concurred in the opinion of Dr. Halley, undertook the
calculation of the disturbance it must suffer from the action of Jupiter. This
immense undertaking was however beyond the powers of one individual. Clairaut
undertook the discovery of the plan to be pursued in these calculations and
Lalande and Madame Lepante executed the calculations themselves. After 12 months
of fatiguing calculations it was found that the action of Saturn was so
considerable that it could not be neglected. The labour was therefore renewed.
In November 1758 these immense calculations were completed and Clairaut was
able to announce that the period of the comet which was just about to terminate
would exceed the preceding one by 618 days. 500 were caused by the attraction
of Jupiter and 100 were the result of the action of Saturn. He also announced
that the comet would be at it nearest distance from the Sun on the 13 March
1759. It in fact only exceed the specified time by 22 days and arrived there on
the 4th of April. Thus did the most celebrated of all the comets confirm the
theory of Newton and afford a proof that they revolve round the Sun like
planets. It must, however, be observed that this is the only one whose periodic time is well ascertained. The
periods of the revolution of many other comets have been conjectured and their
returns expected but with respect to them there is much uncertainty.
The comet
which appeared in 1264 and 1556 is expected in 1848. It may perhaps be the same
as those recorded to have appeared in 975 and 395. But the observations of 1264
are too imperfect for us to depend much on its reappearance. The comet which
appeared in 1770 occupied considerable attention. It was observed for along
time, nor could any parabolical orbit be found which suited its motions. After
immense calculations it was found by Lexell that it moved in an ellipse and
that its period of revolution was 5 years.
The terror which was excited by the
comet of 1773 is one of the most singular circumstances in their history. It
was occasioned by a paper of Lalande presented to l'Academie des Sciences,
Paris. This memoir was not read at the time, but a report soon spread that
Lalande had announced the termination of the world. It was supposed that it
would take place in less than a year. As the report spread the time became
shortened to a month and then it soon came to a week. The populace were alarmed
and the police applied to Lalande to contradict the report. His explanation
appeared in the gazette in a few days, but as this was not sufficient to
justify him from the numerous absurdities which had been imputed to him he
resolved to publish whole paper. It consists of an investigation into the
probability of the contact of one of these bodies with the Earth. From a
consideration of the orbits of all the comets which had at that time appeared
he plainly showed the great improbability of such an occurrence. And since the
more recent observation the improbability of the injuring [of] our globe is
most materially increased.
If a
comet equal in magnitude to our Earth were situated at the distance of about
40,000 miles it would cause a tide of 12,000 [ft.] above the level of the sea,
which would be quite sufficient to overflow in succession the whole globe, but,
if we consider that the comet is in motion and the earth [is also] in motion,
both very rapidly, it will be found that the effect of the comet, during the
very short time it would be at the distance, will be wonderfully diminished,
and, if to this it be added that as yet we have had no instance of any comet
approaching to this magnitude, we shall find that the effect of a comet, even
at this short distance, would be comparatively trivial.
Of all the comets which have been
observed that of 1770 approached nearest to the earth. Laplace found that by
the attraction of the Earth its time of revolution was diminished two days, and
that supposing it to have been of the same magnitude as our globe its reaction
would have shortened the length of our sidereal year 2 hours 40 minutes. But
according to the most accurate observations the length of the year was
certainly not shortened 3 seconds by this comet, from which we may conclude
that its mass was not equal to the ?th
of our Earth. These bodies appear in general to exert very little action on the
planets they approach. Their wandering courses do not disturb the harmony of
the system and though frequently announced by the ignorant as the presages of
misfortune they do not appear to have received the power of doing mischief.
There has
been much question as to the solidity and planetary nature of these bodies. It
has been doubted whether they possess a real nucleus of solid material or
whether their centre may not be the densest and most compact part of their
nebulosity. According to observations on the comets of 1799 and 1807 by
Schroeter and Dr. Herschel it appeared that they possessed solid nuclei of a
round form distinct from the nebulosities which accompany them. This nucleus
was not subject to the same variations as the vapours which surrounded them. It
did not always occupy the centre but generally appeared to incline to wards the
Sun. Dr. Herschel is of opinion that the body of the comet shines by its own
light, for he observed that when from its situation with respect to the Sun we
could not see the whole of its illuminated side, yet the light of the comet
appeared by no means diminished but the whole surface shone with one uniform
light much more resembling by its vivacity irradiance of the stars than the
reflected light of planets and their satellites. This observation however would
be satisfied by supposing the centre to consist of a dense mass of vapours
through which the Sun's rays are refracted.
