3 <24. Gen. Roy’s Account of 
rallel to C b in the fphere, or WB in the fpheroid. Hence, if 
from G, the point where the vertical AG meets the axis, we 
draw Gr parallel to the vertical BW, it will give the point r in 
the meridian EP, making the horizontal angle PAr equal to 
the angle pah, or what the horizontal angle would be on the 
fphere. 
In like manner, if the angle PB'U is to be made equal to the 
angle pbq, Wv muft be drawn parallel to GA, ancj the plane 
<nWB will be parallel to the plane AGr ; and therefore the 
angles of the fpheroidical triangles PAr, PuB, as mealured by 
the inclination of the planes, are equal to each other refpec- 
tively, and equal to the fpherical angles of the triangle pab. 
From hence it follows, that if A be the place of an inftru- 
nient which meafures horizontal angles in the meridian NP on 
a fpheroid, and BT a flag-ftaff fet perpendicular to the furface 
of the earth on another meridian EP, the obferved horizontal 
angle PAB, between the meridian PA and the flag-ftaff BT, 
will be greater than it would be on a fphere (the latitudes and 
longitudes being the fame in both) as long as the latitude of 
the flag-ftaff is greater than that of the inftrument, the excefs 
being the angle BAr ; but if the latitude of the inftrument is 
the greateft, as fuppofe it was at B, and the flag-ftaff at A, 
then the obferved angle PBA will be lefs than it would be on 
the fphere, the defed being the angle AB^, which, becaufe 
the planes W*uB, GAr, are parallel, will be the fame as the 
excefs on the other fide. 
If the latitudes of the points A and B are the fame, the 
planes WvB, GAr, will coincide, or the verticals will meet in 
the fame point in the axis, and therefore the obferved angles 
will be equal to each other, and the fame as they would be if 
obferved on a fphere. 
Becaufe 
