Measurements have been made of adsorption isotherms of He-3 and of He-4 on copper and on a monolayer of argon deposited on copper in the temperature range 6.18-18.55 K and in the pressure range 0.25 to 75 Torr. From these many isotherms, calculations have been made of the isosteric heat of adsorption Q(st)/R. In the limit of zero coverage on the argon monolayer Q(st)/R = 76 +/- 2 K for He-3 and 76 +/- 2 K for He-4. For adsorption on the bare copper, Q(st)/R is difficult to extrapolate to zero coverage, but it probably lies (for both He-3 and He-4) between 135 and 165 K. At theoretical monolayer helium coverage, Q(st)/R = 44 +/- 2 K for He-3 on the argon monolayer and 47 +/- 2 K for He-4. At theoretical monolayer helium coverage on the bare copper, Q(st)/R = 61 +/- 4 K for He-3 and 77 +/- 5 K for He-4. The results are compared with theoretical evaluations for helium adsorbed on an argon monolayer and with dome previous experimental data, and the agreement is found to be fair. All the data are summarized in tables. Finally, a review is given of evaluations, including those from this work, of the monolayer capacity of He-3 and He-4 on the substrates studied.