. The Decorator's assistant. Counter-Gage (in carpentry), a methodused for measuring joints. For example, thebreadth of a mortise is transferred to theplace in the timber where the tenon is to be, inorder to make them fit each other.(To be continued.) No. 25.—Vol. I. 194 THE DECORATOR S ASSISTANT. {Concluded from page 190.) PROBLEM XVI. • To find the area of a ring included betweenthe two circumferences of two concentriccircles. 1. Multiply half the sum of the circum-ferences by half the difference of their dia-meters, and the product will be the area. Example 1.—What will be the area of theri
. The Decorator's assistant. Counter-Gage (in carpentry), a methodused for measuring joints. For example, thebreadth of a mortise is transferred to theplace in the timber where the tenon is to be, inorder to make them fit each other.(To be continued.) No. 25.—Vol. I. 194 THE DECORATOR S ASSISTANT. {Concluded from page 190.) PROBLEM XVI. • To find the area of a ring included betweenthe two circumferences of two concentriccircles. 1. Multiply half the sum of the circum-ferences by half the difference of their dia-meters, and the product will be the area. Example 1.—What will be the area of thering A F c H A, the diameter a c being 72 inches,and the diameter e g 40 inches 1. 72 6283182199113 = circumf. a b c d a. = circumf. e f g h e. 2) = half sum of two circumf. 7240 2) 32 16 = half difF. of the two diam. sq. in. = area. Example 2.—The diameter a c is 30 inches,and the breadth of the ring a e 2^ inches : de-termine its area. 3030 90O .7854900 = area of circle a b c d a. 305 25 25 125 50 625 = F G. .7854 392701570847124 = area of circle e f g h a, sq. in. = area of ring. Example 2 is done by the following rule :—Find the areas of tlie two circles separatelythen the difference of these areas gives thearea of the ring. PROBLEM XVII. To find the area of an ellipse. 1. Find the sum of the areas of the sectorsA F G B, F K E L, B I c M, and E G c D, fromwhich subtract the area of the lozenge a i h k,and the difference will be the required area.
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