In the
comet of 1811 the central body was remarkably distinct from the surrounding
vapour. In its appearance this was one of the most splendid which have been
visible for many years. Its tail or the luminous train which it carried with it
in one part of its orbit was 100 million of miles in length and about 15
million in breadth, yet notwithstanding this enormous atmosphere the solid
nucleus of the comet was according to the observations of Dr. Herschel not more
than 428 miles in diameter. This body would according to the observations made
during it appearance describe an ellipse round the Sun in about 2620 years at
the mean distance of 190 that of the Earth [is] from the Sun. This period might
however be very much altered from the attraction of the planets and if at a
very great distance it should be influenced but in a small degree by any
unknown body it might suffer a total change in its orbit and perhaps never
return to our system.
Of the numerous comets which have
been discovered during the last half century there is scarcely one which on
whose certain return we can rely. Many have been found to move in curves called
parabolas and hyperbolas, and it is impossible for those again to revisit our
system unless some great change take place in their orbits. Laplace has
calculated that supposing a comet to move in such an orbit it is 57 to against
its being visible to our Earth. On the ground its seems probable that in the
last 50 years between 2 and 3 thousand have approached the Sun though the
larger part have been entirely unnoticed by us.
It may
probably be asked what becomes of those comets which retire from the power of
our Sun and never return. Are these bodies lost in the immense deserts which
separate our primary from the nearest of the fixed stars. It rather appears
from mechanical principles that when a comet has by the action of any
extraneous force acquired such a velocity as to cause it to quit the sphere of
our Sun that it would pursue its unimpeded course until some other sun should
exercise its influence on it and attract it towards a new centre. It might then
descend with immense velocity towards this new primary and thus continue to
visit system after system making as it were the tour of the universe. If this
be really the arrangement of Nature there is doubtless some final cause from
which these wanderings are directed. On this we can only form conjecture. It
has been supposed that in the transit of these bodies through the immense
regions which separate our system from the nearest fixed stars the comets pass
through regions of nebulous matter which they convey to distant systems to
supply the waste occasioned by the emission of light.
Lecture 10: On the Theory of Universal GravitationLecture 10
On the Theory of Universal Gravitation
By observation and experiment we gain
the first materials of our knowledge. These are the foundations of all
philosophy. But facts however certain or numerous would by themselves be of
comparatively small importance if the inquiring spirit of Man did not seize him
to generalise his observations, and to form some theory to connect and account
for the various appearances presented to him by Nature. The very number of
these facts would soon overpower his memory unless he made use of method and
arrangement. Thus then the accumulation of his observations would necessarily
produce speculative knowledge and give rise to an attempt at theory.
It is to a legitimate use of theory
that the science of Astronomy is particularly indebted. She presents us with
some of its most happy illustrations. The indiscriminant zeal against
hypothesis so generally avowed by the followers of Bacon has been much
encouraged by the strong and decided forms in which they have been reprobated
by Newton. But the language of this great man must be qualified and limited by
the exemplification he has availed himself given of his general rules. And it
should be remembered that they were particularly directed against the vortices
of Descartes which were purely fictitious and were the prevailing doctrine of
the time. A very learned and acute writer has observed that "the votaries
of hypothesis have been challenged to shew one useful discovery in the work of
Nature that was ever made in that way." In reply to this challenge it will
be sufficient on the present occasion to maintain the Theory of Gravitation and
the Copernican System. Of the former I shall presently endeavour to prove from
a sketch of its history that it took its rise entirely from a conjecture, or
hypothesis suggested by analogy. Nor indeed could it be considered in any other
light until that period of Newton's life when, by a calculation founded in an
accurate measurement of the Earth by Picard, he evinced the evidence to be
true, even the law which regulates the fall of heavy bodies, that power which
retains the Moon in her orbit.
The
Copernican System offers however a still stronger case, inasmuch as the only
evidence which the author was able to offer was the advantage it possessed over
every other hypothesis in explaining with beauty and simplicity all the phenomena
of the heavens. In the mind of Copernicus therefore this system was nothing
more than a hypothesis, but it was an hypothesis conformable to the universal
law of nature, always accomplishing her ends by the simplest means.
