Spoiler Alert: I think this is a W1SS which isn’t so rare as the seller seems to think. There has been a great discussion on the W1 here on Bike-urious.
1968 was the beginning of the end for the Kawasaki W series. Part of the Kawasaki takeover of Meguro motorcycles was a licensing agreement with BSA that resulted in the W1 Kawasaki complete with a four stroke motor in a distinctly British configuration. Relatively low power with a lot of buzz limited sales and the advent of the Triumph Triple, the Kawasaki H series triple two stroke, and, of course, the Honda CB 750 just killed the W series in North America.
The Kawasaki W1SS used a fairly tired design 624 CC (38.1 CID) used a four stroke air cooled overhead valve inline twin with an undamped 360 degree crank (both pistons moved up and down together) along with twin Mikuni carbs that produces 53 HP. Relatively light weight of 400 LBS and a 4 speed transmission made for a top speed of 115 MPH. The W series was basically plagued by outdated design but ran well and didn’t leak.
This particular 1968 Kawasaki W1 is almost undoubtedly a W1SS. It is located in Valencia, California (VIN # W1G03272) and is listed as a super rare 1968 original W1. My research shows that 1968 was clearly W1SS and would clear up the carb discrepancy. Buyer Beware! The bike is currently bid at $3,599.99
This photo clearly shows the badging on the bike as an SS model. It really pays to research any bike you are selling particularly an uber rare model.