of the Angle Jub tended by T’wo QbjsMs, See. 42 y 
* 9 ^ - o 
ED = 2 a + 2pb x %/ 1 - p L — 2 pc x/i - /) ’ — v 7 2 p“ d. 
9 
It appears from the firft term 277, that an error in the arc 
pointed to by the index, caufes an equal error in the obferved 
angle; whereas a double error is caufed by it in Hadley’s 
fextant, which gives the new conftrudlion confiderable advan- 
tages : to counter-balance thefe the errors in hadley’s conftruc- 
tion, caufed by a wrong politlon of the reflecting planes, &c, are 
almoft evanefcent ; whereas the three laft terms in the value of 
ED juft found, may become considerable, unlefs great care be 
taken in making the adjuftments : the Separation alfo of the 
images, when in contadl, caufed by any unfteadinefs of the in- 
ftrument will be greater than in Mr. hadley’s conftrudion * ; 
but 
* The variation of the obferved angle ED will fhew how much the images feen 
in contadt in the field of the telefcope will appear to divaricate on any motion of 
the entire conftrudrion. For example, while the images of the obferved objedts 
are coincident in the field of the telefcope, fuppofe that Mr, hadley’s inftrument 
were turned round' in its own plane through a fmall angle here s, n , and p , not 
© • * 
being affedied by this motion, it follows,, that jr, n, andp nr o, m ~ the fine of the 
angle of incidence on the fixed fpeculum, being the only quantity which fuffers 
alteration : let its variation n m, which will give from art. 26. the correfponding 
variation in the cofine of the obferved angle, or 
Cof. EDrz -f 16 s ? "p 2 /nm X i-n z — p z zp 2 ri'—s l p 2 ‘ n 2 zpnX^V i—tf'Xj i-j-'x \X 1 —p A 
—o, becaufe nzzs ~ x. Wherefore any motion of the images in the plane of 
the inftrument will not caufe the leaf; feparation of them. Now fuppofe the whole 
to be turned on an axis fituated in the plane of motion, and perpendicular to the 
telefcope’s axis : if the angular motion be meafured by an arc of which the verfed 
\vp X ^ 1 — p 
1-2/ 
p being the fine of one quarter of the angle obferved ; but the quantity v being 
very fmall, when the angular motion does not exceed 30', the divarication of the 
images will be inconfiderable. All oblique motions of the telefcope’s axis, and 
confequeratly of the image feen by cliredt rays, may be refolved into thofe that 
ha vs 
fine —V, the points in contadf will be feparated through an angl 
