It is evident that, in such case, the string, while vibrating as a whole between its fixed extremities, is at the same time executing subsidiary oscillations about its middle point, its points B FIG.
"Great" circles may also be defined as circles on a sphere which pass through the extremities of a diameter; they are familiar as the meridians or lines of longitude of geographers; lines of latitude are "small circles."
, but also a sufficient number of the ordinates obtained by continuing the series outside the trapezette, at both extremities, we can use central-difference formulae, which are by far the most convenient.
The most simple case is that in which the trapezette tapers out in such a way that the curve forming its top has very close contact, at its extremities, with the base; in other words, the differential coefficients u', u", u"',.
When a stranger claimed his hospitality, Procrustes compelled him, if he was tall, to lie down on the short bed, and then cut off his extremities to make him fit.