A T ) T. r n R
u
M o u A R T U M
»
\S
Si accipiendo hancdifferentiam in vi ccncrifuga contemnatur tcrmlnuc
•i
ctx
exiguus rcfpcftu rcliquoVtitn binorum , differentia ipfa tota virium
evadet U l L i - H
~ d x
~
{ i
eti
«+«
) ; & fi pariter in vi tot»
in aquatore omittatur vis ccncrifuga exigua rtfpc hi fumma reliquarum dua­
rum , & in harum pofleriore contemnatur fecu dus terminus—
ctx
cxi"uus
J lf
D
rclpcftu praccdeiuis > relinquetur vis in aquatore tota
_
Ugu
1
_ Differentia illa virium pcr hanc divifa >evadit
+
jl<r?j
3
r
1
7«ir-+- lr^
»*.
~
, qua erit fraftio gravitatis . Addatur ipfi cllipticitas —
, & rctluclis
prioribus terminis ad eundem denominatorem fiet . 'f?"1*+~
6tri*
... 2L . cd
>i v, ,(r*
4
-
Ifli* r
.
m
autem
x ~ ?\
— j
10?uj <•'* num.za? juxta numerum » a j . Igitur illa
fumma remanet
£• X
y
^ >
<lui
v:ilor
At
duplus valoris
*~-
exprimentis fratlionem gravitatis , & cllipticitatem lcfpondcntcm homoge-
ncitatl ; oportet idem fic medius arithmetici proportionalis inter fractionem
gravitatis. & ellipticitatem refpondentcm nucleo heccrogeneo , quod erat
alterum dcmonftrandum .
2 j 7 Hoc paflo Clcrautianuin theorema remanet dcmonflratum pro quavis
nuclcifpharici magnitudine, quodquidem in illo Expeditionis Licteraria opu-
fculo dcmonllravcram folumpro cafu, in quo effet nuclei radius aquali» femia-
xi . Facile aucem illud fiatim inn»tefcic non poffe in cafu nuclei fpharici a &
Fraftionein gravitatis,
&
ellipticitaccm c(fe fimul majorem, vel fimul minorem,
quamin cafu homogcncitatis , fed alteram majorem , alteram minorem . Ucra
autem major effe debeat data nucleidenfitate , & magnitudine refpe&u fluidi
facilc deduci poteric e fuperioribus formulis . Nam e formula exhibente el-
lipticitatcm
~r
= = , ^ ^ 4(7/+* iof »J Jivl,"l0" e inflicuta habetur ~ —
— ¥ J —
; qui valor erit minor , vel mafor valore — , nrout uoflerior
Irrl-H- aof»*
terminus line fuo figno confidcratus fuerit pofitivus, vel negativus , Por-*
ro fi Jcnfitas nuclci fuerit major denficatefluidi , femper valor
q
erit pofi­
tivus , adeoque ille fecundus terminus pofitivus totus . Si autem denfitas
nuclci fuerit minor, valor ^ erit ncgativu.v, & idcirco numerator
ne­
gativus femper, denominator autem 8£? ? -H 20
qu\
eric pofitivus, vel ne­
gativus, prouc
2oqttl
fueric minor , vel major, quam 8/. J , five valor
minor ,
yc
I
major, quami l i . Porro in iifdcm cafibus erit etiam pofitU
vus, vel negativus denominator
t f r l ^
1
oqu
* ellipticitatis > cujus nume­
rator 5fr
7
debet elTc femper pwlitivus , cum debeat radius nuclci
H
effe minorradio aquatoris r , &: differentia denfitatum
q
Huidi , ac nuclei
nen major denfitate
t
Huidi , ubi, exiftente
q
negati vo , nucleus minorem
denfitatem habet, vel nullam • Quamobrcm quotiefeunque cllipticitas fuerit
Tom,
//.
A a
pofi-
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