NZ5919011019 Go through the gate on the southern side of the road and follow the wide gravel track of the Cleveland Way steadily uphill into coniferous woodland. Captain Cook's Monument soon comes into view, and the path leads right up to this grand structure. This spot provides a panorama of the Cleveland Hills. Now take a sharp right, downhill to the north-east, aiming for twin stone gateposts in the tumbledown drystone wall. About 100m after these gateposts, the path forks. At this point, take the left fork, diagonally downhill.

NZ5877510305 This path is initially through bracken, but before long leads into Ayton Banks Wood. Stay on the main path, ignoring minor trails, and soon descend steeply through the conifer plantation. Shortly after leaving the wood, pass through a gorse hedge and follow the bridleway right, downhill. Go straight ahead at the crossroads on Dike Lane, onto Aireyholme Lane, and follow this minor road uphill. At the edge of the wood, shortly before the road reaches Aireyholme Farm, turn left on the public footpath, which has a newly-built ramp leading up the grass verge to a wooden gate.

NZ5783611487 Now follow the waymarked footpath around the edge of the wood. Amongst larch trees, an interpretation board tells the story of a recently discovered photograph, which suggests that a cottage at this site might have been the family home of a young James Cook, when his father was manager at Aireyholme Farm. At this board, the path bends right, then at the end of the group of larches the footpath continues ahead through a gate, but the way on is left, uphill on the permissive footpath. The path that skirts around the top of Cliff Rigg Quarry is enclosed by a fence on either side, and if you look to your left you'll see what happened to the old path, mostly slumped into the quarry below.

NZ5733311778 Beside more larch trees, the path starts to go downhill. After passing an in situ photo frame, go down some steps into the dip straight ahead and follow this small but clear path into the deciduous wood. In spring, there is a violet carpet of bluebells here, and in summer look for purple hairstreak butterflies in the oak canopy. At a crossroads, turn right through a wooden gate and on to the open fell. A shooting box to the right of the broad grassy path may be a useful shelter if needed, but otherwise follow the obvious path up to the top of the distinctive summit of Roseberry Topping.

NZ5790112577 Roseberry Topping is not a big hill - the summit is a mere 320 metres above sea level - but nonetheless you can expect extensive views from here. The Cleveland Way is now followed all the way back to Cribdale Gate. First walk east on the sandstone paving stones to Newton Moor. Through a gate, the path splits into three. Take the right fork and follow the obvious, easy track along the edge of Great Ayton Moor.