.[,'4 j 
between the two former, only by .0068 ; that is, by 
aboiit , - 8 th part of the attraction of the oblate 
fpheroid at the equator. 
This reafoning is more fhortly expreffed ( Pri?icip . 
lib. iii. Prop. 19.) as follows: 
.... “ Gravitas in loco A in fphaeroidem, con- 
4t volutione ellipfeos ( ApBq ) circa axem AB de- 
ic lcriptam, eft ad gravitatem in eodem loco A in 
“ fphaeram centro C radio AC defcriptam, ut i2y 
<c ad 126. Eft autem gravitas in loco A in terram 
“ media proportionalis inter gravitates in diCtam 
“ fphaeroidem et fphaeram ; propterea quod fphaera, 
“ diminuendo diametrum P$jn ratione 101 ad 100, 
“ vertitur in figuram terras; et hasc figura, diminu- 
<c endo in eadem ratione diametrum tertiam, qua dia- 
tc metris yfP,P^perpendicularis eft, vertitur in dic- 
<c tain fphaeroidem ; et gravitas in A, in utroque cafu t 
i( diminuitur in eadem ratione quam proxime.” 
In which the expreffion u eadem ratione' occurring 
a fecond time has milled F. Frifi and others, to think 
this laft ratio to be likewife that of the axes, or of 
10 1 to 100: Whereas the identity of ratio’s here af- 
ferted is to be referred only to the words a utroque 
cafu the ratio itfelf being not that of the axes, or 
of m to n ; but the half of that ratio (whatever it is 
found to be by Prop. 91. lib. i.) which the attraction 
of the fphere has to the polar attraction of the in- 
fcribed fpheroid. 
This inadvertence, however, of his own F. Frifi 
charges upon Sir Ifaac Newton ; and files it up, as 
the fixth of the errors, which he fays have been 
difcovered in the Principia. . . . “ Ita dum ftabilitas 
“ in ij? lib. iii, propofitione terreftrium axium pro- 
* ( portionis 
