424 Afr. atwood’s Ihetiry fer the Menjur at ion 
defcribed in art. 1 5. and 1 6. let it be required to affign what error 
is occafioned in observing a given-angle with a hadley’s fe&ant, 
in which the telefcope is parallel to the plane of motion, but 
the two refiedlors deviate from their perpendicular to that plane 
by a fmall angle b. Suppofe the error of half the arc pointed 
to by the index to be <2, and confequently the error of the fine 
of half that * arc =a x \/ 1 — p 1 —p in this cafe, becaufe the 
inclination of the refledlors to the plane of motion is nearly 
5= po°, the variation of the fine will be equal to the verfed fine of 
the fmall arc /, by which the inclination deviates from 90° ; let 
v be the verfed fine of b , then will - s ~ v (r 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 , and will be dependent on each 
other. To inveftigate their relation let FO — b (fig- 7-) be the 
fmall arc which meafures the deviation of the refle&ors from 
the perpendicular to the plane of motion : then, becaufe fin. 
DG=w, and fin. DOF = n =■ 1 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 F properties of fpherics, cof. DFO = 
^.a£DF = ^x ; Vg, and FQ beb fmall, the 
fin. Db m 0 J 
* p here, as in the general folution, denotes the fine of half the arc to which 
the index on the plane of motion is directed, that is, p — the fine of one-fourth 
of the angle obferved in Mr. kadley’s conftru&ion. 
t Fig* j- f as rad. : cotang. DF :: tang? FO : cof. DFO, that is, FO being very 
fmall, and therefore FO zz 2 x verfed fine of FO, as rad. : cotang. DF :: V iv : coft 
DFO : by the problem fin. DF zrw, and cof. DFr^i — m , wherefore cot. DFz^ 
which gives cof, DFO -V~oY, — 
