Joined: Jan 2010
Posts: 9,831
Likes: 1,809
From: Northern California
Bikes: Cheltenham-Pedersen racer, Boulder F/S Paris-Roubaix, Varsity racer, '52 Christophe, '62 Continental, '92 Merckx, '75 Limongi, '76 Presto, '72 Gitane SC, '71 Schwinn SS, etc.
Should be 5/32" as oddjob2 alluded.
Take care not to damage the original cages when replacing the balls, or dispense with the cages and just fill the races with loose balls, full-complement, using extra-heavy grease to retain the balls and to prevent the grease from falling out while riding.
Be sure that the headset isn't the slightest bit too tight, which puts heavy pinching loads into the bearings (which can dent the races) when the steer tube inevitably flexes over bumps in the road.
Bearing cages for 1" headsets are made in slightly different sizes for different headsets, so you definitely don't want to have to go searching for the right ones.