Nor is the use of hypothesis
confined to these cases in which they have subsequently received confirmation.
It may be equally great where they have completely disappointed the
explanations of their authors. Indeed any hypothesis which possesses a
sufficient degree of plausibility to account for a number of facts will help us
to arrange those facts in proper order and will suggest to us proper
experiments either to confirm, or refute it. Nor is it solely by the erroneous
results of his own hypothesis that the philosopher is assisted in his enquiry
after truth.
Similar
lengths may often be collected by the errors of his predecessors: it was from a
review of the endless and hapless wanderings of preceding enquirers that Bacon
inferred the necessity of avoiding every beaten track, and it was this which
encouraged him with a confidence in his own powers, amply justified by the
event, to explore and to open a new path to the mysteries of Nature.
In this respect the maturity of
reason in the species is analogous to that in the individual. It is not the
consequence of any sudden or accidental cause but the fruit of re-iterated
disappointment connecting the mistakes of youth and inexperience. "There
is no subject," says [Bernard le Bouvier de] Fontenelle, "on which
men ever come to a reasonable opinion till they have once exhausted all absurd
views which it is possible to take of it. What follies" he adds,
"should we not be repeating this day if we had not been anticipated in so
many of them by the ancient philosophers."
Those
systems which are false are therefore by no means to be regarded as altogether
useless. That of Ptolemy, for example, as has well been observed by the elegant
historian of Astronomy, is founded on a prejudice so natural and so unavoidable
that it may be considered as a necessary step in the progress of astronomical
science, and, if it had not been proposed in ancient times, it would infallibly
have preceded among the moderns the system of Copernicus and have retarded the
period of its discovery.
Among the numerous discoveries which
have rendered illustrious the name of Kepler there are none more important than
those with which he enriched Astronomy at the commencement of the 17th century.
Galileo had begun the investigation and cleared away some of the difficulties
but it was Kepler who transported geometry to the heavens, who discovered the
laws of their movement. Let us for a moment follow Kepler in the ideas and
conjectures which led him to these memorable results.
By
comparing the different velocities of the Sun at different seasons of the year
with variation of its apparent diameter, he found that it was impossible to
account for the phenomenon by supposing the Earth to revolve [around the Sun]
in a circle. He therefore supposed that it might move in an oval, but of this
figure there are various kinds, and the first one he hit upon did not answer
his purpose. He was however more successful in the next trial and found that
the common ellipse would satisfy all the conditions. From this period we may
date the knowledge of the elliptic motion of the planets and the destruction of
the ancient prejudice which attributed to the heavenly bodies a uniform
circular motion which by its simplicity had seduced the ancient philosophers of
Greece.
After discovering that the planets made
an ellipse Kepler wished to find some law which might regulate their motions.
He knew that when they were nearest the Sun they moved fastest, but was not
acquainted with the law of the change of velocity. After numerous trials he
found out the following analogy. If we conceive a line drawn from the Sun to
the centre of any planet this line will always pass over equal areas in equal
time.
Kepler
observed that the more distant a planet was from the Sun the longer time it
required to perform its revolution round that body, and this led him to the
discovery of another law which prevails throughout the planetary system. He
found that the square of the time of any planet's revolution always bore a
certain proportion to the cube of its distance and that this ratio is constant.
Mercury [=
0.13050] 39 x 39 x 39
Venus [=
0.1356] 72 x 72 x 72
Earth [= 0.1332]
100 x 100 x 100
Mars [= 0.1344]
152 x 152 x 152
Jupiter [= 0.1335]
520 x 520 x 520
[Table of
the square of the number of days required by a planet to revolve round the Sun
divided by the cube of its mean distance from that body in millions of miles]
The laws
which I have just mentioned were discovered by Kepler after many trials and numerous
failures. They rested on no other foundations than experiment and were in
precisely a similar situation to the laws relating the planetary distances
which I endeavoured to explain in a former lecture. That is to say Mankind were
astonished at their coincidence with Nature, but were unable to divine the
cause which produced it.
Kepler is particularly distinguished
from the philosophers of his time by the great boldness and frequently by the
great correctness of his views in enquiring into the cause which produces the
phenomena of Nature. He considered the Sun as the supreme moderator of the
celestial bodies. "This star" says he, "is possessed with a power of moving bodies, which it
spreads with immense rapidity throughout all space and hence arise the motions
of the planets."
