This section is from the book "School Needlework. A Course of Study in Sewing designed for use in Schools", by Olive C. Hapgood. Also available from Amazon: School Needlework: A Course Of Study In Sewing Designed For Use In Schools.
1 . Begin as for hemming, but make the stitch vertical on the side towards you.
3. Take the next stitch by inserting the needle into the next gather (which should be directly under the place where the thread comes out of the band) and at the same time take up a thread of the band.
4. Take a stitch in each gather.
5. When this side is finished, fasten securely, and cut off the gathering thread.
6. Baste and sew the under part of the band in the same manner, taking care that the edge of the band corresponds exactly with the edge on the opposite side, in order that the band may not be twisted.
7.Do not let these stitches show on the right side.
The shape of the stitch is like the letter N, as in overhanding, but the slant here is underneath, while in overhanding it is on the top. A binding is more easily sewed on in this manner, if there is a double row of gathering. To strengthen a binding, where a button is to be placed, turn in one inch at the end of the band before folding it, and baste pieces of cloth on the under side where other buttons are to be placed; at the button-hole end, turn in half-an-inch. Cut a button-hole in a binding nearer the gathers than the folded edge, so that the garment will be held in place firmly.