428 Mr. atwood’s ’Theory for the Menfuratlon 
but in meafuring the fmaller angles, this reparation of the 
images, as well as the errors exprefled by the three laft terms 
« 
will be greatly diminiihed while that w T hich is denoted by 2 a con- 
tained in the fi-rft term is not in-creafed. On the whole, from 
the properties which have been demonftrated to belong to this 
conftruiftion defcribed in art. 15. it may feem worthy of atten- 
tion in practice, for fome aftronomical as well as other ufes. 
3 1. By the fame way of examination it may be judged, whether 
the method of oblerving by two reflections from plane furfacesbe 
applicable to the meniuration of fmall angles, according to the 
conft ruction defcribed in art. 16. Let the errors of the four given 
quantities (as in the laft article) be 2 a — 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 Hup at fea does not much difturb the obfer- 
vation of angles by Mr. hadley’s inftrument. 
The new, conftrudion delcribed in art. 15. is not fo well adapted for obfervation 
where it cannot be fteadily fixed. When the images are in contad, if the inftru- 
nient be' turned in its own plane through a fmall angle e" the reparation of the 
images will be ~ ze"p x (becaufe d" — ^2 vid. p. 426.) p fignifying the fine 
of half the obferved angle : this it is evident will moft afted 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 reparation of the images will be nr ze"pX — p z , p. 426. which 
it is plain will moft difturb the obfervations of angles about 90°, but will fcarcely alter 
the eontad of the images, when the angles meaiured are very fmall, or near 180 0 . 
The objeds obferved and their images are here underftood to be phyfical 
points : thus, when the two images of the fun are feen by dired and reflected 
rays, and the limbs appear precifely in eontad, if by any motion of the inftru- 
ment the contact is difturbed, the points which before touched, being the obferved 
objeds, are laid to be feparated, whether the centres of the folar images approach 
or recede from each other, the reparation being eftimated in the direction of 
an arc which pafies through the centers of the two folar images. 
Experience muft determine in what degree this, reparation of the images will 
jdiiturb obfervations taken at fea with the new conftrudion. 
pointed 
