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 the arrow. If now I draw a line x y, and divide it into equal parts, representing equal periods of time, say tenths of a second, and if I drop a perpendicular line from the curve down to x y, say from o to o, I will see at once where my pen point was at that instant of time. Suppose, again, I extended my fingers and then relaxed them so as to draw a line on the paper at rest, I would again draw a line like a b; but if I repeated the experiment, with the paper moving quickly from right to left, I would describe a curve thus—

and if time were indicated in tenths of a second by a line x′ y′, the position of the pen point at any instant between x and y would be found by dropping perpendiculars, as from x″ to x″ or from x‴ to x‴. If my pen point travelled faster in going up than in coming down, supposing the paper moved with the