196 On a Calculating Apparatus based on Napier's Rods. 

 Ex. 2. The reciprocal of '74628394. 

 Three trial Slides. 



Dividend . . . 10000000000000 



Written work . . 617594672085 



„ „ 237752446776 



Quotient . . . 1*33997255789 



10. Square Root. — In the process for square root a new 

 tablet as well as a new slide is introduced at each stage. 

 Hence in the diagram it will be necessary to represent what 

 intervals are at each stage occupied by tablets. This is done 

 by inserting an asterisk. Also some of the elements must be 

 doubled ; these are indicated by accents. 



I avoid length of description by giving only the diagram, 

 hoping that it will be sufficient explanation of the process. 

 The first digit is obtained in the usual way. 



Plan for finding Square Root, using two trial Slides. 

 012345678 



1*1 F 



2'* 2 * 1 F 

 3'* 3 * 2 * 1 F 

 &c. 



Plan for changing from two to three trial Slides. 

 012345678 



1*1 F~ 

 2'* 2 * 1 F 



* * 2 1 F 

 3' * 3' * 3 * 2 1 F 

 4'*4'*4*3*2 1 F 

 &c. 



^ After the first two stages the process is as easy as that for 

 division. 



11. Example of process for Square Root. Two trial Slides. 

 Given number . . 12*34567890000 

 Written work . . 319533940908 



11 



Square root . . 3*51364182864 



The same, using three trial slides after the second stage: — 

 Given number . . 12*34567890000 

 Written work . . 319551504526 

 243162653 



