based on Napier's Rods. 195 



of the coming digit is sometimes less certain ; but there is 

 usually only one figure of remainder to record, and the result 

 of the first subtraction need not be recorded at all. 



8. If a doubt occurs at any stage, it may be solved in several 

 ways : — 



(1) By pushing forward the frame for a moment and so 

 ascertaining what would be carried from the next rank. 



(2) By increasing the number of trial slides. Thus, sup- 

 posing that we have made the first subtraction, and trying for 

 the new digit we are in doubt. Put back the trial slides, ap- 

 pend another figure from the dividend, push on the frame a 

 step, and subtract the sum of the elements shown. Then try 

 again, using one more trial slide than before. 



For example, 



012345678 



Fourth stage . 4 4 3 2 1 F 



4 3 2 1 F 

 Fifth stage . 55543 2 1 F 



shows the plan of changing from two to three trial slides after 

 4 figures of quotient have been obtained. 



(3) By finding the complete remainder, recording the digits 

 of the quotients already obtained, and beginning the division 

 again with this complete remainder as dividend. 



With three trial slides it is very unlikely that any difficulty 

 will occur before 12 figures of quotient have been obtained, 

 and then only if the divisor have more (sayY than 7 figures. 

 The method of computing should in all cases be exactly that 

 given in Sonnenschein and Nesbitt's 'Arithmetic,' part i. p. 105. 



9. Examples of Division. 



Eos. 1. In these examples the divisor is 74628394, so that 

 the process may with patience be followed on fig. 2. 



Two trial Slides. 



Dividend . . . 3249683142966 

 Written work . . 345599775883 

 Quotient. . . . 435448623344 



The partial dividends are to be read obliquely 34, 49, 56, 

 &c, and in the following example, 260, 310, &c; so that in 

 the above only one figure was recorded at each step : and the 

 result was very quickly verified by reversing the motion of the 

 frame for the purpose of multiplying divisor and quotient. 



