The enquirer. [volume] (Richmond, Va.) 1804-1815, 1811-01-03
20 rux ..IroR or rue rnevIREa {:


New Jersey, which you have published in The
Enquirer, have afforded NE much satisfaction.
It would, however. have been still more crafty
ing if that gentleman had favored me with his
information sooner. wish neither the reputa-
zion of ingenuity, the honor of establishing
Aew systems. My sole motive in publishing the
essay on the tides, was what ] expressed i'm the
preface, viz the hope Of exciting the attention
OF lnathematicians to a subject which believed
Co be " and Of the utmost Importance in ply.
sizes I was we'll aware that my performance
was extremely imperfect but imperfect as it is,
1t 1t orly prove the means ofinducing either Mr..
Adraih or any other To give to the public full
and satisfactory demonstration Of the consequent.
ces resulting from unequal velocity in the
same point Of the earth then my views will he
accomplished. So far from regretting that the
principle assumed was started by Calico, and
adopted by Dr. Wallace l regard it as a cir
cumstance which ought to afford me real gratfi.
cation. For although as Mr.. Adrain Justly OBJ.
serves, mo authority of great names can coun-
terpoise the weight OF demonstraton," yet un-
fortunately the great majority of mankind are
more prone TO listen to the whims and fances of
The great tn ian to the geometry of Euclid.
The last OF Mr.. Abrams observations is one
which merits my particular attention Mr.. A.
drain says" Let Mr.. Wood once for ali, de.
monstrate that from the unequal velocity, there
arises variable tendency towards the centre of
the earth, and let him investigate the precise
measure OF this tendency. In the second place
let him shew clearly that this variable tendency
to the centre can or cannot produce such pheno.
mena as those OF the tides (for what he has
SAID in his book on both these problems is totally
inappiicable )and then mathematicians will readi-
iy admit his conclusions. Should he not do this.
he VIII not, presume, have any objection to seq
The demonstration by anotar.'
AS the purpose of the essay which / publish
ed was to excite farther investigation, the lead
ing outlines OF the theory were only given INV
other engagements, together with the difficulty
ofpubishing mathematical works in this countrv
not permitting complete treatise on the subiect
The first part of Mr.. Abrams observation. viz
that from the unequal velocity there arises avs
riabic tendency towards the centre of the earth
appeared to me proposition sc Obvious as nor
70 require demonstration. However since this
proposition forms the basis of the whole theory
and since objections have been made TO what an.
peared to me evident from the principal of New
ton, have determined upon composing treatise
in which not only this, but the precise measurt
OF this tendency shall be demonstrated in the
most rigid manner At present beg leave m
request the attention of Mr.. Adrain, and those
who are OF his opinion. to the following theorem.
"a a" essay on the laws of centripetal force, by
Mr. John Keill, in the Goth volume of the Philo.
sophicai Transactions, for the year 17Oe, and
which may be found in page $50, ofthe 18th vol
Ofthe last abridgem ent.
At a body urged by centripetai force move
IN any curve then, in every point of the curve
that iorce VIII De IN ratio compounded of the
direct ratio of tine body's distance from the cen
tire OF force, and the reciprocal ratio of the cbe
OF the perpendicular on the tangent TO the same
point OF the curve, drawn into the radu. of c,r
vature of the same point"
Ihereiore, IT we suppose the whole gravity of
the eAith 90 De placed at the centre, the particle
on the surface may be considered as a detached
body moving in an cpcycioidai curve and -.
tendency OF this particle towards the centre will
be Ia ratio compounded of the direct ratio of
the radius of the earth, and the reciprocal Rio
OF tue cube OF the perpendicular from the
centre OF the earth on the tangent the point of
the epicycloid, drawn into the radius of curya
ture of the same point.
This theorem IS strictly demonstrated by Ke
ILL., but the same may also be deduced from the
81 and I'll, CorOliaries of the 9th Proposition of
the LIST book Of Newton's Principia
MIR. Adrian may, however, reply, that the cen
tripetal force which urges the moving BODY. ;s
supposed by Mr. kei, to be stationary but
that the centre OK the earth is in motion, while
the particle OF. the surface is describing an cpl
cycloid but l pledge myself to demonstrate
that the same viii be the measure OF the tenden-
oy OF The particle in thi; c.se also.
In order to discover the particular Epicyclo,d
any point OF the Earth describes, there cannot be
nure simple mode than that pointed out by
NJ McLaurin, with respect to the uoons path
which mentioned in my book but for thf, sa
SsfactioH OF those who have not seen it shall
the Al, book of hcLsurin on Sir Isaac Newtonis
discoveries is as follows:
50 She path the satellite, on an immoyea.
BILE Plane, is the Epicycloid that is described by
a given point in tue plane OF circle, which re.
wolves ON circular base, having its centre in
she centre of the sun, and ITS diameter in the
same proportion to the diameter of the revolving
circle as tie periodic time OF the primary about
the sun, TO the time the synodic revolution of
the teiite about the primary The Tangent
OF the path is perpendicular to the right line
that joins the satellite to the contact OF tire two
sirCles and lie absolute velocity OF the sate!-
lite is always It's distance from that con-
TACT
Therefore to apply the reasoning to the
points OF the earth we may suppose each point or
partfcle to be satellite revolving round the AK
Is IN The plane of circle parallel TO the EQUATOR
and IN place Of the time Of the synodic revoluti.
OIL the satellite about the primary, we may
substitute tue time of the diurnal rotation OF The
Earth about its axis.
mentioned in my essay that this would be
correct, with respect TO the Earth, if the plane
Of tue equator were the same with the plane. Of
tie Ecliptic, but since fndit will also hold
whatever tie obliqui,y of the EcpGc may be-
There cannot, III my opinion, be 4 more bcauti-
fii solution of the Problem winch Mr. Atlrain
says was proposed la the Ladies Diary for I749,
chan this which MIR. Mel surn has given with
respect TO the Moons path The reason did
not adopt il, was because did not find il so con
venient when applied TO practice as supposng
the earth TO move along the chord Of an Ellipse
IN place of tie Arc. The formula used in my
book ~ certainly not so correct as t3at ,vhici