VOL. LXII.] PHILOSOPHICAL TRANSACTIONS. ' 293 



bending of the index, that follows the setting it off the arch, is a very disagree- 

 able circumstance, having a tendency, especially on board of ship, to expose 

 both the index and centre work to damage; and may even, without extraor- 

 dinary precautions 4aken by the instrument maker in placing the plane of the 

 index glass exactly according to the length of the index, disturb its perpendicu- 

 larity to the plane of the quadrant: on these accounts it would be much better 

 if this adjustment of the back horizon glass could be performed, like those of 

 the fore horizon glass, with the index remaining on the arch of the quadrant. 

 Fortunately, this desideratum has been lately effected by an ingenious contrivance 

 invented by Mr. Dollond, which he has given an account of in the preceding 

 paper, by means of an additional index applied to the back horizon glass; by 

 which both the adjustments may be made by the same observations, and with 

 nearly the same exactness, as those of the fore horizon glass. 



Besides the difficulty of adjusting the back horizon glass, the want of a method 

 of directing the line of sight parallel to the plane of the quadrant, has proved 

 also a considerable obstacle to the use of the back observation : this will easily 

 appear from the following proposition, that the error of the angle measured, 

 arising from any small deviation of the visual ray from a parallelism to the plane 

 of the quadrant, is to twice an arch equal to the verse sine of the deviation ; as 

 the tangent of half the angle measured by the quadrant, is to radius, very nearly. 

 Thus a deviation of 1° in the line of sight, will produce an error of about 1' in 

 measuring an angle of 90°, whether by the fore or back observation ; but the 

 same deviation will produce an error of 4' in measuring an angle of 130°, of 6' 

 in taking an angle of l6o°, and 12' in taking an angle of 1 70°. Hence a pretty 

 exact adjustment of the line of sight, or axis of the telescope, is requisite in 

 measuring large angles, such as those taken by the back observation ; and there- 

 fore a director of the sight ought by no means to be omitted in the construction 

 of the instrument (as it commonly has been since Mr. Hadley's time, though 

 recommended by him), except a telescope be made use of, which, if rightly 

 placed, answers the same purpose better, especially in observing the distance of 

 the moon from the sun between the first and last quarter. The director of the 

 sight may be placed exact enough by construction, but the telescope cannot; and 

 Mr. Hadley, not having been aware of the importance of an exact position of 

 it, has accordingly given no directions for the placing it. Mr. M. therefore en- 

 deavours to supply this defect in the following remarks. 



In the first place, he would by all means recommend an adjusting piece to be 

 applied to the telescope, by which its axis may be brought parallel to the plane 

 of the quadrant: in the next place, the back horizon glass ought to be silvered 

 in the same manner as the fore horizon glass: and thirdly, 2 thick silver wires 

 should be placed within the eye tube, in the focus of the eye glass, parallel to 



