16 Mr. J. Edmondson on Calculating Machines. 



machine similarly produces each succeeding column,, the upper 

 line being the term required for the table. 



The apparatus consists of identical parts, equal in number 

 to the digits required for the last column of the tables it is to 

 compute. It is therefore very complex and very costly, and 

 will not serve the purpose of computers in general, who must 

 have recourse to the semi-automatic class of instruments. 

 These are portable, of moderate cost, allow of very rapid 

 working, and require no special mathematical skill. 



In 1663 Sir Samuel Moreland produced an instrument by 

 which additions and subtractions could be worked, digit by 

 digit ; but it took more time than the ordinary mental opera- 

 tion. It was left to Viscount Mahon (afterwards Earl of 

 Stanhope) to produce the first really practical instrument. 

 Besides a machine dated 1780, which was a great advance on 

 that of Sir Samuel Moreland, though on the same lines, he 

 invented three machines. Those of 1775 and 1777 were on 

 the table for inspection after the lecture, and abound in beau- 

 tiful and effective contrivances. The third machine the lecturer 

 had not seen, and it has never been described. In that of 

 1775 is found the " Stepped Reckoner," the basis of the only 

 instruments that have come into extensive use. 



The reckoner of the modern machines, patented in 1851 by 

 M. Thomas de Colmar, consists of a cylinder divided into 

 10 sections, on which there are respectively 0, 1, 2, 3, 4, 5, 6, 

 7, 8, and 9 teeth. The teeth of one section being coincident 

 with an equal number of those of the next section, the whole 

 presents a stepped appearance. Each revolution of this 

 reckoner moves a pinion of 10 teeth, in gear with one of its 

 sections, as many teeth as there are upon that section. The 

 motion of the pinion is communicated to a dial with the digits 

 to 9 in orderly succession upon it. Thus, if the figure seen 

 through an aperture in the covering of the dial were 0, and 

 the pinion were in gear with the section having 3 teeth, the 

 first revolution of the reckoner would move the dial to 3 ; the 

 second to 6 ; the third to 9 ; this result being the multiple of 

 3 (teeth on the reckoner) by 3 (revolutions). A series of, 

 say, 8 reckoners, pinions and dials, each pinion being set to 

 the section having 3 teeth, would give in 3 revolutions the 

 product 99,999,999. The next revolution would bring in a 

 new feature — the carrying of the tens. Here lies the great 

 difficulty of Calculating Machines ; but the difficulty has been 

 overcome, though not without leaving room for improvement. 

 The 1 that will have to be carried from each dial to that im- 

 mediately on its left cannot be added while the latter is being 

 operated upon by its reckoner. The machine must therefore 



