Here's what she, Judy Martin, said
",,,Lengthwise strips are not only more stable and follow the print better, but they are also less stretchy. This is an especially important consideration for Log Cabin quilts because you want to cut the long sides of the rectangular logs following the more stable grain."
And from the other book: "...Your grandma would marvel at your fancy sewing machine and your rotary cutter and all the wonderful fabrics you have. And they she'd wonder what in tarnation you are doing cutting crosswise strips! If you are not already doing it, the time has come to rediscover the wisdom of your grandma and her peers. Gran would say, 'My lands, girl! Lengthwise strips would give you more stable grain....'" Later she says "Still not sure? Try these tests. Hold a piece of fabric with your hands 6" or 8" apart on the crossgrain. Bring your hands together, then quickly pull the fabric outward with a snap. Now repeat on the lengthwise grain. Even with the selvage removed, the lengthwise grain is significantly firmer, as you will note by the crisp snap on the lengthwise grain as opposed to the dull thud on the crosswise...."
And "Lengthwise strips have the long side of the strip parallel to the selvedge. Strips can be any length, but I generally use 18" strips, which can be cut from fat quarters or half yard lengths...."
I cut out many pieces for my barn quilt tonight--and tried cutting some lengthwise. It was convenient because they were small pieces.... I'll see if I notice any improvement.