  The primary emphasis of this work on kinetics is to illustrate the a
posteriori approach to applications, where focus on data leads to novel
outcomes, rather than the a priori tendencies of applied analysis which imposes
constructs on the nature of the observable. The secondary intention is the
development of appropriate methods consonant with experimental definitions. By
focusing on gradients, it is possible to determine both the average and
instantaneous rate constants that can monitor changes in the rate constant with
concentration changes as suggested by this theory. Here, methods are developed
and discussed utilizing nonlinear analysis which does not require exact
knowledge of initial concentrations. These methods are compared with those
derived from standard methodology. These gradient methods are shown to be
consistent with the ones from standard methods and could readily serve as
alternatives for studies where there are limits or unknowns in the initial
conditions, such as in the burgeoning fields of astrophysics and
astrochemistry, forensics, archeology and biology . All four reactions studied
exhibited semi sinusoidal-like change with reactant concentration change which
standard methods cannot detect, which seems to constitute the observation of a
new effect that is not predicted by current formulations, where the possibility
that the observations are due to artifacts from instrumental errors or the
optimization method is reasoned as unlikely since the experiments were
conducted by different groups at very different times with different classes of
reactions.
