The roles played by mesons in the electromagnetic form factors of the nucleon are explored using as a basis a model containing vector mesons with coupling to the continuum together with the asymptotic $Q^2$ behavior of perturbative QCD. Specifically, the vector dominance model (GKex) developed by Lomon is employed, as it is known to be very successful in representing the existing high-quality data published to date. An analysis is made of the experimental uncertainties present when the differences between the GKex model and the data are expanded in orthonormal basis functions. A main motivation for the present study is to provide insight into how the various ingredients in this model yield the measured behavior, including discussions of when dipole form factors are to be expected or not, of which mesons are the major contributors, for instance, at low-$Q^2$ or large distances, and of what effects are predicted from coupling to the continuum. Such insights are first discussed in momentum space, followed by an analysis of how different and potentially useful information emerges when both the experimental and theoretical electric form factors are Fourier transformed to coordinate space. While these Fourier transforms should not be interpreted as charge distributions, nevertheless the roles played by the various mesons, especially which are dominant at large or small distance scales, can be explored via such experiment--theory comparisons.
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