A roof covering apparatus for a structure having a plurality of upright supports (22, 24, 26, 28) and at least one pair of parallel cross beams (32, 36) secured to the upright supports(22, 24, 26, 28), the apparatus comprising: a plurality of elongated parallel slat assemblies, each slat assembly comprising: a pivotal shaft mounted for pivotal movement between said at least one pair of parallel cross beams (32, 36), wherein the pivotal shaft extends transversely to longitudinal axes of the at least one pair of parallel cross beams (32, 36), and a pair of elongated slat members (104, 106), the pair of elongated slat members (104, 106) being pivotally attached in common to the pivotal shaft along their upper edges, each of the slat members (104, 106) having a J-shaped profile with a curved bottom, wherein each of the pair of the slat members (104, 106) is a mirror image of another slat member, and is secured to the pivotal shaft along its upper longitudinal edge, wherein each of the slat members (104, 106) has an upwardly turned lower edge (105, 110), and wherein the upwardly turned lower edge of one of the pair of slat members faces in a direction opposite to the upwardly turned lower edge of another of the pair of slat members said slat assemblies being pivotally movable between an open position in which the slat members (104, 106) are in a substantially upright orientation and a closed position in which the slat members (104, 106) of each of the slat assemblies extend in a covering relationship over the structure; and a pair of sliding rails (120; 122) positioned below the slat assemblies and extending in a transverse relationship to longitudinal axes of the slat assemblies; wherein each of the sliding rails (120; 122) comprises: a first inclined rail member positioned adjacent the bottom of one slat member, a second inclined rail member positioned adjacent the bottom of an adjacent slat member, and a middle rail member positioned between the first inclined rail member and the second inclined rail member. a plurality of elongated parallel slat assemblies, each slat assembly comprising: a pivotal shaft mounted for pivotal movement between said at least one pair of parallel cross beams (32, 36), wherein the pivotal shaft extends transversely to longitudinal axes of the at least one pair of parallel cross beams (32, 36), and a pair of elongated slat members (104, 106), the pair of elongated slat members (104, 106) being pivotally attached in common to the pivotal shaft along their upper edges, each of the slat members (104, 106) having a J-shaped profile with a curved bottom, wherein each of the pair of the slat members (104, 106) is a mirror image of another slat member, and is secured to the pivotal shaft along its upper longitudinal edge, wherein each of the slat members (104, 106) has an upwardly turned lower edge (105, 110), and wherein the upwardly turned lower edge of one of the pair of slat members faces in a direction opposite to the upwardly turned lower edge of another of the pair of slat members said slat assemblies being pivotally movable between an open position in which the slat members (104, 106) are in a substantially upright orientation and a closed position in which the slat members (104, 106) of each of the slat assemblies extend in a covering relationship over the structure; and a pivotal shaft mounted for pivotal movement between said at least one pair of parallel cross beams (32, 36), wherein the pivotal shaft extends transversely to longitudinal axes of the at least one pair of parallel cross beams (32, 36), and a pair of elongated slat members (104, 106), the pair of elongated slat members (104, 106) being pivotally attached in common to the pivotal shaft along their upper edges, each of the slat members (104, 106) having a J-shaped profile with a curved bottom, wherein each of the pair of the slat members (104, 106) is a mirror image of another slat member, and is secured to the pivotal shaft along its upper longitudinal edge, wherein each of the slat members (104, 106) has an upwardly turned lower edge (105, 110), and wherein the upwardly turned lower edge of one of the pair of slat members faces in a direction opposite to the upwardly turned lower edge of another of the pair of slat members said slat assemblies being pivotally movable between an open position in which the slat members (104, 106) are in a substantially upright orientation and a closed position in which the slat members (104, 106) of each of the slat assemblies extend in a covering relationship over the structure; and a pair of sliding rails (120; 122) positioned below the slat assemblies and extending in a transverse relationship to longitudinal axes of the slat assemblies; wherein each of the sliding rails (120; 122) comprises: a first inclined rail member positioned adjacent the bottom of one slat member, a second inclined rail member positioned adjacent the bottom of an adjacent slat member, and a middle rail member positioned between the first inclined rail member and the second inclined rail member.