Though, in these cases, the direction taken by any one whale be straight as a surveyor’s parallel, and though the line of advance be strictly confined to its own unavoidable, straight wake, yet the arbitrary VEIN in which at these times he is said to swim, generally embraces some few miles in width (more or less, as the vein is presumed to expand or contract); but never exceeds the visual sweep from the whale-ship’s mast-heads, when circumspectly gliding along this magic zone.
There are no more uses of "arbitrary" in the book.
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It was an arbitrary decision.
The speed limit seems to be arbitrary. I can’t imagine why it is so slow.