Lancaster daily intelligencer. [volume] (Lancaster, Pa.) 1864-1928, 1886-11-06

ro va,,or.of IN, iNrxlLioxscrn.

"a Ia not satisfied Win 1uNSuiie
b,uuders, but will turn right about and in
sist he il right did, indeed, think the
hints given before about tho reckless use Of
tables we're sufficient but here We are again
confronted by the assertion that the proper
lion and tbe formula are at fault instead OF
himself lie says e" The tests applied are
entIrelv I'm harmony with the manner In
san,,,, a., - - -, a., ges,on.,,.,inn ~ ,ar
, - :, -, q, a., -, ,a.,,i,. ,,r,
fieu iorwafu' anu y the apSuiu iosuio' P'o-
duced are entirely due 10 the INCORRECT tise OF
the Iigonometrical functions, aud the funda-
mental radius, " there IS Que In the demon
.,r.,,o, ~
-, A. ,,.,,,,,.., ,..,,,,,,,, ,,,, ,,,o, In,
he"a 'niS iuo'"''o" '"'o'"i'y wiz '"oa 'e'
us eAhnihe' St, "hero Anu VIE" ~ my i'u'
damenta radius ? After stating 'he rropor'
ton pc: PC: PC: AC, ! say, then, by
tripopome,ry, with Bp as a radius of unity"
Now I suppose much trouble might have
80, n, AZ t,.,a,, ~ s.y,,o 'S,,y,,,, oJ
-, -, =, r,-,,,.,,.,,, 81 .,'.tn,,
"H.g' IA" Saiu "Hn',"'et'.'t r',,.'.s,
My way oi stating things may, ihuecn, .ke
myself be somewhat old-iashioneu, but In
spite OF my lack OF culture I would not TAIL
to understand one of these on pressons about
:. al, -. ,no ,,h.r mi. ,bep ahould ,st.
wen as 'he o'no,. a'',.,,., =.
ue INC Point 'hat '"''" i'" -.
dius used IN the ueniohslia'ioi'' H"o 'Aa' i~
dius IL BP. More than this, | repeat, as as-
serted before, there In no torn pertaining TO
,,,u,,onetrical functions used during the
So, ,a,,,,n.,,a,io, a,,e,, ,hose pcrtainino
.".ie s.,1As,.t -, pp I,a,,.r,., -.
10 the iuiIuaihen.N ,,,s iauIu' pt sI,S's ,,',
unity. Win BP AZ fund ainentai rauius ~
~ surely sin PBA, and AC IL vers fBA, re-
sultiny by substitution In the iron clad pro.
portion. and one which Prof. X. no doubt
teaches in essence to every college student,
Vi
or v.,s,n pRA. sin pBA ain pBA
vers pBa.
r. shnx. that ce raad not la afraid ,o have
,h,. nronoytinn tss,od nv the npplication OF
numbers. we will submit Il, tirst, TO a proper
,aa, sna ,be,, n, Mao the uuf.irnes. a, nur
,,i,,c
Raf,ra ,,,u,asdi,y f.rtb,r I pro,est that n
,snnwoythv of tho dignity of a college pro.
fessor to toIre the necessity of making this
o,nosnra SnpnJv;ng ths tey,ps of the pTopor.
zion an harmony with a radius of unity, iarc
3ng as sele,,ted 6y our critic) we derive,
a.laI,.b,.,5 :lsi or u ,25OoiI. Seeing that
IA ia only an appro, innate of yers this result
IA ,n, n "a ,loIa,inn Of aha la w of nronortion -
Va, 10, ~ oS ,hsn .inca ain and var. vary
a,rs.,,I, az ~ ,ha rasJns ibe n,onnrtio, becomes
1o2seS = IG2g iSE (3s'5J :: fq3s 81
I93 y iqn ,,.rry ont ,be oper.tions and vou
A.r,,,a tna sar,s ras,,it as he,ore. Again
s,onaro,,, Ia, ~ ,hsnox" ISiX:bX SbX
siSiS Snar.,. again and vou have ,he same
,e.ut, as bef"re The fact ia the proportion
nR vars ain pBA.. sin pRA yers is a
sS,ni, a.. yaIna ot IA Al ,,nit NAV ne anything
mi, ~a ,nust moi f,,yst io revulste the
,ri,;n,nne,r,csl t,nc,ion accnrdinrly.
