ASTRONOMY. 



at the times 0, m 9 %m, 3m, 4<m 9 &c. and let 



the differences of a, a, a, &c. be taken in 

 their order, and the difference of these dif- 



ferences, as on the mar- a, a, a', a", a"', 



gin, so that |3 is the first of (3, |3', /3", /T', 



the first differences, y of y, y', y", 



the second, d of the third, 5, ^, 



and s of the fourth, &c. z 



m 



&c. 

 where the law of continuation is evident. 



This is Sir ISAAC NEWTON'S theorem, expressed al- 

 gebraically. Math. Princip. lib. in. lemma 5. 



a. If there are only two observations, so that the se- 

 ries of differences goes no farther than /3, then 



. 



y = , . = a - x ; and this is no 

 m m 



other than the common rule for finding a propor- 

 tional part. 



. If 



