Laser heterodyne spectroscopic measurements of the optical isotope shifts between the naturally occurring even-even isotopes of samarium have been made in eleven lines of the Sm I spectrum. These have been used to study the J-dependent differences between the isotope shifts of the levels of the ground term which were recently discovered by Bauche and co-workers (1977). The present work confirms the experimental results of these authors and, by including more than one isotope pair, allows the field and mass shift contributions to the total J dependence to be separated from each other. It is found that the proportion of the observed J dependence due to the field shift is at least four times that due to the mass shift: these results are not quite in accord with the theoretical results of Bauche et al.