171 



And if we take the differences of those products, they will have 

 as many orders of d ifferences as </ + 2r + 3s + &c. and the last of 

 those will be constant and = ]x2x3x4x Scc...{q+2r+3s-i-kc.) 



l%L2>''x l.^.'^xSiC. 



For, the several powers of contents being multiplied by 

 each other, in the horizontal lines in which they correspond 

 together, viz. 



-1.2.3.. .§• y'-Jlfi.'2.3...h n s r 1-2.3. ../c x &c. 



il \2.3.4...(g+l)f Jl I N2.3.4...(A+l)f £^| A2.3..(A;+1) x&c. 

 <H3A.5...{g+2)C i':|*i3.4.5...(/i + 2)( I n3.4.. (A-+2)x&c. 



the results of the multiplication will be as follows, 



1.2. . . .ffX 1.2 . ..e"x&C. till repeated 5 times, 1.2...A X &:C.til' ''epeated i times, 



|2.3...(g-+l)x2.3...('§-+l)x&c 2.3...(A+l)x,?cc 



)3.4...(§-l-2)x3.4...fg + 2) x&c 3.4...('/i + 2) x &c • 



-&c. x&c. x&c &c. x&c 



X 1.2.3 ... .k X 1.2.3 .;. , k X &C. THI repeated j times, X &€.! 



x2.3.4...fA:+l)x2.3.4...f/c+l)x&c. x&c.(^ 



X 3.4.5... CA; + 2) x 3.4.5...('/c+2)x &c. x Scc.C 



x&c. x&c. x&c. X&C.3 



In which the Involution producing a repetition of contents,, 

 each of which has several factors, the series resulting from the 

 multiplication of the powers of the corresponding contents 



VOL. XI. 2 a will 



