ARITHMETICAL COMPUTATIONS. 1Q 5 



** prime numlers cofitained in an unlimited series of odd numbers 



* ' in succession, and at the same time, the simple divisors of 



" those which are not primes. This latter memoir is probably 



the method pursued by the boy to find prime numbers, and 



to resolve numbers into their factors. Of tiie method of M. 



Rallier, he himself says, " In a word, we do not hesitate to 



" assert from experiment, that ly this method, in a single day , 



" and in the way of amusement, computations may be effected, 



" which by the old methods, would require months of severe 



" labour." I will only now add this observation. As the 



above rules depend upon the two or three first, and the two last which are 



figures of any number, it follows that the change of the inter- ^he^ame^s 



mediate ones cannot affect the result. If it should have those practised 



occured to anyone, as it has to me, to have altered anyof h l thehoy > mi ? 

 J J J ot easy acqtn- 



these, and yet to have obtained the true result ; it will, I think, sition by any 

 not be unfair to conclude, that either of these very methods, b °y of taleut * 

 or some similar to them in principle, are those adopted. Let 

 me add, that I have no doubt, but that any clever boy would, 

 in a week's time, learn to apply those given above with the 

 utmost facility. 



I am, Your's, &c. . 



A. H. E. 



[The following is from the same respectable daily Journal 

 of the 18th.] 



SIR, 

 I agree with your correspondent A. H. E. that the young Remedy for 

 American is a very clever boy, but no prodigy, as one visit to tlie ambiguity, 

 him has convinced me. The ambiguity of the cases A. H. E. 

 mentions, in extracting the cube root, may be readily cleared 

 by any one conversant in figures in a few seconds, by finding 

 B in the common formula for the cube root, which is the cube 

 of the binomial A + B ; namely, A 3 -f-3A' 2 B, &c. which is, no 

 doubt, perfectly well known to A. H. E. though to some of 

 your readers, who may be interested in this matter, it may not 

 be so familiar. For such the following directions may be use- 

 ful. The first fig. of the root being known by inspection, 

 take its cube from the millions given, then the remainder 



being 



