260 DETERMINATION OF AN ORBIT FROM [BOOK II. 



system of determinate values for r, s, etc. will be proportional to the integral 



extended from g=: oo up to ^ = -j- co , which is 



or proportional to the function e~ hhw &quot;. Precisely in the same way, if r also is 

 considered as indeterminate, the probability of the determinate values for the rest, 

 s, etc. will be proportional to the function e~ hhw &quot;, and so on. Let us suppose the 

 number of the unknown quantities to amount to four, for the same conclusion 



will hold good, whether it is greater or less. The most probable value of s will 



i if 

 be -- YT-,, and the probability that this will differ from the truth by the quantity 



0, will be proportional to the function e~ hH &quot; a&amp;lt;! whence we conclude that the 

 measure of the relative precision to be attributed to that determination is ex 

 pressed by \/d &quot;, provided the measure of precision to be assigned to the original 

 observations is put equal to unity. 



183. 



By the method of the preceding article the measure of precision is conven 

 iently expressed for that unknown quantity only, to which the last place has 

 been assigned in the work of elimination ; in order to avoid which disadvantage, 

 it will be desirable to express the coefficient 8 &quot; in another manner. From the 

 equations 



P=p 



it follows, that/, /, r , s , can be. thus expressed by means of P, Q, R, S, 



