412 Mr. Atwood's theory for the Menfuratlon 
the angle meafured or arc ED will become fmailer at the fames 
time, becaufe FI decreafes with KF, the angle IKP remaining. 
This property feems applicable to good purpofe in mea Hiring 
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 conilrudion the fixed plane of reflection is made 
coincident with the primitive fecondary for various reafons : 
there are only two portions of that fixed plane which admit of 
eafy and exact adjufrments ; thefe are when the fixed plane of 
reflection is either perpendicular (art. 1 1 .) 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 adjuftmeht of 
the inclination of the refleding planes to the plane of motion, 
that is, of the arc KF ; for if the primitive fecondary OKMD 
(fig. 1 2.) 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 direded 
to i 8 o°, the objed E obferved by two refiedions will coincide 
with G, becaufe BF = PD and BM = MG by conffrudion. If 
then two given objeds be obferved when the index points to 1 8o°, 
the inclination of the plane refledors to the plane of motion 
will be one fourth part of the angle fubtended by thefe objeds. 
Concerning the magnitude of the arc FE, being the meafure of 
'the angle of incidence on the fixed fpeculum, and of KF — the in- 
clination of the refledors to the plane of motion, it will appear, 
by the computations*, that the fmailer they are both taken, every 
thing elfe being the fame, the more exad will be the refult of 
The obfervation ; but both are limited by circumftances which 
* Infra. 
(herald 
