412 Mr. Atwood’s Theory for the Merfuration 
the angle meafured or arc ED will become fmaller at the fame 
time, becaufe FI decreafes with KF, the angle IKF remaining. 
This property feems applicable to good purpofe in meafuring 
fmall angles, not only from the great extent of fcale, which 
is here obtained, but from various advantageous circumftances, 
which will appear in the fubfequent article, and from the com- 
putations annexed in thofe which follow. 
In this confiruCtion the fixed plane of reflection is made 
coincident with the primitive fecondary for various reafons : 
there are only two pofitions of that fixed plane which admit of 
eafy and exact adjuftments ; thefe are when the fixed plane of 
reflection is either perpendicular (art. n.) to the primitive fe- 
condary or coincident with it. The latter pofition is preferred 
exclufive of the advantages it poflefles in common with the 
other, becaufe it affords means for a very precife adjuftment of 
the inclination of the reflecting planes to the plane of motion, 
that is, of the arcKF ; for if the primitive fecondary OKMD 
(fig. 12.) be produced, and in it DG be taken equal to four times 
KF, it is manifeft, that when the perpendicular Cl coincides with 
M, or, which is the fame thing, when the radius CP is directed 
to 180% the objeCt E obferved by two reflections will coincide 
with G, becaufe BFztFD and BM — MG by confiruCtion. If 
then two given objeCts be obferved when the index points to 1 8o°, 
the inclination of the plane refleCtors to the plane of motion 
will be one fourth part of the angle fubtended by thefe objeCts. 
Concerning the magnitude of the arc FB, being the meafure of 
the angle of incidence on the fixed fpeculum,and of KF — the in- 
clination of the refleCtors to the plane of motion, it will appear, 
by the computations*, that the fmaller they are both taken, every 
thing elfe being the fame, the more exaCt will be the refult of 
the oblervation ; but both are limited by circumftances which 
* Infra, 
{hould 
