a 
910 
For De Laguy gave first to the world the 
N 
‘ ag AE 
expression 2 + a RTE peng 
x 2n for a near valueto the root of the 
number N, where sr is the index of the 
root, and # a near approach to it. By 
bringing this term to a common denomi- 
nator, we have it equal to 
r+ 
rt+i.n +r—I1.Nn+2Nn—2n rt 
r+ i.n’ +r—1.N 
r+t 
whichisequaltor—l.n +r+1.Nn, 
r—1LN+r4+ 1a’ 
r—l1N+r+ 1.2’ 
ter expression is that which Dr. Hutton 
has given in his tracts, but by no means 
supposing that he had made any great 
discovery, for it is merely the reduction 
of a fraction to a common denominator; 
and as, in many cases of this kind, an ex- 
pression is supposed to be simplified by 
such an operation, this change is declar- 
ed to be peculiarly recommended for 
ractice. We apprehend that upon trial 
De Laguy’s will be found to have the 
superiority. Several other methods of ap- 
proximation might have been mentioned, 
which are to be found in the books of al- 
ebra, as that, from Raphson, by which 
ee found the small difference nearly 
between the root andthe number assum- 
ed, this small number is used in the se- 
cond power, and thus a new figure is 
gained with little or no trouble ; and by 
applying the whole number found, in- 
stead of the unknown number, in the 
given equation, and dividing the known 
number by the unk..own side, the powers 
of the unknown number being diminish- 
ed by unity, a still nearer approach may 
be frequently made. An opportunity for 
introducing these improvements will oc- 
cur under the article Equation. 
Under the article dpsides, it is pto- 
perly observed, that Sir Isaac Newton 
has shewn that when the force varies in- 
versely as the square of the distance, the 
line of the apsides is stationary 5 but as 
the equation to the apsides is easily de- 
duced for any law of the force; we would 
rather have seen it introduced in this 
place, whence the truth of Newton’s po- 
sition might easily and satisfactorily have 
beenderived. From the conjecturethrown 
out, that Sir I. Newton was led by Kep- 
ler’s observation, that equal areas were 
or? — len + r+. N 
x2. This lat. 
GENERAL SCIENCE. 
described in equal, times at the apsidess 
to discover that the same held in every 
part of the orbit ; we trust that due juss 
tice will be done to Kepler in this work. 
His merits are not sufficiently known in 
this country ; and from thei? little ac- 
quaintance with him, many lose the pleas 
sure that is derived from tracing the pro- 
gress in science in different ages. 
The article Arch gives us the nature of 
circular arcs in geometry, and arches in 
architecture: for the former, some ex- 
pressions are given without this theory ; 
for the latter, the deficiency of this ar- 
ticle is most deplorable. One would sup- 
pose that the writer of this article had 
never heard any thing of arches since 
Dr. Hutton had written his treatise upon 
bridges ; that he had never been in com- 
pany where the plan of. a bridge with 
one arch over the Thames in London 
was mentioned ; nor knew any thing of 
the various proposals delivered into the 
house of commons; or of the elegant ex- 
periments made by Mr. Atwood ; or his 
scientific treatise, which has explained 
the whole of the difficulties once enters 
tained on this subject in the clearest and 
most satisfactory manner. Mr. Atwood 
has published a treatise on the equilibra- 
tion of arches, known to every mathema. 
tician probably in Europe, except the 
writer of this article. In this treatise he 
has shewn that the source of equilibration 
is to be found in the properties of the 
wedge, and has calculated the force of 
each wedge inthe arch, a3 also the Weight 
of any section of the arch. His theory 
also he. has reduced to practice in the 
most elegant experiment that ever was 
made. A bridge of one arch is construct- 
ed of small polished brass wedges: the 
span is, we believe, less than a yard: the 
weight and form of each wedge is con- 
structed according to the principles of 
his treatise, and thus an atch of equilibra- 
tion’is presented to the eye. 'T’o confirm 
the truth of it, a segment of the arch is 
removed, the remaining segment being 
supported by its abutment, and a hold 
fixed to a string which goes round a puls 
ley, and at the other end of the string a 
weight is fixed, which keeps the segment 
of the arch in equilibrio. This weight 
agrees with, and confitms the truth of the 
principles derived from the properties of 
the wedge. But though the treatise has 
been published a considerable time, has 
been noticed in the Reviews and monthly 
publications, and the experiment has 
been seen and admired by numbers, both 
