80 Scientific Proceedings^ Royal Dublin Society. 



such a paper I apply the term formula-paper. Each row of perforations 

 across the formula-paper directs the machine in some definite step in the 

 process of calculation — such as, for instance, a complete multiplication, 

 including tlie selection of the numbers to be multiplied together. Of course 

 a single formula-paper can be used for an indefinite number of calculations, 

 provided that they are all of one type or kind {i.e. algebraically identical). 



In referring to the numbers stored in the machine, the difficulty arises as 

 to whether we refer to them as mere numbers in the restricted arithmetical 

 sense, or as quantities, wliich, though always expressed in numerals, are 

 capable of practically infinite variation. In the latter case they may be 

 regarded as true mathematical variables. It was Babbage's custom (and 

 one which I shall adopt) when referring to them in this sense to use the 

 term " Variable " (spelt with capital V), while applying the usual meanings 

 to the words " number " and " variable." 



In my machine each Variable is stored in a separate shuttle, the 

 individual figures of the Variable being represented by the relative 

 positions of protruding metal rods or " type," which each shuttle carries. 

 There is one of these rods for every figure of the Variable, and one to 

 indicate the sign of the Variable. Bach rod protrudes a distance of from 

 1 to 10 units, according to the figure or sign which it is at the time 

 representing. The shuttles are stored in two co-axial cylindrical shuttle- 

 boxes, which are divided for the purpose into compartments parallel to their 

 axis. The present design of the machine provides for the storage of 

 192 Variables of twenty figures each ; but both the number of Variables and 

 the number of figures in each Variable may, if desired, be greatly 

 increased. It may be observed, too, that the shuttles are quite inde- 

 pendent of the machine, so that new shuttles, representing new Variables, 

 can be introduced at any time. 



When two Variables are to be multiplied together, the corresponding 

 shuttles are brought to a certain system of slides called the index, by means 

 of which the machine computes the product. It is impossible precisely to 

 describe the mechanism of the index without drawings ; but it may be 

 compared to a slide-rule on which the usual markings are replaced by 

 movable blades. The index is arranged so as to give several readings 

 simultaneously. The numerical values of the readings are indicated by 

 periodic displacements of the blades mentioned, the duration of which 

 displacements are recorded in units measured by the driving shaft on a 

 train of wheels called- the mill, which performs the carrying of tens, and 

 indicates the final product. The product can be transferred from thence to 

 any shuttle, or to two shuttles simultaneously, provided that they do not 



