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ELLIPTICAL DUNGEONS.

will render the words pronounced at F, distinctly audibleat the other focus f

A cruel use has been made of this echoing propertyof ellipses. Prisons have been constructed, in which theprisoners were chained near the focus F, and could not pro-nounce the least word without being heard at the otherfocus of an elliptical arch, separated from F by a par-tition, which hindered the prisoner from seeing the gaoler,who was appointed to listen in secret to every word heuttered.

The curves described by the course of the planetsround the sun are ellipses, having the centre of the sunin one of their foci. Thirty centuries, passed in study-ing astronomy and geometry, were necessary to discoverthis truth, now confirmed by experience ; which preparedthe way for the great and beautiful discoveries in modernastronomy.

If we make the ellipsis revolve round the large axisAF/B, which passes through both foci, we shall form asurface of revolution possessed of the following property ;every luminous ray, or every vibration of sound, FC,which emanates from the focus F, will be reflected inthe direction of a right line which passes through the se-cond focus f

In the same manner as all ellipses are constructed bythe circle, elongated or flattened proportionably at everypoint, so with the ellipsoid of revolution, constructed bymaking an ellipsis revolve on one of its axes, we mayform every ellipsoidal surface, whether elongated or flat-tened. It is sufficient to point this out, without enter-ing into farther details.

There is a mode of tracing an ellipsis by a continuedmotion, which is sometimes employed by artists. AOB,COD, fig. 16, being the two axes, if we draw a rightline, MN = OA, and take in it, produced, if necessary,N —- OC, the point M always remaining on the small,and the point N on the large axis, and making the right