  In the seminal paper by Dahlen et al. the authors formulate an important
expression as a first-order estimate of traveltime delay. The authors left out
a term which would at first glance seem nontrivial, on the basis that their
intention was to derive the Fr\'echet derivative linking the observed delay to
the model perturbation (Nolet 2009, pers. comm.). Here we show that the
derivation by Dahlen et al. results in a first-order estimate even without
anticipating a Fr\'echet derivative, but instead remaining deductively in their
Taylor-series formulation. Although a mathematical technicality, this
strengthens the result of Dahlen et al. by showing that it is intrinsically
valid, requiring no external justification. We show also that ignoring the
aforementioned term is not valid in general and needs to be supported by
careful argument.
