AVI, 
On Certain Forms of Interpolation. : 
By W. P. G. BARTLETT, A. M. 
Communicated bj Proressor B. Perce, May 13, 1862. 
Tur quantity to be interpolated being a function of t, the following scheme shows 
the notation and arrangement seins aoe for a series of its values and their differences. 
Fear my 
EE 
e TO R e tuse 
(1) to : 4, 4; 4; 
Luss 4 a 
Se 8s 
in which ; E em | | 
: An = Ya — Y hn = ha = h, 
rever the subscript numbers are omitted in midig ie +11 is to be 
understood for all odd orders, and 0 for all even ones. 
It may be observed that, if we put 4_, in place of Y,, we shall have the following 
relations between ifs differences and the original ones of Y,: 
[ 4, (44) = h; 44) = 4^, dec. ; 
(3) 4 and similarly, if we put 4? in place of Y, 
AG) = dy c Té se Rer 
and so on with higher orders of differences, the law of this symbolic multiplication 
being to add the subscript numbers of the factors.to form, that of the product, as 
well as their (exponential) indices to form its index. 
