1 N V 



Here a = 150, d' = 97, d" = 36, d"> = 1, d"" 2 ; hence y 150 -f 



1 2 



97 X 2,25 + ~ X 2,25 X 1,25 -{- X 2,25 X 1,25 X ,25 -f * -f- 



2,25 X 1,25 X ,25 X ,75 = 418', 96 = 6. 53'. 57", the place required. 



But besides the use of the above equation, to find the value of any 

 term of a series from its position being- given, the converse is often re- 

 quired, i. e. having given any term, to find its position or distance from 

 the first term. 



Ex. On March, 1783, the sun's declination at noon at Greenwich was 



as follows : On the 19th, N. 28'. 41" =. 1721" ; on the 20th, N. 5' = 300" ; 



on the 21st, S. 18'. 41" = 1121" ; to find the tune of the equinox. 



1721, 300, 1121 



1421, 1421 







Here a - 1721, d' 1421, hence y 1721 1421 X x ; now when 

 the sun comes to the Equator, y the declination becomes o ; .'. 1721 



1721 

 1421 x = o, and x = j^ = Id. 5. 3m. 53*., the time from the 19th j 



hence 20d. bh. 3m. 53*. is the time required. 



We have here supposed that the quantities to be interpolated were 

 taken at equal intervals of time ; for a formula when the intervals are 

 unequal, see fence's Astronomy, vol. 2. 



INVOLUTION and Evolution. 



TABLE of the first nine powers of numbers. 



