MATHEMATYCATO PAPERS. %& 
mid-heaven added to 360°, or, which is the fame thing," by dr 
ing the dcc of the mid-heaven to QO i92 eu 
The right dtedton of the mid-heaven being between 90° 
and 180°, and between 180° and 270°, the neareft equinoc- 
tial point is = ; and in the firft cafe, angle pPZ is obtufe, in 
bs fecond acute, and in each cafe the angle is found, by fub- 
ftra&ing the right-af cenfion. of the mid-heaven from 270°. 
Thefe rules are to be ufed when the latitude of the given 
place is north ; but when it is fouth, they muft be inverted to 
find the. pening bis as will xn evident * a 
diagram. - 
following rules may be obferred n 
_ When the right afcenfion of the mid-heaven is between I So o* 
and 270^, or between 270* and o*, that i is, when angle PPZ, 
is diem the Meme will fal] upon _ 
pour ; ý i 
ie ae: is ake the pepe s will fall es the fide 
of E Papotite to p. snl ME 4 i ENIM m. ate 
For sther Bie: Py EE EFIA M ome 
Radius : Sine co-angle PEL.: Tangent fide PZ : Tangent 
fide Px. - Then, if the perpendicular be on.the fide of P next 
to f, the. difference between Pp and Px will be px ; but if. 
it fall on the fide of P oppofite to p, the fum of Pp and Px 
will 
