524 Mr. W. H. Walenn onUnitation, 



then 

 also 



Example II. Given 



14 

 7'854 



5 



,-_14 W83+ -004172 



V D x= 



tt/-. .00 ■ -004172 \ TT /_ 5\ 5 



thus checking- the above division by a direct process. 



Example III. Given 



239406 Vni 9506 

 #= _ n , jz - =19 + 



then 

 also 



12100 ' 12100 ' 



V 9 x==l=V 9 (6x^ = V 9 (6x7)=6; 

 /.- 9506 \ TT >. 2\ "' ■ " - 



U 9 



In this instance advantage is taken of U 9 J = U 9 4~ 1 = 7*. 

 Example IV. Given 



_ 29137062 _~i-~q 5219 

 *- — 5317 "" + 5317 ; 



then 

 also 



lV=j|=U n (9x3)=lX n 27 = 5; 

 U 11 (5 4 79 + |g)=U 1 ,(l + |) = U 1 ,(l + 5xi) 



= U li (l + 5x3)=U 11 16 = 5. 



Here advantage is taken of U n J = 3. 



In reference to the practical advantage of unitation for check- 

 ing calculations, it must be borne in mind that the obtainment 

 of unitates and the calculations therewith can be performed 

 mentally with ease. It is more laborious to set down the steps 

 of the unitation, or of the operation with unitates, in order, than 

 to do them mentally. 



15. In the eleventh volume of the ( Mechanics' Magazine' a 

 discussion upon a property of numbers ran through nearly the 

 whole volume. The proposition first advanced was that if the 

 digits of a given number were reversed in their order (251 made 



* Phil. Mag. S. 4. vol. xlvi. p. 40. 