At one time he compares the weight
of heavy bodies on Earth to the gravity of the planets towards the Sun. In
another place he suspects that the combined action of the Sun and the Earth
produces the irregularities of the [motion of] the Moon. And he imagines that
the tides may possibly arise from the attractions of this body. One of his
fundamental doctrines is the motion of the Sun on its axis, an hypothesis which
was completely justified a few years after by the discovery of the spots which
cover its surface. These ideas and conjectures bear the evident stamp of
genius, the daring flight of a powerful and comprehensive mind, and they opened
to Newton that glorious path which led him to the most sublime discoveries.
Before
however we take the steps which led this great philosopher to his theory of
gravitation, it will be proper to pass in review the theory of Descartes, which
at the time universally prevailed. Philosophers of the highest antiquity had
recognised the existence of the heavenly bodies. They had each calculated their
distances and appreciated with some accuracy the motions by which they are
animated. But no one before the 17th century, had endeavoured to snatch from
Nature the secret mechanism by which they hold together the planetary system.
The honour of this bold enterprise was reserved for Descartes. Determined to
produce a system entirely novel in which everything should be reconciled with
his ideas of the harmony of Nature, he conceived himself at the formation of
the Universe, and thus presented to himself the spectacle of Creation -an
infinity of molecules of matter repose in the immensity of space. All possess
an extreme hardness, and their infinitely varied form victoriously opposes the
existence of a vacuum. "Creative power" says Descartes, "imposes
on them a force, which at the same time carries them forward in space, and
causes them to revolve on their axis. And certain laws are prescribed to them
by which their actions are to be regulated." Such is the chaos from which
Descartes conceives a universe like ours might arise, whose spectacle, although
habitual, daily excites fresh reason for surprise and admiration. It is
needless to pursue the speculations of this philosopher through their varied
course to the existence of vortices of extremely subtle matter, through whose
assistance the planets and satellites were conceived to revolve.
We have
already seen that they are totally devoid of proof, and are, in fact,
physically impossible. Yet were not the speculations of Descartes without their
use in the progress of philosophy? They were errors, but it must be confessed
that they were splendid ones, and that the mind which could frame such a theory
might under better guidance have arrived at more accurate results.
Kepler, Galileo and Descartes
contributed to dissipate the darkness which had for a long time enveloped
mankind. They became the benefactors of the human race, but for the shame of
the age which produced them, they received as the reward of their labours
nothing but injustice, persecution and disgrace. Galileo, whose brilliant
discoveries had merited a better fate, was dragged to an unworthy prison.
Kepler surrounded by the glory he had acquired by the his sublime views of
Nature experienced in his old age all the misery of want and indignance. And it
was not until 100 years after the death of Descartes that his grateful country
raised even a monument to his memory.
Doubtless
nothing would be more satisfactory to the mind than the physical system of Descartes
if it could sustain the process of examination and observation. Those vortices,
that is to say, those torrents of ethereal matter, which according to this
philosopher carry with them the planets round the Sun, present to the mind an
intelligible mechanism which enchants by its simplicity. But this theory, which
at first glance is so seducing, is subject to many difficulties. It is
unfortunately found to agree so little either with the phenomena or with the
laws of mechanics that notwithstanding the efforts of many ingenious writers,
it is universally allowed that the system of Descartes is not that of Nature.
Newton pursued a different course,
and on the ruins of this system he has erected a new, more solid one, which
presents every appearance of the greatest durability. In fact his system
exhibits a perpetual coincidence between theory and observation. Whether we
regard the grander laws which regulate the Universe, or whether we examine
these minute and almost insensible ramifications of observation and geometry
[it] has nothing to fear from the vicissitudes of time, or from the more
changeable opinions of men. The system of Newton is founded on the principles
of Universal Gravitation.
Every
particle of matter, whatever may be the mechanism or cause which produces this
effect, tends, according to this philosopher, to every other particle with a
force which decreases inversely as the square of the distance. This gravity
causes on the surface of the Earth the weight of a body, and among the celestial
bodies it is the source of the most complicated motions. I shall endeavour to
explain the proofs of this principle and the reasoning which lead Newton to it
after shortly stating what was known on the subject before the time of his
writings.
