. Machinery and processes of the industrial arts, and apparatus of the exact sciences. carried along the lines of the figure to be measured. Theinstrument rests, therefore, on the roller D, and the revolution of thisroller is produced by friction upon the paper. The point E being fixed,and all other parts of the instrument free, the movement is necessarilycircular; and on this account the instrument is sometimes called thepolar planimeter. If we suppose the joint connecting the two rods atC to be inflexible, and the tracer F to be carried round E as a center, itwill be perceived that the movin
. Machinery and processes of the industrial arts, and apparatus of the exact sciences. carried along the lines of the figure to be measured. Theinstrument rests, therefore, on the roller D, and the revolution of thisroller is produced by friction upon the paper. The point E being fixed,and all other parts of the instrument free, the movement is necessarilycircular; and on this account the instrument is sometimes called thepolar planimeter. If we suppose the joint connecting the two rods atC to be inflexible, and the tracer F to be carried round E as a center, itwill be perceived that the moving point will describe a circular arc, ofwhich the line joining E F is the radius. This moving radius E F willsweep over a sector, of which the arc is the base, and the radii in theinitial and final positions the lateral boundaries. In the mean time theroller D will turn by friction on the paper, and the geometrical fact uponwhich the usefulness of the instrument depends, is that the extent ofthe arc developed by the roller is a simple function of the area of thesector swept over. c.
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Keywords: ., bookcentury1800, booksubjectmachinery, booksubjectscientificappa
