A Rational and Humane Science 



amazing accuracy. Yet every tyro in Mathe- 

 matics knows that the equations which give these 

 results can only be solved by what is called 

 " neglecting small quantities " — that is, the prob- 

 lems cannot be solved in their entirety, but by 

 leaving out certain terms and elements, which do 

 not appear important, a solution can be approached. 

 And naturally it has been an important point to 

 show that these small quantities may be safely 

 neglected. In the case, for instance, of the orbits 

 of the planets round the sun, and of the moon 

 round the earth, it was for a long time taken as 

 proved that the small variations in the shape and 

 position of each elliptic orbit would never be 

 accompanied by any permanent increase or dimi- 

 nution in its size — that is, that the mean distances 

 of the planets from the sun, and of the moon from 

 the earth, would always remain within certain 

 limits. Of late years however Professor George 

 Darwin, taking up one of these poor little neglected 

 quantities in the theory of the moon, found that 

 it indicated after all very vast and very permanent, 

 though of course very slow, changes in her mean 

 distance from the earth ; so that now it appears 

 probable that the Moon's true orbit, instead of being 

 a limited ellipse, is a continually though gradually 

 enlarging Spiral, which may some day carry the 

 Moon to a great distance from the earth. If an 

 eclipse were calculated for twenty years in advance 

 on the Elliptic theory or the Spiral theory, it would 

 probably — so slow would be the divergence — make 

 no perceptible difference ; but in a hundred 



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