Reason and Invention. 851 



in a position to execute. There was certainly in this conclusion nothing 

 to excite surprise in any one having an inkling of the general facts of 

 the case. It seemed more wonderful that the mathematicians were able 

 to calculate the position of the stranger in the heavens with such ac- 

 curacy that it was actually found within one degree of the place indi- 

 cated. But here again the most obvious analogies were followed. Ac- 

 cording to Bode's law, the new planet should be almost twice as far from 

 the sun as the planet Uranus, and in making their calculations the astron- 

 omers assumed the correctness of the law. It was afterwards shown that 

 in this case Bode's law signal!}" fails, since Neptune is not so far from the 

 sun by 758 millions of miles as Bode's law would make it. It was, 

 therefore, after all, mere luck that this enormous error in their assump- 

 tions did not throw the calculators entirely off the track. They hap- 

 pened to take their observations at a time in the revolution of the planet 

 when the assumed distance gave it nearly the same direction from the ob- 

 servers as the correct distance would have given. 



If the discovery had remained to be made 40 or 50 years later, when 

 the planet was in a different part of its orbit, the assumption of the errone- 

 ous distance would have thrown them wide of the mark, because the 

 relative positions of the planet, then due to the assumed orbit and to the 

 real orbit, would have differed far more. So that the discovery after 

 all was, as remarked by some mathematicians, the result, to a large ex- 

 tent, of a happy accident. 



Invention involves prediction, and both rest upon memory. From the 

 memory of things experienced and seen, particularly those things which 

 have recurred often and regularly, we predict future recurrences. And 

 the more facts we have in memory relating to anything, the more con- 

 fident we become of the predictions we make concerning it. A savage 

 will predict a to-morrow and a next year, purely from the experience of 

 yesterdays and years gone by. He cannot give any other reason for it. 

 But a man of science makes a like prediction based on a more extended 

 knowledge of related facts. He knows better than the savage the past 

 repetitions of the days and years, for he has the testimony of recorded 

 history going back far beyond the traditions of savages, and he has, be- 

 sides this, the observations of himself and others of the phenomena of 

 the motions of the earth on its axis and in its orbit, and these, he per- 

 ceives, are indissolubly associated with the recurrence of da} r and season. 

 Discovering nothing likely to disturb or terminate these motions, he 

 may be more confident than the savage in predicting the indefinite re- 

 currence of the daily and annual periods. Knowing from past obser- 

 vation that certain phenomena are always seen together, we come to 

 regard them as related, and when one appears we are reminded of the 

 other, and look for its appearance also. 



