84 The Arithmometer. 



The large knobs G and D, are known respectively as 

 the " result effaeer," and the " quotient effaeer," and operate 

 upon a very simple and ingenious arrangement of wheels 

 and racks, whereby all the result and quotient discs can be 

 brought to zero, preparatory to undertaking a new calcu- 

 lation. 



It is impossible to convey by a mere verbal description, 

 unaided by detailed diagrams, an adequate idea of the 

 numerous and ingenious mechanical contrivances with 

 which this instrument abounds. To give an idea of the 

 intricacy of the mechanism, I ma}^ state that in the smaller 

 of the two arithmometers exhibited on the present occasion, 

 and which has but twelve result discs, there are no less 

 than 120 separate cogged wheels, and 44 different springs, 

 all essential to its proper working. In spite of this apparent 

 complexity, the machine has never yet got out of order, has 

 never made a mistake ; while of the springs, which are 

 regarded by the makers as the w T eak point of the whole 

 affair, not one has given way. 



The machine, as will be seen from what has preceded, 

 essentially a difference engine, adding to or subtracting 

 from the number in the result, an equal difference at every 

 revolution of the handle. Hence, it is capable of computing 

 tables having a constant difference with great rapidity, 

 exhibiting successive results, at the rate of one for each 

 revolution. 



Tables of this kind are very common, and although their 

 computation requires but very little arithmetical skill, yet 

 the operation is fatiguing and disagreeable, and an error 

 in any one item will vitiate all that follows ; hence a 

 mechanical aid is by no means to be despised. 



In many tables the difference, though not absolutely 

 constant, varies so slowly that it may safely be taken as 

 constant for a considerable number of successive items. In 

 such cases also the arithmometer can be used with 

 advantage. 



Another large class of tables has for its fundamental 

 formula y = ax 2 . Here it can be shown that the difference 

 of the difference, or second difference, is constant, and by 

 altering the buttons by the amount of the second difference 

 with one hand, and turning the handle with the other, 

 results twelve figures long can be obtained very much 

 more rapidly than the most expert writer can copy them 



