EFFECTS OF INSENSIBLE MODIFICATIONS. 369 



Arguing the matter some time since with a learned pro- 

 fessor, I illustrated my position thus: — You admit that 

 there is no apparent relationship between a circle and an 

 hyperbola. The one is a finite curv^e ; 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 difiers 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 : 



