This section is from the book "Cassell's Cyclopaedia Of Mechanics", by Paul N. Hasluck. Also available from Amazon: Cassell's Cyclopaedia Of Mechanics.
For umbrella covers, first make the pattern by which to cut out the sections or gores. This may be of strong paper, but for permanent use sheet zinc is best. First cut a square of paper, each edge of which is exactly the same length as the frame on which the cover is to be placed - that is, a 2"i-in. frame would take a square of paper with edges 25 in. long. Cut this across from one corner to the opposite corner to produce a piece shaped like A B C in the illustration. Measure from A towards C the same distance as from A to B (in this case 25 in.), and then cut along the line 1) B. The part ABB now forms the complete pattern. By measuring down the centre as shown by dotted line, the width of cloth necessary to cut the cover will be discovered. For 25-in. covers cloth 22 in. wide is required. Always place the edges 15 D towards the selvedge edges of the cloth being cut, and allow a margin for hemming and sewing together. Sew the top of the cover witn strong thread alter machining.

Pattern for Umbrella Covers.
 
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