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 hascol- 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.
