carlfogel wrote:
> Peter wrote:
> > Carl Fogel wrote:
> > > Peter <
[email protected]> wrote in message
> > > news:<Lcv8c.87617$1p.1331107@attbi_s54>...
> > >
> > > [snip Carl and Peter and Lord Kelvin]
> > >
> > > Dear Peter,
> > >
> > > Thanks for the calculations. While the mathematics
> > > are beyond me, I can at least return the favor by a
> > > spattering of lurid biographical quotes and sites
> > > about Lord Kelvin that might intrigue people.
> > >
> > > Some of these sites mention the various ranges for
> > > the age of the earth that puzzled you--Gould was
> > > just repeating what Lord Kelvin kept publishing.
> > It was the age of the sun estimate where Gould's
> > numbers were puzzling. He indicated a range from 100 -
> > 500 million years, but Kelvin's paper which I cited
> > and you also cite below actually gave a calculation
> > that came out to 20 million years. Kelvin then figured
> > that it would likely have been hotter in earlier times
> > and that might reduce the age to only 10 million
> > years. OTOH, if most of the mass were actually in a
> > dense core the age could be greater but probably not
> > as much as 100 million and certainly not as much as
> > 500 million. The actual probable age in his published
> > paper is in the range of 10 - 100 million years, not
> > Gould's quoted 100-500. The only time Kelvin has
> > numbers that large is when he's bending over backward
> > to give as long an age as conceivable under the stated
> > assumptions (no unknown energy sources), but they
> > aren't his estimate of the likely age.
> > > That some form of the meteoric theory is certainly
> > > the true and complete explanation of solar heat can
> > > scarcely be doubted, when the following reasons are
> > > considered:
> > >
> > > 1. No other natural explanation, except by chemical
> > > action, can be conceived,
> > >
> > > 2. The chemical theory is quite insufficient,
> > > because the most energetic chemical action we
> > > know, taking place between substances amounting
> > > to the whole sun's mass, would only generate
> > > about 3,000 years' heat . . .
> > A few paragraphs down is where he gives his probable
> > range: "We may, therefore, accept, as a lowest
> > estimate for the sun's initial heat, 10,000,000 times
> > a year's supply at the present rate, but 50,000,000 or
> > 100,000,000 as possible, In consequence of the sun's
> > greater density in his central parts."
> > >
> > > It seems, therefore, on the whole most probable that
> > > the sun has not illuminated the earth for
> > > 100,000,000 years, and almost certain that he has
> > > not done so for 500,000,000 years. As for the
> > > future, we may say, with equal certainty, that
> > > inhabitants of the earth can not continue to enjoy
> > > the light and heat essential to their life for many
> > > million years longer unless sources now unknown to
> > > us are prepared in the great storehouse of creation.
> > >
> > > --from Kelvin's brief essay on the age of the sun:
> > >
http://home.att.ne-
> > > t/~a.caimi/Kelvin.dochttp://home.att.net/~a.caimi/K-
> > > elvin.doc
>
>
>
> Dear Peter,
>
> Here's how I think Gould arrived at this comment in "The
> Flamingo's Smile":
>
> "He [Lord Kelvin] never ventured a precise figure for the
> sun's age. He settled on a number between 100 million and
> 500 million years as a best estimate, probably closer to
> the younger age."
>
> This seems like a fair description of what Lord Kelvin
> wrote below, which takes a bit of re-reading. He gives no
> specific number, explains that he considers 100 million a
> "few millions," and says that "it is almost certain" that
> the sun hasn't been going for 500 million years, which
> Gould seems to take as an upper limit. This 100-500 range
> seems to be as close as anyone can pin things down from
> Lord Kelvin's remarks, particularly when by his reckoning,
> it's only a few millions:
>
> "We may imagine that to be the case, and that he [the sun]
> is continually burning from the combustion of elements
> within himself; or we may imagine the sun to be merely a
> heated body cooling; but imagine it as we please, we
> cannot estimate more on any probable hypothesis, than a
> few million years of heat. When I say a few millions, I
> must say at the same time, that I consider one hundred
> millions as being a few, and I cannot see a decided reason
> against admitting that the sun may have had in it one
> hundred million years of heat, according to its present
> rate of emission, in the shape of energy. An article, by
> myself, published in Macmillan's Magazine, for March 1862,
> on the age of the sun's heat, explains results of
> investigation into various questions as to possibilities
> regarding the amount of the heat that the sun could have,
> dealing with it as you would with a stone, or a piece of
> matter, only taking into account the sun's dimensions,
> which showed it to be possible that the sun may have
> already illuminated the earth for as many as one hundred
> million years, but at the same time also rendered it
> almost certain that he had not illuminated the earth for
> five hundred millions of years.
