88 Hcientific Proceedings, Royal Dublin Society. 



should be worked out in detail iti tlie formula-paper. To obviate the necessity 

 of so doing the machine is provided with a special permanent dividing 

 cj/Under, on which this formula is repi-esented in the proper notation of per- 

 forations. When the arrangement of perforations on the formula-paper 

 indicates that division is to be performed, and the Variables which are to 

 constitute divisor and dividend, the formula-paper then allows the dividing 

 cylinder to usurp its functions until that cylinder has caused the macliine to 

 complete the division. 



It will be observed that, in order to carry out the process of division, the 

 machine is provided with a small table of numbers (the numbers A) whicli 

 it is able to consult and apply in the proper way. I have extended tin-'' 

 system to the logarithmic series, in order to give to that series a considerable, 

 convergency ; and I have also introduced a logarithmic cylinder whicli has the 

 power of working out the logarithmic formula, j'ust as the dividing cylinder 

 directs the dividing process. This system of auxiliary cylinders and tables 

 for special formulae may be indefinitely extended. 



The machine prints all results, and, if required, the data, and any note- 

 worthy values which may transpire during the calculation. It may be 

 mentioned, too, that the machine may be caused to calculate and print, quite 

 automatically, a table of values — such, for instance, as a table of logs, sines, 

 squares, &c. It has also the power of recording its results by a system of per- 

 forations on a sheet of paper, so that when such a numJjer-jjaper (as it may 

 be called) is replaced in the machine, the latter can " read " the numbers 

 indicated thereon, and inscribe them in the shuttles reserved for the purpose. 



Among other powers with which the machine is endowed is tliat of 

 changing from one formula to another as desired, or in accordance with a 

 given mathematical law. It follows that the machine need never be idle ; 

 for it can be set to tabulate successive values of any function, while the work 

 of the tabulation can be suspended at any time to allow of the determination 

 by it of one or more results of greater importance or urgency. It can also 

 " feel " for particular events in the progress of its work — such, for instance, as 

 a change of sign in the value of a function, or its approach to zero or infinity ; 

 and it can make any pre-arranged change in its procedure, when any such 

 event occurs. Babbage dwells on these and similar points, and explains their 

 bearing on the automatic solution (by approximation) of an equation of the 

 ifi^ degree ;' but I have not been able to ascertain whether his way of 

 attaining these results has or iias not any resemblance to my method of so 

 doing. 



1 C. Babbage : " Passages from the Life of a Philosopher," p. 131. 



