of the Angle fult ended by Two ObjeSls , &c. 
JiiJ = 2 a + 2pb x s/ 1 -f _ 2 p c x %/\ 
It appears from the fort term za, that an error in the arc 
pointed to by the index, caufes an equal error in the obferved 
angae , whereas a double error is caufed by it in hadley’s 
extant, which gives the new conftrudKon confiderabie advan- 
tages : to counter-balance thefe the errors in hadley’s conftruc- 
tion, caufed by a wrong pofit.on of the reflecting planes, & c a r e 
aimoft evanefcent ; whereas the three laft terms in the value of 
LD juft found, may become constable, unlefs great care be 
taken in making the adjuftments : the reparation' alfo of the 
images, when in contact, caufed by any unfteadinefs of the m- 
ftrument will be greater than in Mr. hadley’s conftrudion * ; 
but 
. * The va ™‘ io " of obferved angle ED will fhew how much the images fee* 
“ CODtaa m f fidd ° f the tdefC0 P e Wiil W- to divaricate on any mm ill of 
e entire conftrua,on. For example, while the images of the obferved objeft- 
are coincident in the held of the te.efcope, fuppofe that Mr. h ADLEY > s inft« 
, .urned round ,n its own plane through a fmall angle : here ,, », and p, not 
emg affedted by this motion, it follows, that 7 n,- m ip = o, *= the fine of the 
gle incidence on the fixed fpeculum, being the only quantity which fuffers 
alteration: let its variation = *, which will give from art. a6 . the correfpondin. 
variation in the cofine of the obferved angle, or a 
Cof. ED = + 16 rfmm x - 
7°’ beCaufe »='='■ therefore any motion of the images in the plane of 
e .nftrument Will not canfe the leaf! feparation of them. Now fuppofe the whole 
be turned on an ax.s f.tuated in the plane of motion, and perpendicular to the 
efcope s axis : it the angular motion be meafured by an arc of which the verfed 
4 vp X^i — p 
~ V 
fine the points in contaft will be feparated through an angle - 
c: in ^r n ; of r q “° ftheang,e ^ the 
. y mal1 ’ When the an gnlar motion does not exceed ,o', the divarication of u 
images will be inconfiderahle Ail t,r . 3 ! tne aivanc ““°n of the 
have 
