]|24 COMMUTATION OF saUAREf AND CITBES; 



On the compu- Jn the rule laid down by me in p. 150 of your Journal for July 

 ff i^uafestld' ^»'^' w^'<^^ ^''^ ^® correaed by fubftituting the, word given 

 c»k9« for the word next. 



But he does not feera to be aware that the rule I propofed 

 for finding the fquares of roots in an arithmetical progreffion 

 of thofe roots, is^ precifely the fame as that he has ufed and 

 elucidated in pages 5 and 6 of your Journal for this month. 



Neither has he made me a convert to his dodlrine, that ad- 

 dition ftiould be ufed in preference to fubtradion ; for the one 

 appears to me as eafy an operation as the other, for all the 

 purpofes to which it is applied in the conftrudion of the tables 

 in queftion. 



, With refpedl to the conftru6lion of the table of cubes, I 

 will barely ftate my method of computing the cubes of the 

 fame roots E. O. has calculated, in pages 8 and 9 of your 

 Journal for this month, and will leave it to thofe who may be 

 inclinable to enter on the inveftigation, to determine which 

 method will be raoft advantageoufly pra6lifed, his or mine, 

 only obferving, that E. O. has a continual repetition of the 

 firft differences, which I have entirely avoided without adding 

 any figures, \n other refpe^ls, to thofe he has ufed. 



I ftill think my method of computing the table of cubes is 

 not more liable to inaccuracy than that E. O. has adopted ; but 

 in order to avoid almoft the poffibility of error in my computa- 

 tion, and at the fame time to add to, examine, and corred 

 Mr. Councer's table, I would place the cubes of half the given 

 roots X 8, at fuch diftances under each other, as would en- 

 able me to interpolate my calculations of the cubes of twice 

 thofe roots, as it is done in the left hand part of the following 

 « elucidation ; and then it is evident, every other cube obtained 



by the calculation muft be the fame as that obtained from the 

 table; and thus a proof of the accuracy of Mr. Councer's 

 tablei and of the continuation of it, would go hand in hand. 



TABLE. 



