112 Solutions of Sir H. C. Englefield’s Mathematical Question. 
perform in arithmetical computations is the result of tuition ; and. 
that he will not discover his methods. This however, so far as 
my observations have been extended, in several examinations of 
him both in company and in private, I can positively contradict. 
All his ideas were obviously intuitive, yet in most cases correct : 
indeed the only instance in which I found that he proceeded on 
false principles was in resolving numbers into their factors; and 
even here he would succeed in the greater number of cases. 
These examinations were undertaken for the purpose of giving a 
sketch of his methods or rules (if they may be so called), in a work 
which his father intended, and I believe still intends, to publish 
by subscription, containing an account of this remarkable boy ; 
and I therefore do not wish to enter into further particulars in this 
place, lest his father should imagine it to be injurious to the 
interests of that publication. But if that plan should be ultimately 
given up, I may at some future time furnish you with what I 
have been able to ascertain on this subject; not that I conceive 
any one of his methods can be employed to any useful purpose ; 
they are peculiarly his own, and can only be adv antageously em- 
ployed by himself; but as a subject of curiosity they may be ac= 
ceptable to some of your readers. 
I am, sirs, yours, &c. 
To Messrs. Nicholson and Tilloch. PrrER BaRLow. 
—=>— 
Plymouth, Feb. 8, 1814. 
Sims,—Every attempt to simplify and abridge. calculation 
deserves attention, and I cannot therefore but view the question. 
proposed by Sir H. Englefield, in your number for January, with 
particular pleasure and satisfaction. 
In order to resolve it, I would first Papal 2 that when the unit’s 
place in any hoebiss 3 dcactd Orly 2, 3, 4, o2-6, is 8, 9, 
the unit’s place i in the cube will be 0, 1, 8, 7, 4, 5, 6, 3, 2, 9. 
This table, of course, can be acquired i ina “few hinatee by me- 
mory. To exemplify its use, we may briefly state, that when 
the unit’s place in any cube is 8, the unit’s place in the root 
will be 2; or when the unit’s figure in the cube is 3, the unit’s 
place in the root will be 7. 
Moreover it is a well known law existing amongst cube num- 
bers, that if any cube number be divided into periods of three 
figures commencing with the unit, the number of these periods 
will show the number of figures in the root, which’ in the case 
before us never can exceed two; that is, the root of every cube 
number under a million consists but of two figures, the first of 
which, or that in the unit’s place, being readly obtained by the 
application of the above table, there remains only to discover 
the other figure, which is the cule root of the greatest cube num- 
ber contained in the first period. An 
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