conservatism/conservative

Thu May 19 09:20:28 UTC 2011

As we tend to identify various "isms" with political movements or
philosophical trends, a more plain use often escapes attention:

http://goo.gl/xzL9j
The Entwined Lives of Miss Gabrielle Austin, Daughter of the Late Rev. Ellis
C. Austin, And of Redmond, the Outlaw, Leader of the North Carolina
"Moonshiners." By Bishop [Edwin B.] Crittenden. Philadelphia: 1883
p. 21

> In the arrangement of the incidents of this truly wonderful history, I have
> adhered closely to conservatism, and if the reader stands amazed at the
> fearfully dramatic character of the situations, it will go to prove that
> "Verily truth is stranger than fiction."

This does not match any of the OED definitions of "conservatism" that is
attached either to a philosophical ideas (as opposed to "liberalism") or to
political ones (the Tories). The usage here corresponds to the main
definition of conservative, adj.:

B. adj.
>  I. That conserves, or tends to conserve.
>  1. a. Characterized by a tendency to preserve or keep intact or unchanged;
> that conserves something; preserving. Now rare except as merged with
> sense B. 2, or retained in specialized uses at Branch B. II.

The main definition of conservatism (1.a.) corresponds to the second
definition of conservative, adj.:

2. a. That conserves, or favours the conservation of, an existing structure
> or system; (now esp.) designating a person, movement, outlook, etc., averse
> to change or innovation and holding traditional ideas and values, esp. with
> regard to social and political issues.

There is another conservative, adj. B.II.4.

> 4. Math. and Physics. Of a vector field: equal to the gradient
> (gradient n. 5) of a scalar potential, so that the integral over a path in
> the field depends only on the end points of the path, not on the route
> between them; (of a physical property) describable by or associated with
> such a field.

[Note: In most cases a conservative field has a curl (curl n. 3e) of zero
> (is irrotational), so that the integral around a closed path is zero.]

 Indeed, Wiki has an entry for "conservative vector field". But it also has
an entry for "conservative force", which attracted my attention by its
glaring absence from the OED list.

A conservative force is a force with the property that the work done in
> moving a particle between two points is independent of the path taken.
> Equivalently, if a particle travels in a closed loop, the net work done (the
> sum of the force acting along the path multiplied by the distance travelled)
> by a conservative force is zero. ... Informally, a conservative force can be
> thought of as a force that conserves mechanical energy.

Another entry--conservative system (which is a commonly used
term)--redirects to "conservation law". In general, "conservative" is used
as a descriptor of something that functions in a conservative system or is
subject to conservation of energy or some other conservation law. There are
other math/science uses of "conservative" that are not related to
conservative systems (e.g., conservative extension), but these are far less
important. Note that the OED definition is actually derivative of the more
general one--a conservative force has a path integral of zero, a
conservative field is or is a part of a conservative system--in fact, the
very first example is from a Thomson&Tait comment on [mechanical]
conservative /systems/, not fields.

Incidentally, a related term "gradient field" has no entry, but appears in
three quotations. Nor do "path-independence" and "path-independent", which
is what the conservative B.4. lemma describes but fails to mention.

http://goo.gl/wB2Bj
The Popular Science Monthly. Volume 6. January 1874
The Primary Concepts of Modern Physical Science. By J. B. Stallo.
IV--Inertia and Force. p. 353

> A corollary from, or rather an application of this is the well-known
> theorem that the forces within a body or conservative system can alter only
> the positions of its constituent parts, but cannot change the position of
> the body as a whole; and that, whenever such an internal change takes place,
> the momentum accruing in one direction has its counterpart in an equal
> momentum accruing in the opposite direction. If we apply this theorem to the
> universe as a whole, i. e., as a single dynamical system, and if we bear in
> mind that, mechanically speaking, all force properly so called, i. e., all
> potential energy, is energy of position, we see at once that whatever energy
> is spent in actual motion is gained in position--that the system, therefore,
> is absolutely conservative; and we are thus led, by a very simple approach,
> to the principle of the conservation of energy.[1]

[Footnote [1]]