We find among the writings of the
ancients a glimpse of several of the most brilliant truths. This is
particularly the case with the principles of Universal Gravitation, of which we
discover some decided marks. Anaxagoras as we have already seen attributed to
all the heavenly bodies a tendency towards the Earth, and other traces of the
same opinion may be found among the writings of Democritus and Epicurus. It was
from this principle that Lucretius drew the bold conclusion that the world is
without bounds.
As soon
the true system of the world revived by Copernicus arose from its ashes that of
Universal Gravitation threw some rays of light. This celebrated astronomer
attributed the round figure of bodies to the attraction of their parts. He did
not extend this attraction from planet to planet. But Kepler more bold and more
systematic made this step. He attributed to the Moon a tendency towards the
Earth and said that they could meet in their common centre of gravity if they
were not prevented by their rotation. Nobody however before the time of Newton
so clearly perceived the principle of that attraction, or more nearly
approached in making a proper application of the system of the Universe than
Dr. Hooke. The philosophers whom we have mentioned had some of them seized one
branch, some another, but Hooke embraced it in all its generality.
His anticipation of that theory of
planetary motions which was soon after to present itself with increased and at
length demonstrative evidence to a still more powerful mind furnishes a
remarkable instance of this philosophical sagacity. This conjecture I shall
state in his own words, and it affords a decisive reply to the undistinguishing
censures which have so often been bestowed on the presumptuous vanity of
attempting by means of hypothesis to penetrate into the secrets of Nature.
"I will explain" says Dr. Hooke, in a communication made to the
P[resident of the Royal Society?] in 1666, "a system of the world very
different from any yet received. It is founded on the three following
positions."
"1st
that all the heavenly bodies have not only a gravitation of their parts to
their own centre, but that they mutually attract each other within their
spheres of action."
"2ndly that all bodies having a
simple motion will continue to move in a straight line unless continually moved
out of it by some extraneous force."
"3rdly that as this attraction
is so much greater as the bodies are nearer, as to the proportion in which
those forces diminish by an increase of distance."
Dr. Hooke
adds "I [on my] own have not discovered it although I have made some
experiments for this purpose. I leave this for others who have time and
knowledge sufficient for the purpose."
It should be observed that there is
a wide difference between the conjecture of Hooke and the proofs and sublime
demonstrations by which Newton supported this law of the Universe. Such however
was the state of the question when this profound philosopher appeared. It was
in 1666 that he first [began] to suspect the existence of this principle and to
endeavour to apply it to the motions of the heavenly bodies. He had retired
into the country to avoid the plague, which at that time prevailed in London.
His meditations were one day accidentally directed toward the weight of bodies.
His first
reflection was that the cause which produced the fall of heavy bodies always
acts upon them to whatever height we convey them. It may then be extended much
further than we think, possibly as far as the Moon or even beyond. From this he
conjectured that it might possibly be this same force which retains the Moon in
her orbit. At the same time he considered that though Gravity does not sensibly
alter at different heights to which we can attain, yet at greater distances it
may vary and these altitudes are too small to conclude that it is the same at
all distances. It now remained to discover the law by which it varied,. For
this purpose he argued that if gravity retained our Moon in her orbit round the
Earth, it must be a similar cause which retains the sattelites of Jupiter in
their orbits round that body, and by comparing the periods of these bodies with
their distances, he found that gravity must decrease inversely as the square of
the distance.
Newton
did not however rest here. He continued to examine an account of the Moon's
distance from the Earth: the force by which she is attracted will be 3,600
times less than that by which a body falls on the surface of the Earth. If we
can compare the space through which the Moon falls towards the Earth in a given
time with that through which a body on the Earth's surface falls, we shall have
a criterion by which to judge of the truth of our theory. But here arose a
difficulty, how shall we find how much the Moon falls towards the Earth in a
given time? This difficulty Newton overcame, and these are the means he made
use of. This had nearly overthrown his whole edifice. He supposed the
terrestrial degrees to contain 60 miles and in consequence of this the two
quantities (on whose relation the truth of his theory was to be tried) did not
afford a result favourable to it.
Many philosophers would have been
but little troubled by this disagreement and would have continued to construct
their theoretical edifice. But this incomparable man, whose object was the discovery
of truth and not the formation of a
system, when he found that a single fact overthrew all his conjectures which
had hitherto been so well founded, immediately relinquished them.
