ARITHMETICAL INSTRUMENTS. 25 



inducement has existed to supersede the labour involved in such 

 calculations by means of mechanical appliances. 



Counting machines, however, for certain purposes have been 

 found indispensably necessary. A clock is defined by Sir John 

 Herschel as a machine for counting and recording the number 

 of the oscillations of a pendulum ; though to this definition we are 

 obliged to add that every clock must also contain a mechanism 

 adapted to maintain the state of oscillation of the pendulum 

 against friction and the resistance of the air. A pedometer is an 

 instrument for counting and recording the number of steps taken 

 by the person carrying it. Distances along a road are approxi- 

 mately measured by rolling a wheel along the road, an apparatus 

 being annexed to the wheel which counts and records its revolutions. 

 In the same way a turnstile may be made to record the number 

 of its own revolutions, i.e. the number of persons admitted 

 through it. 



The above are simple instances of counting machines employed 

 for the common purposes of life ; but the construction of calculating 

 engines, adapted to more varied and complicated purposes than 

 that of simple counting, is to be reckoned among the great achieve- 

 ments of mathematical and mechanical skill. The first idea of 

 such a machine appears to have been due to the celebrated Blaise 

 Pascal ; the apparatus constructed by him was arranged for the 

 addition and subtraction of sums of money. Two calculating 

 machines, constructed in 1775 and 1777 by James Bullock for 

 Viscount Mahon, are included in the Exhibition. But the idea 

 of a difference engine, which should serve to calculate tables of 

 analytical functions, was first successfully realised by Charles 

 Babbage ; the analogous contrivances which had previously been 

 proposed having been designed merely for the performance of 

 single arithmetical operations, such as addition, subtraction, mul- 

 tiplication, and division. The later years of Babbage's life were 

 devoted to the construction, or rather to the design, of a great 

 analytical engine, which was intended to possess a range of calcu- 



