The Meafure of the Earth.                       25

neceffrily be diredced in the level line; fo that if by chance they
are at firl fight fo pointed, there xili be found no other than the
Lime point before and after the reinverfion.
  The reafon of this method is eafic to be comprehended, becaufe
W ithout confidering wx hat pafkes in the Telefcope, if we fuppofe that
the right line A B (\x hich paftes by the center A) tends towards
the OIbjed to which the Tclefcope is direded, then the two Angles
Whlich the plumb line makles with the line A B, the one under, and
the other above, flial1 be either right Angles or equal to two right
Angles ; they flulil be right Angles x when one has dire6tcd in the level,
but if one has direCt ei'hlc r too high or too low, the half of the
difference of the tWo Anglcs taken from the grcateft Angle, or ad-
ded to the leafl, flall retlore or give the level linc.
  This pradice is very ufeful, not only for placing the Degrees up-
on the limb of an Infirument, following the effect of the Telefcope
whatever it may be ; but 'tis yet further for verifying from time
to time, xw hehter the Telefcope agree with the Divifion which we
have fuppofed good and xwcll centred. But to the end this Verifica-
tion mav be made with the more eafe, the Degrees ought to be
continued from C towards E, even to the end of the limb, which
for this purpofe ought to be greater than it need to be for go De-
grees only,
  One may verifle a Sextant very near after the fame manner as
a Q.uadrant, as we may eafily fee by confidering, that if before the
reinverfing of the InfIrument there be fufpended from the middle
of the line A B, a plumb line which falls upon the poiut of, the 6oth
Degree, counting from B towards D, and afterwards the Jnflru-
ment being reinverfed, the fame line hanging oi the point of 6o
Degrees, fills upon the middle of the line A B. In the one aif in
the other of the(e pofitions the line A B liall be in the lcvel, and
by conlequcncc the Tclefcopc ought to have remained pointed at
the fame dlilant Objed which did mark .the level line. But jf on
the contrary the Telefeope be found to point to two Objeas,. of
which one is above the other, the middle between the two 1aljbe
the level line. Now the Angle of difference between the level line
and the one and the other of thofe Objeds, or indeed the half of
the Angle of the appearing diflance between the two Objeats, Sall
after be eafily meatured with a great Telekope in the manner as
we meafure the Diameters of the Planets: And by this means we
know the error of the Inifrument, the which fiall augment the
heigthl, if before the reinverfiment, and in the ordinary pofition,
the InfIrument be pointed at that Objet which is loweft, and on
the contrary it fhall diminiflh the heigths, if the Jnflrument is found
at firfi pointed at that Obje6t which was the higheft.
  The firiP and fecond Figures of the 4thPl ate reprefent an InfIrument,
PIlt 4th.
which conaining fewer Degrees than aStytant, cannot be verified to
the level,, but only to the Zenith. This d h1rument is pointed in two
differing manners to the fame Star near the Zenith. For in the firft
                                 E                        Figure