10 SEC. 1. ARITHMETIC. 



Iu the third place comes subtraction, and it must first of all be understood 

 that the red numbers are to be used on the larger discs ; for the rest the 

 method is very easy. 



The following is an example: 



The numbers 5,786, as the larger numbers are placed in red figures 

 5,786 in the openings of the large discs ; (6) in the units, (8) in the tens, 

 3,524 and so on. The smaller number, which is to be subtracted, must 



be placed on the arcs, in the same order as was shown for addition. 



2,262 And in the same manner likewise must the handle be turned round 

 =: once, and then all is done, and the remainder appears in the 



openings in which the larger amount was previously to be seen. 



For multiplication (as for addition) the black numbers must be used on the 



large discs, and before anything else, plain noughts must be placed in the 



openings. And because in this method of reckoning small discs are also 



used, noughts must at first be placed on them. Let the numbers 



365 365, as in the case of addition, be placed on the arcs. One of the 



24 hands, working from the centre, points to the units on the small 



discs, and shows that multiplication will be effected with the units 



1,460 as long as the hand is unaltered. Now if the handle be turned 

 7,300 round once, the numbers 365 will appear on the larger discs, instead 



of the noughts which were there previously. But on the smaller 



8,760 discs where the hand points, the number (1), and this proves, that 

 = the numbers 365 have been carried once under the aperture of the 



large disc. The handle is again turned, and there will be seen on 

 the large disc the numbers 730 and on the smaller one the number (2). But 

 it must in the units' place be multiplied by (4), and so the handle has to be 

 turned four times round, and there will then appear on the large disc the 

 number 1,4CC, and on the smaller the number (4), and therefore, in this 

 problem, enough has been done with the units. Since 365 had to be multi- 

 plied by 24, the operation is repeated twice in the tenfold numbers, and the 

 desired result obtained ; this is effected in the following way : 



The hand acting from the centre must be placed on the second disc, which 

 corresponds to tens. Near to the spot where the handle has its resting- 

 point, there is at the circumference of the machine a steel catch pressed down 

 in a notch;' this must be lifted up, and so turned round at the circumference of 

 the machine that the hand working from the centre comes to point on the 

 tens disc, and as in this case the catch will be pressed into the newly found 

 notch, the handle being turned round twice, the product 8,760 will be found 

 in the openings of the large discs. 



For division the red figures must be used, as in the case of subtraction. 

 As an example take the number 8,760, which was obtained by the first 

 multiplication, and divide it by 365. The number 8,760 must be placed on 

 the large discs, in red figures, under the openings. The divisor 365 must be 

 placed on the arcs ; the first digit of the divisor (3) must be turned round 

 under the first digit of the dividend, viz., under the number (8) ; on the 

 small discs noughts must everywhere be placed. The catch must be left in 

 the notch. Now 3 can be taken from 8, the handle is turned once round, 

 and the numbers 5,110 appear, which is the remainder after 3,650 has 

 been taken from 8,760. 3 can again be taken from 5 ; the handle is again 

 turned round once more, and the remainder 1,460 appears. Since 3 cannot 

 be taken from 1, the catch is lifted, and 3, the first digit of the divisor, 

 brought under the 4 in the dividend. The handle is then turned 4 times, 

 and the remainders, 1,095, 730, 365, and 0, appear in succession, being those 

 due to the successive subtractions of 365 from 1,460. The value of the 

 quotient is seen to be as follows, 3,650 or 365 x 10 is subtracted twice, giving 

 20 as the first part of the quotient, then 365 is subtracted 4 times, giving 4 

 as the second part, with no remainder ; thus the quotient sought is 24. 



