96 BROOMALL : 



as vertical ordinates, the resulting curve will be a parabola. 



Another physical application of the parabola is found in 

 its use as a reflector to concentrate parallel rays of light 

 to a focus, or vice versa. It is a characteristic of the para- 

 bolic reflector that parallel rays of light striking its surface 

 in a direction parallel to its axis are concentrated at a single 

 point called the focus. Conversely, light from the focus is 

 reflected forth in a parallel beam. It is interesting to note 

 that a related phenomenon exists in the case of the ellipse. 

 Thus, if a light is placed at one focus of an elliptic mirror, 

 the rays after reflection will be concentrated again at the 

 other focus. In the case of the hyperbola, with the source of 

 light at one focus, the beam of light projected forth after 

 reflection will be divergent, but the directions of its rays pro- 

 duced backwards will meet at the focus of the conjugate 

 hyperbola. These facts, of course, are all due to the charac- 

 teristic of the conic sections that the lines from a given point 

 to the foci make equal angles with the tangents. 



Another form of the parabola, known as the rectangular 

 parabola, whose mathematical characteristic is that the pro- 

 duct of the ordinate and the abscissa at any point is constant, 

 is met with in the phenomena of capillarity. If two glass 

 plates, with two of the edges together and their planes making 

 a slight angle, are dipped in water with the joining edge ver- 

 tical, the water will rise up between the plates to a distance 

 dependent upon the width of the opening. In this case it 

 will be found that the surface of the water assumes the form 

 of a rectangular hyperbola, whose axes are respectively hori- 

 zontal and vertical. 



The Catenary. — This is another one of the curves which, 

 like the cycloid, is physical even in its mathematical deriva- 

 tion. It is that curve which is assumed by a perfectly flex- 

 ible body of equal weight per unit of length, as for instance 

 a heavy rope or chain, when suspended loosely between two 

 points. This curve, it may be noted, is not the curve assumed 

 by the cables of a suspension bridge, as in the latter case the 



