OF ARTS AND SCIENCES. 439 



ing is much greater than this, it indicates that the components of each 

 group were together in consequence of some common cause determining 

 them to nearly the same position. Vice versa, if the stars are equally 

 spaced over the heavens, it would indicate that some constant cause had 

 operated, tending to prevent them from occupying positions near each 

 other. Law and chance are not necessarily the antithesis of each other 

 in the mathematical expression of their effects. Law is indicated by a 

 deviation from what ought to he the results of chance, in whatever di- 

 rection this deviation may be. 



Let us in this connection return to the second objection of Professor 

 Forbes, to see in what sense a uniform distribution is the most probable 

 result of chance. It is so only when, supposing the heavens to be di- 

 vided into a given number of equal spaces, we are required to specify 

 exactly how many stars each sjjecial division contains. Suppose the 

 heavens to be divided into 100 portions, and 200 stars to be distributed 

 at random ; then, if a person is required to guess how many stars the 

 first space contains, how many the second contains, and so on to the 

 hundredth, he ought to guess two for each space. Yet the chances are 

 millions to one against the correctness of such a guess ; but they would 

 be still greater were he to guess differently. But suppose he were 

 simply required to guess how many spaces contained no stars, how many 

 contained one, &c., without specifying the particular spaces which con- 

 tained the several numbers. Theory shows that, in the case supposed, 

 the probability that a space selected at random contains n stars is very 



nearly —r—^, e being the Neperian base. The individual ought, there- 

 n ! e' 



fore, to guess that 14 spaces were devoid of stars, 

 27 spaces contained 1 star each, 



27 " " 2 " 



18 " " 3 « 



9 « « 4 " 



4 " "5 " 



1 " "6 stars. 



This guess, however, would include a number of guesses of the first 

 class, equal to the number of possible permutations of 100 things, 14 

 of which were of one class, 27 of another, &c., to express which num- 

 ber would require ninety-seveii significant figures. Yet the guess would 

 in all probability be wrong in some respects, although there is no rea- 

 sonable probability that it would differ much from the truth. 



