110 Solutions of Sir H.C. Englefield’s Mathematical Question. 
mentally to substitute noughts in the places of the unknown in~ 
termediate figures. 
I shall subjoin three examples, which comprehend all the va- 
rieties of the question ; and am, sirs, your obedient servant, 
Francis ELLIs. 
Given 94...2. Here the number of places being six, the 
first period (according to the rule for extracting the cube root) 
must consist of three figures, which after the mental substitution 
of noughts will be 940, whose nearest less cube root is 9, and 
the final digit 2, indicating S for the remaining figure of the 
root: the entire root is ‘“‘ins/anily and without any aid of 
wriling’’ perceived to be 98. 
Given 50..3. The number of places being five, the first pe- 
riod must consist of only two figures, which are (50), the two 
first given, whose nearest less cube root is 3, and the final digit 3, 
indicating 7 for the other figure of the reot : the whole reat is 37. 
Given 6,8. 9. The number of places being only four, the 
first period consists of the single figure 6, whose nearest less cube 
root is 1, and the final digit 9, indicating 9 for the other figure 
of the root: the whole root is at once found to be 19. 
The number 438976, given by Sir H. C. Englefield, is not a 
cube number*. 
Yo Messrs. Nicholson and Tilloch. 
ees Fs 
Royal Military Academy, Woolwich, Feb. 12, 1814. 
Sins,—Ir gave me great pleasure to observe the sentiments 
with which Sir H. C. Englefield introduced his question in your 
last number, relative to the extraction of certain cube roots. He 
there justly states, that it is not common to introduce questions 
of this kind to the public through the medium of periodical 
“Journals, though it was not unusual in the early part of the last 
century; and every one acquainted with the progress of the 
sciences at that period will admit that much of it was to be 
attributed to such communications. I made a similar remark 
some little time back, in proposing a question in the Philosophi- 
cal Journal, under the signature of “¢ Mathematicus;” and though 
I failed in my attempt to bring the subject under examination at 
that time, | am not without hopes that the example of a gentle- 
man, so well known and esteemed in the scientific world as Sir 
H. E. is, may be followed by others, and that we may thus see, 
at times, a few pages of your valuable Magazine employed on 
subjects of this nature. 
With respect to the question proposed, it is far from difficult, 
nothing further being necessary for its solution, than that of re- 
* Probably a typographical error, Read 438996,—Enrr. 
membering 
