Sometimes called right hands, By the right is the most common way for two Scottish Country Dancers to Take hands when Crossing or Turning or Travelling together, side by side. When Travelling together, the joined right hands should be in front at chest height; for all other movements, the hands should be as described in Take hands with relative movement.
By the right is also-
A qualification of a Figure, such as Cross, to indicate that the dancer should pass to the right of (i.e., Give left shoulders to) the approaching dancer (or Couple).
For example, here are some Scottish Country Dances in which the term, By the right, is used in either the Minicrib or the Maxicrib Dance instructions or both -
Belle Of Bon Accord
Blue Mess Jacket
Cadgers In The Canongate