/. 
428 Mr . atwood’s Theory for the Menfuratlon 
but in meafuring the fmaller angles, this feparation of the 
Images, as well as the errors expreffed by the three laft terms 
will be greatly diminifhed while that which is denoted by 2 a con- 
tained in the firft term is not increafed. On the whole, from 
the properties which have been demonft rated to belong to this 
conftrudtion defcribed in art. 15. it may feem worthy of atten- 
tion in pradtice, for feme aftronomical as w^eli as other ufes. 
3 1 . By the fame way of examination it may be judged, whether 
the method of obferving by two reflections from plane furfacesbe 
applicable to the menfu ration of fmall angles, according to the 
conftruclion defcribed in art. 1 6. Let the errors of the four given 
quantities (as in the laft article) be2tf = the error of the arc 
have been confidered, which are perpendicular to each other: and from hence the 
reafon appears., why the motion of a fliip at fea does not much diihirb the obfer- 
vatiomof angles by Mr. h ad-ley’s inftrument. 
The new conftrudlion defcribed in art. 15. is not fo well adapted for obfervation 
where it cannot be fteadily fixed. When the images are in contad, if the infiru- 
ment be turned in its own plane through a fmall angle e" the feparation of the 
images will be — 2e"p z (becaufe d" — ^ 2 e\ vid. p. 426.) p fignifying the fine 
of half the obferved angle : this it is evident will moil affect the obfervation of 
the larger angles ; but in meafuring thofe that are fmall, the divarication will be- 
come inconfiderable. Moreover, if the angular motion of the inftrument be e " „ 
when it turns round an axis in the plane of motion, and perpendicular to the tele- 
fcope’s axis, the feparation of the images will be zi 2 e"pX — p z , p. 426. which 
it is plain will moft did urb the obfervations of angles about 90°, but will fcarcely alter 
the contact of the images, when the angles meafured are very fmall, or near ioo°. 
The objedfs obferved and their images are here underftood to be phyfical 
points : thus, when the two images of the fun are feen by diredt and reflected 
rays, and the limbs appear precifely in contadf, if by any motion of the inftru- 
ment thecontadl is difturbed, the points which before touched, being the obferved 
.qbjedts, are faid to be feparated, whether the centres of the folar images approach 
•or recede from each other, the feparation being eflimated in the direction of 
an arc which palfes through the centers of the two folar images. 
Experience mull determine in what degree this feparation of the images will 
,difturb obfervations taken at fea v» r ith the new conftrudfion* 
3 pointed 
