26 



THE PHILOSOPHY OF BIOLOGY 



parabola having the equation y=J 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 



yns 



y s 



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 OX . 5 , 0X lt 

 0X V5 , 0X 2 , and so on, the small numerals indicating 

 the distance of each point (OX . 5> 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 , 0X ly 

 etc., and then we mark off these calculated lengths 

 along the perpendicular lines. The point A, for 

 instance, is J(o.5) 2 from the point X . 5 , B is J(i) 2 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. 



