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A bishop moves "diagonally" -- that's good one-word description.
Is there a generally accepted one-word description of how a rook moves? "Horizontally", "vertically", and "perpendicularly" don't seem correct. "Straight" seems too vague.
P.S. I'm going with "orthogonal".
modified 14-Oct-15 23:10pm.
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I've seen horizontally, vertically mentioned in the same breath, as Ive seen 'forwards, backwards and to the sides', and then 'horizontally and vertically both forwards and backwards' - so if you want one word, horizontally and vertically arnt too bad
Perpendicularly .. hmmmm
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Garth J Lancaster wrote: horizontally and vertically
But I seek one word that covers both.
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Yes, a very good word for this situation. 
The pieces cross the divisions of the board at right angles to them.
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Over yonder!
New version: WinHeist Version When you have eliminated the JavaScript, whatever remains must be an empty page. Unknown
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That sounds more like a shuffle board term. You've been in Florida too long.
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PIEBALDconsult wrote: You've been in Florida too long.
30 years! I think I'm starting to rub off on them! 
New version: WinHeist Version When you have eliminated the JavaScript, whatever remains must be an empty page. Unknown
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Which way does your chad hang? 
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To the south of course!
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It hangs so far south it's started to go north.
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This [^] might give you a general idea. 
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A rook moves to an adjacent[^] location.
/ravi
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No, rooks aren't limited to adjacent squares. And I would include diagonally adjacent as adjacent. The King can move to any adjacent square.
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That just sounds like "side-to-side" to me.
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Right side, left side, front side, back side, side-to-side
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A "lateral" pass in (American) football goes across the width of the field; it doesn't move the ball down the length of the field (or not much anyway).
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As opposed to longitudinal?
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Lateral encapsulates longitudinal
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How about "Axially (in 2D)" or "Tranverso-Longitudinally"? 
You have just been Sharapova'd.
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That doesn't sound right either; that seems more like "corner-to-corner".
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PIEBALDconsult wrote: That doesn't sound right either; that seems more like "corner-to-corner".
No, "axially" means "along" an axis. So in 2D, it's either along X (left-right) or Y (forward-backward) - assuming the rook at (0,0). It doesn't have to be corner-to-corner.
The other term I mentioned is related to anatomy and is also correct, although it's not a proper word. (ref[^])
You have just been Sharapova'd.
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But if I had to draw axes on a chess board, I'd draw them diagonally. These are the only bisecting lines a chess piece may travel.
"Transverse" might suffice for my purpose, but I was hoping for a more widely used term.
I see "crossing from side to side; athwart; crossways" and "at right angles to the long axis" (a chess board has no long axis of course).
So I'll use "transversely" for now; no one will see it but me anyway.
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