EFFECTS OF INSENSIBLE MODIFICATIONS. 3.G9 



Arguing the matter some time since with a learned pro- 

 lessor, I illustrated my position thus: You admit that 

 there is no apparent relationship between a circle and an 

 hyperbola. The one is a finite curve ; the other is an in 

 finite one. All parts of the one are alike ; of the other no 

 two parts are alike. The one incloses a space ; the other 

 will not inclose a space though produced for ever. Yet 

 opposite as are these curves in all their properties, they 

 may be connected together by a series of intermediate 

 curves, no one of which differs from the adjacent ones in 

 any appreciable degree. Thus, if a cone be cut by a plane 

 at right angles to its axis we get a circle. If, instead of 

 being perfectly at right angles, the plane subtends with the 

 axis an angle of 89 59 , we have an ellipse, which no hu 

 man eye, even when aided by an accurate pair of compasses, 

 can distinguish from a circle. Decreasing the angle min 

 ute by minute, the ellipse becomes first perceptibly eccen 

 tric, then manifestly so, and by and by acquires so im 

 mensely elongated a form, as to bear no recognisable re 

 semblance to a circle. By continuing this process, the 

 ellipse passes insensibly into a parabola ; and ultimately, by 

 still further diminishing the angle, into an hyperbola. Now 

 here we have four different species of curve circle, ellipse, 

 parabola, and hyperbola each having its peculiar proper 

 ties and its separate equation, and the first and last of which 

 are quite opposite in nature, connected together as mem 

 bers of one series, all producible by a single process of in 

 sensible modification. 



But the blindness of those who think it absurd to sup 

 pose that complex organic forms may have arisen by suc 

 cessive modifications out of simple ones, becomes astonish 

 ing when we remember that complex organic forms are 

 daily being thus produced. A tree differs from a seed 

 immeasurably in every respect in bulk, in structure, in 

 colour, in form, in specific gravity, in chemical composition : 



