See Agapanthus praecox Willd. for a discussion of the species.   Macarthur’s ‘f. var.’ is probably a foliage variant of the species. Such a plant was described by Allen as less vigorous than the species, its leaves being less broad and long than the type and almost pure white with a few green bands and delicate blue flowers. [Allen, RHSD, Hortus]. Macarthur’s plant is possibly the variety listed by Steudel in 1840 as Agapanthus variegatus Hort., considered by him to be a form of A. umbellatus [Nomencl. Bot. – Steudel vol.1, p.33/1840]. Although Macarthur was obviously familiar with a foliar variety the only reference I have found to such a plant in the contemporary literature is the brief mention by Steudel. Today there are many variegated garden forms.