FAMILY CHARACTERISTICS. 117 



formula, the most similar forms may belong to 

 entirely different systems, when their derivation 

 is properly traced. 



Our great mathematician, in a lecture delivered 

 at the Lowell Institute last winter, showed that 

 in his science, also, similarity of outline does not 

 always indicate identity of character. Compare 

 the different circles, the perfect circle, in which 

 every point of the periphery is at the same dis- 

 tance from the centre, with an ellipse in which the 

 variation from the true circle is so slight as to be 

 almost imperceptible to the eye ; yet the latter, like 

 all ellipses, has its two foci by which it differs from 

 a circle, and to refer it to the family of circles 

 instead of the family of ellipses would be overlook- 

 ing its true character on account of its external 

 appearance ; and yet ellipses may be so elongated, 

 that, far from resembling a circle, they make the 

 impression of parallel lines linked at their ex- 

 tremities. Or we may have an elastic curve in 

 which the appearence of a circle is produced by 

 the meeting of the two ends ; nevertheless it 

 belongs to the family of elastic curves, in which 

 may even be included a line actually straight, and 

 is formed by a process entirely different from that 

 which produces the circle or the ellipse. 



But it is sometimes exceedingly difficult to 

 find the relation between structure and form in 

 Families. I remember a case which I had taken 



