th function of (5.), would have to be determined from the combined consideration of these equations and of (5.) itself.
The algebraical nature of the engine (so strongly insisted on in a previous part of this Note) would enable it to follow out any of these various modes indifferently; just as we recently showed that it can distribute and separate the numerical results of any one prescribed series of processes, in a perfectly arbitrary manner. Were it otherwise, the engine could merely compute the arithmetical
th function, a result which, like any other purely arithmetical results, would be simply a collective number, bearing no traces of the data or the processes which had led to it.
Secondly, the law of development for the
th function being selected, the next step would obviously be to develope (5.) itself, according to this law. This result would be the first function, and would be obtained by a determinate series of processes. These in most cases would include amongst them one or more cycles of operations.
The third step (which would consist of the various processes necessary for effecting the actual substitution of the series constituting the first function, for the variable itself) might proceed in either of two ways. It might make the substitution either wherever
