364 PROBLEMS ON CAUSES. [CHAP. XX. 



It has been observed that there exists in the heavens a large 

 number of double stars of extreme closeness. Either these ap- 

 parent instances of connexion have some physical ground or they 

 have not. If they have not, we may regard the phenomenon of a 

 double star as the accidental result of a " random distribution" of 

 stars over the celestial vault, i. e. of a distribution which would 

 render it just as probable that either member of the binary sys- 

 tem should appear in one spot as in another. If this hypothesis be 

 assumed, and if the number of stars of a requisite brightness be 

 known, we can determine what is the probability that two of 

 them should be found within such limits of mutual distance as 

 to constitute the observed phenomenon. Thus Mitchell,* esti- 

 mating that there are 230 stars in the heavens equal in brightness 

 to ]3 Capricorni, determines that it is 80 to 1 against such a 

 combination being presented were those stars distributed at ran- 

 dom. The probability, when such a combination has been ob- 

 served, that there exists between its members a physical ground 

 of connexion, is then required. 



Again, the sum of the inclinations of the orbits of the ten 

 known planets to the plane of the ecliptic in the year 1801 was 

 91 4 1ST, according to the French measures. Were all inclina- 

 tions equally probable, Laplacej determines, that there would be 

 only the excessively small probability .00000011235 that the 

 mean of the inclinations should fall within the limit thus as- 

 signed. And he hence concludes, that there is a very high 

 probability in favour of a disposing cause, by which the inclina- 

 tions of the planetary orbits have been confined within such narrow 

 bounds. Professor De Morgan, J taking the sum of the inclina- 

 tions at 92, gives to the above probability the value .00000012, 

 and infers that " it is 1 : .00000012, that there was a necessary 

 cause in the formation of the solar system for the inclinations 

 being what they are." An equally determinate conclusion has 

 been drawn from observed coincidences between the direction of 



* Phil. Transactions, An. 1767. 



t Theorie Analytique des Probabilites, p. 276. 



t Encyclopaedia Metropolitana. Art. Probabilities. 



