This free pattern originally published in the Woolco Knitting & Crocheting Manual, in 1916.

MATERIAL-6 skeins white and 1 skein color Woolco Shetland Floss. No. 4 Woolco hook.
With white, chain 56.
1ST ROW-Skip 2 chain, make 1 double crochet in each chain stitch. Turn, chain 2 at end of every row.
2D ROW-6 double crochet, taking both loops, *6 double crochet around the stitches; that is, putting the hook between the stitches and out through the next space. Then draw through. 6 double crochet, taking both loops. * Repeat between *'s 3 times.
Repeat 2d row 10 times.
12TH AND 13TH ROWS-With color, using cross stitch, make 1 double crochet in 2d stitch, 1 double crochet in 1st stitch, 1 in 3d stitch, and 1 in 2d stitch. Repeat to end of row.
14TH ROW-White. Double crochet.
Repeat 12th, 13th and 14th rows twice.
Then work 2d row 86 times. Reverse directions for border.
Cut 4 strands of each color 12 inches long, knot in every other stitch.
Other great scarf patterns from Woolco Knitting & Crocheting Manual.
Scarf
Sport Scarf I
Sport Scarf II
Sport Scarf III
Nubia