Came across some very interesting imformation regarding these strange metal rings we all find, they could have been used for the making of The Dorset Button 1680s known as High tops and Nobs. Orginally the button was made on a Bone ring.
Its most likely that the rings with Chamfered sides like the examples shown are the type used for these embroidered buttons. The group of copper-alloy rings shown here show the different thickness's and sizes which Detectorist's come across and are used in these buttons. allot of these copper-alloy rings have been manufactured for many other purposes.
http://forum.treasurenet.com/index.php/topic,272310.0.html
Not only were thread buttons less expensive than bone, wood or metal but they would not break during the strenuous beating and scrubbing. Unlike buttons made of other materials, thread buttons are soft and comfortable to lay against while sleeping.
During the early-to-mid-eighteenth century some such officers and official's are described as having worn buttons of embroidered gold or gilded metallic cord or thread. These buttons would have been either made with cut bone centres or with supporting circular metallic loops like those shown here right of picture. The loops formed circular frames around and over which could be sewn/ threaded or embroidered the knotted pattern of the buttons, the completed buttons would then be sewn to the uniform.
This type of embroidered button is known as the Dorset Button. The Dorset button began in Shaftesbury, Dorset probably between the years 1680 - 1700, The first buttons were known as "High Tops" and "knobs" and were made from a disc cut from Dorset Horn sheep.
The disc was covered by a small piece of material and worked with a needle and thread to make a conical shape or knob shape depending on the type of button required. The high-tops were worn by gentlemen on their hunting waistcoats and also used for ladies dresses, other types of buttons were then developed using copper wire twisted on a spindle with the ends cut and dipped in solder, children of both sexes were employed as "Winders & and Dippers" others threaded the rings and were called Stringers.
An alloy for the rings was invented and old buttons made, these rings show no signs of rust. There were three grades of ring the lower two grades were sold in this country. In 1850 a button making machine shown in the greta exhibition of London brought a tragic end to the industry. Another name used for these rings are fabric covered or thread cartwheel buttons.
SS