Lancaster daily intelligencer. [volume] (Lancaster, Pa.) 1864-1928, 1886-10-23

Let APN be the circumference OF the circle
the given point to which the centIipetal
force tends PN the chord OF the circle drawn
through s from r, the position OF the BODY at
any time, and VOA the diameter through '
join PA, and draw sI perpendicular to
Ply, the tangent to the curve at T.
By prop. vi, cor. s. II + be the measure OF
the acce!erating effect of the centrlPetal
force.
F-sy5pv- and since the angles SPY VA
p are equal, and also the right angles SYP,
APV, the trlangles SPY, NAP are similar,
and sY: sP:: Pv: VA: F. =557ST5
therefore, since h and VA are gissn varies in
versely as SP-PNs.'
tits mot needful TO trace his demOnstra-
ton through all its reference. The expression
~ nv ~ in which represents twice the
al ca described by the radius yectOr in a unit
of time is properly derived. The error which
Newton commits is simply an oversight
II is conceded that iu an expression OF Yaria-
ton only varIables should be retained. Will
any one dispute that the chord OF a given
circle drawn through two given points
is a constant? In the course OF the dem
OnstratiOn Newton says, let L be the
chord drawn through from +. and
L are points fixed before the chord PV
il drawn. PN can only be what it is
and nothing else.
The supposition that the places of S and P
NAV be changed will not change the chord
PV, for then the chord drawn from p
through s will be an entirely other
chord. The chord drawn in this latter
case will also be constant as Will indeed
any chord OF which two fixed points are
given.
1t is evident that SP is variable, since it is
the radius vector, but we must not coniOund
SP the radius vector with SIP az a part OF the
chord PV. As vector SP is variable as a
part of the chord it is constant
BY applying this, so righuully test, to the
expression F. C6-pv, in which Newton
recognizes the constancy of b and VA but
tails to acknowledge the equally evident con-
stancy OF PV, the final expression of varia-
ton and the true expression is, varies in.
yersely as spa, which is the law of gravita-
ton face to face. Had Newton not commit
ted this oversight in his demonstration, Re
would have spared me the task of intrOduc-
ing the true doctrine Of orbits- Had he
made this announcement in his day, il
would have been accepted without the hos
tile demonstrations which confront an hum
BILE instrument whe happens not to be "good
authority" Had he announced this tn cory,
astronomers would long since have recon
Gil ed themselves 1t isimpotent to maintain
that a series Of observations Is worth
more than a volume OF demonstration, but
my article is growing too long and must be
brought TO close.
By way of conclusion, let me say that If |
have not shown sufficient respect tor the criti-
cism from the observatory, have, at least,
displayed no worse behavior than the dis
tinguished professor himself The tone Of
his entire prod uction Is remarkable for its
manifestation OF spleen and rejudice, no less
| than tor its absolute steriiity OF argument
He will, have no doubt, mud some "difti-
| Guilty in seeing just where Newton is wrong"
| Might not add, that judging from the dis
play in public, it does not require very diffi-
| cult task TO give him some trouble The pro-
| fessor is not very candid in saying that he is
| not supposed to know, wherein propose TO
| assail Sewton's demonstration. ] personally
directed his attention TO the point, SHORTY after
| my original announcement During that in
| terview 4 asked him TO assent to the fact that
a chord drawn through two fixed points is a
| constant, to which he simply replied "not
| necessarily" a third or fourth time Finally
| he agreed so far, but fairly indicated by re-
| marks and manner, that, whether right or
| wrong, he proposes to follow Newton any
| how, because he is good authority. Prof.
| Kershner Is not correct in saying that col
| league and himself were uHnocentiy drawn
into controversy with me. Surely not By me.
| Their comment appeared in connection with
| my first announcement 10 which did not
| at all object. i want criticism, but let It be
| worthy OF the name. If 1t Is TO be a game OF
| bluff, IL is certainly two sided play, and our
| friends must not think harsh If try 10 play
| my side Successful contradiction will re-
| ceive acknowledgement at once, and want
| no one to suppose from the tone OF this reply,
that 1 will take unfair advantage OF any criti.
cism that is offered with due degree OF
courtesy. III. u. PUsH.
| New Dsnville, Oct 23.