101 



which M. Monge supposes to take place between two strata of air 

 of different density, is by no means consistent with that continued 

 ascent of rarefied air which he himself admits ; and that the expla- 

 nation founded on this hypothesis will not apply to other cases, 

 which may all be satisfactorily accounted for, upon the supposition 

 of a gradual change of density, and successive curvature of the rays 

 of light by refraction. 



The subject being of far greater importance than may at first sight 

 appear, since the variations in the dip of the apparent horizon, on 

 which all observations of altitude at sea necessarily depend, must be 

 influenced by this variable refraction, our author has been vigilant 

 in availing himself of every incident that might serve to throw some 

 light on the subject : among these, the first that occurred was an ap- 

 pearance he saw on the river Thames; when being seated in a boat, 

 with his eye about half a yard above the surface of the water, he per- 

 ceived the oars of barges at some distance, bending inwards, the point 

 of curvature or angle taking place at a small height above the sen- 

 sible horizon. 



He now recollected that the warmth of the summer having been 

 very considerable, the temperature the water had acquired, and still 

 retained when the atmosphere had become cooler, must occasion a 

 rarefaction of the stratum of air above its surface greater than those 

 at higher elevations. 



This led him to a series of further observations, which he has col- 

 lected in a table, from which we learn that, taking in likewise the 

 hygrometrical changes in the atmosphere, the depression of the 

 horizon is greater the higher the temperature of the water is above 

 that of the air ; but that this depression is materially diminished by 

 the increasing dryness of the air. 



That these refractions (which in the above-mentioned observations 

 were by no means at all times consistent,) must be affected by the 

 vicinity of land influencing the temperature of the air, will be easily 

 admitted ; and hence the observations at sea may, it is thought, af- 

 ford some more accurate conclusions, though the quantity of depres- 

 sion may not be so great. Thus much however is evident, that the 

 error in nautical observations, arising from a supposition that the 

 horizon is invariably according to the height of the observer, stands 

 greatly in need of correction. 



How to apply this correction is the object of the close of this 

 paper. This consists in measuring, by a back observation, the whole 

 vertical angle between any two opposite points of the horizon, either 

 before or after taking an altitude, and calculating half the excess of 

 this angle above 180, which will of course be the dip required. 



A few cautions are lastly given for correcting some inaccuracies in 

 the instruments, especially the index error in the back observations, 

 which it is owned had been some years since suggested by Mr. 

 Ludlam. 



