What is reduced momentum in "A Dynamical Theory of the Electromagnetic Field" by James Clerk Maxwell? I was reading Maxwell's paper titled [A Dynamical Theory of the Electromagnetic Field][1]. In part 2, section 3 ("Dynamical Illustration of Reduced Momentum"), Maxwell discusses a mechanical illustration for reduced momentum:
![§"Dynamical Illustration of Reduced Momentum" (pp. 467-468)][2]
What is Maxwell trying to convey in this section:

As a dynamical illustration, let us suppose a body $C$ so connected
  with two independent driving-points $A$ and $B$ that its velocity is
  $P$ times that of $A$ together with $q$ times that of $B$. Let $u$ be
  the velocity of $A$, $v$ that of $B$, and $w$ that of $C$, and let
  $\delta x$, $\delta y$, $\delta z$ be their simultaneous
  displacements, then by the general equation of dynamics,
$$C \frac{dw}{dt}\delta z = X\delta x + Y \delta y,$$
where $X$ and $Y$ are the forces acting at $A$ an $B$. But,
$$\frac{dw}{dt} = p\frac{du}{dt} + q\frac{dv}{dt}$$ and $$\delta z =
> p\delta x + q \delta y.$$
Substituting, and remembering that $\delta x$ and $\delta y$ are
  independent,
$$X=\frac{d}{dt}(Cp^2u+Cpqv),$$ $$Y=\frac{d}{dt}(Cpqu+Cq^2v).$$
We may call $Cp^2u+Cpqv$ the momentum of $C$ referred to $A$, and
  $Cpqu + C q^2 v$ its momentum referred to $B$; then we may say that
  the effect of the force $X$ is to increase the momentum of $C$
  referred to $A$, and that of $Y$ to increase its momentum referred to
  $B$. If there are many bodies connected with $A$ and $B$ in a similar
  way but with different values of $p$ and $q$, we may treat the
  question in the same way by assuming, $$L=\sum (Cp^2), \quad M=\sum
> (Cpq), \quad \mathrm{and} \, \, \, N=\sum(Cq^2),$$
where the summation is extended to all the bodies with their proper
  values $C$, $p$, and $q$. Then the momentum of the system referred to
  $A$ is, $$Lu+Mv$$, and referred to $B$, $$Mu+Nv,$$ and we shall have
  $$X=\frac{d}{dt}(Lu+Mv),$$ $$Y=\frac{d}{dt}(Mu+Nv),$$ where $X$ and
  $Y$ are the external forces acting on $A$ and $B$. To make the
  illustration more complete we have only to suppose that the motion of
  $A$ is resisted by a force proportional to its velocity, which we may
  call $Ru$, and that of $B$ by a similar force, which we may call $Sv$,
  $R$ and $S$ being coefficients of resistance. Then if $\xi$ and $\eta$
  are the forces on $A$ and $B$
$$\xi=X+Ru=Ru+\frac{d}{dt}(Lu+Mv),$$ $$\eta = Y + Sv=Sv +
> \frac{d}{dt}(Mu+Nv)$$
If the velocity of $A$be increased at a rate of $\frac{du}{dt}$, then
  in order to prevent $B$ from moving a force, $\eta=\frac{d}{dt}(Mu)$
  must be applied to it.
This effect on $B$, due to an increase of the velocity of $A$,
  corresponds to the electromotive force on one circuit arising from an
  increase in the strength of a neighbouring circuit. This dynamical
  illustration is to be considered merely as assisting the reader to
  understand what is meant in mechanics by reduced momentum. The facts
  of the induction of currents as depending on the variations of the
  quantity called electromagnetic momentum, or electronic state, rest on
  the experiments of Faraday, Felici, &c.

 A: Maxwell is referring to a mechanical system composed of two rods connecting three points. Consider the following diagram A----------C-----------B where A, C, and B are points (you can consider them to be balls). Then, the motion of A and B influence C the way Maxwell as just described. He is constructing an analogy between the upper mechanical system and that of two circuits, where a change in current in one current induces an electromotive force on another circuit (induction). The quantities L, M, and N are mechanical quantities Maxwell invented to correspond to the three coefficients of induction. 
Coefficients of induction were used in Maxwell's time to construct a geometric relationship between electromagnetic quantities. In Part 3, Maxwell's equations are put in scalar form, though they look different from the modern equations because the magnetic potential and other extra variables are discussed. Part 2 has these arcane mechanical illustrations to discuss about induction, and I would recommend for you to skip Part 2, unless you want a thorough understanding of archaic systems and archaic physics terminology. Note: Heaviside vastly simplifies Maxwells equations to the four we know today; I would recommend physical lines of force by Maxwell, Part 3 of Maxwell's treatise as well as Heaviside's papers on the matter for an understanding of the equations and there derivation. Part 2 of "A dynamical Theory of the ELectromagnetic Field" deals only with induction and serves to create mechanical analogies and use them to derive experimentally verified relations, as a backdrop for the vastly more important Part 3 of the treatise.
