74 THE PRINCIPLES OF SCIENCE. 



perfect correspondence must be purely accidental, and 

 should give rise to suspicion rather than to satisfaction. 



One remarkable result of the approximate character of 

 our observations is that we never could prove the existence 

 of perfectly circular or parabolic movement, even if it 

 existed. The circle is a singular case of the ellipse, for 

 which the eccentricity is zero ; it is infinitely improbable 

 than any planet, even if undisturbed by other bodies, 

 should have a circle for its orbit ; but if the orbit were 

 a circle we could never prove the entire absence of ec- 

 centricity. All that we could do would be to declare the 

 divergence from the circular form to be inappreciable. 

 Delambre was unable to detect the slightest ellipticity 

 in the orbit of Jupiter's first satellite, but he could only 

 infer that the orbit was nearly circular. The parabola is 

 the singular limit between the ellipse and the hyperbola. 

 As there are elliptic and hyperbolic comets, so we might 

 conceive the existence of a parabolic comet. Indeed if an 

 undisturbed comet fell towards the sun from an infinite 

 distance it would move in a parabola ; but we could never 

 prove that it so moved. 



Substitution of Simple Hypotheses. 



In truth men never can solve problems fulfilling the 

 complex circumstances of nature. All laws and explana- 

 tions are in a certain sense hypothetical, and apply exactly 

 to nothing which we can know to exist. In place of the 

 actual objects which we see and feel, the mathematician 

 invariably substitutes imaginary objects, only partially 

 resembling those represented, but so devised that the 

 discrepancies may not be of an amount to alter seriously 

 the character of the solution. When we probe the matter 

 to the bottom physical astronomy is as hypothetical as 

 Euclid's elements. There may exist in nature perfect 