His writing style is certainly verbose, but in this passage
as in the paper itself it is clear that both 100 million and
500 million are to be taken as *upper limits* - just with
differing degrees of certainty, i.e. he's pretty sure it's
less than 100 and almost certain it's less than 500 million
years. However, Gould takes the 100 million figure and uses
it as a lower limit on the range. This is not consistent
with either Kelvin's statement above "as many as one hundred
million years" nor with the statement from his paper "It
seems, therefore, on the whole most probable that the sun
has *not* illuminated the earth for 100,000,000 years ..."
The estimates here are necessarily very vague, but
> yet, vague as they are, I do not know that it is possible,
> upon any reasonable estimate, founded on known properties
> of matter, to say that we can believe the sun has really
> illuminated the earth for five hundred million years."
>
> On Geological Time Transactions of the Geological Society
> of Glasgow, vol. iii, 1868
>
>
http://zapatopi.net/kelvin/paper.php?id=9
>
> While rummaging about to find the quote above, I found the
> following example of Lord Kelvin's geological theorizing,
> which so far I hadn't noticed anyone mentioning in my
> browsing.
>
> Based on a slowing down of the earth's rotation, the exact
> amount of which he later states doesn't matter, he
> calculated that the earth must have been "all fluid not so
> many millions of years ago."
>
> I suspect that it's the kind of thing that my professor
> had in mind, since the physics of rotating bodies haven't
> changed much.
His theorizing below, while rather rambling, isn't far off
the mark either under the assumption that the interior of
the earth has no energy source keeping it hot. This line of
reasoning is discussed by Gould as the third method used by
Kelvin to put some bounds of the age of the earth. He
estimated the amount of tidal friction that would be slowing
the earth's rotation and then determined that if the earth
had solidified 10 billion years ago it would have been
spinning fast enough to result in a much more flattened
shape than is observed. I note that he really doesn't derive
an estimated age from this calculation with any precision
other than to say that the degree of flattening is
consistent with an earth that's as old as 100 million years
but inconsistent with one that's 10 billion years old or
more. Nothing wrong with his conclusion that the earth is
less than 10 billion years old. The main thrust of his
argument is summed up in the last sentence "The earth is
filled with evidences that it has not been going on for ever
in the present state, and that there is a progress of events
towards a state infinitely different from the present." This
shows that his argument is with those who were claiming a
totally steady-state view with an infinite age of the earth
with no major changes occuring over time. He was entirely
correct to have taken issue with that view even if some of
his other calculations on the ages were on the low side due
to a lack of knowledge of radioactivity and fusion.
The physics of rotating bodies hasn't changed much, but at
issue here is the question of how much the earth has
solidified. That is dependent on the source of heat in the
earth's interior and brings us right back to the energy of
radioactive decay which Kelvin did not and could not have
included in his models some decades before it was
discovered.
The discussion below by Kelvin doesn't apply to our current
model of the earth's structure with continental plates
drifting on semi-fluid portions of the mantle. But it seems
unfair to criticize his theories from the 1860s for failure
to foresee the plate tectonics of the 1960s.
>
> Carl Fogel
>
> Recently all-fluid earth:
>
> "Now, if the earth is losing angular velocity at that
> great rate, at what rate might it have been rotating a
> thousand million years ago? It must have been rotating
> faster by one-seventh part than at present, and the
> centrifugal force must have been greater in the ratio of
> the square of 8 to the square of 7, that is, in the ratio
> of 64 to 49. There must have then been more centrifugal
> force at the equator due to rotation than now, in the
> proportion of 64 to 49. What does the theory of geologists
> say to that? There is just now at the equator one two-hundred-
> and-eighty-ninth part of the force of gravity relieved by
> centrifugal force. If the earth rotated seventeen times
> faster bodies would fly off at the equator. The present
> figure of the earth agrees closely with the supposition of
> its having been all fluid not many million years ago."
>
> "The centrifugal force a hundred million years ago would
> be greater by about 3 per cent. than it is now, according
> to the preceding estimate of tidal retardation; and
> nothing we know regarding the figure of the earth and the
> disposition of land and water, would justify us in saying
> that a body consolidated when there was more centrifugal
> force by 3 per cent. than now might not now be in all
> respects like the earth, so far as we know it at present.
> But it you go back to ten thousand million years ago --
> which, I believe, will not satisfy some geologists -- the
> earth must have been rotating more than twice as fast as
> at present -- and if it had been solid then, it must be
> now something totally different from that it is. Now, here
> is direct opposition between Physical astronomy, and
> modern geology as represented by a very large, very
> influential, and, I may also add, in many respects,
> philosophical and sound body of geological investigators,
> constituting perhaps a majority of British geologists. It
> is quite certain that a great mistake has been made --
> that British popular geology at the present time is in
> direct opposition to the principles of natural philosophy.
> Without going into details, I may say it is no matter
> whether the earth's lost time is 22 seconds, or
> considerably more or less than 22 seconds, in a century,
> the principle is the same. There cannot be uniformity. The
> earth is filled with evidences that it has not been going
> on for ever in the present state, and that there is a
> progress of events towards a state infinitely different
> from the present."
>
>
http://zapatopi.net/kelvin/paper.php?id=9
