92 eeport— 1878. 



Report of the Committee, consisting of Professor Cayley, Dr. Fare, 

 Mr. J. W. L. Gtlaisheb, Dr. Pole, Professor Fuller, Professor 

 A. B. W. Kennedy, Professor Clifford, and Mr. C. W. Merri- 

 field, appointed to consider the advisability and to estimate the 

 expense of constructing Mr. Babbage's Analytical Machine, and of 

 printing Tables by its means. Draivn up by Mr. Merrifield. 



We desire in the first place to record our obligations to General Henry 

 Babbage for the frank and liberal manner in which he has assisted the 

 Committee, not only by placing at their disposal all the information with- 

 in his reach, but by exhibiting and explaining to them, at no small loss of 

 time and sacrifice of personal convenience, the machinery and papers left 

 by his father, the late Mr. Babbage. Without the valuable aid thus kindly 

 rendered to them by General Babbage it would have been simply impos- 

 sible for the Committee to have come to any definite conclusions, or to 

 present any useful report. 



We refer to the chapter in Mr. Babbage's ' Passages from the Life of a 

 Philosopher,' and to General Menabrea's paper, translated and annotated 

 by Lady Lovelace, in the third volume of Taylor's ' Scientific Memoirs,' for 

 a general description of the Analytical Engine. 



I. The General Principles of Calculating Engines. 



The application of arithmetic to calculating machines differs from or- 

 dinary clockwork, and from geometrical construction, in that it is essen- 

 tially discontinuous. In common clockwork, if two wheels are geared 

 together so as to have a velocity ratio of 10 to 1 (say), when the faster 

 wheel moves through the space of one tooth, the angular space moved 

 through by the slower wheels is one-tenth of a tooth. Now in a calcu- 

 lating machine, which is to work with actual figures and to print them, 

 this is exactly what we don't want. We require the second wheel not to 

 move at all until it has to make a complete step, and then we require that 

 step to be taken all at once. The time can be very easily read from the 

 hands of a clock, and so can the gas consumption from an ordinary 

 counter ; but a moment's reflection will show what a mess any such ma- 

 chinery would make of an attempt at printing. 



This necessity of jumping discontinuously from one figure to another 

 is the fundamental distinction between calculating and numbering machines 

 on the one hand, and millwork or clockwork on the other. A parallel 

 distinction is found in pure mathematics, between the theory of numbers 

 on the one hand, and the doctrine of continuous variation, of which the 

 Differential Calculus is the type, on the other. A calculating machine 

 may exist in either case. The common slide-rnle is, in fact, a very power- 

 ful calculating machine in which the continuous process is used, and the 

 planimeter is another. 



Geometrical construction, being essentially continuous, would be quite 

 out of place in the calculating machine which has to print its results. 

 Linkwork also, for the same reason, is out of place as an auxiliary in any 

 form to the calculation. It may be of service in simplifying the construc- 

 tion of the machine ; but it must not enter into the work as an equivalent 

 for arithmetical computation. 



