8 ON THE FO UNDA TIONS OF 



affinity which in a greater or less degree appears to exist among 



them. 



This is so natural a reflection, that Lacroix, in calculating 

 the mathematical value of the presumption, omits the rotatory 

 movements, and, I believe, those of the secondary planets, in 

 order, as he expressly says, to include none but similar move- 

 ments. But in the admission thus by implication made, that 

 regard must be had to the similarity of the movements, too 

 much is conceded for the interests of the theory. For are the 

 retained movements absolutely similar ? The planets move in 

 orbits of unequal eccentricity and in different planes : they are 

 themselves bodies of various sizes ; some have many satellites 

 and others none. If these points of difference were diminished 

 or removed, the presumption in favour of a common cause deter- 

 mining the direction of their movements would be strengthened; 

 its calculated value would not increase, and vice versa. 



Again, up to the close of 1811, it appears (Laplace) that 

 100 comets had been observed, 53 having a direct and 47 a 

 retrograde movement. If these comets were gradually to lose 

 the peculiarities which distinguish them from planets we should 

 have 64 planets with direct movement, 47 with retrograde. The 

 presumption we are considering would, in such a case, be very 

 much weakened. At present, we unhesitatingly exclude the 

 comets on account of their striking peculiarities: in the case 

 supposed we should with equal confidence include them in the 

 induction. But at what precise point of their transition-state 

 are we abruptly, from giving them no weight at all in the 

 induction, to give them as much as the old planets ? 



15. It is difficult to acquiesce in a theory which leads to 

 so many conclusions seemingly in opposition to the common 

 sense of mankind. 



One of the most singular of them may, perhaps, serve as a 

 key to explain their nature. When any event, whose cause is 

 unknown, occurs, the probability that its ci priori probability 

 was greater than % is f . Such at least is the received result. 

 But in reality, the <i priori probability of a given event has no 

 absolute determinate value independent of the point of view in 

 which it is considered. Every judgment of probability involves 

 an analysis of the event contemplated. We toss a die, and an 



