$04 Mr. Boteditch on the altitude and longitude, &e. 
gives the distance from the north pole of the ecliptic to the zenith, 
which may sometimes be obtuse and equal to the supplement of the 
actual altitude. oe 
Cor. From the above demonstration it is evident, that the differ- 
ence of the arches F,, G (or its supplement to 360°) is equal to the 
angle PZ p. This angle is useful in finding the correction of the al. 
titude and longitude of the nonagesimal, from an error in the latitude 
of the place. Thus if the latitude were increased by the quantity Za 
(m the case of Fig. 3) and the perpendicular a 4 were let fall on the 
arch p Z, the altitude of the nonagesimal would be decreased by Z 6 
=ZaX cos. PZp,and as ab=Z ax sine P Z p, the longitude ofthe 
honagesimal would be decreased by the angle Z p a = es ax 
Sine PZ p 
Sine Z p 
Thus in the ice example the difference of the arches G, F 
is 31° 38’ 33" = P Z f, its cosine is *851, its sine *525. Hence if the 
increment of latitude Z @ be 100’, the decrement of the altitude of the 
nonagesimal Z 6 will be 85”*1, and thé arch ab = 59” J ‘which divid- 
ed by the sine of the altitude p Z +7511 will give the decrement of the 
longitude of the nonagesimal 69”*9, 
