390 Mr. Y. A. Bailey on the Mental Multiplication 



rational coefficients. The most natural ways of well- 

 ordering these are such that those of low order and degree, 

 and involving no numerical constants other than small 

 integers and fractions with small numerators and deno- 

 minators, come earliest in the sequence. Accordingly, 

 the practice of adopting the simplest law that fits the 

 availahle observations appears to* be closely related to the 

 possibility of a satisfactory theory of inference. 



XLIII. The Mental Multiplication and Division of Large 

 Numbers. By Y. A. Bailey, M.A.. Queens College, 

 Oxford *. 



THE current methods of long multiplication and division 

 have been in existence practically since the twelfth 

 century, when they were given by the Hindoo Mathematician 

 Bhaskara. 



Some of the modifications of these methods are given in 

 the Encyclopedia Brittanica, 11th edition. Article "Arith- 

 metic." In particular, mention is made of a process of long 

 multiplication which may be performed wholly mentally, 

 though w T ith some difficulty. 



The process described below may be regarded as a develop- 

 ment and simplification of this last, though originally arrived 

 at independently. 



After very little practice w r ith this new method the author 

 has found it to possess the following other advantages over 

 the ordinary method : — 



(1) It is speedier. 



(2) Less liable to error. 



(3) Less fatiguing for large numbers. 



(4) By reversing the process we can perform long 



division mentally. 



The method is best explained by indicating the steps in an 

 actual example. 



Let us evaluate 24968 x 4352. 



On a slip of paper write down the multiplier backwards, 

 taking care to give the figures the same spacing as the 

 multiplicand. Start with the left-hand digit on the slip 

 placed under the right-hand digit of the multiplicand 

 thus : — 2 4 9 6 8 



| 2 5 3 4 | . 



* Communicated bv the Author. 



