Capricorn's share is the knees positionally, and the bones, the joints and the skin by inheritance from Saturn, its ruling planet. Saturn's associations in this tradition are consistent and dark: the slowest of the seven planets, the outermost known, the greater malefic, and the significator of cold, dryness, age, restriction and everything hard and enduring. The bones are the body's hardest and most enduring tissue, and the skin its limit and boundary, so both fall to it.
The knee is a joint that carries weight and wears, which fits the same set of associations, and this is one of the assignments where the positional and planetary arguments reinforce each other rather than pulling apart.
The tradition's treatment of Saturn is a good corrective to the idea that these schemes are uniformly consoling. Saturn's parts were not lucky parts, Saturn's hours were not good hours to begin anything, and the Saturnine temperament, the melancholic, was a burden rather than a gift. Only later, and largely through the Renaissance reading of Aristotle's Problemata by Ficino and his circle, did melancholy acquire its association with genius.
The atlas records the doctrine as history. Nothing on this page concerns the actual condition of joints, bones or skin, and nothing in it is guidance.
Sources AstronomicaMarcus Manilius with Saturn and Melancholy: Studies in the History of Natural Philosophy, Religion and ArtRaymond Klibansky, Erwin Panofsky and Fritz Saxl