Johnston (1986) proposed that the global geometry of the striate cortical map in primates can be understood with reference to a conic surface in visual space oriented with its base in the plane of the eye and axis along the line of sight. Here, cortical magnification data from the macaque, squirrel and cebus monkeys and distance data from topographic maps of the macaque and owl monkey cortex are used as a further test of this proposal. Though there is a substantial difference in the emphasis placed on foveal vision in the owl monkey and the macaque topographic maps, both can be accommodated by the conic model with a change of parameter. The theory has also been extended in an attempt to model the differential changes in mean cortical receptive field size and inverse magnification with eccentricity found in the macaque. Though cortical receptive fields increase in size with eccentricity when measured on a spherical screen, mean receptive field size should be constant if measured on a tangent planes to a cone with an apical half angle of around 6.4 deg.