``XXX`` -> :class:`XXX`

principle -> principal... I'm a bozo.

docs-source/usersguide/theory.rst

@@ -1399,7 +1399,7 @@ normal distribution).
 
 What this means is that the random numbers used by integrators and forces within
 OpenMM cannot have any discernible pattern to them.  Patterns can be induced in
-PRNGs in two principle ways:
+PRNGs in two principal ways:
     1. The PRNG uses a bad algorithm with a short period.
     2. Two PRNGs are started using the same seed
 
@@ -1421,23 +1421,24 @@ only within a single simulation, but between two different simulations of the
 same system as well (including any restarts of previous simulations).
 
 Every stochastic force and integrator that does (or could) make use of random
-numbers has two instance methods attached to it: ``getRandomNumberSeed()`` and
-``setRandomNumberSeed(int seed)``. If you set a unique random seed for two
-different simulations (or different forces/integrators if applicable), OpenMM
-guarantees that the generated sequences of random numbers will be different (by
-contrast, no guarantee is made that the same seed will result in identical
-random number sequences).
+numbers has two instance methods attached to it: :class:`getRandomNumberSeed()`
+and :class:`setRandomNumberSeed(int seed)`. If you set a unique random seed for
+two different simulations (or different forces/integrators if applicable),
+OpenMM guarantees that the generated sequences of random numbers will be
+different (by contrast, no guarantee is made that the same seed will result in
+identical random number sequences).
 
 Since breaking simulations up into pieces and/or running multiple replicates of
 a system to obtain more complete statistics is common practice, a new strategy
 has been employed for OpenMM versions 6.3 and later with the aim of trying to
 ensure that each simulation will be started with a unique random seed. A random
 seed value of 0 (the default) will cause a unique random seed to be generated
-when a new ``Context`` is instantiated.
+when a new :class:`Context` is instantiated.
 
 Prior to the introduction of this feature, deserializing a serialized
-``System`` XML file would result in each stochastic force or integrator being
-assigned the same random seed as the original instance that was serialized. If
-you use a ``System`` XML file generated by a version of OpenMM older than 6.3
-to start a new simulation, you should manually set the random number seed of
-each stochastic force or integrator to 0 (or another unique value).
+:class:`System` XML file would result in each stochastic force or integrator
+being assigned the same random seed as the original instance that was
+serialized. If you use a :class:`System` XML file generated by a version of
+OpenMM older than 6.3 to start a new simulation, you should manually set the
+random number seed of each stochastic force or integrator to 0 (or another
+unique value).