Thank you everyone for responding, I have found out from Katie
White Sewing Machine Company did not begin to use model numbers
until 1929 which was not unusual among sewing machine manufacturers.
That being said, we hobbyists have set up a system to refer to this
differing VS types ourselves and I modified that system last year. Your
machine -- 1,355,640 -- is a model VI under this system and was made
in 1902.
Model VI was introduced in mid-1900 so yours is an earlier VI. You have
one of the beautiful Theodor Kundtz cabinets [ATTACH=CONFIG]596166[/ATTACH]