LuDGATE — On a Proposed Analytical Machine. 79 



step of the work (together with the proper algebraical signs) ; and, lastly, a 

 means of recording the result or results. It must be capable of submitting 

 any two of the numbers stored to the arithmetical operation of addition, 

 subtraction, multiplication, or division. It must also be able to select 

 from the numbers it contains the proper numbers to be operated on ; to 

 determine the nature of the operation to which they are to be submitted ; 

 and to dispose of the result of the operation, so that such result can be 

 recalled by the machine and further operated on, should the terms of the 

 problem require it. The sequence of operations, the numbers (considered 

 as abstract quantities only) submitted to those operations, and the disposition 

 of the result of each operation, depend upon the algebraical statement of the 

 calculation on which the machine is engaged ; while the magnitude of the 

 numbers involved in the work varies with the numerical data of that 

 particular case of the general formula which is in process of solution. The 

 question therefore naturally arises as to how a machine can be made to 

 follow a particular law of development as expressed by an algebraic formula. 

 An eminently satisfactory answer to that question (and one utilized by 

 both Babbage and myself) is suggested by the Jacquard loom, in which 

 interesting invention a system of perforated cards is used to direct the 

 movements of the warp and weft threads, so as to produce in the woven 

 material the pattern intended by the designer. It is not difficult to imagine 

 that a similar arrangement of cards could be used in a mathematical machine 

 to direct the weaving of numbers, as it were, into algebraic patterns, in 

 which case the cards in question would constitute a kind of mathematical 

 notation. It must be distinctly understood that, if a set of such cards 

 were once prepared in accordance with a specified formula, it would possess 

 all the generality of algebra, and include an infinite number of particular 

 cases. 



I have prepared many drawings of the machine and its parts ; but it is 

 not possible in a short paper to go into any detail as to the mechanism by 

 means of which elaborate formulae can be evaluated, as the subject is 

 necessarily extensive and somewhat complicated ; and I must, therefore, 

 confine myself to a superficial description, touching only points of particular 

 interest or importance. 



Babbage's Jacquard-system and mine differ considerably ; for, while 

 Babbage designed two sets of cards — one set to govern the operations, and 

 the other set to select the numbers to be operated on — I use one sheet or 

 roll of perforated paper (which, in principle, exactly corresponds to a set of 

 Jacquard-cards) to perform botli these functions in the order and manner 

 necessary to solve the formula to which the particular paper is assigned. To 



