ON BABBAGE’S ANALYTITICAL ENGINE. 731 
means of a subtraction; and so on; but we shall not enumerate fur- 
ther. It is desirable in all calculations, so to arrange the processes, 
that the offices performed by the Variables may be as uniform and fixed 
as possible. 
__ Supposing that it was desired not only to tabulate B,, B,, &e., but 
_ Ao, A,, &e.; we have only then to appoint another series of Variables, 
Vai» Via, &e., for receiving these latter results as they are successively 
produced upon Vj. Or again, we may, instead of this, or in addition 
to this second series of results, wish to tabulate the value of each 
successive éotal term of the series (8), viz: Ay, A, B,, A; B,, &c. We 
_ have then merely to multiply each B with each corresponding A, as 
produced ; and to place these successive products on Result-columns 
appointed for the purpose. 
The formula (8.) is interesting in another point of view. It is one 
_ particular case of the general Integral of the following Equation of 
_ Mixed Differences :— 
— nia) = (2n+1)(2Qn+ 2) 2" 2 
LR FEARED. 
a 
for certain special suppositions respecting z, # and x. 
The general integral itself is of the form, 
" Zn =f (n).c+f,(n) +f (2).a-1 + fo(m).a73 +... 
_ and it is worthy of remark, that the engine might (in a manner more 
_ or less similar to the preceding) calculate the value of this formula 
upon most other hypotheses for the functions in the integral, with as 
_ much, or (in many cases) with more, ease than it can formula (8.). 
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