TESTS OF AN IMPERFECT CIRCLE. 227 
the adjoining groups (a fact which experience and 
critical examination alone will teach), then we have 
presumptive evidence for considering them as so 
many fragments or indications of a circle, the de- 
ficiencies of which we may form some idea of, by 
looking to the adjoining circles. To illustrate such 
a nice and somewhat abstruse subject more clearly, 
let us suppose there are two groups apparently fol- 
lowing each other ; one of which is perfect, and con- 
tains five principal variations of form; the other is 
imperfect, and contains but three, between which 
the intervals are of course much wider than between 
the other five. Now, if we are able to trace an 
analogous resemblance between three of one, and 
three of the other, we may fairly presume that the 
other two, which are deficient in the imperfect 
group, will, when discovered, exhibit a correspond- 
ing analogy. And we are thus not only justified in 
forming a theoretic notion on the nature of the 
forms of these missing types, but also in concluding 
those which we already have, to be parts of a dis- 
tinct circle of their own, although its circularity is 
incomplete. 
(158.) There is, indeed, one certain rule of de- 
ciding, in such cases, with almost mathematical 
precision, this is, by the law of representation ; but 
to enter upon this subject at present would violate 
the main object we have endeavoured to keep in 
view. We are proceeding on that gradual mode of 
induction, which all who wish to understand or to 
benefit science must inevitably follow. We throw 
aside all theories, and assume nothing as granted’ 
but the circular progress of affinities. What has 
Qa 2 
