This is an example of the calculating planisphere introduced in the early 1830s by James McFarlane, a mathematics teacher in Glasgow. It consists of three metal plates that revolving around a central axis, and on which are printed various numerical tables. One advertisement boasted that this planisphere “facilitates and is a ready and efficient check on all other methods of calculation” and was “strongly recommended to Merchants, Engineers, Mechanics and School Masters.”
Ref: “Calculating Planisphere,” <i>The Year-Book of Facts in Science and Art</i> (London, 1842): 18.
James McFarlane, <i>Rules, Directions, and Examples, Illustrating the Use of McFarlane’s Calculating Cylinder</i> (Edinburgh, 1837); this is third ed; the first ed was dated 1833.