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APPLICATIONS.—LIGHT HOUSES.

extends rounds this focus, will come gradually to resemblea parabola, and at length will be of the same figure asthis curve.

The orbits described by comets seem to be parabolas,the sun being at the focus; they are ellipses very muchelongated.

In the elongation of the ellipsis, the vector radii drawnfrom the focus, removed to a distance, towards the otherfocus, approach more and more to parallel lines, as the fociare separated; and they become parallels, if we supposethe two foci at an infinite distance from each other. Theellipsis is then, rigorously speaking, a parabola, and theradii proceeding from the focus where the spectator issituated, are so reflected by this curve, as not to meetthe axis, except in infinite space, where the other focus issupposed to be. In the parabola, therefore, the raysemanating from the focus are reflected by the curve, pa-rallel to the axis.

The parabola is made use of accordingly, to receive thelight proceeding from one focus, and to reflect it in onebeam parallel to the axis, in place of allowing it to dis-perse itself towards all the points of space.

IJght-houses on this principle, are erected at variousplaces on the sea-coast, at the entrance of harbours, atthe mouths of rivers, over or near dangerous shoals, andin various other situations, in which it is necessary to pointout to the mariner a safe path, or warn him against dan-ger. Both fires and lamps are employed for this purpose.It is necessary they should be seen as far off as possible,they are placed, therefore, in the focus of a piece ofplated copper, having the form of a parabola, which re-volves on its axis, fig. 18, pi. 13. It is the paraboloid ofrevolution. All the rays reflected from the surface, calleda paraboloidal reflector, form a beam of parallel rays,having for their base, the parallel circle ABCD, whichforms also the base of the surface of the reflectorABCDN.

Sometimes the paraboloid is fixed, and in that case the