approximation techniques or model
systems. For some problems, such as
the three-body problem in classical
mechanics, it is possible to obtain
qualitative information about the sys-
tem. If there are a great many bodies
interacting, such as the molecules in
a gas, the problem can be analysed
using the techniques of *statistical
mechanics.marbleA metamorphic rock com-
posed of recrystallized *calcite or
*dolomite. Pure marbles are white
but such impurities as silica or clay
minerals result in variations of col-
our. Marble is extensively used for
building purposes and ornamental
use; the pure white marble from Car-
rara in Italy is especially prized by
sculptors. The term is applied com-
mercially to any limestone or
dolomite that can be cut and pol-
ished.
margaric acidSee heptadecanoic
acid.
marijuanaSee cannabis.MarkofÜan process (Markov
process) A random process (see sto-
chastic process) in which the rate
of change of a time-dependent quan-
tity ∂a(t)/∂t depends on the instanta-
neous value of the quantity a(t),
where t is the time, but not on its
previous history. If a random process
can be assumed to be a Markov
process, an analysis of the process is
greatly simpliÜed enabling useful
equations in *nonequilibrium statis-
tical mechanics and disordered solids
to be derived. Problems involving
Markov processes are solved using
statistical methods and the theory of
probability. Markov processes are
named after the Russian mathemati-
cian Andrei Andreevich Markov
(1856–1922).
Markovnikoff’s rule When an
acid HA adds to an alkene, a mixtureof products can be formed if the
alkene is not symmetrical. For in-
stance, the reaction between
C 2 H 5 CH:CH 2 and HCl can give
C 2 H 5 CH 2 CH 2 Cl or C 2 H 5 CHClCH 3.
In general, a mixture of products
occurs in which one predominates
over the other. In 1870, Vladimir
Markovnikoff (1837–1904) proposed
the rule that the main product would
be the one in which the hydrogen
atom adds to the carbon having the
larger number of hydrogen atoms
(the latter product above). This oc-
curs when the mechanism is *elec-
trophilic addition, in which the
Ürst step is addition of H+. The
electron-releasing effect of the alkyl
group (C 2 H 5 ) distorts the electron-
distribution in the double bond, mak-
ing the carbon atom furthest from
the alkyl group negative. This is the
atom attacked by H+giving the car-
bonium ion C 2 H 5 C+HCH 3 , which fur-
ther reacts with the negative ion Cl–.
In some circumstances anti-
Markovnikoff behaviour occurs, in
which the opposite effect is found.
This happens when the mechanism
involves free radicals and is common
in addition of hydrogen bromide
when peroxides are present.Markush structure A generalized
formula or description for a related
set of chemical compounds, used in
patent applications. It is named after
Eugene Markush (1888–1968), an
American manufacturer of dyes and
pharmaceuticals. In 1924 he was
awarded a patent for “The process
for manufacture of dyes which com-
prises coupling with a halogen-
substituted pyralazone, a diazotized
unsulphonated material selected
from the group consisting of aniline,
homologues of aniline, and halogen
substitution products of aniline”.
Note that the patent was for
processes to produce a range of com-marble 342m