Periodical Literature 339 



metric measure as a unit, being too large to keep in one's eye, and, 

 in cubic meters, requiring the handling of fractions which the 

 mind does not grasp readily. Nevertheless, by using the decimeter 

 for lineal measurement and square decimeter and liter for basal 

 area and volume, and the are for sample area expression, this 

 difficulty may be reduced. 



He then develops aids for rapid mental calculations which form 

 part of the art of estimating. These are naturally given for 

 meter measure, but similar short cuts could be devised for our 

 own measures. We give some of the rules. 



1. Avoid multiplications except by 10 and its multiples and the 

 small numbers 2, 3 and 4. Substitute rather division and addition 

 and subtraction. 



ino 

 E. g., instead of 17x25 = 17 X- 



" 5.7 X. 7854 



= 5.7-10x2% = 4.56 



73 



" 73X1.25(=V2) = 73X:4 =91.25 



" 26X.57 (form factor) =26X^+7x2%= 14.82 



This is the secret of rapid mental calculation. 



2. To check a calculation mentally do not repeat the same 

 calculation, but make a different kind of calculation, or at least 

 follow a different sequence of calciilation, when also any errors in 

 the factors (height, form factor, etc.) reveal themselves more 

 readily. 



3. Since exponential expressions are needed so frequently, it is 

 worth while to memorize second and third potencies ; or in cubing, 

 the memory may be assisted by the rule 



(10+a)3 = 2a3+(10-a)3+600a 

 E. g., 143 = 2X43+6^+600x4 = 2744 



Or squaring larger numbers : 



(10a±6)2=10a(10a±2t)+62 

 E. g., 542 = 50X(50+2X4)+42 = 2916 



