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 

 Q 2 