It was
not till 10 years after that he resumed the train of his ideas. In this
interval the opinion of Dr. Hooke had been published and a very important step
had been made by Ricard in ascertaining the magnitude of the Earth. From this
Newton learned that the terrestrial degree was nearly 70 miles in length, and
not 60 as he had considered it in his calculations. He now therefore again
returned to his theory and having calculated the magnitude of the lunar orbit,
he found to his great satisfaction that the space fallen through by the Moon
precisely agreed with what it ought from his theory. After this demonstration
Newton no longer hesitated to consider the force by which heavy bodies fall at
the surface of the Earth and that by which the Moon is retained in her orbit as
one and the same.
He assumed gravity as a well ascertained
fact and proceeded to reason upon it. He showed that it followed necessarily
from his theory that the planets move in ellipses and he demonstrated the laws
which Kepler had only found by induction. By a skillful application of
mathematical calculation to the phenomena of Nature aided by the theory of
gravity, he unravelled numberless irregularities to which the heavenly bodies
are subject. Yet such was the excessive modesty of this great man that it was
with the greatest difficulty that he was persuaded to publish his profound
discoveries.
At the
urgent request of his friend, Dr. Halley, and at the entreaty of the Royal
Society, he was persuaded to collect together his discoveries, which he did in
his Principia, a work which also is alone sufficient to immortalise its author.
This work however in which this great
man has built a new system of natural philosophy upon the most sublime geometry
did not at first meet with all that applause it deserved and was one day to
receive.
Two reasons concurred to produce
this effect. Descartes' system had at that time got full possession of the
world. His philosophy was indeed the creature of a fine imagination; he had
given her some of Nature's features and had painted the rest to a seeming
resemblance to her. Newton, on the otherhand, had with unparalleled penetration
and force of genius pursued Nature up to her most secret abode and was intent
to demonstrate her residence to others rather than anxious to describe
particularly the way by which he arrived at it himself. But at last that
approbation which had been so slowly gained became universal, and nothing was
heard from all quarters but one universal burst of applause [and] admiration:
"Does Mr. Newton eat, drink or sleep like other men?" said the
Marquis de l'Hospital, one of the most enlightened foreigners of the age, to
his English visitors, "I represent him to myself as a celestial genius
entirely disengaged from matter."
Yet in
the midst of these profound enquiries Newton had leisure for other pursuits. When
the privileges of the University [of Cambridge] were attacked by James II he
appeared as one of the most strenuous defenders. And he made a very successful
defence before the high commission court. He was also a member of the
Convocation Parliament in which he sat till it was dissolved.
In his private life Newton was
modest and unassuming in the highest degree. His temper was so mild and equal
that no accident could disturb it. He would have rather chosen to remain in obscurity
than to have the calm of life ruffled by the storms and disputes which genius
and learning so frequently draw on those who are eminent for them. From this
love of peace arose that unusual horror which he felt for all disputes, and
that steady unbroken attention which was his peculiar felicity; he knew and
well esteemed its value.
When some
objections hostily made to his discoveries concerning light and colours induced
him to lay aside his design of publishing his optical lectures, we find him reflecting
on that dispute into which he was unavoidably drawn in these terms: "I
blamed my own imprudence" said Newton, "for parting with so real a
blessing as quiet, to run after a shadow." Yet this shadow was one of the
most splendid and most original of these discoveries which have contributed to
make his name so illustrious.
In contemplating the genius of
Newton the penetration, the strength and the originality of his mind, in his
moral capacity the pre-eminent trait is his modesty and love of quiet. In his
intellectual character the most predominant feature is the astonishing power
which he possessed of concentrating his attention to the object on which he was
employed. It was to this almost supernatural power that he himself attributed
his profound discoveries. When he declared that if he had done the world any
service it was due to nothing but industry and patient thought; that he kept
the subject of consideration constantly before him and waited till the first
dawning opened gradually, by little and little into a clear and full light.
Such was Newton as a man, and as a philosopher both characters were tinged with
a similar colouring. As a man he did not possess that warmth and enthusiasm
which we should admire in a friend, but he displayed that calm unruffled
serenity, which we should reverence in superior beings. As a philosopher he was
not led away by the fire of genius whose too daring grasp by sometimes
fostering error, reminding us of his mortal origin. But he was the patient, the
accurate investigator of Nature, the deep, the profound philosopher.
