426 Mr DE morgan, ON A QUESTION 



the Encyclopaedia Metropolitana. By means of this table, and its dif- 

 ferences, and the formulae 



Aar ^ = Ay - i A'jr + 1 £i.hj - 



nearly. 



(A.rf g = A=y - A^y + 



we can also determine with sufBcient accuracy 



9 1 



Thus, u. Am, &c. being taken positively as in the table (remembering 

 that A'w is really negative, and that A a; = 01), we have 



-^ / 6-' dt = u, 



^^ = 100 (A?/ + i A^M + \ A^u) 

 Vtt 



*^JL = 10000 (A-M + A'm) 



In the case before us we have, writing or for X, 



w = ir° (1 - xY, nr = — ^^ — . 



Differentiate log y four times in succession ; 



y' = /- _ M' \ 



y U (1 - ^)J ' • 



yl - (ylx = _ ll + ^ \ 



y \yl W^(l-x)=J' 



y y y^^\y) ' ^V (i-^)')' 



y y y \yl y \yi \yl \^' {^-x)\ 



