256 



DETERMINATION OF AN ORBIT FROM 



[BOOK II. 



the event E or some other event, should occur, a system of the different cases is 

 formed, each one of which cases is to be considered as equally probable in itself 

 (that is, as long as it is uncertain whether the event E, or some other, will occur), 

 and that these cases be so distributed, 



Then we shall have 



m 



j 



m -\- n 



moreover, before the event was known the probability of the hypothesis II was 



m -\- n 

 m _|_ n _|_, n _|_ w _|_ m &quot; _|_ n &quot;&amp;gt; 



but after the event is known, when the cases n, n, n&quot; disappear from the number 

 of the possible cases, the probability of the same hypothesis will be 



in the same way the probability of the hypothesis H before and after the event, 

 respectively, will be expressed by 



+ n and m 



i i &quot; / i r~\ Ti i fr cm*-! / i 7/ 



tn ( n } w* f- n j w j w wz j ni -j w 



since, therefore, the same probability is assumed for the hypotheses H and If 

 before the event is known, we shall have 



m -j- n = m -\- n f , 



whence the truth of the theorem is readily inferred. 



Now, so far as we suppose that no other data exist for the determination of 

 the unknown quantities besides the observations V=M, V = M , V&quot; = M&quot;, 