> 1 If the term " force" is restricted, as it ought to be, to the designation
> of potential energy, or mere tension, the expression " persistence or
> conservation of force " becomes inaccurate; for the sum of the forces in the
> universe, in this sense, is by no means constant. The "persistence
> of force," or, more properly, the " conservation of energy," simply imports
> that the sum of actual or kinetic energy (energy in motion) and potential
> energy (energy of position or energy in tension) in the material universe is
> invariable. This, as is shown in the text, is but an amplification of the
> theorem that in any limited conservative system the sum of the potential and
> kinetic energies of its parts is never changed by their mutual actions.

p. 359

>  Molecular forces, therefore, are the agencies which determine the
> particular state of the body in its physical relations, considering it as an
> independent whole--or, as it is termed in modern mechanics, as an
> independent conservative system—while the molar forces determine the
> physical relations of the body to other bodies which, together with it, are
> integrant parts of a greater whole, i . e., of a more
> comprehensive conservative system.

p. 360

> Now, what is this molecular motion, in the light of the insight which, as I
> hope, has been gained in the foregoing discussion? Simply an exhibition of
> the struggle involved in the formation or constitution of a body as a
> distinct conservative system.

Proceedings of the Royal Irish Academy. Series II. Volume I: Science.
1870-1874
The Theory of Screws.--Part I. A Gemetrical Study of the Kinematic
Equilibrium and Small Oscillations of a Rigid Body. By Robert Stawell Ball.
Read November 13, 1871. p. 237

> The forces which hold a body in equilibrium form a conservative system. A,
> B are a pair of displacement screws; X, T'' the corresponding restoration
> screws. If A be reciprocal to Y, then B is reciprocal to X. This appears to
> be an important property of a conservative system.
>
> A free body is in equilibrium under a conservative system.

http://goo.gl/sRnAC
The Quarterly Journal of Pure and Applied Mathematics, Volume 10. 1870
An Interpretation and Proof of Lagrange's Equations of Motion Referred to
Generalized Coordinates. By R. B. Hayward. p. 375

> In fact /kQ[delta]q/ is the work done by the forces acting on /m/, when a
> displacement is made by giving an arbitrary increment /[delta]q/ to /q/, and
> therefore [Sigma](/kQ/) /[delta]q/ is the total work done by all the forces
> throughout the system corresponding to the variation /[delta]q/ : but if
> the system be a conservative system, this total work may be expressed as
> /[dU/dq [delta]q]/,  U being a function of the coordinates only
> termed the force-function. Hence
>
[Sigma (kQ) = dU/dq]

and equation (7) becomes
> [dp/dt - dT_q/dq = dU/dq]................ (8).
> This equation is the type of /n/ equations obtained by attaching the
> suffixes 1,2, ... /n/ to the letters /p/ and /q/, and the /n/ equations thus
> obtained are identical with Lagrange's equations of motion for
> a conservative system.
> Harrow, Jan., 1870.
>

Transactions of the Royal Society of Edinburgh. 1867
On the Application of Hamilton's Characteristic Function to Special Cases of
Constraint. By [Peter Guthrie] Tait. (Read 20th March 1865.) p. 147

> It is there shown that the complete solution of any kinetical problem,
> involving the action of a given conservative system of forces, and
> constraint depending upon the reaction of smooth guiding curves or surfaces,
> also given, is reducible to the determination of a single quantity called
> the /Characteristic Function/ of the motion.

p. 164

> Here the velocity depends only upon the direction of the ray, as in
> homogeneous doubly refracting media, and the problem has no analogy with
> the conservative case which is treated above.

IIRC, the very terminology of a "conservative system" might have been
introduced by William Thomson (Lord Kelvin) and/or P.G. Tait, although I am
hesitant to say that either of them coined the term. Thomson & Tait were
certainly responsible The Treatise on Natural Philosophy (1867, "T and T")
that served as a vector for the terminology and I found no other physical
references so far prior to the 1865 lecture on the characteristic function.
 This was later extended to a "conservative field" by Maxwell. Tait is
responsible for recognizing, popularizing and contributing to many
innovative mathematical and scientific ideas of the 1860s-80s, including
Hamilton's quaternions, Cayley's notions of abstract algebra, thermodynamics
and kinetic theory of gases--along with Kelvin and Maxwell, etc. Prior to
that, "conservative system" is used almost exclusively in the political or
philosophical sense.

VS-)

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