Lancaster daily intelligencer. [volume] (Lancaster, Pa.) 1864-1928, 1886-10-30

rs being taken to radius X That is, In
addition to the errors vi hich we pointed out
before, there Is one OF magnitude X which
would not sppeat here II the functions in the
hrst proportion were taken to radius unity,
ss we took them. All the evidence oil the
whole work is against the idea that Il as
there used Is applied as fundamental radius
TO the junction. For that proportion by
itself Il will do, but not in its connection with
the remainder. Ii will work in better alter
the frst proportion II the functions are taken,
as they commonly are, to radius UNITY IN
other words We were more liberal i'll our IN
terpretation ot the work than the suthot IL
himself when he compells us to use X ~
fundamental radius aud angle pBA for fSA.
Our last objection to III not being constant
and is not at all met by the reference To
LOOMS treatise on astronomy. We did not
deny that the radius vector describes constant
areas in equal times We claim, however,
now as then that the sector IL rs computed
even with the correct formulas Is not the true
area that is con slant We have in our htst
review OF the theorem clearly pointed out
what area is constant aud also by what
amount IL differs from as produced by the
formulas This is not met 10y the reference
since the reference is nothing to the point at
issue.
l Now let us also look briefly at the correc-
ton To Newton's corresponding proposition.
Here We beg to say the objection to the
theorem is certainly not valid and more than
this very unreasonable. The reader Will ob-
serve thst there Is no objection made to the
thtOrem except In the Interpretation Of the
final result That is, Newton regards
quantity variable which the author OF the
new theorem claims Is constant This guam
tity is the chord PV. In the objection II is
stated that in the course of the demonstration
Newton says let PN be the chord drawn
through from r." This Newton certainly
says, and he says also more, viz: "The
position of the body at any time" How then
does 1t follow that L Is a fixed point Is
fixed but I is point the position OF which Is
| variable since II represents the position OF
| the body at any time There is very
| strange aud unnatural distinction between L
| as u point in P> and rs point in PN. The
| chord is no more an entirely other chord
| when 1t changes its position than the radius
| veCtor PS is an entirely other radius yector
| when it changes its position. The point L
| certainly is movable. Tho corresponding
| trisugles can be drawn In any position both
| for chord aud radius vector and consequent
| ly the same relation between the quantities
| considered will hold in all petitions, and the
| law Is precisely as stated in NewtOn's con
clusion. Any reader can easily satisfy him
| self that the proposition is true tor all posi-
| tiOns of Z by drawing different hgures in
| which p is taken at intervals from A along
the cirCum ference. 1t is evident that an in
| finite number of positions for 7 could be Sc
| lected and hence the veCtOr and chord are
| both variable.
We entirely dislike to make any reference
\ to any personal remark, but as We are
Il
| plain few points. We said in our last con-
| tributioa We were not supposed TO know what
the OBI hjeCtiOns were. We claim this was en-
| tirely proper leaving any one fairly open to
the inference that we did know in general
| terms AT least hat the objections We're But
| since they were not published we certainly y
| could not reply to them in public.
l. Neither does the author OF thene theorem
l represent us correctly at the time of our
| meeting. He came out TO the college and IN
| about i've minutes wanted TO convince us
| that Newton was wrong. He pulled out his
| book in exact new theory mau style and just
| wanted 10 ask US very simple question, az
he states. We do not remember everything
that was said, although we are quite sure we
| told him that the point z could be taken any
where in the circumference OF the circle He
evidently was very anxious to get us to make
| some admissions before he told US what hi:
| objections were to the theorem. This again
IL thoroughly characteristic OF the new theory
| man. When he stated the question about the
| fixed points 2 and we could not see where
| Newton said fixed points and We will le
| any person try 10 find where Newton ssyI
| anything about fixed points and then alsc
we are perfectly willing that the same person
shall judge of the propriety of asking the
| question about q chord passing through
| fixed points. Also We beg to say that W.
| certainly did not expect to see our opinion 4
| appear in the paper with the first announce
ment We thought the reporter simply
| wanted our opinion for his own use. W.
| beg to add yet for the sake OF our friend, tht
reporter, that we do not pretend even to b.
| offended, only we did not care to appear il
| public with any demonstration that prove
| that Sir Isaac Newton Is wrong before VI
| know what that demonstration is and W her
| 1t comes from very definitely. X.
SCHoLL OBSERVATORY.