1890 BABBAGE'S CALCULATING MACHINE 277 



discussed the origin of the story, and criticised the attempt 

 of the essayist in Lux Mundi to treat this and similar stories 

 as " types," which must be valueless if typical of no under- 

 lying reality. These things are of moment in speculative 

 thought, for if Adam be not an historical character, if the 

 story of the Fall be but a type, the basis of Pauline the- 

 ology is shaken ; they are of moment practically, for it is 

 the story of the Creation which is referred to in the " speech 

 (Matt. xix. 5) unhappily famous for the legal oppression 

 to which it has been wrongfully forced to lend itself ' in 

 the marriage laws. 



In July 1890, Sir J. G. T. Sinclair wrote to him, call- 

 ing his attention to a statement of Babbage's that after a 

 certain point his famous calculating machine, contrary to 

 all expectation, suddenly introduced a new principle of 

 numeration into a series of numbers,* and asking what 



* Extract from Babbage's Ninth Bridgewater Treatise. 



Babbage shows that a calculating machine can be constructed 

 which, after working in a correct and orderly manner up to 100,000,- 

 ooo, then leaps, and instead of continuing the chain of numbers 

 unbroken, goes at once to 100,010,002. "The law which seemed at 

 first to govern the series failed at the hundred million and second 

 term. This term is larger than we expected by 10,000. The law thus 

 changes 



100,000,001 100,100,005 



100.010.002 100,150,006 



100.030.003 100,210,007 



100.060.004 100,280,008 



For a hundred or even a thousand terms they continued to follow the 

 new law relating to the triangular numbers, but after watching them 

 for 2761 terms we find that this law fails at the 27&2nd term. 



If we continue to observe we shall discover another law then com- 

 ing into action which also is different, dependent, but in a different 

 manner, on triangular numbers because a number of points agreeing 

 with their term may be placed in the form of a triangle, thus 



(one, three, six, ten). 



This will continue through about 1430 terms, when a new law is 

 again introduced over about 950 terms, and this too, like its prede- 

 cessors, fails and gives place to other laws which appear at different 

 intervals." 



