Ellsworth American. [volume] (Ellsworth, Me.) 1855-current, 1858-11-19

system OF the universe, determining the
masses, the FERNS. and the motions of ali it,
parts by the iasra inspect " # ahstrirt cat
cnlatiJns and formulas anaiyticallv deiurcd
Inc two great Improvements in this instru-
ment which h1vc ban u,2da-thc clicuiuS of
variations It Eul and l.agr ing ,the method
Of partial diitr,ncas ltv Il ,Al Hnheft we
have every rcas N to believe wer, known at
least in pirt t. NawtIa hinsalf His htving
solved an i-pperin 'tricl lri'"n t6niinZ
the line whose revolution t)rms the : iil e.
least resistance. shaws clearly that l1 mast
have made the c,-trdinates q the generating
curve vary ,tn mis- construction agr5 EXACTLY
with the cqusi)n given BIZ fla, ca'e4lus -
That he must have lied the process Of in.
t1gra.in. by nlrts il attempting - g'a.r =
=, tie inverse prob IN Of ee1'rl t,g.'S b.
r,rc he Ind recourse I, ~ caln '.f'rt'
approximation which h has giy,a. api IL
when he s,asht the ue..ns VI asetrtti1ia.
/ the c5uet'.plth. which h. has t,yGeI h.
fertha N 1t di.hcalt OF prohlans. is emin,n-
tIv Iro1tble, when we consider how natHr-
ally that meth d flows from the ordinary
process for dill 'rentiItin- compound quau-
titi's,hy >upp'sins each vlrithc in sacc2ssi n
constant: iH short. diif.r.rti,tin5 by parts
- n.;',lI, a.n ,,,,,, >, Vim, n, 1,,,T. ca,
H., a,,,a,. ,;,..j ~. j., cst;,n,.i,., +ha
..,,;nt,e;,, ,r ~. oor,h h, p-,(. n.Iol NV,
the assumption Of 4 Proposition, Of which he
gave M demonstration, t4ny more than he
mad done -! the is)pari II 'tricll problem, J
tt.r Tho r,tio ,r tIr e,atyif,.,,l fore. +
,,r,,;f,t;,, d.tay,,ioa. ~, a)fi,,T;.i.v Nh
= csnt,,r,. I,t,r thot which n, ON, br,ra
t,o,. ;, he tr.n v,,;.I, ,,,, rr.,, Nv c,,-
sider,d +, l., ornaments v,. examined nv
ona of hi, most 6i.tinyui.hel f,l|,v,rs
NIc,Trin AMI den,n,tr5t,J m,st .3tisf,c-
.-..t,...zli, 49,, w.. 1T Sill :,
''!'N = tn -" -. Law ''o' 49,.
'sfs,''i we nS'.s5,.s Lu.e'S u Ia; 49, -,
Ia -, = i,.l,1 ti,.;n.,..I
litcs in their course RUM f1.ir .;,rll CEN
tres Of attraction. u,aof tbrs, n'Ieaomcna.
wholly unsusp,cte,i before the discovery of
tho rc,eral law. i tbe alt rnata movement
II and fr5 of the e.rta'- axis, ia consequence
If The s,lAr llal Blsa ot the lunar attraction
combined with the e.rth's m9.im. This
liberation. nr mutation. distinctly announced
hv him as the result O. III, th79fv. was not
found by actuai o5Saryati n to exj,. till go
Years and UPWARDS hld elapsed, when Rradlv
proved the Etct. Ths VI at discoveries which
have hen mad, by la-raugs ana L1place
uron the results vi disturbing forces have
est,biishcl tn, law OF /. ri5dical variation Of
orbits. which secure, I u stability Of the sys-
ten bv prescribinr ,galipual and a MINI
mum amount of deviation; and this is Not A
CONTINGENT but necessary truth .by rirarou.
demonstration, the inevitable result Gf un-
deubted do,s IN n5int IF fact. The ncceptriti-
tics Of Tho ,rbif. th,-1;-,cfi ms or tse mn
tons, aud tie movement IN one plane OF Il
certain position. Inat wonderful PROPOSE
tim OF Newton, which, with It's corollarles
may be sand TO give the whole doctrine OF
disturbing forces. has beea little more than
applied aad extended by the lahors OF succeed
ing geometriciAns. Indeed. la Place ,struc X
with wonder at on, of his c5nprehensIye
GENERAL statements on disturbing forces in
another proposition. has ~. hasitated t.
assert that it contains tn, r,rm oil tagranrs's
celebrated inaairy exactly a century after
I'm P,iar;gid Wis ciy,n !, the world. The
wonderful n,yars decentralization. combined
,v;.b IL \ 1i},ass n 1,,,er sLrinkinr from n
,>o,,,.s,,n SOD th, l,rit1nrt, result
! e II. ;,,,efir,ti ,7e--Y,y S,v MI e,a,
s.,r4l;,r s,,r,, Il ,o;f.,t ,r,,a,r--v,ss civil.
;orl,. -, !, - ~ ~, ;,f,r,,,.,
win ~, Ir,,,- c-,,., o.,t.a,I ,,L5,,r,sv,, +b,.
tLa j;a,r,n5 +. - ,,9et'',,s s@,ls.,nce o.
- sI,I,.,a,.,.+ ,1;.o,,sr;,s bo,;n.-
~ ,ts,, 49,, tE,t s,.L s1is,a,1' - A., rsr.
h,csan. ~, ,5,. .,a 5,,r,''.1 i ,.g,.ta.
- 49,, e .,,a.l,o,,
,,i ~, LII -. III, ,ritl 80
,oi3os. ;,3,,:ti,, - f:a;s,,s a,,ti.;
r. ,rL1+ 49, -. h,.n lfoo,sI =
~ ;.,.a,..a ~ IF Ia
f,r5;n i., f'r,a IN. -, ~ 49, md 4dns
t5tbn 5is,,,.a, - -, ~.
d,,ircti#,ns g., tbs 49, =, ,r5;eE H.