90 PHILOSOPHICAL TRANSACTIONS. [ANNO 17Q7. 



and I could see a small opening above the horizon of the sea, in the angle made by 

 the gaff and mast; and had the mast been shorter by 10 feet, to the height of y, 

 the whole would have been elevated above the horizon of the sea, and from y to d 

 an open space. This drawing was taken from a sketch I took at the time, and re- 

 presents the proportion of the inverted to the erect object, as near as I could take 

 it by the eye, the former being about -§- of the latter in height, and the same 

 breadth respectively; though at one time during the observation, which was con- 

 tinued about an hour, I thought the inverted nearly as tall as the erect object. The 

 day was fine and clear, with a very light air of wind, and I found very little tremor 

 or oscillation in viewing her through the telescope. 



Fig. 4 is laid down for explaining the above phenomena, in which a represents 

 the window whence I viewed the vessel b; ho, the curved surface of the sea; cd 

 parallel to ho, the height of the maximum of density of the atmosphere; the lines 

 marked with the small letters aa, bb, cc, dd, the pencils of rays under their various 

 refractions from the vessel to the eye, or object-glass of the telescope. The pencil 

 of rays aa, from a point near the head of the main-sail, is wholly refracted in a 

 curve convex upwards, being everywhere above the maximum of density; and the 

 pencil of rays dd, which issues from the same point in the sail, and passes near 

 the horizon of the sea at x, is convex upwards from the sail to w, where it passes 

 the line of maximum of density, which is the point of inflection ; there it becomes 

 convex downwards, passing near the horizon at x to y, where it is again inflected,, 

 and becomes convex upwards from thence to the eye. The pencil of rays bb, 

 from the end of the boom, passing nearly parallel to the horizon, and near the 

 maximum of density, suffers very little deviation from a right line in the first part; 

 but in ascending, from the curvature of the sea, will be convex upwards to the 

 eye. The pencil of rays cc, from the same point in the boom, may have the small 

 part to c convex upwards, from c to z it will be convex downwards, and from z to the 

 eye convex upwards. From this investigation it appears, that 2 pencils of rays 

 cannot pass from the same point, and enter the eye, from the law of refraction, 

 unless 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 10 

 feet of height above the surface of the sea at the time these observations were 

 made. 



Respecting the hull of the vessel being confused, and ill defined in the teles- 

 cope, as by fig. 3, it arises from the blending of the rays, from the different parts 

 of the object, refracted through the 2 mediums; some parts of the hull appearing 

 erect, and some inverted. Suppose the dotted line ii, 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, unless the angles at the 

 eye aAC and aAd, exceed the angle aAi ; for the intermediate space could only be 

 contracted by the secondary pencils of rays. The lengths of the inverted, com- 



