THE INDUCTIVE OB INVERSE METHOD. 289 



is the near approximation of all the orbits of the planets 

 to a common plane. Daniel Bernouilli roughly estimated 

 the probability of such an agreement arising from accident 

 at r^c, the greatest inclination of any orbit to the sun s 



(12) J 



equator being i-i2th part of a quadrant. Laplace de 

 voted to this subject some of his most ingenious investi 

 gations. He found the .probability that the sum of the 

 inclinations of the planetary orbits would not exceed by 

 accident the actual amount (&quot;914187 of a right angle for 

 the ten planets known in 1801) to be j$ ( Qi/j-iS/) 10 , or 

 about 00000011235. This probability may be combined 

 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 11 . 



If the same kind of calculation be applied to the orbits 

 of comets the result is very different y. Of the orbits 

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

 or in the same direction as the planetary motions z . 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 become accidently 

 attached to the system by the attractive powers of the 

 sun or Jupiter. 



Statement of the General Inverse Problem. 



In the instances described in the preceding sections, 

 we have been occupied in receding from the occurrence 



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

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

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

 sions by the late Dr. Boole, see the Philosophical Magazine, 4th Series, 

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



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



z Chambers s Astronomy, 2nd ed. pp. 346-49. 



U 



