On definite Proportions in Chemical Affinity. 118 
An example or two will make this clear. Let the cube num- 
ber whose root is required be 804857. Here the first figure of 
the root will be 3, and the root of the greatest cube contained 
in 804 is 9. Hence the root required is 93. 
» Again. Required the cube root of 74088. Here 2 is the 
first figure of the root, and the root of the greatest cube con- 
tained in 74 is 4; hence 42 is the root required, 
If ouly the figure of the unit, the two first figures, and the 
number of places be given, as stated in the i beh the opera- 
tion will be precisely the same. For by taking the example 
given in the question, the first figure of the reot is 6; and as the 
number consists of 6 places, it remains only to find the root of 
the greatest cube number contained in 430, which is 7. Hence the 
root is 76. {It may be proper however to remark, that this mode 
of stating the question fails when the given cube number ter- 
minates with a cypher. 
Concerning the performing this “instantly and without any 
aid of writing,’ I beg to observe, that when I first discovered 
the principle, I explained it to’ two or three young gentlemen, 
pupils of mine, about twelve years of age, and who, after practising 
it for the short time of half an hour on a slate, would tell without 
the aid of writing, the root of any cube number under a million, 
instantly, and without the smallest hesitation. 
The wnethod applies also to any cube number above a million, 
when it terminates in a eypher; but I have not been able to ex- 
tend it to cube numbers in general. I make no-doubt but that 
with a little pains many other arithmetical operations might be 
simplified; and it would perhaps explain in a way not the most 
unsatisfactory, the truly astonishing powers of the “wonderful 
American boy.” Iam, &e. 
Gzorce Harvey. 
To Messrs. Nicholson and Tilloch. 
XXIV. Observations on the Doctrines of definite Proportions in 
Chemical Affinity By Witttam ae Jun. M.D. of 
Boston, Lincolnshire*. 
I, is often a pleasing task to view the progressive improvement 
that is attendant upon different departments of science ; in doing 
which we sometimes meet with hypotheses that were considered 
at first as crude, ridiculous, and soon almost forgotten, again re= 
Vived, more clearly iNdstrated; and not unfreguently advanced 
as entirely new. Among many ‘others that have been proposed in 
the science of chemistry, that of bodies uniting in definite pro- 
portions to form chemical compounds holds a distinguished place. 
* (oO wunieated by the author, 
~ Vol. 43. No, 190, Feb. 1814, a ae Mr, 
