We study the available measurements of the solar constant made at ground sites and from recent space observations to determine whether sunspots or faculae produce a detectable modulation of either the solar flux or the earth's atmospheric transmission. The data from radiometers on Mariners 6 and 7 rule out any relative change of the solar constant in space due directly to faculae or spots exceeding 0.03%. This limit is two orders of magnitude smaller than previous values obtained from ground measurements. The measurements made at mountain stations of the Smithsonian Astrophysical Observatory between 1923 and 1952 show a marginally significant increase of solar constant at the level of 0.1%, related specifically to high projected facular area. Since this increase is not seen in the space measurements, we suggest that it may reflect a change in the earth's atmospheric transmission, possibly due to a change in ozone concentration induced by variation of facular ultraviolet radiation.