To trace
the consequences of the law of Universal Gravitation through its numerous and
almost endless ramifications would lead us in succession through every branch
of astronomical science. Each seeming objection which has successively been
brought against its truths has furnished new arguments in its favour and
afforded new ground of triumph to the followers of Newton. It has frequently
anticipated observation and has predicted to future astronomers irregularities
that are yet to be recognised. To such a point of perfection has this science
been carried, that there does not now remain one single irregularity of the
heavenly bodies of any magnitude which does not follow as a consequence of this
law, and whose quantity cannot be calculated by it. It is obvious that an
enumeration of these varied irregularities would be of little improvement, but
there are some important questions which present themselves and which relate to
the law of gravity.
There are many of the planetary
irregularities, which increase and decrease alternately in longer and shorter
periods. Some however, since we have observations of them recorded, have been
found uniformly to decrease. Such for instance is the obliquity of the ecliptic.
If this obliquity were to decrease continually, the ecliptic would at last
coincide with the equator. This would not take place until after the lapse of
millions of years, but when it did the days and nights all over the world would
become equal; the Earth would possess a perpetual spring. Whether this change
would be for the advantage of the human race if it then existed, or whether it
would not render nearly half the globe uninhabitable, are doubtful questions;
yet remote as this change may be it is interesting to enquire whether it is
possible, because there are other irregularities which increase much more
rapidly and which might if they continued to increase totally derange the
system. The question then in the most general sense is to investigate whether
the irregularities of the planetary system will continually increase or whether
after attaining a certain point they will not decrease and return again in the
same order.
This
question which is a very important one has occupied some of the greatest philosophers
of the age. The progress was very gradual but the solution is complete. It is
to the united labours of Lagrange and Laplace that we are indebted for the
solution of this interesting question. It has been demonstrated that every
irregularity to which the planetary [system] is subject must from its nature be
periodical: that is, it will increase to a certain point and then decrease to
another point, between which two it will constantly oscillate, never exceeding
either of them, just in the same manner as a pendulum which constantly moves to
and fro, but never exceeds a certain fixed distance from its point of rest.
Almost everything in the system will therefore be in motion, but admidst this
universal change some few elements will remain constant: thus the mean distance
of each planet from the Sun will be unaltered. Thus then it appears that unless
some foreign force disturb the harmony of our System, it will forever continue
in its present arrangement, that it does not contain within itself the seeds of
destruction, but on the contrary that it is destined to an eternal duration,
unless the mechanical laws which govern matter be subverted or some influence
foreign to the System be exerted on it.
There
were, however, in its original constitution some conditions necessary, that the
inclination of the orbit of the planets to the Sun's equator be small, that the
ellipses which they describe should be nearly circular and that they should all
move round the Sun in the same direction. And if these conditions had not been
fulfilled it is possible that the beautiful system from its own action have
produced its destruction. If we enquire from the doctrine of chances whether it
is probable that the conditions should have been accidentally accomplished we
find that the contrary is indicated with the highest possible degree of
probability. In fact Laplace, when speaking on this subject, says that we have
stronger grounds for believing that the planetary motions and inclinations were
all influenced by the same primitive cause, than we have for giving credit to
any of the most authentic accounts in history. This wonderful contrivance of an
intelligent mind by which the permanence of our System is secured is highly
calculated to excite our admiration, yet it has been perverted to the worst,
the most unphilosophical purposes. It has been urged as the supporter of fate
and of necessity, and has been inconsiderately advanced as an argument against
the superintendence and existence of a first cause. It is a singular circumstance
that a fact which had a tendency so directly contrary should have been so
misunderstood, and it would perhaps be needless to refute it, but that it has
been said, though I believe falsely, to have received the sanction of one of
the most eminent of the continental philosophers. The difficulty is easily
removed. We have only to ask ourselves this question: which is the most skilful
artist? he who makes a clock which requires winding up every day and cleaning
every year, or he who contrives one which winds itself up and never requires
cleaning, to which
it may be
further added that among the infinite number of laws by which gravity might
act, all equally possible, this of Nature alone aided by the conditions already
specified will ensure the stability and permanence of the System. Had there
been any other originally established this Universe the beneficent result of
creative power would have long since have returned to its primitive chaos.
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