THE LOGICAL MACHINE. 123 



whence it is apparent that A must be B, the true conclusion 

 of the argument. 



In my previous Essay 11 I have described the working of 

 two other logical problems upon the abacus, which it 

 would be tedious to repeat in this place. 



The Logical Machine. 



Although the Logical Abacus considerably 'reduced the 

 labour of using the Indirect Method, it was not free from 

 the possibility of error. I thought moreover that it would 

 afford a conspicuous proof of the generality and power of 

 the method if I could reduce it to a purely mechanical 

 form. Logicians had long been accustomed to speak of 

 Logic as an Organoii or Instrument, and even Bacon, while 

 he rejected the old syllogistic logic, had insisted, in the 

 second aphorism of his ' New Instrument/ that the mind 

 required some kind of systematic aid. In the kindred 

 science of mathematics mechanical assistance of one kind 

 or another had long been employed. Orreries, globes, 

 mechanical clocks, and such like instruments, are really 

 aids to calculation and are of considerable antiquity. The 

 arithmetical machine of Pascal is more than two centuries 

 old, having been constructed in 1642-45. M. Thomas of 

 Colmar has recently manufactured an arithmetical machine 

 on Pascal's principles which is extensively employed by 

 engineers and others who need frequently to multiply or 

 divide. To Babbage, however, was entirely due the 

 merit of embodying the Calculus of Differences in a 

 machine, which thus became capable of calculating the 

 most complicated tables of figures. It seemed strange 

 that in the more intricate science of quantity mechanism 

 could be applicable, whereas in the simple science of 



h ' Substitution of Similars,' pp. 56-59. 



