292 PHILOSOPHICAL TRANSACTIONS. [aNNO 1772, 



or palest I imagine will be of use in taking the sun's altitude when the horizon 

 appears glaring, which I believe often happens by the reflection of the sea. 



Xf^. . Remarks on the Hadlerfs Quadrant, tending principally to Remove the 

 Difficulties tvhich have hitherto attended the Use of the Back-observation, and 

 to Obviate the Errors that viight arise from a Want of Parallelism in the 

 two Surfaces of the Index Glass. By N. Mashelyne, F. R. S. p. 99. 



The back observation with Hadley's quadrant being founded on the same 

 principles, and in theory, equally perfect with the fore observation, and being at 

 the same time necessary to extend the use of the instrument up to 180 degrees 

 (it being impracticable to measure angles with any convenience beyond 120 de- 

 grees with the fore observation) it may seem surprising that it has not been 

 brought equally into general use, more especially as the method of finding the 

 longitude by observations of the moon has been practised at sea for some years 

 past; since this method would receive considerable advantage from the use of the 

 back observation in taking distances of the sun and moon between the first and 

 last quarter, could such observations be as much depended on as the fore obser- 

 vations. The causes of this seem to have been principally these two, the diffi- 

 culty of adjusting the back horizon glass, and the want of a method of directing 

 the sight parallel to the plane of the quadrant. The back horizon glass, like the 

 fore one, requires 2 adjustments: the first, or common one, disposes it at right 

 angles to the index glass, when the index stands at on the arch; which is 

 usually performed by setting O of the index of the arch of the quadrant by double 

 the dip of the horizon of the sea, and then holding the quadrant vertical with the 

 arch downwards, and turning the back horizon glass about, by means of its 

 lever or perpetual screw, till the reflected back horizon appears to coincide with 

 the fore horizon seen directly. But this operation is so difficult in practice with 

 the back horizon glass wholly silvered, except a small transparent slit in the 

 middle, as it has been usually made, that few, if any, persons, have ever 

 received proper satisfaction from it. If the back horizon glass was silvered in 

 every respect like the fore horizon glass, which it ought to be, the upper part 

 being left unsilvered, and a telescope was applied to it, perhaps this adjustment 

 might be rendered somewhat easier and more exact; but it could not even thus 

 be made so exact as the adjustment of the fore horizon glass may, by making 

 use of the sun's limbs. 



The 2d adjustment of the back horizon glass, in the common construction of 

 the quadrant, is still more troublesome, since it cannot be executed without 

 setting the index 90 degrees off^ the arch, in order to place the index glass parallel 

 to the back horizon glass; when this adjustment may be performed in the same 

 manner as the corresponding adjustment of the fore horizon glass. But the 



