34 
Mr. Huddart's Observations 
from c to % it will be convex downwards, and from £ to the 
eye convex upwards. 
From this investigation it appears, that two pencils of rays 
cannot pass from the same point, and enter the eye, from the 
law of refraction, except one pencil pass through a medium 
which the other has not entered ; and therefore the maximum 
of density was below the boom, and could not exceed ten feet 
of height above the surface of the sea at the time these obser- 
vations were made. 
Respecting the hull of the vessel being confused, and ill de- 
fined in the telescope, as by fig. 3, it arises from the blending 
of the rays, from the different parts of the object, refracted 
through the two mediums ; some parts of the hull appearing 
erect, and some inverted. Suppose the dotted line i i, fig. 4, 
an indefinite pencil of rays, passing from between the inverted 
and erect parts of the object, or the upper part of the hull of 
the vessel, to the eye, (for the lower part of the hull could not 
be observed) : the objects cannot appear inverted, except the an- 
gles at the eye a Ac and a Ad, exceed the angle aAi; for the 
intermediate space could only be contracted by the secondary 
pencils of rays. The lengths of the inverted, compared with 
the erect image of the sail, is as the sines of the angles at the 
eye aAi to iA d; and the angle at the eye a Ad, made by the 
two pencils of rays from the same point near the head of the 
sail, must be double the angle aAi, when the inverted image 
is as tall as the erect. In this case, the sines of the angles aAb, 
a Ac, a Ad, fig. 4, are proportional to the altitudes ab, ac , ad , 
in the magnified view of the vessel, fig. 3. 
Under this consideration no inverted image of the sail will 
be formed, until the angle at the eye, made by the two refracted 
