C 4049 ) 
reprefent the places of Comets for fome time oftlieir appari- 
tion, but not for th^ whole time : as we have fiisw'd io that 
Theory. 
Having therefore ehofen two of our firft ObferTatioos3(be» 
caufe the latter are not fo proper for this piirpofe/^ and h;iV* 
ing taken a Mean between the firft Obfervatipiif of the Msihe* 
raatician? of la FlefeheyWQ have found by this method^ that the 
Goraet had been in his Perigee iht i2tlh of March u8:z 
clock ija^ihe morning tba in that time 3 which is that o( his 
grcateft app^rentcelerity,he made about 1. deg.52'.a day in the 
great Circle of his ^//'^rm motion ^ and-^^, of his perigee- 
diftanceJn the line of his e^ual mot ion : that he was in bis great- 
eftDeclination the i itknid i2//^.ofMarch5and/^^if at that time 
he pafs'd through the inferiour Meridian at about two a clock 
after midnight* Wherefore, if the weather hath been favoura.* 
ble, he muft have been obferv'd by Mr. Hevelius^who hath feen. 
himjwitnefs his Letter^from the 6ch. o^March 5 * at ^gumM^ 
which time he was ia perigee and made the biggeft Moiy- 
fliew* 
If we have rightly determined his Perigee^ and that the ^y- 
pthefs oixhz equality of his motion be juft for that time^nor he 
hath begun to appear but when he was fufficiently nigh to the 
Earth 3 then he hath been vifible jSnce the middle of February^ 
at which time he waj as far diftahV from his perigee by ap- 
proaching to the Earth^as he is at the prefent by receding from 
it* He muft then have been at the extremity of the Southern 
wing of the Srvan^ and arrived at the Southern foot of Pegafus 
on the ^^th^of Febrmry, of the fame bignefs that he was feen to 
beofj March 28. He muft have arrived at the Stars of the Npr* 
thern Arm of Andromeda^ March the^ihi at thofe of her Girdle^ 
the I ith. when he was in his Perigee 5 and in his greateii dccli-- 
nation ; to her Southern Legg, March i %th ^ between her Sou- 
thern Legg and the Tv\2Lng\c^March iBtk very near as he was 
obfervM at la Flefche^znd under the head o£M£dufa,March2 $fh. 
The dayes enfuing he muft have arriv'd at the places marked in 
pur firft Obfervations ; But in thelaft^he hath been fwifter than 
ihi$ Hypothefis will bearjo reprefent thefe latter Obfervations, 
the Line of the motion ought to have been made curve^ as we 
did for the end of the apparent motion of the Gomet 0(16^57 
with this difference^that inftead of thai: lines being convex in re- 
