[ 3+o ] 
But, if the fun or ftar lie not in the celeflial meri- 
dian P D, but in fome other meridian P S, at S, 
then the fpherical angle S P D is the diftance of the 
fun from the meridian P D, when the pole is at P, 
and S QJD is his diftance from the fame meridian, 
when the pole is tranflated to Q^ Let P T, QJT, 
meeting in T, be tangents of the meridians P S, 
QJ 3 , in P and Qj T QJD being the external angle 
of the rectilineal triangle T P Q, the angle P T Q^_ 
is — T QJD —TP D = SQD — SPD, and, 
therefore, is a meafure of the alteration of the time 
of any meridian of the earth’s coming to the fun at 
S, produced by the tranflation of the pole from P to 
Q^ Now the fine of P T Qjs to the fine of T P Q, 
as P Qjo T Qj whence, calling the radius unity, 
and taking P Q, on account of its fmallnefs, — the 
fine of P Q, and the angle P T Q_~ the fine of 
PTQ.we have P T Q^= p Q- x gg T p Q -— t h e 
tranflation of the pole x the fine of the right af- 
cenfion of the fun or ftar reckoned from the meri- 
dian in which the pole moves, -f- the tangent of the 
polar diflance, or, which is the fame thing, x the 
tangent of the declination. Therefore, as P Q, 
ariflng from the nutation of the earth’s axis, never 
exceeds q " JL, the greateft value of P T Q, for the 
fun can never exceed 9 " 4. x tangent of 23 .1 the 
fun’s greatefl declination, — 4", 1 which antwers to 
about 4 of afecond of time: and fo much, and no more, 
may the fun come fooner or later to the meridian, 
on account of the nutation of the earth’s axis : 
whereas, if the equation of the equinoxes was to be 
applied diredfly in the computation, according to 
M. Delalande’s 
