io Dr. Wollaston's Observations on horizontal Refraction; 
taking angles in general, with much reason ; but he has thereby 
overlooked a means of determining the dip, which I am inclined 
to think might be employed with advantage in all latitudes, 
without any occasion to hurry the most inexperienced or cau- 
tious observer. 
By the back observation, the whole vertical angle between 
any two opposite points of the horizon may be measured at 
once, either before or after taking an altitude. Half the excess 
of this angle above 180°, should of course be the dip required. 
But, if it be doubtful whether the instrument is duly adjusted, 
a second observation becomes necessary. The instrument must 
be reversed, and, if the apparent deficiency of the opposite 
angle from 180° be not equal to the excess before obtained, the 
index error may then be corrected accordingly ; and, since the 
want of adjustment, either of the glasses at right angles to 
the plane of the instrument, or of the line of sight parallel to it, 
will affect both the larger and smaller angle very nearly in an 
equal degree, the \ part of their difference will be extremely 
near the truth, and the errors arising from want of those adjust- 
ments may with safety be neglected. 
This method of correcting the index error for the back obser- 
vation at sea, was many years since recommended by Mr. 
Ludlam ;* yet I do not find that it has been noticed by subse- 
quent writers on that subject, or suggested by any one for 
determining the dip ; but I can discover no reason for which it 
could be rejected as fallacious, and I should hope that in prac- 
tice it would be found convenient, since in theory it appears to 
be effectual. 
The most obvious objection to this, as well as to Mr. Huddart's 
* Directions for the Use of Hadley’s Quadrant, 1771. §82, p. 56. 
