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 iv 
Families. I remember a case which I had takeu 
