Astronomical and Nautical Collections. 357 



and when SAD is a right angle, — _ c : and this, according 



d 



to the values of c and d akeady assigned [that is c = -^^^ and d ^ 

 .00052828, according to Hawksbee], becomes about 5SA ; and 

 the curvature is -J of the curvature of a great circle of the earth, 

 [consequently the depression from refraction Jj^.] But the velo" 

 city of light being to that of a body revolving in a great circle by 

 the force of gravity nearly as 40,000 to 1, the refractive force of 

 the " air" [atmosphere] is to that of gravity about as 320 000 000 

 to 1 : the forces being as the curvatures and as the squares of the 

 velocities. 



[Remarks, If we now attempted to compute the horizontal re- 

 fraction by these methods, we should have to substitute SA =: a 

 = 1 = SD = 6 =: SE = f, 2, at A = 1, at B or C, = : then 

 X =■ ^ Qt — zz) ~ at A, and at B — 1, and y the density de- 

 creasing from d at A to at B. Here it is obvious, that the series 

 for FHG cannot be directly applied, each of its terms containing x 

 and 3/ : and for a similar reason, the first series for FGH fails : 

 the series for GFH is intended by the author for small zenith 



distances only : and the last series being multiplied by ^ is also 



zz 



incapable of direct application without some further explanation. 



The remark respecting the series for GFH appears however to 

 be somewhat hasty, since it is the only one which does not altoge- 

 ther fail for the horizontal refraction : its singularity is, that it 

 ought to afford the same result, whatever values of z and x may be 

 employed ; the two parts of which it is composed, beginning at 

 the opposite ends of the curve and meeting at the given point : it 

 appears in no case to converge very rapidly, but with proper ma- 

 nagement it might, no doubt, be employed with success, unless it 

 were thought better to obtain the result by means of differences 

 from the series of refractions in the lower altitudes, which is by no 

 means impracticable. Perhaps, indeed, the fourth series, though 

 somewhat awkward, would in fact afford the most compendious 

 mode of computation, taking z the reciprocal of the height of the 

 middle of the effective part of the atmosphere, and computing for a 



