VOL. LXXXVII.] PHILOSOPHICAL TRANSACTIONS. gi 



pared with the erect image of the sail, is as the sines of the angles at the eye aAi 

 to iAd ; and the angle at the eye aAd, made by the 2 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, aAc, aAd, 

 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, till the angle at the eye, made by the two refracted pencils of rays aa and 

 dd, exceed the angle made by aa, and bb, the apparent height of the sail of the 

 vessel; for were those angles equal, the inverted sail would only be contracted into 

 the parallel of altitude of the boom b, and render the appearance confused, as in 

 the hull of the vessel. 



Respecting the existence of 2 pencils of rays entering the eye from every point 

 of an object not more elevated than a, or less than i, fig. 3, in this state of the 

 atmosphere, I cannot bring a stronger proof than that of the strength of a light 

 when the rays pass near the horizon of the sea, proved by the following observa- 

 tions. Going down Channel about 5 years ago in the Trinity yacht, with several of 

 the elder brethren, to inspect the light-houses, &c. I was told by some of the gen- 

 tlemen, who had been on a former survey, that the lower light of Portland was 

 not so strong as the upper light, at near distances, but that at greater distances 

 it was much stronger. I suspected that this difference arose from the lower light 

 being at or near the horizon of the sea, and mentioned it at the time; but after- 

 wards had a good opportunity of making the observation. We passed the Bill of 

 Portland in the evening, steering towards the Start, a fresh breeze from the north- 

 ward and clear night; when we had run about 5 leagues from the lights, during 

 which time the upper light was universally allowed to be the stronger, several gen- 

 tlemen keeping watch to make observations on them, the lower light, drawing 

 near the horizon, suddenly shone with double lustre. Mr. Strachan, whose sight 

 is weak, had for some time before lost sight of both lights, but could then clearly 

 perceive the lower light. I then went aloft, as well as others, but before I got 

 half mast up, the lower light was weaker than the upper one; on coming down on 

 deck, I found it again as strong as before. We proceeded on, and soon lost the 

 lower light from the deck; and on drawing the upper light near the horizon, it like 

 the former shone exceeding bright. I again went aloft, when it diminished in 

 brightness; but from the mast head I could then see the lower light near the 

 horizon as strong as before. This is in consequence of the double quantity of 

 light entering the eye by the 2 pencils of rays from every point. To illustrate 

 which, we compare the vessel, fig. 4, to a light-house built on the shore, and a 

 the place of the observer; and having brought down the light so low as to view it 

 in the direction aa, another light would appear in the horizon at x from the pencil 

 dd; and had the vessel been still enough to have observed it at this time with a 

 good glass, I doubt not but the 2 images might have been distinctly seen: as the 

 light dropped, by increasing the distance, the 2 images would appear continually 



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