CURVATURE. 



every side limited, and one which must therefore have such a 

 surface that a traveller or navigator can completely surround it in 

 one continuous course. 



4. Let us see, however, whether we may not obtain evidence 

 more distinct as to its form. If we stand on the deck of a ship at 

 sea, and out of sight of land, the view being bounded only by sea 

 and sky, and look at the horizon when a ship (A, fig. 1) approaches, 

 we shall at first see its topmast rising out of the water like a pole. 



Fig. I. 



As it gradually comes nearer to us (as at B), more of the mast will 

 become visible, and the sails will be seen cut off, however, 

 horizontally, by the line at which the water and sky unite. Upon 

 the nearer approach of the ship (as at c and D), the hull will at 

 length become visible. Xow since this takes place on all sides 

 around us, it will follow that when the ship is at a distance, there 

 must be something interposed between the eye and it which inter- 

 cepts the view of it ; but as the surface of the water is generally 

 uniform, and not subject to sudden and occasional inequalities like 

 that of the land, we can only imagine its general form to be 

 convex, and that its convexity is interposed between the eye and 

 the object so as to intercept the view. 



Since the same effects are observed from whatever direction the 

 ship may approach, it will follow that the same convexity must 

 prevail on every side. 



If, on the contrary, the surface extending from the eye to the 

 ship were a plane, the ship would be rendered invisible only by 

 reason of its distance ; whereas it is ascertained that a ship 

 frequently is invisible at a distance at which it must be seen but 

 for the interposition of some other object; this may be tested, and 

 in fact is frequently tested at sea by mounting to the masthead, 

 whence the seaman being enabled to overlook the convexity, sees 

 vessels which are invisible from the deck, although, strictly 

 speaking, he is nearer to those vessels on the deck than at the 

 masthead. 



When the mariner, after completing a long voyage, discovers by 

 his observations and reckonings that he is approaching the desired 

 coast, he ascends to the topmast and looks out for the appearance 

 of mountains or other elevated land, and he invariably sees them 

 from that point long before they are visible from the deck. He 



E2 51 



