250 THE PRINCIPLES OF SCIENCE. [CHAP. 



satellites, and it is only slightly weakened by the fact that 

 some of the outlying satellites are exceptional in direction, 

 there being considerable evidence of an accidental dis- 

 turbance in the more distant parts of the system. 



Hardly less remarkable than the uniform direction of 

 motion is the near approximation of the orbits of the 

 planets to a common plane. Daniel Bernoulli roughly 

 estimated the probability of such an agreement arising 

 from accident as I -j- (i2) 6 the greatest inclination of any 

 orbit to the sun's equator being i-i2th part of a quadrant. 

 Laplace devoted to this subject some of his most ingenious 

 investigations. He found the probability that the sum of 

 the inclinations of the planetary orbits would not exceed 

 by accident the actual amount (-914187 of a right angle' 

 for the ten planets known in 1801) to be [jy (x^^iS/), 10 

 or about '00000011235. This probability may be com- 

 bined with that derived from the direction of motion, and 

 it then becomes immensely probable that the constitution 

 of the planetary system arose out of uniform conditions, 

 or, as we say, from some common cause. 1 



If the same kind of calculation be applied to the orbits 

 of comets, the result is very different. 2 Of the orbits 

 which have been determined 48-9 per cent, only are direct 

 or in the same direction as the planetary motions. 3 Hence 

 it becomes apparent that comets do not properly belong 

 to the solar system, and it is probable that they are stray 

 portions of nebulous matter which have accidentally become 

 attached to the system by the attractive powers of the 

 sun or Jupiter. 



Tlie General Inverse Problem. 



In the instances described in the preceding sections, 

 we have been occupied in receding from the occurrence 

 of certain similar events to the probability that there 



1 Lubbock, Essay on Probability, p. 14. De Morgan, Encyc. 

 Netrop. art. Probability, p. 412. Todhunter's History of the Theory 

 of Probability, p. 543. Concerning the objections raised to these 

 conclusions by Boole, see the Philosophical Magazine, 4th Series, 

 vol. ii. p. 98. Boole's Laws of Thought, pp. 364-375. 



- Laplace, Essai Philosophique, pp. 55, 56. 



3 Chambers' Astronomy, 2nd ed. pp. 346-49. 



