424 - Mr. atwogd’s theory for the Menjuration 
defcribed in art. 1 5.- and 1 6. let it be required to affign what error 
is occafioned in obferving a given angle with a hadley’s feclant, 
in which the telefcope is parallel to the plane of motion, but 
the two refledbors deviate from their perpendicular to that plane 
9 ■ 
by a fmall angle b. Suppofe the error of half the arc pointed 
to by the index to be a, and consequently' the error of the fine 
of half that * arc =nVi ~p z —p : in this cafe, becaufe the 
inclination of the refledbors to the plane of motion is nearly 
= po°, the variation of the fine will be equal to the verfed fine of 
the fmall arc b , by which the inclination deviates from 90° ; let 
• ® 
v be the verfed fine of b, then will - s = v (j varying by a de- 
crement of v). Moreover, becaufe a condition is annexed^ which 
is, that the line of obfervation is parallel to the plane of mo- 
tion, the variations s, m, and n, will be dependent on each- 
other. To invefbigate their relation let FO = b (fig. 7.) be the 
fmall arc which meafures the deviation of the reflectors from 
the perpendicular to the plane of motion : then, becaufe fin. 
DO — m, and fin. DOF'=»~i by the problem, when F from 
having been coincident with O has moved through the arc OF, 
© • 
it is plain, that n = fin. DFO - fin. DOF - (n being a decre° 
ment) ; but, by the + properties of fpherics, cof. DFO = 
v "iv x ccf. Dy __ ^ iv x ^ : and FO being very fmall, the 
fin. DF m & a 
* p here, as in. the general foliation, denotes the fine of half the arc. to which 
the index on the plane of motion is dir.eft.ed, that is, p ~ the fine, of one-fourth 
of the angle obferved in Mr. hadley’s conftruftion. 
-j- Fig. 7. as rad. : cotang. DF :y tang. FO : cof. DFO, that is, FO being very 
fmall, and therefore FQ^~ 2 x verfed line ofFO, as rad. : cotang; DF :: V zv : cof. 
DFO : by the problem fin. DF — ot, and cof. DF — ^ \ wherefore cot. DF trr 
m which gives cof. DFO zv X — d — 
m 
fine- 
m 
m 
