The Arithmometer. 85 



down. To this class belong tables of squares, weights of 

 square and cylindrical rods of various materials, strength 

 of ditto, kc. kc. 



In order to understand the operation of the machine 

 when multiplying, it will be neccessary to observe that 

 multiplication is but a form of addition, e.g., if we wish to 

 multiply 63 by 4, we may proceed thus — 



63 

 63 

 63 

 63 



252 



and the method, though tedious, will be admitted to be 

 perfectly accurate. The corresponding operation will be 

 performed by the instrument, by setting the units button 

 to 3, and the tens button to 6, and turning the handle four 

 times, when the result discs will exhibit the number 252, 

 and the multiplier 4 will be presented by the unit quotient 

 disc. If the multiplier were 24, we should need to shift 

 the slide one notch to the right, and turn the handle twice, 

 the result discs would then give 1512, while the quotient 

 discs would show the multiplier 24. The operation being 

 similar to the subjoined addition : 



63 



63 



63 



63 

 63 

 63 



1512 



In this way long multiplication can be performed 

 expeditiously and accurately, a result 20 figures long being 

 obtained by actual trial in 45 seconds, with a machine 

 having 20 result discs. 



By means of a simple algebraical artifice results containing 

 many more figures than the machine has result discs may 

 be obtained, e. g., a result 24 figures long, expressing the 

 product of two factors, each 12 figures long, was obtained 

 from an arithmometer having only 12 result discs, in about 

 2 minutes. 



