26 



THE PHILOSOPHY OF BIOLOGY 



parabola having the equation y=h x. Now a parabola 

 is defined as " the locus of a point which moves, so that 

 its distance from a fixed point is in a constant relation 

 to its distance from a fixed straight line." How do 

 we construct such a curve ? 

 y 



y/t2 



yo5 



We proceed to fix the positions of a series of points 

 in this way : there are two straight lines, OX and OY, 

 at right angles to each other, and we measure off certain 

 steps along the line OX ; these steps are OXq.^, OXi, 

 0X15, 0X2, and so on, the small numerals indicating 

 the distance of each point (OXo-s, etc.) from the origin 

 0. We then draw lines perpendicular to the X-axis 

 through these points. We have now to calculate one- 

 half of the square of each of these lengths OX 05, OX^ 

 etc., and then we mark off these calculated lengths 

 along the perpendicular lines. The point A, for 

 instance, is ^(0.5)2 from the point Xo-^, B is \(iY from 

 Xi, and so on. In this way we obtain a series of points, 

 A,B,C, D, E, etc., and these are points on the locus of 

 the " moving " point. 



