APPENDIX B. 



OP INTERPOLATION AND EXTERMINATION. 



387. Theorem. The fluxions of any 

 quantity u may be found from its finite diffe- 

 rences, taken at equal intervals with respect 

 to another flowing quantity x^ by the theorem 



^ h=Au~-iA^U +lA^U—i^''U -\-i-A^U—Wu +... 



dV 



dV 

 dx5 



-4 /i^= A^w — f A7f/ 4- . . . 

 dx^ ^ 



g^A^=:A7W-iABl/+... ^ 



We obtain, for the value of u„, first u+nAu-^n . — ^— 



lit 



A^u + . . . (245), and secondly, putting the finite difference 

 orxzznh, u-{-Au=:nh — "^i2"'d^"^***^ ^* The first 





