Unfortunately there are two different methods that are called scything - the one you describe, and this one:
http://straightrazorpalace.com/shavi...tml#post313829
http://straightrazorpalace.com/attac...le-slicing.jpg
The image on the left is what most of us (and the old barber texts) mean by scything. On the right you see the guillotine method.
And if you look closely you will see they are the same diagram! The two methods are one and the same. However, I believe it is safer to think of it as a guillotine action, you only need to think about movement in one dimension and you are less likely to mess up as a result of thinking about a sideways motion.