CHAELES BABBAGE. 169 



one longitudinal, wMch is the tcarp, the other transverse, which is the 

 ivoof. 



Of course the analytical engine could not originate. It would have 

 always been the servant — never the master. It could have done what- 

 ever its inventor Jcnew Iww to order it to do. No more. It assisted — 

 marvelously indeed, but it only assisted — in making the Ictiown available. 

 It could hskyefoUouied analysis, never anticipated it. But had it been con- 

 structed, it would have achieved three desiderata of science — economy 

 of time, economy of intelligence, rigid accuracy. It would have made ob- 

 servations fertile that are now barren for lack of computing powers ; 

 it would have saved time for contemplation that is now wasted in arid 

 calculations by men of genius, and it would have made certain arith- 

 metical numbers, without the aid of which the veil that envelopes the 

 mysteries of nature can never be raised. 



As illustrative of the estimate put upon the operations of the analytical 

 machine, it may not be inappropriate to quote here Mr. Babbage's own 

 remarks : " An excellent friend of mine," he wTites, " the late Professor 

 MacCullagh, of Dublin, was discussing with me the various powers of 

 the analytical engine. After a long conversation he inquired what the 

 machine could do, if, in the midst of algebraic operations, it was required 

 to perform logarithmic or trigonometric operations. My answer was, that 

 whenever the analytical engine should exist, all the developments of 

 formula would be directed by this condition, that the machine should, 

 be able to compute their numerical value in the shortest possible time; 

 I then added that if this answer was not satisfactory, I had provided 

 means by which, with equal accuracy, it might comx^ute by logarithmic 

 or other tables. 



"I explained that the tables to be used must, of course, be computed 

 and punched on cards by the machine, in which case they would un- 

 doubtedly be correct. I then added, that when the machine wanted a 

 tabular number it would ring a bell and then stop itself. On this the 

 attendant would look at a certain part of the machine and find that it 

 wanted the logarithm ,of a given number, say of 2303 ; the attendant 

 would then go to the drawer, take the required logarithmic-card, and place 

 it on the machine. Upon this the engine would first ascertain whether 

 the assistant had or had not given it the correct logarithm of the num- 

 ber 5 if so, it would use it and continue its work. But if the engine 

 found the attendant had given it a wrong logarithm, it would then ring 

 a louder bell and stop itself. On the attendant again examining the en- 

 gine, he would observe the words, WRONa tabular number, and then 

 discover that he really had given the wrong logarithm, and of course 

 would have to replace it by the right one." 



As between the two engines, the difference and the analytical, their 

 powers and principles of construction, the capabilities of the latter would 

 have been immeasurably the more extensive. They hold to each other, 

 in fact, the same relationship that analysis holds to arithmetic. The dif- 



y 



