FAMILY CHARACTERISTICS. T17 
formula, the most similar forms may belong to 
entirely different systems, when their derivation 
is properly traced. 1 
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 