Hut what did the professor do with this
r,nrsr,,inn9 OneTsting nv a method IA
tho,oh wa had a ruIe 10 the effect that in.
rreasiny mr. decreasinp tho radius of A circle
does not alter the value of the functions at
least be says Inv fair substitution,
~. ,gI. -. -. tqI ,asuIti,g n, oue
49,. IT, ,s6i y, "a Yat .f,ay ,Smnititn,
,hia n,nr,,,. tJunaar 10 ,S,nts 10 m aka Z
, s ,'I 80 =, - Ii ,ha r,,,y ~ ~
soou os Wy Twas ma' , ~ ,,,,, ano ~, o,Ign,,,I, %
~. ,u.u ,,a, p n,raas,I,s ~, instsaS -,
he fioesspi y, t.iJ w bIsi' .na -
s,i an n " p, ,ti' i',,P 10 nynna a'
~. - -, 80, ,no u, -, ln,i ha ,,iaa =,
ny tne same styie % oi mlaesirnS no u,'s 81, W
eAL,o,e hinhsoii s,, ,,uh t,io hi'.n ba al III
Siraoi, i,"o'' p''''''"S :" "'o' '' f''
hiiiisoi'' ,.t.
since 80 great ano Is ihhue aoout ms to' eCt
tests OF incorrect formul5o let US briefly re-
view his uiai OF me expression arr
sin ny "hich neah a. a,e 81 a. -. .in
rba. ms elua,ion Is oouainea py assunns .,s
tne arc Al lnnni'e'y shaa,, , a,iu sui VIZ pr
lessor MAKES 'no ,ch.iuisn n anu "nSS
ehot' W tes' ~ ~ 'U ,S ,at". '''eti t,io
aio Al Is inhh,teiy suAi me Po' o'lonuicuiaI al
tno sih % ~ .i' .u"iu ~ ~ a., 49,, NU ~, ~, ~
nsuIes anu any ,no a,o a,o ,o, ~, p"' .,o r
ovsn less, The area of the infini,eiy small
sector PSA, is certainly Isr arc AP. ObserCe
noW, are APz ihordAf=,in PBA in the
limit Why ihsl, when &C AP=sin PBA
should not I5r arc AP=3r sin PBA. /
might even say more and be correct 0. e.
ar arc apr peudicular PC=J5r chord
aP= "a sin PBA. Since the are PSA-eitber
of these values why should they not be
equal to each other (axiom). Ia all these
forms and com parisons san Gas repeated so
often) means the sin OF the infinitely small
angle PBA In spite of the fact that tn
matter was clearly emphasized in my last
comment, tie professor insists that l say
and assume what do not only not say aud
assume, but most emphatically deny saying
or assuming. He appears to think, talking
about "man choosing his own place for
making mistak es }" and " becoruing entangled
in the meshes OF his infnitessimals," will
have quite good effect in his favor even
though il must be said at the expense OF
yeracity and fairness. The whole of his
sayings about these formula, which he
simply does not understand, are about rs
incoherent aud incorrect as possible. see
nothing more in what he says In reference TO
the demonstration OF Th VIII that IL worthy
Of comment. He cannot even see that
PSA II, Ia the constant area lie refers me 10
demonstration in Loomia. There Is moth
ing new and nothing collecting IN IT.
word with reference to my criticism on
Newton's demonstration. The professor
takes pains to refer the reader to the TACT thai
do no not object To more than the interpre
tation of the final result varies as pp,,,,
p,x,o,, o o. ,i,,. Lin, ua.,.r ,Sa,I a,
20, ,onsia.r i, s,aod 'I,n 49, To- .,r,,;n 10 Il nd
,a,,i, ,.i,h aysrstbira r;oht 10 90 mrnnm " 90
70 . ~, VII t,,,' ", ,ss " III - ;',i :" "
sa.,,,' anu % H. ~ ou, 4pauine"S ~ ,,nr, ,,ablp,
sh"N ny opJoSeoh 10 hot N"i'